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New solid state laser crystals created by epitaxial growth Kumaran, Raveen 2012

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New Solid State Laser Crystals Created by Epitaxial Growth by Raveen Kumaran B.A.Sc, e University of British Columbia,                Doctor of Philosophy in       (Physics)  e University Of British Columbia (Vancouver) September  © Raveen Kumaran,   Abstract Rare-earth-doped oxide crystals such as Nd:YAG are oen used as the gain medium in solid state lasers because they produce a collection of sharp emission peaks, some of which have strong gain. Rather than the typical bulk form of these crystals, thin films with planar waveguide geometry are promising alternatives for compact devices with lower lasing thresholds and better heat extraction. Such benefits motivated the growth of these oxide films by molecular beam epitaxy, a technique capable of films with precise composition, thickness and structure due to its independently controlled elemental sources. Two sets of material systems were attempted, Al-Ga-O and Y-Al-O, with Nd as the sole dopant. e films were grown on sapphire substrates of various orientations, then analyzed by x-ray diffraction and photoluminescence where peaks signaled long-range and short-range order respectively. Work on the Al-Ga-O system yielded Nd:α-Al2 O3 (Nd:sapphire) and Nd:αGa2 O3 , two new laser crystals with unique collections of sharp emission peaks only observable from single-crystal films grown at temperatures far below the melting point. ese conditions were required to confine the much-larger Nd dopants into Al and Ga sites with short-range order, and are unlikely reproducible by bulk methods. Due to their shared corundum structure, the emission spectra from Nd:sapphire and Nd:α-Ga2 O3 appear similar but wavelength-shied. e dominant Nd:sapphire peak has strong gain comparable to its counterpart from Nd:YVO4 , one of the highest available, while the blue-shied Nd:α-Ga2 O3 peak is likewise comparable to Nd:YAG. Alloying both produced corundum-structure crystals with peaks that shied linearly with unit cell volume, which in turn depended on Ga/Al ratio and film stress. ese Al-Ga-O crystals are promising for applications involving compositional-tuning and graded-index layers. Ternary Y-Al-O is not tunable because it has three stable phases YAM, YAP and  ii  Abstract YAG with different compositions, structures and thus emission spectra. Singlephase films of each phase were grown without single-crystal structure but still yielded sharp peaks consistent with their bulk counterparts. Short-range order was achievable because the Nd dopants were size-compatible with the Y sites. While the peaks did not shi with Y/Al ratio, peak sharpness improved when the ratio approached bulk stoichiometric values.  iii  Preface With few exceptions, all the work presented in this thesis is my own. is includes the growth of the samples as well as most of the characterization data. All exceptions are explicitly stated. e MBE system used to grow the films was jointly managed by three graduate students: Scott Webster, Shawn Penson and me. e shared responsibility included configuring the system (sources, pumps, control systems, etc.) and maintaining its operational status. Certain measurements regarding the system such as RHEED geometry and plasma source efficacy are therefore attributed to my colleagues. All the samples characterized in the data portion of this thesis, i.e. chapters –, were grown by me. Likewise for growth experiments that did not produce samples e.g. desorption tests. During the growths, I also ran the in-situ measurements such as RHEED and thin film reflectometry. Post-growth characterization involving XRD, PL and AFM were all done by me. is work exclusivity was possible because Scott and Shawn were largely focused on Y2 O3 while my research involved ternary Y-Al-O and the corundum-structure films. Samples were sent out of the group for analysis when those desired techniques were unavailable to us. is included XPS by Ken Wong and RBS by Peng Wei. Both are mentioned at relevant locations in the text. e main results of this thesis have been published in four journal articles, three of which I am listed as first author. Listed chronologically, the four are • I. C. Robin, R. Kumaran, S. Penson, S. E. Webster, T. Tiedje, and A. Oleinik. Structure and photoluminescence of Nd: Y2 O3 grown by molecular beam epitaxy. Optical Materials ():, , []; which has my analysis of the optical properties of Nd:Y2 O3 films. • R. Kumaran, S. Webster, S. Penson, W. Li, and T. Tiedje. Molecular beam epitaxy growth of neodymium-doped yttrium aluminum perovskite. Journal iv  Preface of Crystal Growth, (): – , , []; which has my results from high-quality Nd:YAP as well as thermal radiation measurements yielding the substrate temperature. • R. Kumaran, S. E. Webster, S. Penson, W. Li, T. Tiedje, P. Wei, and F. Schiettekatte. Epitaxial neodymium-doped sapphire films, a new active medium for waveguide lasers. Optics Letters, ():–, , []; which describes my growth and characterization (optical and structural) of Nd:sapphire films. • R. Kumaran, T. Tiedje, S. E. Webster, S. Penson, and W. Li.Epitaxial Nddoped α-(Al1−x Gax )2 O3 films on sapphire for solid-state waveguide lasers. Optics Letters, ():–, Nov , []; which describes my growth and characterization (optical and structural) of Nd:α-Ga2 O3 and Nd:α(Al1−x Gax )2 O3 films. While these results have been published in those journals, the text or figures describing them have not been reproduced here. is thesis is a stand-alone document that covers the entire research process (including results) with greater detail, and is written from scratch to produce a more coherent document. Furthermore, the figures used in those journal articles have been updated (for better clarity, more accurate data, etc.) for the thesis, and are sufficiently different for copyright concerns.  v  Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vi  List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ix  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Rare-earth luminescence and the solid state . . . . . . . . . . . . . RE3+     ..  Electronic structure of the  free ion . . . . . . . . . . .    ..  Effect of local atomic structure on free ion levels . . . . . . .    ..  Effect of solid state host on emission spectra . . . . . . . . .    .  Crystallinity considerations for optical devices . . . . . . . . . . . .   .  Planar thin films for making solid state lasers . . . . . . . . . . . . .   .  ..  Bulk lasers . . . . . . . . . . . . . . . . . . . . . . . . . . .   ..  in film advantages . . . . . . . . . . . . . . . . . . . . .   ..  in film growth . . . . . . . . . . . . . . . . . . . . . . . .   Epitaxial films by molecular beam epitaxy (MBE) . . . . . . . . . .  ..  Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . .   ..  Research scope . . . . . . . . . . . . . . . . . . . . . . . . .    Epitaxial growth of single-phase Nd:sapphire . . . . . . . . . . . . . . .  .  MBE growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vi  Table of Contents ..  Substrate preparation . . . . . . . . . . . . . . . . . . . . .   ..  Substrate and effusion cell heating . . . . . . . . . . . . . .   ..  Oxygen plasma ignition . . . . . . . . . . . . . . . . . . . .   .  In-situ monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . .   .  Surface morphology . . . . . . . . . . . . . . . . . . . . . . . . . .   .  Structural analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .   .  Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . .    Structural and optical properties of Nd:sapphire . . . . . . . . . . . . .  .  .  .  Structural properties . . . . . . . . . . . . . . . . . . . . . . . . . .  ..  Film thickness and density . . . . . . . . . . . . . . . . . .   ..  Effect of Nd doping on lattice spacing . . . . . . . . . . . .   ..  Example relating lattice expansion to Nd concentration . . .   ..  Film–substrate epitaxial relationship . . . . . . . . . . . . .   Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . .  ..  Temperature-dependent emission . . . . . . . . . . . . . .   ..  Product of emission cross-section and lifetime . . . . . . . .   ..  Lifetime measurement . . . . . . . . . . . . . . . . . . . . .   ..  Absorption cross-section from fluoresence excitation . . . .   Post-growth annealing . . . . . . . . . . . . . . . . . . . . . . . . .  ..  Motivation, process and ◦ C anneal . . . . . . . . . . .   ..  Anneal at ◦ C . . . . . . . . . . . . . . . . . . . . . . .    Epitaxial Nd:Al-Ga-O in the corundum phase . . . . . . . . . . . . . .  .  Ga2 O3 growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ..  Gallium desorption . . . . . . . . . . . . . . . . . . . . . .   ..  Monitoring film quality by reflection high energy electron diffraction (RHEED) . . . . . . . . . . . . . . . . . . . . .   .. .  In-situ characterization by thin film reflectometry . . . . . .   Structural and optical properties of Nd-doped Ga2 O3 . . . . . . . .  ..  β-Ga2 O3 on C-plane sapphire . . . . . . . . . . . . . . . .   ..  α-Ga2 O3 on A-plane sapphire . . . . . . . . . . . . . . . .   ..  Emission properties of Nd:α-Ga2 O3 . . . . . . . . . . . . .   vii  Table of Contents .  Nd-doped α-(Al1−x Gax )2 O3 alloys . . . . . . . . . . . . . . . . . .  ..  Composition and density . . . . . . . . . . . . . . . . . . .   ..  Structure and emission . . . . . . . . . . . . . . . . . . . .    Epitaxial films of the popular Y-Al-O system . . . . . . . . . . . . . . .  .  Nd-doped Y2 O3 . . . . . . . . . . . . . . . . . . . . . . . . . . . .   .  Mixed Y-Al-O growth considerations . . . . . . . . . . . . . . . . .  ..  Al desorption . . . . . . . . . . . . . . . . . . . . . . . . .   ..  Single-phase Y-Al-O films . . . . . . . . . . . . . . . . . . .   ..  Parameters affecting film Y-Al-O phase . . . . . . . . . . .   .  Emission spectra dependence on phase stoichiometry . . . . . . . .   .  Effect of growth temperature on phase stoichiometry . . . . . . . .   .  Nd-doped YAP film with high degree of crystallinity . . . . . . . . .   .  Crystallinity of Y-Al-O films and effects of post-growth annealing .    Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . .  .  Comparison of Y-Al-O and Al-Ga-O films . . . . . . . . . . . . . .   .  Comparison of laser properties . . . . . . . . . . . . . . . . . . . .   .  Comparison of growth conditions . . . . . . . . . . . . . . . . . . .   .  Ideas for future work . . . . . . . . . . . . . . . . . . . . . . . . . .   Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   APPENDICES    A Sapphire lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  B Simulated TEM patterns for RHEED . . . . . . . . . . . . . . . . . . .  C X-ray diffraction data . . . . . . . . . . . . . . . . . . . . . . . . . . . .  D Artwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   viii  List of Tables Table .  Popular methods for planar waveguide laser (PWL) deposition compared to MBE . . . . . . . . . . . . . . . . . . . . . . . . . .   Table .  Nd3+ states in the 4 F3/2 , 4 I9/2 and 4 I11/2 manifolds responsible for the Nd:sapphire emission peaks near  and  nm. . . .   Table .  Ionic radii comparison of octahedral (-coordinated) rare-earth dopants and host elements. . . . . . . . . . . . . . . . . . . . . .   Table .  Comparison of the Nd-doped corundum-structure materials to popular bulk crystals. . . . . . . . . . . . . . . . . . . . . . . . .   Table .  Density comparison between the set of α-(Al1−x Gax )2 O3 films with those expected from bulk sapphire, α-Ga2 O3 or a linear interpolation of the two. . . . . . . . . . . . . . . . . . . . . . .   Table .  Plane spacings of α-(Al1−x Gax )2 O3 alloys along various orientations enabling the calculation of the unit cell volume. . . . . . .   Table .  MBE growth conditions for single-phase Y-Al-O films. . . . . . .   Table .  Growth sets investigating the effect of single parameter variations on the Y-Al-O film phase. . . . . . . . . . . . . . . . . . .   Table .  Comparison of the Nd-doped corundum-structure materials to bulk Nd:YAG and Nd:YVO4 . . . . . . . . . . . . . . . . . . . . .   Table A.  Equivalent planes in sapphire . . . . . . . . . . . . . . . . . . .   Table C.  Relevant Y-Al-O and Al-Ga-O space groups and their allowed x-ray diffraction (XRD) reflections. . . . . . . . . . . . . . . . .   Table C.  Partial list of sapphire diffraction data, calculated using a hexagonal lattice with a = 4.759 Å, c = 12.991 Å . . . . . . . . . . .   ix  List of Tables Table C.  Partial list of γ-Al2 O3 diffraction data, calculated using a cubic lattice with a = 7.914 Å. . . . . . . . . . . . . . . . . . . . . . .   Table C.  Partial list of α-Ga2 O3 diffraction data, calculated using a hexagonal lattice with a = 4.9825 Å and c = 13.433 Å. . . . . . . . .   Table C.  Partial list of β-Ga2 O3 diffraction data, calculated using a using monoclinic lattice with a = 12.2140 Å, b = 3.0371 Å, c = 5.7981 Å and β = 103.83◦ . . . . . . . . . . . . . . . . . . . . .   Table C.  Partial list of Y2 O3 diffraction data, calculated using a cubic lattice with a = 10.6056 Å. . . . . . . . . . . . . . . . . . . . . . .   Table C.  Partial list of Y4 Al2 O9 diffraction data, calculated using a using monoclinic lattice with a = 7.4579 Å, b = 10.531 Å, c = 11.1498 Å and β = 108.806◦ . . . . . . . . . . . . . . . . . .   Table C.  Partial list of YAlO3 diffraction data, calculated using an orthorhombic lattice with a = 5.17901 Å, b = 5.32663 Å and c = 7.36971 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . .   Table C.  Partial list of Y3 Al5 O12 diffraction data, calculated using a cubic lattice with a = 12.016 Å. . . . . . . . . . . . . . . . . . . . . .   x  List of Figures Figure .  Electronic structure of Nd3+ as a (a) free ion, and (b) as a dopant in a YAG crystal. . . . . . . . . . . . . . . . . . . . . . .  Figure .  Site symmetry of the (a)  Y3+  site in YAG and the (b)  Al3+  site  in sapphire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure .  Emission spectra showing the  4F 3/2  →4 I  9/2     transitions from  Nd-doped (a) glass fiber, (b) nanocrystalline YAG powder, and (c) single-crystal YAG. . . . . . . . . . . . . . . . . . . . . . . .  Figure .  MBE growth chamber . . . . . . . . . . . . . . . . . . . . . . .   Figure .  Deposition rate of Al and Nd metal onto a quartz crystal microbalance (QCM) placed in front of the substrate at various cell temperatures. . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  (a) Setup relating the sample heater and thermal radiation monitor. (b) Spectra corresponding to various substrate temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  Oxygen plasma emission spectra captured from the glowing quartz tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  RHEED patterns showing the surface structure evolution during the growth of a  nm Nd:sapphire film. . . . . . . . . . . .   Figure .  Atomic force microscopy (AFM) scans showing the surfaces of the starting substrate and  nm Nd:sapphire film post-growth.  Figure .    (a) XRD geometry and (b) Reciprocal space map (RSM) example showing the diffraction condition being satisfied . . . . . . .   Figure .  XRD θ-θ scans of Nd-doped Al2 O3 films grown on sapphire substrates of different orientations. . . . . . . . . . . . . . . . .   Figure .  Photoluminescence (PL) measurement apparatus . . . . . . . .   Figure . PL emission spectra produced by 4 F3/2 →4 I11/2 transitions from Nd-doped Al2 O3 films. . . . . . . . . . . . . . . . . . . .  xi  List of Figures Figure .  Detailed X-ray structural data from a  nm thick Nd:α-Al2 O3 film grown on R-plane sapphire. . . . . . . . . . . . . . . . . .   Figure .  High resolution XRD θ-θ scans of nearly  nm thick sapphire films with various Nd-doping levels. . . . . . . . . . . . . . . .   Figure .  High resolution θ-θ scan and Rutherford backscattering spectrometry (RBS) scan of a  nm thick Nd:sapphire film grown on A-plane sapphire. . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  RSM of the (030) peak showing that the Nd:sapphire film is fully strained to the A-plane sapphire substrate. . . . . . . . . .   Figure .  Comparison of Nd:sapphire PL emission spectra at room temperature and at  K. . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  Product of emission cross-section σ and lifetime τ for Nd:sapphire derived from the PL emission spectra. . . . . . . .   Figure .  Pulsed luminescence from Nd:sapphire generated by mechanically chopping a continuous wave pump laser at  kHz. . . . . .   Figure .  Room temperature absorption cross-sections of Nd:sapphire measured using excitation spectroscopy. . . . . . . . . . . . . .   Figure .  PL emission spectrum from an Nd:sapphire film aer furnace annealing in air. . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure . PL emission spectra showing the contribution of pump laser scattering and inhomogeneous broadening to the broad spectrum of furnace-annealed Nd:sapphire. . . . . . . . . . . . . . .  Figure .  Schematic showing the residual gas analyzer (RGA) detection of desorbed Ga . . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  RGA scans identifying the desorbed material from a ′′ sapphire wafer heated to ◦ C when the Ga cell shutter is closed/open. . . . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  Effect of O2 overpressure on Ga and Ga2 O desorption from the ′′ sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  Similar to figure . showing instead the effect of sample temperature on Ga and Ga2 O desorption. . . . . . . . . . . . . . .   xii  List of Figures Figure .  Evolution of RHEED patterns during the growth of Ga2 O3 on different sapphire substrate orientations. . . . . . . . . . . . . .   Figure .  Schematic showing thin film reflection from a two layer dielectric   Figure .  Specular reflection from Ga2 O3 samples during growth showing the influence of various parameters. . . . . . . . . . . . . .   Figure .  Structural and optical properties of Nd-doped Ga2 O3 grown on C-plane sapphire. . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  Possible orientations of monoclinic β-Ga2 O3 on C-plane sapphire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure . Structural and optical properties of single-phase Nd-doped αGa2 O3 grown on A-plane sapphire. . . . . . . . . . . . . . . . .  Figure . Product of emission cross-section σ and lifetime τ for Nddoped α-Ga2 O3 and α-Al2 O3 films grown on A-plane sapphire.  Figure . X-ray photoelectron spectroscopy (XPS) spectrum used to identify the Ga/Al ratio of a mixed Nd-doped α(Al1−x Gax )2 O3 film. . . . . . . . . . . . . . . . . . . . . . . .  Figure . Density and thickness of a set of mixed Nd-doped α(Al1−x Gax )2 O3 films obtained using x-ray reflectivity (XRR). .  Figure . Effect of varying the Ga/Al ratio of Nd-doped α(Al1−x Gax )2 O3 on PL emission spectrum and XRD peak. . . .  Figure . RSM showing the off-axis () peaks for Nd-doped α(Al1−x Gax )2 O3 films grown on A-plane sapphire. . . . . . . . .  Figure . Effect of composition and unit cell volume of Nd-doped α(Al1−x Gax )2 O3 films on emission peak wavelength. . . . . . . .  Figure .  PL spectra from a  µm thick Nd:Y2 O3 film grown on C-plane sapphire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   Figure .  PL intensity of the 4 F3/2 →4 I11/2 transitions for varying concentrations of Nd:Y2 O3 . . . . . . . . . . . . . . . . . . . . . . .   Figure .  RGA scans showing Al desorption. . . . . . . . . . . . . . . . .   Figure .  PL spectra of the 4 F3/2 → 4 I11/2 transition from Nd-doped YAl-O films grown on sapphire. . . . . . . . . . . . . . . . . . .   xiii  List of Figures Figure .  Map showing the phase of Nd-doped Y-Al-O films grown on sapphire at ◦ C under different growth conditions. . . . . . .   Figure .  XPS survey scan showing the surface composition of an Nd:YAG film grown on sapphire. . . . . . . . . . . . . . . . . .   Figure .  PL spectra from Nd-doped Yx Aly O films grown on sapphire with varying Al/Y ratios as measured by XPS. . . . . . . . . . .   Figure .  Effect of substrate temperature on Al incorporation during the growth of a YAG film on sapphire. . . . . . . . . . . . . . . . .   Figure .  Structural and emission properties of a high quality Nd:YAlO3 film grown on R-plane sapphire. . . . . . . . . . . . . . . . . .   Figure . Effect of a  hr, ◦ C furnace-anneal on Nd-doped YAG, YAP and Y2 O3 films grown on sapphire. . . . . . . . . . . . . . . . .  Figure .  Estimated wavelength of the dominant PL peak for the other candidate corundum-structure oxides. . . . . . . . . . . . . . .   Figure A.  Hexagonal lattice of sapphire showing the  most popular substrate orientations C, R, A and M. . . . . . . . . . . . . . . . . .   Figure B.  Simulated transmission electron microscopy (TEM) patterns produced using an electron beam directed towards different sapphire substrate orientations along the denoted azimuths. . .   Figure B.  Continuation of fig. B. showing M and R-plane sapphire. . . .   xiv  Glossary is glossary uses the handy acroynym package to automatically maintain the glossary. It uses the package’s printonlyused option to include only those acronyms explicitly referenced in the LATEX source. AMPEL Advanced Materials and Process Engineering Laboratory UBC  University of British Columbia  AFM  atomic force microscopy  CCD  charge-coupled device  FEL  fast-entry load lock  FWHM full width half maximum LPE  liquid phase epitaxy  LRO  long-range order  MBE  molecular beam epitaxy  MIG  monitoring ion gauge  MRO  medium-range order  PFC  pressure/flow controller  PL  photoluminescence  PLD  pulsed laser deposition  PWL  planar waveguide laser  QCM  quartz crystal microbalance xv  Glossary RBS  Rutherford backscattering spectrometry  RE  rare-earth  RHEED reflection high energy electron diffraction RGA  residual gas analyzer  RMS  root mean squared  RSM  reciprocal space map  SRO  short-range order  TEM  transmission electron microscopy  UHV  ultra high vacuum  XPS  x-ray photoelectron spectroscopy  XRD  x-ray diffraction  XRR  x-ray reflectivity  YAG  yttrium aluminum garnet or Y3 Al5 O12  YAM  yttrium aluminum monoclinic or Y4 Al2 O9  YAP  ytrrium aluminum perovskite or YAlO3  xvi  Acknowledgments First and foremost, thanks to my parents Jeya and Nair for their loving support and steadfast belief in me. ey taught me to aim high, and that great things are possible given hard work and trust in the Lord. anks also go to my sisters Sunita and Seetha, and my brothers-in-law Steve and Todd for their wonderful and entertaining company. You are the go-to people in my life! I am joyful for the time spent with Rayna, my lovely and hilarious niece, and Rohan, my rambunctious but oh-so-amusing nephew. I am extremely grateful to my fellow researchers at the Molecular Beam Epitaxy lab. ey created a vibrant collegiate atmosphere of stimulating ideas, helping hands and in general good times for all. ree cheers for Shawn Penson, Scott Webster, Daniel Beaton, Michael Whitwick, Ryan Lewis, Wei Li, Erin Young, Anders Ballestad, Ivan-Cristophe Robin, Eric Nodwell, Xianfeng Lu, Nikolaj Zangenberg and Jens Schmid. Special thanks go to our resident engineer / MBE-whisperer Jim MacKenzie for his help and advice on fixing the MBE on the numerous occasions when a critical subsystem failed. Personal shout-outs go to Shawn Penson, for teaching me how to use the Xray system and for lively discussions on gaming and books; Scott Webster, linux guru and my MBE MVP – we established a smoothly running MBE with minimal risk even during a power outage!; Dan Beaton, my NY Times crossword compadre, MBE ideas man, and all-round sounding board; and Mike Whitwhick a.k.a. Captain Morphology, who taught me cleanroom techniques before being certified himself as well as the fun of tinkering with optical setups (the exception being a Spectra Physics Wavetrain). Tom Tiedje, you a terrific supervisor and it has been a privilege to work with you. Your broad expertise and keen instincts in the field of crystal growth were pivotal for a great many ideas and research directions that helped define my work. More importantly, however, your emphasis on the quality of ones work as well as its  xvii  Acknowledgments presentation is a personal goal that I continually strive to emulate. I hope it comes through in this thesis. I would also like to thank the members of my PhD committee Lukas Chrostowski, Andrew MacFarlane and Kirk Madison for their valuable input over the course of my research and especially for the feedback on this thesis. Likewise for my thesis examiners Tom Trocynski and Peyman Servati from UBC as well as Zetian Mi from McGill. It is very likely that my research would not have happened without the funding support provided by NSERC. eir CGS D and PGS M post-graduate awards, as well as their USRA undergraduate award heavily influenced my decision to pursue graduate studies all the way to a PhD. e degree is merely the icing on the cake; the chance to research a field and create something new was immensely rewarding on its own.  xviii  1– Introduction e race to demonstrate the first laser device was won by Ted Maiman of Hughes Labs in , who used a synthetic ruby crystal grown by Ralph Hutcheson as the laser gain medium[]. Ruby, a luminescent material with the chemical formula Cr:α-Al2 O3 (i.e. Cr-doped sapphire), produces optical emission from the low concentration of optically active chromium dopants dispersed throughout the sapphire host. ese dopants also give the otherwise transparent sapphire the characteristic pink–red colour of ruby. ere are many other luminescent materials that use optically active dopants, available through the combination of: suitable dopants, typically transition-metal or rare-earth atoms; and plentiful hosts, most commonly oxide compounds. e large overall selection gives access to a wide range of emission wavelengths and has been exploited for various display and lighting applications. When making devices, luminescent materials in their naturally occurring form are unsuitable due to the likelihood of extraneous impurities and structural defects. Instead, they are replicated synthetically with specifications required by the target application including composition, structure as well as form e.g. powder, thin film, optical fiber, bulk crystal, etc. In the late s, General Electric began selling fluorescent lamps that used an inner coating of luminescent powders to produce visible light[]. Colour television became viable in the early s aer RCA succeeded in arranging powders of three different luminescent materials (for red, green and blue) into a discrete pixel array[, chap.]. In contrast to these earlier devices, Maiman’s criteria for the laser gain medium was a large and uniform piece of luminescent material that could support optical propagation with minimal losses. He settled on ruby because synthetic crystals were available at the time from the Linde division of Union Carbide, grown by people like Hutcheson using a flame fusion process first reported by Auguste Verneuil in []. Initially intended for replicating gems, Verneuil’s growth method proved so successful at mass-producing synthetic ruby and sapphire crystals that it un-    – Introduction locked industrial uses including jewel bearings and watch windows[]. Maiman’s laser success spurred the search for other materials offering better laser performance and different emission wavelengths. e search, which still continues today, initially unveiled a rich selection of laser gain media encompassing the various forms of matter: gases (e.g. HeNe in []), liquids (e.g. organic dye in []) and solids (e.g. Nd:glass in [], semiconducting GaAs in [])¹. Attempts at new solid state gain media in particular oen motivated improvements to material synthesis techniques including crystal growth. A notable achievement was made in  by Geusic et. al., who used a  cm long Nd-doped Y3 Al5 O12 (Nd:YAG) crystal rod to produce laser emission in continuous-wave mode[]. e large crystal was possible due to advancements in the Czochralski method of growing bulk crystals. Nd:YAG proved to be a high-gain laser medium, and has since become the established choice for ∼ µm emission. It gained further popularity when the flash lamps used for optical excitation were replaced with more efficient diode sources. e wide availability of sources designed to excite Nd in turn made Nd the preferred optically active dopant for testing new solid-state laser hosts. Besides new materials, new laser geometries were also explored. Snitzer made the first waveguide laser using a ′′ long glass fiber in []. e fiber consisted of a  µm diameter core of Nd-doped barium crown glass (the gain medium) and a cladding of soda lime silicate glass. e lower-index cladding was essential for waveguiding, which confines the beam and reduces the threshold power needed to initiate lasing. In Snitzer’s case, a waveguide was necessary because solid-state lasers based on glass hosts have much weaker gain compared to their crystal counterparts. Nevertheless, advancements in fabrication over subsequent decades led to longer and better optical quality fibers (likewise for crystals), such that high power laser output in the kW range is now possible from metre-long fibers[]. e idea to combine the high gain of doped laser crystals and the efficiency of waveguiding was first implemented in the early s by van der Ziel el. al using a garnet variant of YAG with holmium and then later neodymium dopants[, ]. Unlike amorphous fiber, the crystals were in the form of planar thin films, having ¹e term “solid state”, when referring to gain media, is only used for solids doped with lightemitting elements. e term is not used for semiconductors, which despite also being solids, use a different physical process involving the recombination of electrons and holes to generate light.    – Introduction been grown on a planar YAG substrate that provided a template crystal for the film to follow. Ordered growth in such a manner is referred to as epitaxy. e multilayer operated as a waveguide, where the YAG substrate and doped film layers were analogous to the cladding/core layers in an optical fiber. In common practice, a top layer would be deposited on the doped film to complete the cladding and improve waveguiding. e high gain and efficient geometry of a planar waveguide with a doped crystalline core make it a compact alternative to optical fiber devices. Advances in the field have led to a YAG planar waveguide laser producing  W output from a  µm thick core layer with a length of only  mm[]. Setting aside optical gain, luminescent devices based on thin films have multiple advantages associated with the planar geometry in general: excellent heat extraction from the large surface-area-to-volume ratio; high fabrication yield because of its support for mass-processing steps; and suitability for incorporation into integrated optoelectronic circuits. As an example of the mass-processing benefits, multiple devices are produced from a single thin film deposition step, depending on the area of the substrate. Further savings can be made by processing the thin film (e.g. polishing, coating) before cutting it into the individual devices. ere are many ways of making crystalline, luminescent thin films, not all of them by epitaxy. e research presented in this thesis covers my work to extend the current capabilities in the field using the molecular beam epitaxy (MBE) growth technique. A review of the various techniques and the advantages of MBE are provided in sections . and .. e thesis shows how MBE was used to create new luminescent materials such as Nd-doped sapphire, a promising laser material with a unique emission spectrum and strong, sharp emission peaks. e material may appear simple, consisting of a common laser host and a popular dopant, but it had never been created by bulk crystal growth methods due to the size of the Nd dopant. Sapphire is typically doped with the much smaller transition-metal elements. Other new materials created include Nd-doped gallium oxide and Nd-doped alloys of sapphire and gallium oxide. Existing materials were also attempted, namely the phases in the Y-Al-O system, which include the ever popular YAG. e thesis highlights the interesting properties of these materials, characterized both during and aer growth. e rare-earth neodymium was used exclusively as the optically active dopant   – Introduction in all the MBE growths. is provided a basis of comparison for the various host materials grown because the rare-earth optical emission spectrum is highly dependent on the host. Section . will cover the physics behind the emission spectra, with a special focus on neodymium.  .  Rare-earth luminescence and the solid state  When used as optically active dopants, the rare-earths typically exist in the form of trivalent cations (e.g. Ce3+ , Nd3+ , Er3+ ) that have an electron configuration of [Xe]fN . Here [Xe] is the electron configuration of the noble gas xenon: s2 s2 p6 s2 p6 s2 d10 p6 s2 d10 p6 , and N is the number of f electrons corresponding to the position on the rare-earth (or lanthanide) row of the periodic table e.g. N = – for Ce3+ –Lu3+ respectively. Electrons in the partially filled f shell are localized closer to the nucleus than those in the filled s and p shells, and are thus shielded from external interactions such as chemical bonding. is leads to fN electronic states with discrete energy levels that produce sharp optical transitions characteristic of atomic spectral lines. e fN states can be derived by first finding the states of the RE3+ free ion from the quantum theory of atomic spectroscopy, then perturbing those states to simulate the effect of the solid state host.  .. Electronic structure of the RE3+ free ion e approach to determine the electronic states of a RE3+ free ion with the fN configuration is rather involved, so a brief overview will be provided here based in part on details provided by Guokui Liu and a summary by Miniscalco[, ]. e energy levels of the electronic states are determined by the Hamiltonian operator, which for a RE3+ free ion is dominated by the following terms:  H = H0 + HC + HSO  (.)  Here H0 is the central field approximation, HC is the electrostatic interaction and HSO is the spin–orbit coupling. e main contribution comes from the central field approximation, which treats each f electron as independent and hydrogen-    – Introduction like, moving in the spherically symmetric potential of the nucleus and the average potential of the other electrons. H0 therefore evaluates the kinetic and potential energy of the n electrons as well as part of the inter-electron repulsion. e rest of that repulsion is captured by the HC term, while HSO describes the magnetic interaction between the spin and angular momentum of the electrons. Both HC and HSO are small compared to H0 , and are thus treated as perturbations. From the central field approximation, the fN electron configuration has a single specific energy regardless of the orbital and spin angular momenta possible by the ensemble of N -f electrons. is degeneracy is lied by the HC and HSO perturbations, which splits the configuration into multiple energy levels. e 2S+1 LJ notation of the LS coupling (a.k.a. Russell-Saunders) scheme is used to describe these levels. Here L and S are the respective quantum numbers for the total orbital and total spin angular momentum of the ensemble, where L (or S) is obtained from a vector sum of the orbital (or spin) number from each f electron. While each f electron has an orbital number of  and a spin of /, care must be taken while deducing L and S to avoid having electrons with the same angular momentum projections (Pauli exclusion principle). e overall total angular momentum J is then obtained by coupling both L and S together such that J= |L-S|, |L-S|+, ..., L+S. As an example, the ground state of Nd3+ following Hund’s rules is 4 I9/2 , where S=/, L= and J=/. Note that L is specified in alphabet form with labels of L=S,P,D,F,G,H,I,.. representing values of L=,,,,,,,.. and so on. In the typical LS coupling approach, the energies of the 2S+1 LJ levels are solved by applying the perturbations in successive steps[, chap.]. e electrostatic interaction HC first lis the degeneracy of the electron configuration to produce terms of 2S+1 L, then the weaker spin-orbit coupling H SO  splits those terms into the 2S+1 LJ  levels. e magnitude of the splittings are smaller for the latter, and thus have minimal effect on the former. However, in the case of RE3+ ions, the heavy nucleus induces a strong HSO perturbation comparable to HC , which causes the mixing of levels with the same J but different L or S. e 2S+1 LJ notation scheme is still used though, with the levels labeled based on their leading contribution. For example the ground level of Nd3+ has components from 4 I9/2 and 2 H9/2 , but the former is dominant and so the level is labeled accordingly. e LS coupling approach works better for light atoms, so here an intermediate coupling approach is neces  – Introduction Nd3+, [Xe] 4f3  2H -1 11/2 16161 cm 4F -1 9/2 14995 cm 4F 4 -1 7/2 , S3/2 13720, 13793 cm 4F 2 -1 5/2 , H9/2 12748, 12800 cm 4F -1 11699 cm  4F  3/2  R2 = 11506 cm-1 R1 = 11421 cm-1  3/2  4I  X7 = 4494 cm-1 13/2 X1 = 3925 cm-1  4I 4I  15/2  5989 cm-1  13/2  3907 cm-1  Y6 = 2515 cm-1  4I  11/2  4I  9/2  1897 cm  4I  11/2  Y1 = 2003 cm-1  -1  0 cm-1  Z5 = 852 cm-1 4I  9/2 Z1 = 0 cm-1  Electrostatic + Spin - orbit  Central field  Crystal field (b)  (a)  Figure .: Electronic structure of Nd3+ as a (a) free ion, and (b) as a dopant in a YAG crystal. Only the crystal field manifolds popular for optical emission are shown. sary whereby the Hamiltonian containing elements of both perturbations is solved simultaneously rather than in stages. In practice, the free ion Hamiltonian is simplified into terms of effective operators that are parametrized based on the type of rare-earth. Various corrections to better fit experimental results are then added, leading ultimately to a -term Hamiltonian. e set of + parameters for each rare-earth ion have been observed to vary only by ∼ when using different hosts, which is further evidence that the fN electrons are shielded from interactions with their environment. While the parameters are not a focus of this thesis, they help identify and evaluate the energy levels of the free ion. As an example, Nd3+ in the configuration [Xe]f3 has the   – Introduction spectroscopic terms 4 I, 4 F, 2 H, 4 S, 2 G, 4 G, 2 D, 2 P, etc.[, chap.]. Its lowest energy levels are plotted in figure .(a), based on vacuum spark measurements by Wyart[]. e overlap between levels of the 4 F, 2 H and 4 S terms shown are a consequence of the strong spin–orbit coupling mentioned above.  .. Effect of local atomic structure on free ion levels When a rare-earth is doped into a solid state host and chemically bonds as a trivalent (+) ion, the electrostatic interaction with its bonding partners (e.g. O2− anions) destroys the free-ion spherical symmetry. Since the fN electrons are shielded, the electric field generated by the partners (a.k.a. crystal field) is weak and thus treated as a perturbation HCF to the free-ion Hamiltonian of the previous section. HCF lis the degeneracy of the angular momentum J, splitting each 2S+1 LJ level into a number of states depending on certain criteria. For example, 2J + 1 states are created if the RE3+ ion has an even number of f electrons, but only (2J + 1)/2 when f is odd. e difference is attributed to Kramer’s degeneracy, which persists for half-integral J[, chap.]. Using an oxide host as an example, the geometry of the surrounding O2− cage (i.e. local atomic structure) determines the crystal field. As such, the symmetry of the cage also affects the splittings, where dopant sites with high symmetry have fewer split states because they approach the ideal spherical symmetry of the free ion. For example, Nd3+ doped into a site with cubic symmetry would have its 4I  9/2  ground level split into  states, but  if the symmetry was lower[, chap.].  However, the large size of Nd precludes cubic site doping; Nd dopants are typically in sites of octahedral (-coordinated) or dodecahedral (-coordinated) symmetry. Pauling’s rules provide approximate guidelines for determining the coordination number. When doped into a YAG (Y3 Al5 O12 ) crystal, Nd3+ ions substitute into the dodecahedral sites of the Y3+ ions that have a D2 point group symmetry (fold rotation with two additional -fold rotation axes perpendicular to the primary axis)[, chaps.,]. at site is shown in figure ., and can be compared to the -fold rotation C3 site of Al3+ in sapphire. e plots were made using the Jmol chemical structure viewing soware[]. e manifold of states split from each J level usually covers a small energy range    – Introduction (b)  (a)  Y3+  Al3+  O2-  Figure .: Site symmetry of the (a) Y3+ site in YAG and the (b) Al3+ site in sapphire. Nd3+ dopants are substituted into these sites, the latter being the result of research presented in this work. such that there is a clear separation between manifolds. As an example, the 4 I9/2 , 4I  11/2 ,  4I  13/2  and 4 F3/2 manifolds of Nd-doped YAG are shown in figure .(b),  based on room temperature measurements by Walsh et. al.[]. In cases when states with different J overlap (result of strong spin–orbit influence mentioned earlier), the outcome mostly involves a shi in energy level positions. Calculating this, however, requires a more elaborate treatment of the Hamiltonian[]. e manifolds split from the J levels are responsible for the spectroscopic properties of the rare-earth (RE)-dopant including optical absorption and emission. For example, a transition from a higher energy state to a lower one could produce light (i.e. a radiative transition), where the wavelength is specified by the energy difference between those states. To be remotely useful, these optical transitions should involve the electric dipole, which is orders of magnitude stronger than the magnetic dipole. Such optical transitions are impossible for the RE3+ free ion because an electric dipole transition requires a parity change but all the levels of the fN con-    – Introduction figuration share the same parity. e parity of a configuration is essentially a test of ∑  odd or even spatial symmetry and is determined from −1(  l) , where l is the orbital  quantum number of each electron[, chap.]. A parity change therefore requires transitions between different electron configurations. e crystal field surrounding the RE3+ dopant overcomes this limitation by creating admixtures between states of the fN configuration with those from higher–lying, opposite–parity configurations (e.g. fN −1 d). ese admixtures depend on the odd-parity components of the crystal field, which therefore excludes dopant sites with inversion symmetry. e admixtures only contribute a small electric dipole component, albeit one dominant compared to the other electromagnetic components[, chap.]. e crystal field Hamiltonian taking the admixtures into consideration can be solved using approximations by Judd and Ofelt. ey also identified the selection rules for fN transitions made possible by the crystal field: ∆J ≤ 6 but J = 0 → J ′ = 0 forbidden, ∆S = 0 and ∆L ≤ 6. As an example, the states shown in figure .(b) are responsible for the popular Nd:YAG optical emission wavelengths near ,  and  nm, which involves transitions from the excited R1 and R2 states of the 4 F3/2 level to the Zi , Yi and Xi states within the 4 I9/2 , 4I  11/2  and 4 I13/2 manifolds respectively.  .. Effect of solid state host on emission spectra e crystal field acting on an individual dopant produces states with discrete energy levels that yield sharp emission lines during optical transitions. ese levels are unique for a particular local atomic structure. When the dopant is part of an ensemble distributed within the solid state host, it can be treated as an isolated optical centre because the interaction between dopants is minimal for typical dopant concentrations (∼ at. for Nd). e emission spectra from the ensemble is therefore the sum of the emission from every dopant, and thus may not resemble sharp emission lines because the local atomic structure and consequently the crystal field may vary for each dopant. Instead of tracking individual dopant sites, it is more practical to evaluate the local structure in aggregate, which to some extent can be associated with the level of order/disorder of the host structure. In general, structural order can be categorized by the existence of short, medium    – Introduction or long-range order (SRO, MRO and LRO respectively)[]. SRO pertains to the arrangement of a site’s nearest neighbours (e.g. O2− relative to Y3+ in YAG), which include the coordination number as well as bond lengths and bond angles among others. Given SRO, the site and its nearest neighbours can be visually simplified to a polyhedron (e.g. a dodecahedron or octahedron in fig. .), which together with nearby polyhedra determine the level of MRO from their mutual orientation. e polyhedra can be interconnected by sharing vertices, faces or edges, so MRO is more evident given a fixed relationship[, chap.]. Vertex-sharing may not have the best chances for MRO since adjacent polyhedra can be rotationally offset. e range for MRO is not well-defined, though covering a few of these structural units should be adequate. Finally, LRO exists when remote parts of the material have a correlated structure. Here the polyhedra should be arranged in a repetitious pattern that maintains the interconnected distances and angles. LRO is commonly associated with crystals, where a number of polyhedra form into a unit cell that repeats across the material with translational symmetry. To illustrate the various scenarios of structural impact, the emission spectra from Nd in three different hosts are shown in figure .. e optical fiber host composed of silica glass is considered a disordered material because it lacks LRO, having instead SRO and elements of MRO. Silica glass consists primarily of a disordered network of [SiO4 ] tetrahedrons that are bridged by oxygen atoms. e network, however, tends to depolymerize due to the various glass-improving additives, which break up the O–Si–O chain and form ionic bonds with the resulting non-bridging oxygens[]. When doped into glass, the RE-ion is too big for the -coordinated Si site and thus will be excluded from the partially ordered, glass-forming chains. Instead, the dopants bond preferentially with the non-bridging oxygen ions and are higher-coordinated depending on size e.g. – for Nd3+ and  for the smaller Er3+ []. is variety in Nd3+ coordination renders the local atomic structure inhomogeneous across the ensemble, producing a broad emission peak because the individual electronic states now have a distribution of energy level positions. Inhomogeneity may exist even for dopants with the same coordination, especially when the bond lengths are not uniform. According to Wang et. al., dopant homogeneity in glasses improves when using a smaller-sized rare-earth (more uniform coordination) and   – Introduction  Emission Intensity (arb. units)  (a)  (b)  (c)  860  880  900  920  940  960  Wavelength (nm)  Figure .: Emission spectra showing the 4 F3/2 →4 I9/2 transitions from Nddoped (a) glass fiber, (b) nanocrystalline YAG powder, and (c) singlecrystal YAG. Data for the plots were extracted from works by Strek et. al.[, ]. with availability of non-bridging oxygen (more uniform bond lengths)[]. e latter suggests using more additives to depolymerize the network. Compared to glassy hosts, the environment in a single crystal offers SRO, MRO, and LRO. Crystals are typically compositionally pure since additives such as those used in glasses are avoided as they would disrupt the lattice and thus break translational symmetry. In contrast, optically active dopants (e.g. rare-earths or transitionmetals) can be integrated into the lattice with minimal disruption by substituting for the crystal cations. e crystal hosts, however, must satisfy the coordination requirement of the dopant. For example, YAG has the -coordinated Y3+ site suitable for Nd3+ or Er3+ doping and sapphire has the -coordinated Al3+ site for Cr3+ or Ti3+ . Dopants in a crystal are therefore identically coordinated, and having a lattice to enforce atomic positions will ensure uniform bond lengths. As a consequence,   – Introduction the dopant ensemble has a homogeneous local atomic structure where each dopant has states with the same energy level positions. e sharp emission lines of individual RE-dopants now persist for the overall ensemble, and the overall emission spectra features a collection of sharp peaks that uniquely represents the interaction between the RE-dopant and its host structure. While single crystals remain the epitome of excellent LRO, other crystalline environments with only SRO, MRO and limited LRO also exist. An example is the nanocrystalline powder represented by fig. .(b) that consists of Nd:YAG crystallites with an average size of  nm. e crystallites (a.k.a. grains) each mimic the structure of single-crystal Nd:YAG but are oriented non-uniformly, hence the material is considered to be polycrystalline. Even with the weak LRO², the crystallites are better ordered than the MRO of glasses and can accommodate the Nd dopants in homogeneous sites. e emission spectra therefore resembles the spectra of sharp peaks associated with a Nd:YAG single crystal, albeit with subtle differences such as wider peaks. Some level of inhomogeneity thus exists, which for a polycrystalline host likely involves dopants in the disordered regions near the crystallite interfaces (grain boundaries), where sudden changes in orientation occur. While the difference between polycrystalline and single-crystal Nd:YAG in terms of emission may appear minor, other criteria may apply when making optical devices as will be discussed in the next section. However, it should be noted that the similarity of the Nd:YAG pair shown here is a promising result, inspired by the search for better devices, and due to polycrystalline growth with better control over the crystallite parameters[].  .  Crystallinity considerations for optical devices  When designing an optical device based on rare-earth emission, the first step likely involves finding a RE-dopant capable of emission in the desired wavelength. en, a host with a suitable level of structural order should be chosen to provide the emission quality required by the target application. Other considerations also apply at that point, such as the form factor and overall production cost. ²Considering the unit cell of YAG is cubic with . nm long sides, each crystallite consists of a number of unit cells thereby ensuring SRO and MRO. Some element of LRO is also present, albeit weak since  nm is a significant range reduction from the ideal case of a single crystal.    – Introduction In display devices such as TV screens, the visible colour gamut is reproduced using a variety of dopants, one for each colour. Broad emission peaks are acceptable here, but narrower peaks can improve the colour purity. e emitters must be small, isolated and able to populate a dense pixel array, which would be too costly if using single crystals. Fortunately, scattering within the emitters due to optical path distortions does not significantly affect the emission quality. A typical approach is to use polycrystalline oxide powders synthesized from a solution. Examples of rare-earth emitters used in displays such as plasma display panels, cathode ray tubes or projection TVs include Eu3+ :Y2 O3 (red), Tb3+ :Y3 Al5 O12 (green) and Eu2+ :BaMgAl10 O17 (blue)[]. ese and other similar powders have also been used in lighting devices such as fluorescent bulbs and white LEDs. e latter uses Ce:YAG to convert violet light from the GaN LED into yellow light. Aside from polycrystalline powders, amorphous materials also make viable display emitters, as evidenced by the growing popularity of organic LED screens that use solid organic complexes doped with rare-earths[]. For specialized applications where the optical emission is amplified e.g. lasers, the material quality requirements are more rigorous. A crystalline structure ensures higher gain from the sharp and narrow emission peaks, and with a uniform crystal field across the ensemble, specific peaks can be distinguished and exploited e.g. for the lasing wavelength. While these conditions are met by both single-crystal and polycrystalline (subject to quality) materials, size is an important parameter for gain devices, which in turn necessitates a consistent optical path for beam propagation. Since various problems are associated with polycrystal grain boundaries, single crystals have oen been the preferred choice[]. Progress in the s and s, however, yielded successive improvements in polycrystal synthesis leading to high power Nd:YAG bulk lasers made from nanocrystalline powders sintered at high temperature and under pressure[]. is type of process is more sophisticated than those used for display devices, but produces better quality polycrystals. It is also faster and more cost-effective than single crystals pulled from a melt when making bulk devices. Optical scattering at the grain boundaries are mitigated by the dense crystallites that are small relative to the emission wavelength, not unlike the sample of fig. .(b). A drawback of the high-quality polycrystals, however, is that although   – Introduction the grain boundaries are better-ordered, the crystallites still have non-uniform orientations[]. Optical gain devices are therefore limited to crystals with a cubic lattice (e.g. Nd:YAG) because of their optical isotropy, where properties such as refractive index are non-directional. Optically anisotropic crystals are unsuitable because scattering at the grain boundaries is exacerbated by the inconsistent refractive index along the beam propagation path[]. Anisotropic crystals such as Nd:YVO4 are attractive for their higher gain over isotropic crystals, and merit fabrication in single-crystal form[]. e higher gain stems from the local atomic structure, which is typically anisotropic because of the low symmetry of the RE-dopant sites. Since the local structure affects both crystal field splittings and transition strengths, the emission/absorption from each site is likely to be directionally dependent. However, this may not carry through to the overall lattice because the lattice symmetry includes a greater number of elements/sites and may be wholly different from the site symmetry. For example, the YAG lattice has Oh cubic symmetry that is much higher than the D2 symmetry of its Y3+ sites. is contrasts to the rhombohedral lattice of sapphire with D3d symmetry, which is comparable to the C3 symmetry of its Al3+ sites[, chap.]. e YAG unit cell consists of  atoms including  Y3+ sites with an isotropic arrangement that counteracts any directional advantages in emission/absorption. In comparison, anisotropic crystals like sapphire (with its smaller unit cell) are more likely to retain and amplify the anisotropic local structure resulting in polarized emission/absorption that may favour certain peaks. Anisotropic RE-doped crystals in single-crystal form are definitely worth pursuing.  .  Planar thin films for making solid state lasers  .. Bulk lasers Aside from crystal structure, the geometry of the RE-doped medium must also be considered when designing optical devices. When making intense light sources such as lasers, the necessary optical gain can be achieved using a medium with excellent crystallinity and sufficient propagation length. Historically, this involved single crystals in bulk form (e.g. rods) made by methods such as the Czochralski process of   – Introduction pulling crystals from a melt. With the recent advances in sintering, isotropic polycrystalline materials in bulk form are now also viable. In a typical laser assembly, the gain medium (bulk or otherwise) is placed within an optical resonator of at least two mirrors, along a path where repeated reflections of its emission builds into a strong enough optical field that can stimulate it to produce coherent emission i.e. lasing. e RE-doped gain medium is usually excited optically, where the pump power required to initiate lasing is denoted the threshold power. e optical pump has a smaller wavelength than the lasing wavelength so as to excite the RE-ions to a higher-lying state than the state responsible for the emission. Using the popular Nd:YAG and its states in fig. . as an example, a typical pumping–lasing scheme involves an  nm pump to excite Nd3+ ions from the ground state of Z1 in the 4I  9/2  manifold to a state in the mixed 4 F5/2 + 2 H9/2 manifolds. e excited Nd3+  ions then decay non-radiatively to the metastable 4 F3/2 manifold, distributed across the R1 and R2 states. Nd:YAG has a dominant emission peak at  nm, which unlike most lasers is due to two radiative transitions that overlap in wavelength: R1 → Y2 and R2 → Y3 . To complete the -level cycle, the Nd3+ ions then decay non-radiatively to the 4 I9/2 ground manifold. Laser assemblies using bulk gain media typically consist of spatially separate elements (discrete mirrors, etc.), so geometry concerns include the evolving size of both the pump and laser beams due to free space diffraction. For example, a rodshaped gain medium should be wider than the pump beam at its location, and long enough for maximal absorption that excites a large RE-ion population into the upper manifold. e laser beam within the resonator should also be likewise contained for maximal stimulated emission. Since the beam profile within the resonator is largely determined by the optics, the rod would be best placed at the beam waist where the optical intensity is highest. Knowing the segment of the rod excited by the pump as well as the resonator beam profile, the length of the rod required for sufficient gain to overcome the losses of the entire assembly and yield net laser output can be estimated.    – Introduction  .. in film advantages in films are an alternative to bulk media, offering numerous advantages and new geometry possibilities such as the thin disk, microchip and waveguide laser. e films are typically planar, and may sit atop an underlying substrate of similar material. A thin disk laser consists of a thin layer of gain material ∼ – µm thick with a high-reflectivity coating on its underside and a free-space front-facing mirror for the laser output. e disk is optically pumped obliquely from the front, with a series of mirrors used to recirculate the pump beam to improve absorption by the thin layer. e disk is mounted on a cooled heat sink, and can be power-scaled via the disk diameter leading to kW-level output power with good beam quality (nearly gaussian)[]. In contrast, microchip lasers are low-power devices constructed monolithically for deployment in small-sized devices. e gain medium is typically ∼  mm2 by  µm thick and is sandwiched by mirror coatings. e monolithic design allows the use of other functional layers within the resonator e.g. a saturable absorber for pulsed laser output[]. For further compactness, the microchip laser and its pump (typically a diode laser) may be incorporated into the same module. ese two laser examples highlight the advantages offered by the thin film geometry: heat extraction for high power operation, compact design, and wider functionality. Heat is generated during the non-radiative decay transitions of the RE-ion absorption–emission cycle, and more so the greater the difference between pump and laser wavelength. High power operation further exacerbates the heat load, creating problems such as thermal lensing that involve refractive index distortions. All the above-mentioned advantages can be realized by a thin film planar waveguide device, which consist of a core layer sandwiched by top and bottom cladding layers with lower refractive index. e index contrast between core and cladding enable a discrete set of guided modes to propagate within the core, with the modes decided by the optical properties of the layers as well as core thickness, typically in the range of one to tens of micrometers thick[, ]. A compact planar waveguide laser (PWL) with RE-doped core can be made monolithically if mirrors are coated on the end faces. Compared to the microchip laser, high power operation is possible since propagation occurs within the core instead of across it, allowing for higher    – Introduction gain. Like the thin disc laser, the large surface area can be exploited for optimal heat extraction. Wider functionality is also possible by adding layers between the core and cladding e.g. a non-linear layer for frequency doubling[]. Perhaps the greater incentive for PWLs is that they bring the waveguiding benefits of optical fiber to high-gain single crystals. Optical confinement is maintained over the length of the gain medium producing high intensity optical modes superior to the beams in bulk media that diverge due to diffraction. Confinement can be exploited for both the pump and lasing modes, and given certain pumping configurations will allow for excellent overlap of the two. Combining the high gain contribution of crystals with the high optical intensities and high modal overlap possible with waveguides will lead to efficient lasers with low lasing thresholds. PWLs can be much shorter than fiber lasers due to the high gain, and coupled with the planar geometry allows for small-footprint compact devices that are easier to integrate with semiconductor fabrication processes.  .. in film growth ere are various ways to make the devices of the previous section. Since thin disc and microchip lasers have relatively thick but simple structures, the practical approach for their gain media is to use diced pieces of bulk-grown crystals. PWLs are generally thinner with a more complicated multilayer structure better suited for deposition methods, but the thicker PWLs are routinely assembled from bulk materials. e popular bulk approach is contact bonding, where separate core and cladding pieces are bonded by weak Van der Waals forces, then heated (avoiding diffusion) to promote stronger covalent bonding. Prior to assembly, the interfaces are polished to atomic-level flatness to improve adhesion as well as minimize laser scattering losses[]. Examples include an  µm thick Yb:YAG channel waveguide laser capable of  W output and the planar waveguide laser used for frequency doubling in Mitsubishi Electric’s laser television[, ]. in film deposition offers a number of advantages over bulk assembly methods. Although the growth rates are typically slower than those of bulk crystals , the PWL structure may be completed sooner since bulk crystal boules are grown over long durations (weeks for – cm of Nd:YAG at a rate of ∼. mm/hr)[,    – Introduction chap.]. In deposition processes, the PWL is grown onto a substrate in the order of bottom cladding, core, then top cladding, with the processes having some mechanism to switch between the materials used for each layer. e entire growth is essentially a single operation albeit with brief interruptions for layer changes, and is simpler to execute than the multiple steps of growth, cutting, polishing and bonding required for contact bonding. With access to a wide assortment of source materials and precise control of layer thicknesses, deposition processes can make PWL structures tailored for specific parameters such as refractive index contrast and number of waveguide modes. Scalability is yet another advantage, as these processes are capable of uniform growth over areas larger than the cross-section of a typical bulk crystal boule. is is helped by the flexibility in substrate material, which is not restricted to those of the core/cladding, but may be chosen instead based on the availability of large-area substrates. A suitable pairing for scalable mass production would be PWLs with a YAG core grown on sapphire substrates. Aside from deposition processes, thin film waveguides can also be fabricated by defining the waveguide structure from an existing host material. is typically involves processing steps that make local changes to the refractive index or surface morphology. One example is thermal ion indiffusion, where a solid state host with rare-earth metal coating is heated to allow the RE-ions to diffuse into the host to create a gain profile with an elevated refractive index. Other examples include ion-exchange, proton exchange, ion-beam implantation, proton-beam writing and optical writing. Waveguide definition is attractive because the device may retain the optical properties of the solid state host, which is likely bulk-grown and therefore excellent. e downside, however, is the lack of control associated with modifying a structure rather than creating it from scratch. For this reason, deposition processes offer the most promise for advancing PWL devices and similarly related fields. Various processes have been demonstrated such as chemical vapour deposition, sputtering, molecular beam epitaxy, flame hydrolysis deposition and thermal sublimation, but the popular ones are liquid phase epitaxy, sol-gel deposition and pulsed laser deposition. e attributes of some of these processes are presented in table ., summarized from a comprehensive review of PWL fabrication methods by Grivas that covers deposition, waveguide definition and bonding processes[].    – Introduction Table .: Popular methods for PWL deposition compared to MBE  Sol-Gel Deposition Process  • Colloidal suspension (sol) coated on substrate by dipping, spin-coating or spraying • Suspension formed by hydrolysis and condensation of metal alkoxide precursor • Coagulation of colloids leads to porous network of solid gel • Gel densified by sintering  Properties  • Non-vacuum, low-cost, simple and versatile process • Suitable for glasses or organic–inorganic hybrid materials • Popular for silica/silicate glass waveguide doped with heavy elements • ickness limited by cracking during drying stage • Multiple steps required for waveguides Liquid Phase Epitaxy (LPE)  Process  • Single-crystal substrate dipped and rotated in supersaturated molten solution • Before dipping, substrate and furnace in thermal equilibrium • Substrate dipped in solution at above saturation temp. to dissolve surface layer, reducing defects • Solution then cooled to saturation temp. prompting spontaneous crystallization with substrate as seed crystal  Properties  • Non-vacuum, low-cost and simple process • Epitaxial growth of single-crystal films using low supersaturations near thermodynamic equilibrium • Typical growth rates ∼ µm/hr • Important that substrate and film are lattice matched with similar thermal expansion coefficients • Typical films such as KY0.59 Gd0.19 Lu0.22 (WO4 )2 on KY(WO4 )2    – Introduction  Liquid Phase Epitaxy (LPE), continued Properties  • Challenges with precise thickness control and surface uniformity • Multilayers are time-consuming (solution changes etc.) Pulsed Laser Deposition (PLD)  Process  • Vapour deposition of ablated sources under vacuum conditions • Sources prepared by sintering powder with desired film composition • Ablation of solid source by pulsed laser (typically ns pulses at UV wavelengths) • Plume of ejected material directed towards opposing substrate • Background gases: buffer gas to control surface diffusion, and/or oxidizing agent • Multilayers possible by switching target sources (e.g. carousel)  Properties  • Single-crystal films at growth rates up to  µm/hr with precise thickness control • Flexible choice of substrate and film materials, but best if latticematched with similar thermal expansion coefficents. • Growth temperature much lower than melting point, allowing access to materials like Nd:Y2 O3 (◦ C vs ◦ C) • Easier for materials with simple structures: cubic (e.g.  garnets,  sesquioxides) and trigonal (e.g. sapphire) • Unwanted phases form during growth of biaxial materials (e.g. orthorhombic Nd:YAlO3 ) • Problem: micron-size particulates from ejecta increase waveguide propagation loss • Effect of laser pulse rate on particulate formation depends on target material • Film choice subject to availability of target sources    – Introduction  Pulsed Laser Deposition (PLD), continued Properties  • Difficult to create graded-composition layers, system with multiple lasers capable of simultaneous ablation required Molecular Beam Epitaxy (MBE)  Process  • Vapour deposition like PLD but with elemental sources that form compounds on the substrate surface • Metal sources evaporated from individually heated effusion cells • Anions sourced via background gas (e.g. oxygen, fluorine) in either molecular or active (e.g. plasma) form. • Independent control over atomic/molecular beam fluxes by varying cell temperatures and gas overpressure • Multilayers possible by actuating shutters on individual sources to select which material is grown  Properties  • Sophisticated, ultra-high-vacuum process popular for the growth of single-crystal compound semiconductors e.g. GaAs • Suitable for the growth of ionic compounds, though waveguide lasers mostly involved fluorides (e.g. ZnF2 , PbF2 , CaF2 , LaF3 ) • Oxide MBE used for high-temperature superconductors, multiferroics, wide-bandgap semiconductors, etc. • Clean environment and high-purity elemental sources lead to highly pure films • Overall beam fluxes affect film growth rate, while relative fluxes determine composition and doping level (assuming full incorporation) • Rapid shutters enable changes to the film at the atomic layer scale and allows for precise thickness control • Precise composition control over the entire film thickness important for complex multilayer structures such as waveguides with gradedindex layers or non-uniform doping profiles    – Introduction  Molecular Beam Epitaxy (MBE), continued Properties  • Growth from atomic/molecular beams is slow, typically not exceeding  µm/hr  .  Epitaxial films by MBE  .. Rationale Outlined in previous sections, the superior properties of RE-doped single crystals in planar waveguide form became the motivation for the research presented in this thesis. Using MBE exclusively, planar films of various solid state laser oxides were grown and their details are the subject of subsequent chapters. MBE is a mature technique having been refined over the past  years in the field of III-V semiconductor growth, but its use for solid state laser materials mostly involved fluoride hosts that were grown between  and []. e surprising result from the work on fluorides was that the MBE-grown films were more uniformly doped compared to bulk-grown crystals (maximum separation between dopants), thus permitting higher doping levels. Solid state laser oxides had been largely neglected, likely because of more demanding requirements such as higher growth temperature and an active oxygen source. Modifying an MBE system originally intended for III-V semiconductors enabled the oxide growths of this research, which sought not only to reproduce popular oxides like Nd:YAG but also to uncover new discoveries. Inspired by the inventors cited at the start of this chapter, it was expected that the merits of MBE would help further advance the field. To recap the growth comparisons of the previous section, MBE is capable of making anisotropic single-crystal films that are oriented with the substrate. Film composition can be controlled for each atomic layer deposited successively, allowing for complex multilayer structures with precise thickness control. At low growth temperatures compared to the melting point, the films may acquire benefits observed in III-V semiconductor growth such as lower levels of thermodynamic defects and smoother surfaces. e limi  – Introduction tation of slow growth rates may not be a problem for waveguide laser devices as functional devices with cores of a few microns thick are still viable given a sufficient core/cladding index contrast and an efficient optical pumping scheme. A major performance issue affecting most thin film growth methods is waveguide loss resulting from either defects in the propagation medium (e.g. micronsized particulates in PLD) or roughness at the core/cladding interfaces[]. Propagation losses in MBE films can be kept to a minimum by optimizing the crystallinity. Some defects that affect the film stoichiometry (e.g. vacancies) may still occur, but are unlikely to impair propagation because their length scales are much shorter than optical wavelengths. Interface roughness is common because surfaces typically roughen during growth from such factors as heteroepitaxy-induced stress relaxation and insufficient surface diffusion[]. Compared to other methods, however, MBE may be preferable for its graded interfaces. e scattering loss at a rough interface depends on the refractive index contrast, and is mitigated if the index changes gradually between core/cladding. ere is mention of a prototype PLD system in the literature with a complicated layout of multiple laser beams meant for simultaneous ablation of two or more source compounds, but it is unclear if such a system is capable of gradual index changes[]. Such control is natively inherent to MBE, requiring only temperature variations for the relevant sources.  .. Research scope e benefits outlined above prompted a new research project with the goal of making waveguide lasers using RE-doped oxides grown by MBE. e research presented in this thesis focuses on the initial steps of that project, which following the typical roadmap for making devices involves the identification, growth and characterization of suitable materials. My research followed that of Ivan-Christophe Robin, a post-doctoral fellow that initiated film growth for the project with Nd-doped Y2 O3 []. Ivan’s early films proved the viability of the project as they were highly crystalline (i.e. not single crystal, but with limited number of orientations) and produced an emission spectra of sharp peaks similar to those from Nd:Y2 O3 bulk crystals. e latter was measured by me and is shown in chapter . Aer Ivan’s departure, Scott Webster continued the work on Nd:Y2 O3 focusing on the crystalline    – Introduction quality and surface morphology of thin undoped films[]. He found improvements by reducing the growth rate and pre-treating the substrate surface. I joined the growth-side of the project shortly aer Scott did, and decided to branch away from yttria to search for better materials. Ivan’s yttria growths were successful partly because yttrium metal oxidized easily on the substrate, even without a source of active oxygen (i.e. molecular O2 was sufficient). e binary composition of the host oxide also helped, since ternary or higher oxides have a higher risk of structural disorder and unwanted-phase crystallites when the metal ratios deviate from single-phase stoichiometries (e.g. Y3.2 Al4.8 O12 vs Y3 Al5 O12 ). In addition, the cubic crystal structure of Nd:Y2 O3 relaxed the need for single-crystal films because the optical emission was isotropic and thus insensitive to crystallite orientation. Although the initial results were promising, it was unclear if the Nd:Y2 O3 films were suitable for making devices. For one, Nd:Y2 O3 was not an ideal laser gain medium due to its lack of a dominant emission peak. Surface roughness was another problem, increasing steadily during the growth of micron-thick films. Grading the index was not an option here due to the three stable Yx Aly O phases with dissimilar crystal structures and non-trending indices that might form when attempting a sapphire (substrate material) and yttria mixture. e research presented in this thesis covers two ternary oxide systems: Y-Al-O and Al-Ga-O, with Nd as the sole RE-dopant. All the films were grown on sapphire, an ideal substrate choice due to its optical properties, high thermal conductivity for better heat extraction, economical price and popular usage among researchers growing GaN and ZnO. Optically, sapphire has a lower refractive index than popular laser materials making it an attractive cladding choice. In addition, the UV–Vis–IR transparency window permits optical access to the gain layer by various pump geometries and wavelengths (e.g. face pumping with a UV source for IR emission). e research began with Y-Al-O, a reasonable follow-up to Nd:Y2 O3 that required only an aluminum source addition. e Y-Al-O work was motivated by the desire to report the first instance of MBE-grown Nd:Y3 Al5 O12 , the popular laser gain medium with a dominant emission peak at  nm. During the course of the research, however, it was found that MBE was capable of making all three of the stable Y-Al-O phases, Y4 Al2 O9 (YAM), YAlO3 (YAP) and Y3 Al5 O12 (YAG), here listed in order of increasing Al/Y ratio. e wide range of MBE growth condi  – Introduction tions facilitated the growth of single-phase films, which produced a Nd3+ emission spectra unique to each phase/host. e growth and characterization of Y-Al-O films is the subject of chapter . e thesis, however, will begin with the work on the Al-Ga-O system, starting in chapter  with the growth of Nd-doped sapphire, a new and promising laser material. Although the RE-dopant and the host are not new on an individual basis, uniformly doped Nd3+ in sapphire with a unique emission spectra of distinct peaks had not been previously reported. In that chapter, the simple binary oxide host with composition identical to the substrate is used to illustrate the MBE growth technique as well as certain film characterization methods. A more detailed analysis of the structural and optical properties of Nd:sapphire is presented in the following chapter, where the crystal anistropy helps to establish the dominant emission peak as a candidate for strong laser emission. Chapter  covers the growth and characterization of α-phased Ga2 O3 doped with Nd, another new material with a unique emission spectrum echoing that of Nd:sapphire because both materials share the same corundum structure. In a move analogous to the growth of the compound semiconductor AlGaAs, Nd-doped alloys of sapphire and α-Ga2 O3 were also grown. In contrast to the Y-Al-O system, α-(Al1−x Gax )2 O3 films with various compositions retained their α corundum phase, making them viable as graded-index layers. e thesis concludes with recommended future work, which includes new materials that should be attempted as well as attractive laser geometries uniquely suited for MBE growth.    2– Epitaxial growth of single-phase Nd:sapphire Sapphire (α-Al2 O3 ) is an attractive laser host crystal due to excellent thermomechanical properties and wide optical transparency. Solid state lasers made from sapphire typically use transition-metal dopants such as Ti3+ or Cr3+ which are similar in size to the replaced Al3+ ions. ere are no reports of rare-earth-doped bulk sapphire crystals suitable for making lasers. It is likely that the equilibrium solubility of rare-earth ions in sapphire is very low at the melting point due to the disparity in size between the small aluminum ions and large rare-earth (RE) ions. Rare-earth-doped sapphire lasers would be better suited for power scaling since the thermal conductivity of sapphire ( W/m·K) is large compared to other popular hosts such as YAG ( W/m·K) or YVO4 ( W/m·K)[, ]. While rare-earthdoped sapphire grown by bulk methods is unavailable, some progress has been made using thin film techniques. Eu-doped sapphire grown by pulsed laser deposition (PLD) produced distinct emission lines but they were superimposed on broad peaks, which according to section .. suggests greater structural disorder[]. It is possible that their poor films are due to the presence of unwanted Al2 O3 phases (not α or corundum phase). In a  Optics Letters article, my colleagues and I reported the growth of single-phase Nd-doped sapphire (α-Al2 O3 ) films on sapphire substrates by MBE[]. e emission spectra from this new material features sharp lines characteristic of Nd-doped crystalline hosts, implying a uniform crystal field effect on the Nd3+ dopants surveyed. e theory behind RE emission lines and their host effect was shown in section .. Among the Nd:sapphire emission lines, the  nm line in the 4 F3/2 → 4 I11/2 manifold is dominant and a candidate for lasing action. Solid state laser materials deposited in the form of thin films can be fabricated into planar waveguide lasers following methods borrowed from the semiconductor in-    – Epitaxial growth of single-phase Nd:sapphire Sapphire substrate, T = 400-1000oC  RHEED Source  RHEED Screen  O2 Plasma source • 200 W, designed in-house  Al, Ga, Nd, Y effusion cells Optical viewport  Figure .: MBE growth chamber dustry. ese lasers offer numerous advantages as outlined in section .. and have promising applications such as the high power sources in laser televisions[]. In this chapter, the MBE growth of Nd-doped sapphire will be presented together with details on the various growth subsystems. Following that, the methods used to characterize the films in-situ (in place) during and aer growth will be shown. ese methods include in-situ electron diffraction, surface morphology, crystal structure as well as optical emission. Characterization of single-phase Nd:sapphire films will be emphasized.  .  MBE growth  Films were grown by plasma-assisted MBE using a modified VG V-H system designed originally for III-V semiconductor growth. A schematic of the system growth chamber is shown in figure .. As the presence of oxygen or water vapour as residual gases are not a problem for oxide growth, the cryoshroud enveloping the chamber interior was cooled with water instead of liquid nitrogen. Aer this eco-    – Epitaxial growth of single-phase Nd:sapphire nomical switch, the cryoshroud served more as a heat sink rather than a cold surface for condensing residual gases. Ultra high vacuum (UHV) conditions were nonetheless established by a high-throughput Osaka turbomolecular drag pump and an APD cryopump. e growth chamber base pressure was typically ≤ −9 torr as measured by a UHV ion gauge. e system supports growth on wafers up to ′′ in diameter. Each sample i.e. substrate before/aer growth, is held on a molybdenum disc that is in turn mounted and locked into a manipulator unit that can be rotated freely to achieve uniform film growth. e Mo sample holders have cutouts specific to the sample shape e.g. quarter piece of a ′′ wafer,  cm2 square piece, etc., allowing direct access to the back of the sample for radiative heating. e heater sits ∼  cm behind the Mo sample holder in the manipulator unit but belongs to a fixed assembly that does not rotate. e original graphite heater was replaced with a serpentine-shaped SiC heater more resilient in an oxygen environment and capable of higher temperatures. e system has  source ports arranged in a ring and pointed at the manipulator ◦ off its normal. e mounting flanges are . cm away from the manipulator. e source ports are equipped with effusion cells for evaporating the metallic elements: Al, Nd, Ga, and Y, as well as a helical resonator plasma source for generating active oxygen. Designed in-house, the plasma source is powered by a  W tunable VHF amplifier[]. e background oxygen pressure during growth was typically ×−6 torr.  .. Substrate preparation As mentioned in section .., sapphire was chosen as the substrate material for a number of reasons: thermal and optical advantages relevant for waveguide devices, economical prices, availability in multiple crystalline orientations as well as popularity with researchers growing GaN and ZnO. During the course of this research, ′′ sapphire wafers in the  available orientations R, A, M and C-plane (see appendix A) were used. e wafers were either single-side polished (i.e. rough on the back) or double-side polished. Substrate preparation began by first annealing the ′′ wafers in a ◦ C furnace in air for  hours. Annealing generates ordered surfaces consisting of atomically flat    – Epitaxial growth of single-phase Nd:sapphire terraces separated by atomic steps. e back faces of the wafers were then metallized by electron beam evaporation. Approximately  nm of chromium was deposited as an adhesion layer followed by  nm of molybdenum to improve the absorption of thermal radiation from the sample heater. e metallized wafers were then diced into  cm2 squares using a diamond saw. Up to  substrates were made from each wafer. Dicing work was performed by Alina Kulpa at UBC AMPEL. Prior to being loaded into the MBE system, each substrate was boiled in acetone, rinsed in electronic-grade methanol then dried with nitrogen gas. is solvent cleaning step was meant to remove surface contamination from the dicing process. Each substrate was then tied using tantalum wire to a molybdenum sample holder designed for easy mounting onto (and removal from) the sample manipulator in the growth chamber. e samples (on their holders) were loaded into the MBE system via the fast-entry load lock (FEL), typically  at a time. e FEL is a small vacuum chamber that can be valved off from the rest of the system and quickly pumped down or vented for sample loading/unloading. Within the MBE system, samples are moved between the FEL, preparation and growth chambers by a trolley and multiple magnetically actuated wobblesticks. e preparation chamber lies between the other two chambers and contains a seldom-used sample heating unit ineffective for either degassing or annealing (the heaters in the growth chamber and external furnace run hotter).  .. Substrate and effusion cell heating Film growth could be initiated once a sample holder with sapphire substrate was mounted and locked into the sample manipulator and the growth chamber valved off from the rest of the system. To begin, the effusion cells and substrate were heated up to the desired temperatures with ramp rates as high as ◦ C/s. ermocouples were used to measure the temperature and provide feedback for heater control. Temperature measurements were highly accurate in the effusion cells because of the direct contact with the crucibles holding the elemental sources. is was not the case for the substrate because the thermocouple in the sample manipulator lay suspended between the SiC heater and the Mo disc, thereby reporting an intermediate temperature of the two.    – Epitaxial growth of single-phase Nd:sapphire 8  10  torr)  Shutter: Open  Closed  Shutter open  -8  7  o  Flux (x10  Thickness (nm)  6  T 5  =1080 C,  Al  -8  Flux:  6.7x10  torr  5 0 2  4  6  8  10  12  Time (mins) 4  o  T  3  = 1100 C,  Al  QCM = 1.4 nm/min  o  T  = 1080 C,  Al  2  QCM = 1.0 nm/min  o  T  Nd  1  = 1050 C,  QCM = 0.06 nm/min  0 0  2  4  6  8  10  Time (mins)  Figure .: Deposition rate of Al and Nd metal onto a QCM placed in front of the substrate at various cell temperatures. e rate was calculated from the slope. Inset, monitoring ion gauge measurement of the Al flux using the drop in pressure when the Al shutter is closed. Effusion cell fluxes Once a cell reached a suitably high temperature, further adjustments were made using measurements of the elemental flux as feedback. ere were two methods for measuring the flux, the most convenient involving a monitoring ion gauge (MIG), a retractable UHV ion gauge with a backing plate that could be slid into place a few cm in front of the manipulator. With the MIG extended, the flux measurement was started by opening the relevant cell shutter and waiting for the pressure to stabilize. e shutter was then closed and the resulting pressure drop noted. An example measurement is shown in the inset of figure .. For non-dopant metals such as Al, the MIG growth fluxes were typically in the −8 –−7 torr range. e Nd dopant flux was more difficult to detect, being ∼ times weaker, especially when the background pressure was elevated e.g. by residual gases released from the hot effusion cells. e MIG was also less useful for flux ratio measurements since the ionization factor of each element had to be considered. An alternative method involved a quartz crystal microbalance (QCM), which   – Epitaxial growth of single-phase Nd:sapphire uses a quartz crystal that changes resonant frequency depending on the amount of mass deposited on it. e QCM, also retractable, converts its internal measurement of mass to thickness based on the elemental density input by the user (ρAl = . g/cm3 , ρNd = . g/cm3 ). Figure . shows QCM thickness measurements during exposure to Al and Nd fluxes, and how the deposition rate was obtained from the rising slope. e figure also shows that the rate increased with cell temperature as expected, and that the low Nd dopant flux could be measured given more time. In contrast to the MIG, the actual flux in units of atoms cm−2 s−1 can be easily determined from the QCM deposition rate, allowing for an evaluation of the elemental flux ratio as follows: FluxNd QCMNd ρNd MAl = FluxAl QCMAl ρAl MNd  (.)  where ρ is the density and M is the atomic mass. Using the examples in the figure, the ratio of Nd/Al atoms impinging on a substrate during growth would be . for Nd and Al cells at ◦ C and ◦ C respectively. Limitations aside, using the MIG was preferable to the QCM because it allowed for faster flux measurements. Accurate flux ratios, especially for non-dopant metals (e.g. Ga/Al, Al/Y), was possible aer calibrating the MIG with the absolute measurements of the QCM. e MIG was then used in every growth, ensuring consistent fluxes over a long growth campaign despite gradual changes occurring within the cell crucibles. Among the changes observed were the oxidation of the source material at the bottom of the crucible and constriction of the crucible orifice by deposited source material. Substrate temperature accuracy A more accurate substrate temperature was obtained by monitoring the spectrum of the thermal radiation emitted from the front of the substrate. Sapphire by itself has high transmission in the infrared, thus a measurement of uncoated sapphire would essentially yield the SiC heater temperature instead. e Cr and Mo metal layers on the back surface were therefore vital to prevent heater radiation interference. e optical setup involved light collection from a spot within the  cm2 sample, passage through an ARIES FF scanning monochromator, and finally detection by an In  – Epitaxial growth of single-phase Nd:sapphire  (b)  (a) Mo holder  Thermal Radiation Intensity (arb. units)  T = 982oC  Mo Cr Al2O Lens T = 919oC  TC Substrate  Fiber to spectrometer T = 874oC  Serpentine SiC heater  Ta heat shield 900  950  1000  1050  1100  1150  1200  1250  1300  Wavelength (nm)  Figure .: (a) Setup relating the high temperature SiC sample heater and thermal radiation monitor. Revised drawing of a version by Scott Webster. (b) ermal radiation spectra from a metallized, double-side polished, sapphire substrate at different temperatures. Points indicate measured data while lines correspond to fits of eqn. .. For the spectra with temperature fits yielding ,  and ◦ C the thermocouple temperature sensor reading was ,  and ◦ C respectively. GaAs sensor. Spectra were collected within a – nm range and corrected for the non-uniform spectral response of the optical setup. A schematic of the heater and radiation monitor is shown in figure .(a). e temperature was determined by fitting the thermal radiation data to a graybody expression for the photon flux I given by  I(λ, T ) =  Aε(λ) hc  λ4 (e λkT − 1)    (.)  – Epitaxial growth of single-phase Nd:sapphire where A is a scaling constant and ε is the spectral emissivity ε(λ) = 1 − R(λ). e reflectivity R(λ) was calculated for chromium-coated sapphire as follows R(λ) = R1 +  T1 2 R2 (λ) 1 − R1 R2 (λ)  (.)  where R1 and T1 are the respective reflectance and transmittance at the vacuum–sapphire interface, and R2 is the reflectance at the sapphire–chromium interface. e required refractive index data was taken from reference []. e emissivity of chromium-coated, double-side-polished sapphire averaged to . in the wavelength range collected, with a range of ±. due to spectral variations. Figure .(b) shows radiation data collected from a substrate at three different thermocouple temperatures: ,  and ◦ C. e actual temperatures as fitted using eqn. . with the same A value were determined to be ,  and ◦ C respectively. Although the fit was precise to within a few degrees, such accuracy and consistency between samples was not needed because growth temperature effects were typically observed for changes of ∼◦ C. In the interest of preserving the life of the heating element, ◦ C was the maximum thermocouple temperature tested. is corresponded to a heater temperature of ◦ C, measured using an unmetallized sapphire substrate to pass through the heater radiation. Here the emissivity of the SiC heater was assumed to be spectrally independent. At high power operation then, the substrate temperature discrepancy was about ◦ C, which is likely the maximum difference and should shrink/converge with lower heater power. Verification measurements at low temperatures were not performed because the radiation intensity was much weaker and undetectable. For substrates that were single-side polished, calculating the emissivity was not straight forward due to the roughness of the metalized back surface. As an approximation, using the same calculated emissivity and floating the A constant led to a slightly larger discrepancy of ∼◦ C when the thermocouple was at ◦ C.  .. Oxygen plasma ignition Once the cell temperatures/fluxes were finalized, oxygen gas was leaked into the growth chamber via the plasma source. e gas pressure was regulated by an ex-    – Epitaxial growth of single-phase Nd:sapphire ternal MKS  pressure/flow controller (PFC) positioned along the supply line. A PFC setting of  torr would establish a pressure of 4×10−6 torr in the growth chamber, the drop occurring because of the ∼ mm2 inlet and outlet orifices of the quartz discharge tube that the gas flowed through. With an estimated  L/s of effective pumping speed (cryo + turbo), the amount of O2 gas flowing into the system was ∼. sccm. Plasma was ignited by coupling ∼ W into the helical resonator, a /′′ thick, ′′ long copper rod coiled into an  turn, .′′ pitch helix with a .′′ diameter cylindrical cavity for the quartz discharge tube. e helix was grounded at one end for operation as a quarter wavelength resonator. Coupling was accomplished by means of a direct tap i.e. wire connection from the incoming transmission line to a spot on the helix. Surrounding the assembly was a grounded cylindrical copper sheath centred on the quartz tube. e resonator and tap combination can be modeled as an open circuit and short circuit transmission line in parallel. Changing the tap position affects the resonant frequency and input impedance, and is only possible upon removal of the source from the system. A diagram of a similar plasma source albeit with different coupling method and tube material used for generating nitrogen plasma is available in reference []. e tap was typically positioned – turns from the shorted end, resulting in a resonant frequency of ∼ MHz. A sinusoidal signal at that frequency was generated by a VHF oscillator, then amplified by an Amplifier Research  kHz– MHz broadband amplifier to ∼ W forward power. At this point, the EM fields generated by the helix were sufficiently strong to initiate breakdown of the O2 gas flowing through the quartz tube. Plasma ignition changes the impedance as well as quality factor of the resonator. e forward/reflected power (to/from the resonator) was measured by a Bird wattmeter employing directional couplers. Since the tap was fixed, the impedance mismatch, as indicated by the reflected/forward power ratio, could be minimized by changing the frequency, forward power or O2 gas flow. e plasma was sustainable in the broad range between  and  MHz, which implies a drop in the quality factor. Under ideal conditions, forward powers upwards of  W and reflected powers <  W were attainable. e oxygen plasma within the quartz tube glowed bright white, as observed at either ends of the tube. Capping the adjacent shutter port with a glass window permit  – Epitaxial growth of single-phase Nd:sapphire  Forward/Reflected Power (W)  250/0  Intensity (arb. units)  125/35  (1) = O (1)  +  (2) = O  2  (1)  (2) (2)  500  550  (1)  600  (2)  650  700  750  800  850  900  Wavelength (nm)  Figure .: Oxygen plasma emission spectra captured from the glowing quartz tube. Spectrum in red/black are produced using different power settings and O2 pressures (red = ×10−5 and black = ×10−6 torr). ted optical access to the front tip of the tube that sticks out of the resonator. e back end was optically accessible via a miniflange window mounted on the tee that also fed oxygen into the system. Using these optical access points, the plasma emission was analyzed in more detail by means of an ARIES FF scanning monochrometer and Hamamatsu R photomultiplier detector. Examples of the emission spectra are shown in figure .. While the emission appears white, it is not a broad spectrum but rather consists of narrow peaks associated with transitions of excited atomic oxygen (O) or ionized molecular oxygen (O+ 2 ). It is possible that ozone was also present, but undetectable as the setup was only sensitive in the visible (no UV) region and rapidly cut off above  nm. e spectrum suggests that atomic oxygen is the dominant light-emitting component in the plasma. Figure . also shows the influence of net power absorbed by the resonator on the peak intensities. Higher powers produced visibly brighter emission, which was verified by the stronger peaks. For the range of powers tested, the influence on relative peak strength was insignificant i.e. amplification of atomic   – Epitaxial growth of single-phase Nd:sapphire vs suppression of molecular peaks was not achievable. Prior to growth, the heated substrate was exposed to oxygen plasma for about  mins as a final cleaning step. Surface quality was monitored using the in-situ electron diffraction technique RHEED, which will be described in section . below. e plasma exposure period was also useful to ensure the stability of the gas flow, forward/reflected powers and substrate/cell heating. Nd-doped Al2 O3 film growth was initiated by opening the Al cell shutter, thus exposing the substrate to both oxygen and Al. RHEED patterns were observed vigilantly during the initial moments of growth, prompting a growth interrupt should the film appear to be forming poorly. Given sufficient active oxygen and temperature, an Al2 O3 buffer layer was grown, typically with thicknesses of – nm. Nd doping was initiated without interrupting film growth by opening the Nd cell shutter. e deposition of Nd-doped films typically lasted for – hours, with thicknesses determined by the Al flux. e growth was stopped by closing all the metal cell shutters, then ramping down the sample temperature while maintaining oxygen exposure for a few minutes. Alternatively, the sample could remain heated under oxygen as an annealing step, though to minimal effect unless the film was poorly oxidized during growth.  .  In-situ monitoring  An indispensable technique for monitoring the film quality during growth is reflection high energy electron diffraction (RHEED). is technique involves electrons from a hot filament that are accelerated and focused towards the substrate at a grazing angle of less than ◦ . e electrons then elastically diffract off the substrate/film and strike a phosphorescent screen producing diffraction patterns visible outside the MBE chamber. e shallow angle of the electron beam effectively restricts diffraction to the topmost monolayers, thereby providing a real-time window on the structure of each incremental layer deposited. More information on the RHEED technique can be found in []. e system used was a STAIB model capable of generating up to  keV electrons. At such energies, the electron wavelength λ is given by the de Broglie wavelength    – Epitaxial growth of single-phase Nd:sapphire [ ] h 1 √ λ= 2mo eV 1 + 2meVo c2  (.)  with the relativistic correction in square brackets (see reference [] for derivation). e RHEED supply was typically operated at  kV, corresponding to a wavelength of ∼. Å. is is at least  times smaller than the atomic step heights of the main sapphire substrate orientations C, R, A and M-plane (see section .). e electron diffraction geometry as seen from above the sample normal is shown in figure .(a). is viewpoint highlights the ability of RHEED to probe the crystal structure in the lateral direction. e electrons scatter elastically producing a lateral deviation based on the reciprocal lattice and restricted to the Ewald sphere as given by  where kLattice  ⃗kRHEED + ⃗kLattice = ⃗kDiffracted (.) 2π 2π = and kRHEED = kDiffracted = ≡ Ewald radius (.) d λ  where d is the plane spacing and λ the electron wavelength. Since the Ewald radius is much larger than the reciprocal lattice, θ is very small and ⃗kLattice is essentially ⊥ ⃗kRHEED . erefore,  r kLattice ≃ kRHEED R r λ which simplifies to = R d sin θ ≃  (.) (.)  where r is the lateral separation of the diffraction dashes/spots seen on the screen and R is the sample to screen distance. Figure .(c) shows the evolution of RHEED patterns during the growth of a  nm Nd:sapphire film on an R-plane sapphire substrate. e electron beam is ori¯ direction, as shown by the hexagonal cell³ in figure .(b) with ented along the [4¯21] ³Sapphire is customarily described using a hexagonal lattice but is actually a member of the trigonal crystal system with a rhombohedral lattice. More details together with the Miller index conventions for identifying directions and planes in hexagonal sapphire are given in appendix A.    – Epitaxial growth of single-phase Nd:sapphire (a)  RHEED screen  Ewald sphere  (b)  d  kRHEED  k Diffracte kLattice θ  d  ]  21  R  o  2  [-1  [-4 -2 1]  [-4 -2 1]  r  θ  7. =4  [-1 0  0]  Sample, facing up Profile (c) (a)  t= 00 mins mins t=  (d)  [-4 -2 1]  Front  R-plane sapphire  mins t=t= 169mins  t= 97 mins  t= 32 58 mins mins t=  [-1 -2 1]  t= 97 mins  Figure .: RHEED patterns showing the surface structure evolution during the growth of a  nm Nd:sapphire film. (a) Top view of the electron diffraction geometry showing the effect of lateral periodicity. (b) Orientations in R-plane sapphire with highly symmetric RHEED patterns. (c) Evolution of patterns along the [¯4¯21] during film growth. e growth was terminated at t= mins. (d) Comparison of post-growth patterns along the [¯4¯21] and [¯1¯21] with their simulated electron transmission.   – Epitaxial growth of single-phase Nd:sapphire highlighted R-plane. Prior to growth (t = ), the furnace-annealed substrate surface produced a RHEED pattern featuring short dashes surrounding a central specular reflection spot. e dashes represent lattice planes in reciprocal space. eir shape, short streaks pointing normal to the substrate surface, arises from the intersection of parallel rods (reciprocal lattice for a surface) with the large Ewald sphere[, chap.]. Once film growth was initiated, the dashes elongated into streaks while retaining the same substrate pattern. As the pattern denotes lattice spacings, the film therefore shares the same lattice structure as the substrate in a clear demonstration of homoepitaxy. e elongation of dashes into streaks corresponds to the presence of random epitaxial D islands either on the previously flat terraces or possibly on other islands[, chap.]. A streaky RHEED pattern is nevertheless still an indicator of continued smooth conformal growth. Should the growth transition to rough D islands, the streaks would then break up into stacks of spots. RHEED patterns differ depending on the sample orientation relative to the incident electron beam i.e. azimuth angle. In figure .(d), two patterns from the same sample of figure .(c) are shown post-growth, along with their R-plane azimuths in the hexagonal cell. e reciprocal lattice planes in each pattern were identified by comparing them to simulated diffraction spots produced from electron transmission through a thin crystal. e simulation was done using the SingleCrystal program in the CrystalMaker soware package and involved setting the electron beam direction to match the RHEED azimuth angle with the crystal oriented to match the R-plane substrate. e simulated patterns are shown beneath their corresponding RHEED patterns of figure .(d), offering good agreement for the location of the reciprocal lattice planes as well as identifying them. Simulations of other substrate orientations are presented in appendix B. As a check, the (¯210) lattice plane observed in the pattern along the [¯1¯21] azimuth will be analyzed. e separation of that RHEED dash to the central specular dash should follow the diffraction condition of eqn. .. e plane spacing for planes in a hexagonal lattice is given by ( ) 1 4 h2 + hk + k 2 l2 = + d2 3 a2 c2  (.)  where (h, k, l) are the Miller indices and a and c are the lattice constants. Using an   – Epitaxial growth of single-phase Nd:sapphire  Substrate  Film  2 μm  Figure .: Atomic force microscopy (AFM) scans showing the surfaces of the starting substrate and  nm Nd:sapphire film post-growth. e film conforms to the atomically flat terraces of the substrate. on-screen separation r of . cm (measured by Scott Webster) and plane spacing of a/2 for the {¯210} series of planes, the substrate-screen distance R is calculated as  cm, which is consistent with the MBE chamber geometry. On a side note, RHEED features (spots, dashes, etc.) from sapphire tend to be blurrier compared to those obtained off semiconductor materials such as GaAs or Si. is is due to charging of the insulating sapphire substrate. Consequently, the RHEED filaments are operated slightly hotter at . A instead of . A, and the Focus and Grid voltage settings are tweaked to produce high electron emission currents of – µA. For comparison, RHEED off GaAs in a comparable III-V MBE system requires an emission current less than  µA. Such settings, while potentially damaging to the filament, are necessary.  .  Surface morphology  Post-growth, the surface morphology of a sample can be measured with sub-nm accuracy using AFM. Here a silicon cantilever with a downward pointed tip (radius of  nm) is tapped along the sample surface. Deviations in the tip position (i.e.   – Epitaxial growth of single-phase Nd:sapphire local height) are tracked by a laser beam reflected off the back of the tip. With AFM, the step heights of the atomic terraces produced by annealing sapphire was found to vary with orientation e.g. c/ for C-plane, a/ for A-plane and . nm for R-plane sapphire[]. e terrace width depends on the angle that the substrate is miscut from its intended orientation, becoming wider with smaller miscut. Figure . shows the surface morphology of an R-plane sapphire substrate aer furnace annealing as measured by a Digital Instruments Nanoscope. Also shown is a scan of the same sample aer the growth of the  nm thick Nd-doped sapphire film previously shown in section .. e growth rate was . nm/min and substrate temperature was ◦ C. e resulting film is smooth (. nm RMS) and maintains the atomic terrace profile of the underlying substrate. Such conformal (or D island) growth is preferable to D islands (rough), but it would be better still if step-flow growth had occurred. During conformal growth, the adsorbing atoms (adatoms) coalesce on the surface into single-layer-thick islands that grow into a reproduction of the underlying layer. During step-flow growth, the same atoms have more time to diffuse (avoiding other adatoms) and instead stick to the better-coordinated step edges. e atomic terraces as seen by AFM are no longer uniformly spaced but start to appear wavy. While both conformal and step-flow growth may produce smooth layers at the start, conformal growth is more susceptible to evolve into rough D island growth. It may be possible to achieve step-flow growth either by reducing the growth rate or raising the substrate temperature. Attempts at temperatures up to ◦ C or rates as low as . nm/min proved unsuccessful. Reducing the rate much further makes device fabrication impractical and was not pursued. On a side note, good quality AFM scans on sapphire substrates/films are difficult to obtain consistently, possibly because the silicon tips are easily damaged by the much harder sapphire. Consequently, the post-growth scan in figure . lacks the same height resolution as the substrate scan, becoming a convolution of the damaged tip profile and the sample surface instead.    – Epitaxial growth of single-phase Nd:sapphire  .  Structural analysis  e crystal structure of the films was analyzed post-growth by high-resolution x-ray diffraction (XRD) using a PANalytical X’Pert Pro Materials Research Diffractometer. Under normal operation, the system produced Kα x-rays with a wavelength of . Å by colliding electrons into a copper target inside an x-ray tube set to  kV and  mA. e x-rays are transmitted from the vacuum environment via a beryllium window, then focused into a ∼ mm thick line that spans the  mm wide film + substrate sample. e sample holder has  degrees of freedom ( translational and  rotational about the holder normal) allowing for analysis along various crystal orientations in the sample. Diffracted x-rays are collected by a gas proportional detector placed on an articulating arm. Since the x-ray tube is fixed, the diffraction condition is set by the orientation of the sample holder and angular position of the detector arm. e geometry of the diffractometer is shown in figure .(a). XRD provides a useful gauge of the long-range order (LRO) mentioned in section .. by evaluating the translational symmetry of atomic planes. In reciprocal space, equivalently spaced planes are represented as points where their position relative to the (000) origin gives the inverse plane spacing and orientation. Successful diffraction by elastic x-rays requires that their wavevectors confined within an Ewald sphere connect the two reciprocal lattice points. An example is shown in figure .(b) for the (002) planes of an arbitrary crystal. Diffraction peaks (or spots in reciprocal space) observed by XRD will satisfy the Bragg condition 2d sin θ = λ relating the plane spacing d and incident angle θ. Strong diffraction peaks from a sample imply a high frequency of equivalently spaced planes and thus considerable LRO. More information on XRD as well as relevant data such as observable planes and diffraction angles for the materials presented in this thesis are available in appendix C. Perhaps the most popular type of XRD scan is a θ-θ scan. Here the sample is continuously rotated by θ while the detector is simultaneously rotated by θ, effectively probing the plane spacings along the substrate normal i.e. the out-of-plane direction. e peaks in a θ-θ scan can be used to identify the phase of the deposited film by comparing the corresponding spacings to the spacings present in a shortlist of materials likely to have been grown (based on elements used, etc). Given the lat-    – Epitaxial growth of single-phase Nd:sapphire (a)  (b) ω or θ rotation  Sample  axis crystal xis sample a  θ  ψ rotation  (004)  Ewald Sphere, radius = 1/λ  ω From Source  (002)  kreflected 2θ kincident  Δk |Δk| = 1/d (000)  θ ϕ rotation To Detector  reciprocal space  Figure .: (a) XRD geometry and (b) Example of a reciprocal space map (RSM) showing the diffraction condition being satisfied. e use of ω and θ in (a) highlights the routine offset between the XRD sample holder and the atomic planes in the crystal. In contrast to the Ewald sphere of section ., the 2π scaling factor is removed in (b) to conform to RSMs in the more intuitive units of inverse plane spacings. tice constants of a crystal, the plane spacings can be calculated from equations like those of eqn. .. Prior to this type of scan (and most others), the offset between the sample holder at ω = 0 and the planes in the substrate at θ = 0 as shown in figure .(a) must be taken into account. Scans of Nd-doped Al2 O3 films grown on commercially available orientations of sapphire substrates are shown in figure .. Films grown on R, A and M-plane sapphire produce peaks that coincide with the substrate peaks, an indication that they share the same sapphire crystal structure as the substrate. e lack of other peaks suggest that the films are single phase i.e. entirely sapphire. For continuity, the R-plane sample shown is the one analyzed in figures . and .. Films grown on C-plane sapphire with the same conditions (as mentioned earlier in the chapter) were not sapphire but instead γ-Al2 O3 , which is cubic. e films were still single   – Epitaxial growth of single-phase Nd:sapphire  R-plane (0 1 -1 2) (0 2 -2 4) (0 3 -3 6)  A-plane  Intensity (arb. units)  (1 1 -2 0) (2 2 -4 0)  M-plane  (3 0 -3 0)  C-plane (222)  -Al O 2  (0 0 0 6)  (0 0 0 12)  3  (444)  -Al O 2  15  25  35  /2  3  45  (°)  Figure .: XRD θ-θ scans of Nd-doped Al2 O3 films grown on sapphire substrates of different orientations. Single-phase Nd:sapphire films were grown on R-, A- and M-plane sapphire while (111) γ-phase alumina was grown on C-plane sapphire. phase and oriented out-of-plane as (111) γ-Al2 O3 ∥ (0001) α-Al2 O3 . A potential explanation for the non-homoepitaxial growth on C-plane involves surface diffusion. Maeda et. al. grew undoped sapphire on C, A and R-plane sapphire by pulsed laser deposition (PLD), which they referred to as “Laser MBE”, and found that surface diffusion on C-plane sapphire was weakest[]. Limited mobility on the surface could prevent adatoms from reaching the low energy sites of the underlying substrate, forcing them instead to coalesce into thermodynamically stable phases. While studying the formation of Al2 O3 nanocrystals, McHale et. al. determined that γ-Al2 O3 is thermodynamically stable at  K for specific surface areas   – Epitaxial growth of single-phase Nd:sapphire greater than  m2 /g []. Assuming a density of .–. g/cm3 for Al2 O3 , this corresponds to spherical grains with radii of – nm. e γ-Al2 O3 films grown on C-plane sapphire could be comprised of similarly or larger sized grains, oriented differently in-plane but with the same out-of-plane orientation.  .  Optical properties  While XRD is essential for LRO analysis, photoluminescence (PL) is an effective probe for evaluating the short-range order (SRO) introduced in section .. concerning the uniformity of the local atomic structure. In brief, PL involves shining light onto a sample to induce optical transitions and the resulting emission is then collected and analyzed. Since solid state laser materials are customarily transparent hosts doped with rare-earths or transition-metals, the PL emission will be solely due to the optically active dopants. Nd:sapphire is no exception with the sapphire host highly transparent in the wavelength range .– µm except for a dip near  µm[, chap.]. e Nd3+ emission was expected to follow the theory of section ., where the local atomic structure (coordination, bond lengths, etc.) of individual ions yielded discrete optical transitions but the overall emission was dependent on the SRO of the dopant ensemble. For analyzing Nd-doped samples, the pump source of the PL setup was a continuous-wave  nm Spectra Physics diode laser operable at powers up to  mW. e pump wavelength was suitable for the excitation of Nd3+ ions from their 4 I9/2 ground manifold to the 4 F5/2 + 2 H9/2 upper manifold shown in figure .. e pump light was passed through optical fiber then focused into a ∼ mm2 spot on the sample to improve the intensity. e collected PL emission was passed through optical fiber to an Acton SpectraPro- monochromator equipped with  selectable diffraction gratings ( and  lines/mm) mounted on a -grating turret. e monochromator was configured as a spectrograph i.e. exit slit removed, with a Princeton Instruments OMA V CCD detector mounted on the exit port. e InGaAs CCD was sensitive in the broad wavelength range of – nm and consisted of an array of  pixel lines. e PL setup is shown in figure ..    – Epitaxial growth of single-phase Nd:sapphire  Triple grating turret  Fiber coupler  Detector  Polarizer ( if used )  Long pass filter From pump laser Laser line filter Monochromator  Sample  Figure .: PL measurement apparatus. With the  line/mm grating selected, the CCD⁴ registered a wavelength spectrum across a ∼ nm range. is is suitable for measuring Nd emission involving transitions between the 4 F3/2 upper metastable manifold and the 4 I9/2 , 4 I11/2 and 4 I13/2 manifolds also shown in figure .. e  nm wavelength range is sufficiently wide to capture all the peaks from each intermanifold transition. e monochromator grating would be moved to centre the spectrum at either ∼, ∼ or ∼ nm to capture the transitions to the 4 I manifolds listed above, respectively. PL analysis of Nd-doped Al2 O3 films grown on all four orientations of sapphire revealed that two types of emission spectra were produced. e films on R, A and Mplane sapphire that maintained the substrate crystal structure yielded a collection of sharp emission peaks characteristic of other Nd-doped solid state laser crystals (e.g. ⁴ e CCD, like all other optical sensors, measures light intensity in units of photons/sec or some scale thereof. Each photon produces the same response regardless of photon energy. Unless otherwise noted, all PL emission spectra shown in this document are direct measurements from the CCD and will be in the same units.    – Epitaxial growth of single-phase Nd:sapphire  PL Intensity (arb. units)  (a)  (b)  1040  1060  1080  1100  1120  1140  Wavelength (nm)  Figure .: PL emission spectra produced by 4 F3/2 →4 I11/2 transitions from: (a) Nd-doped Al2 O3 film on C-plane sapphire and (b) Nd-doped sapphire film on R-plane sapphire. Nd:YAG, Nd:YVO4 ). Here the primary peak is at . nm with a full width half maximum (FWHM) of . nm as measured with . nm resolution. e films on C-plane sapphire that were of a different phase yielded a broad emission spectrum similar to Nd-doped glass, which is amorphous. In figure ., PL from the R and C-plane samples of figure . are compared. e collection of peaks from the Nd-doped sapphire films are unique and were first reported in the  Optics Letters article[]. At the local atomic structure level, Nd is doped into the octahedral Al3+ sites shown in figure .(b). e crystal field of the surrounding host, established primarily by the  nearest oxygen ions, splits the degeneracy of the J manifolds (e.g. 4 I11/2 ) into a unique collection of energy levels as explained in section ... PL emission from Nd:sapphire has a strong signal-to-noise ratio and contains the appropriate number of peaks corresponding to the number of energy levels ((2J + 1)/2) expected from the low-symmetry Al3+ sites. e sharp emission peaks are an indication of strong SRO where all the Nddopants sampled in that  mm2 laser spot experience the same crystal crystal field and thus produce the same emission. PL emission from the Nd-doped γ-Al2 O3 grown on C-plane sapphire serves as    – Epitaxial growth of single-phase Nd:sapphire a counter-example. Here the broad emission spectrum is due to the non-uniform crystal field experienced by the ensemble of Nd dopants. Although the film is single phase, the peaks measured by the XRD scan shown in figure . are rather weak implying a composition of nanoscale grains. Parallels can be drawn to the Nd:glass fiber discussed in section .., where the broad spectrum of figure .(a) was due to the differently coordinated Nd3+ ions excluded from the glass-forming O–Si–O chains. In the case of the Nd:γ-Al2 O3 film, the larger Nd3+ ions are not suited to the small Al3+ sites and thus likely segregate to the disordered grain boundaries where coordination variety is supported. As will be shown later, the Nd:sapphire films are single crystal, thereby depriving the Nd dopants of grain boundaries and forcing them instead to incorporate within the crystal.    3– Structural and optical properties of Nd:sapphire Following the overview in chapter  of film growth and film quality assessments during and aer growth, attention will now be given to detailed analysis of the Nd:sapphire films. is will primarily involve further measurements using the two key characterization methods previously introduced, x-ray diffraction (XRD) and photoluminescence (PL), for the structural and optical properties respectively. Key parameters such as film thickness and density will be provided, as well as the influence of Nd-doping on the lattice. e single-phase nature of the Nd:sapphire films of chapter  was concluded based on simple out-of-plane XRD measurements. Here, a more rigorous study of the lattice structure in both the out-of-plane and in-plane directions will be presented. Furthermore, the orientation of the film relative to the substrate i.e. epitaxial relationship will be used to decide if the film is single crystal or composed of crystallites with multiple in-plane orientations like the γ-Al2 O3 film of figure .. Since Nd:sapphire is a new material, the energy levels within the important emission manifolds will be identified. Its merit as a laser gain medium will then be evaluated via key parameters associated with optical gain. is involves polarized emission measurements in keeping with the optically anistropic nature of sapphire. Furthermore, excitation measurements will be used to extract the absorption spectrum, thus giving an idea of the best wavelengths for optical pumping. Lastly, attempts at improving the film quality post-growth by annealing samples in an external furnace will be presented.    – Structural and optical properties of Nd:sapphire  .  Structural properties  .. Film thickness and density e  nm thick Nd:sapphire film presented in the previous chapter was further analyzed using the PANalytical x-ray diffractometer. e goal was to compare the structural parameters such as lattice constant and density between film and substrate as well as gauge the film thickness. A more detailed θ-θ scan of the R-plane sample from figure . was done using a longer time interval and narrowed to the vicinity of the film/substrate (01¯12) Bragg peak. e result, shown in figure .(a), features a Nd:sapphire film peak that protrudes from the le shoulder of the substrate peak. e smaller Bragg angle of the film peak suggests that the film has a larger vertical spacing due to the incorporation of the bigger Nd dopant. e lack of a standalone film peak makes it difficult to obtain a precise lattice spacing, and will be calculated for a different sample described later in section ... e fringes on either side of the film/substrate peaks are known as Pendellösung fringes. e term is from the German, meaning “pendulum solution”, and is used because the fringes resemble the oscillations of a compound pendulum[, chap.]. Fringing is due to interference between the x-rays reflected from the film surface with those from the film-substrate interface. eir presence indicates that the film has good crystalline quality with low levels of disorders such as dislocations, mosaicity and surface roughness [, chap.]. e thickness of a single-layer film can be calculated from the spacing between fringe peaks as given by[, chap.] ickness =  λ 2∆θp cos(θB )  (.)  where λ is the x-ray wavelength . Å, ∆θp is the fringe spacing and θB is the Bragg angle. e  nm thickness for the film in figure . was calculated using this equation. Material specific parameters are not present in the equation because most materials have a refractive index at x-ray wavelengths that is very close to, but below unity. e film density was obtained from x-ray reflectivity (XRR), an analysis technique using the same PANalytical diffractometer but with a small incident beam    – Structural and optical properties of Nd:sapphire  Sapphire (0 1 -1 2) substrate  (a)  Intensity (arb. units)  Nd: Sapphire (0 1 -1 2) film  12.4  12.6  12.8  /2  13.0  13.2  (°)  3  Density  (g/cm )  Intensity (arb. units)  4.19 4.09 3.99 3.89  (b)  3.79  Measured Simulated, offset  0.2  0.4  0.6  0.8  1.0  (°)  Figure .: X-ray structural data from a  nm thick Nd:α-Al2 O3 film grown on R-plane sapphire: (a) High resolution θ-θ scan showing the film peak contained within the shoulder of the substrate peak. Pendellösung fringes are an indication of good film crystalline quality and are useful for obtaining film thickness.(b) X-ray reflection (XRR) scan showing that the film density matches bulk sapphire. Simulations of slightly different density films are shown for comparison, which are vertically offset for easier viewing.    – Structural and optical properties of Nd:sapphire angle such that x-rays are reflected specularly rather than diffracted off the sample. e lower-than-unity refractive index permits total external reflection as opposed to total internal reflection commonly observed for optical waves. In XRR, there also exists a critical angle above which the total external reflection ceases and the beam penetrates the material. e critical angle is primarily a function of the electron density of a material as explained in reference [, chap.]. By fixing the chemical composition and porosity, the electron density can be translated into mass density, a more useful parameter. Figure .(b) shows an XRR scan of the  nm Nd:sapphire film compared to simulations of similarly thick Al2 O3 films with slightly different densities. e simulations were performed with the X-Ray Reflectivity soware package from PANalytical. In the scan, the reflected intensity rises up to a critical angle of .◦ before decaying rapidly. e scan matches the simulation of a film with a density of . g/cm3 , which is the bulk density of sapphire. In the other simulations, the Al2 O3 density is varied in . g/cm3 steps producing different critical angles, albeit not by much (e.g. .◦ for a film with density of . g/cm3 ). As further evidence that the film density matches bulk sapphire, interference fringes (a.k.a. Kiessig fringes) would be present if the film–substrate densities were different, especially for such a smooth sample. In the simulations, the oscillations become more pronounced with increasing density contrast. ese oscillations are produced by the same effect as the Pendellösung fringes about a Bragg peak, and can also be used to calculate film thickness.  .. Effect of Nd doping on lattice spacing A set of Nd:sapphire films were grown on A-plane sapphire with varying Nd/Al ratios. e films were grown at ∼◦ C at a rate of . nm/min and under a background oxygen pressure (with plasma) of .×−6 torr. A  nm sapphire buffer layer was grown first, followed by the  nm thick Nd:sapphire layer. Among the set, the Nd concentrations of two samples were measured by Rutherford backscattering spectrometry (RBS). e measurements were done at the University of Montreal by Peng Wei and will be described in section ... XRD θ-θ scans of these samples, an undoped sample and an A-plane substrate are shown in figure .. Wider range    – Structural and optical properties of Nd:sapphire  Nd:sapphire film Nd/Al = 0.76%  0.1  Nd:sapphire film  Intensity (cps)  Nd/Al = 0.33%  0.1  Undoped sapphire film  0.1  A-plane sapphire substrate  0.1  18.2  18.4  18.6  18.8  /2  19.0  19.2  19.4  19.6  (°)  Figure .: High resolution XRD θ-θ scans of nearly  nm thick sapphire films with various Nd-doping levels. e film peak shis to a lower angle, denoting a larger vertical plane spacing, as the Nd concentration is increased. scans (not shown) proved that the films were single-phase sapphire. e scans here are focused in the vicinity of the (11¯20) peak of A-plane sapphire and provide a clear demonstration of the earlier claim that Nd doping increases the vertical lattice spacing. e Nd/Al ratios provided in the figure are RBS atomic ratios. On a point of interest, the undoped sapphire film is sufficiently different from the substrate that it yields a distinct peak and clear Pendellösung fringes. Compared to the Nd:sapphire film peaks in the top two tiles, the undoped sapphire peak is largely centred about the substrate peak, with only a slight shi denoting minor lattice expansion. Possible explanations include point defects such as impurities or   – Structural and optical properties of Nd:sapphire vacancies. Impurities may be present in the source materials or evaporate from the heated elements in the system (cells, substrate, plasma source, etc.). e more likely explanation of vacancies, either Al or oxygen, would result in non-stoichiometric films (e.g. Al2 O2.98 ). Brooks et. al. showed that lattice expansion of SrTiO3 films, a popular oxide MBE material, occurred for both Sr-rich and Sr-poor conditions[]. e undoped sapphire film has well defined Pendellösung fringes compared to the Nd-doped samples where some fringes are flattened out. e undoped film is a simple single layer while the doped samples undergo multilayer interference due to the relatively sizable undoped buffer layer. Measuring the doped film thicknesses from fringe spacings might not be fully accurate, requiring instead simulations that can fit the whole pattern. Commercial soware products (e.g. Bede RADS Mercury, PANalytical X’Pert Epitaxy) are currently unable to do so, as their focus is limited to cubic as well as C-plane hexagonal materials.  .. Example relating lattice expansion to Nd concentration A thicker Nd:sapphire sample was grown on a similar A-plane substrate using the same sapphire growth conditions but lasting  instead of  minutes. An XRD θ-θ scan of the sample is shown in figure .(a). e narrower fringe spacing was a result of the increased thickness, but the noisier fringes suggest a slight degradation in film quality over time. Some fringes remained flattened, probably due to the multilayer effect of the  nm undoped buffer layer. e thickness calculated from the fringe spacing was  nm, which is consistent with the growth rate used for the thinner samples. e film peak is much narrower and agrees with the Scherrer equation t = 0.9λ/(β cos θB ) that shows an inverse relation between the minimum crystallite size t and the FWHM β[, chap.]. e film peak is also well offset and distinct from the substrate peak, indicating a measurable Nd-doping level. By relating both peaks using  d2 d1  =  sin θ1 sin θ2 ,  the out-of-plane lattice expansion in the film  was calculated as .. An RBS scan used to measure the film composition is shown in figure .(b). During the RBS measurement, energetic . MeV He+ ions were bombarded into the sample and scattered off the Nd, Al and O atoms present. e backscattered ions were detected at an angle of ◦ and sorted by kinetic energy. Referring to    – Structural and optical properties of Nd:sapphire  7  Intensity (counts)  10 6  10  Substrate  (a)  Film  5  10 4  10 3  10 2  10 1  10 18.4  18.6  18.8  19.0  80  Normalized Yield  Normalized Yield (%)  /2  60  (b)  O  40  19.2  19.4  (°)  15  10  Al Nd  5  0  20  0.4  Measured  0.6  0.8  1.0  Energy (MeV)  Al  Simulated  Nd  0 0.2  0.4  0.6  0.8  1.0  Energy (MeV)  Figure .: (a) High resolution θ-θ scan of a  nm thick Nd:sapphire film grown on A-plane sapphire. e Nd concentration is . atomic  relative to Al. (b) RBS scan used to determine the Nd composition of the film shown in (a). Inset, a close-up of the Nd peak. RBS measurement and analysis performed by Peng Wei, University of Montreal. the figure in order of decreasing energy, the three atomic species are identified by the respective rapid increases in scatter intensity. A heavy element such as Nd has a high kinematic factor, which is the ratio of scattered to incident energy. For a fixed scattering angle, this factor increases monotonically with the mass ratio of target atom to projectile ion[, chap.]. us the order of detection with decreasing energy is Nd, Al and O. Since the scattering cross-section that affects intensity is essentially dependent on the atomic number squared, heavier atoms like Nd are much easier to detect, which is helpful for such low concentrations[, chap.]. e isolated Nd peak is also useful for depth profiling whereby the film thickness can be extracted. He+ ions experience energy loss as they penetrate and exit the sample aer scattering. e energy loss is reflected in the width of the RBS peak, where the low scattering energy   – Structural and optical properties of Nd:sapphire point coincides with the maximum film depth. A flat peak indicates a uniform depth profile. is RBS scan was performed at the University of Montreal by Peng Wei. A fit he performed on the scan revealed that the Nd-doped film was  nm thick with an Nd concentration of . atomic  relative to Al. Applying Vegard’s law, which proposes that the lattice constant varies linearly with composition, the effect of Nd doping is a lattice expansion of 1.2N + 0.1 percent relative to the substrate. Here N is the Nd atomic  and . is the offset for undoped films. Compared to the . at. doped sample of figure ., the Bragg peak in the thicker . at. sample is shied further implying a larger lattice. is ostensible contradiction occurs because the Bragg condition 2d sin θ = λ does not consider volume effects and is thus inaccurate for the thinner film. A full treatment is provided by dynamical theory, which evaluates Maxwell’s equations in the periodic electron density of the crystal to determine the wave interactions present[, chap.]. According to dynamical theory, the diffraction peak of the thinner film was “pulled” towards its substrate peak because of the proximity of both peaks. is typically occurs for thin, strained films because the wave fields excited in the film and substrate are coupled[, chap.]. It is expected that the substrate influence is dominant until the film reaches a certain thickness when the film peak location converges. Simulations using Bede RADS Mercury on cubic III-V materials suggest that convergence occurs by a thickness of  nm. e  nm Nd:sapphire film should therefore be suitable for lattice analysis. Likewise, the . shi was taken from a sufficiently thick undoped film.  .. Film–substrate epitaxial relationship Analysis of the film lattice structure thus far has been limited to the vertical, outof-plane direction. To form a complete picture of the structure, the in-plane orientation and lattice constants are needed. Since measurements of the sample on its side are not feasible, a Bragg peak with an angle between the substrate normal and plane must be used instead. e angled or off-axis peak provides information on both the out-of-plane as well as in-plane axis. ree main criteria affect the choice of an off-axis peak: strong intensity as seen from a powder diffraction pattern; inplane projection that is oriented along a low-index plane to simplify analysis; and    – Structural and optical properties of Nd:sapphire detectability by reflection XRD, which depends on the angle between the substrate normal and off-axis peak. e interplanar angle for a hexagonal lattice can be calculated from the Miller indices (hi ,ki ,li ) using the following equation given by reference [, app.]:  cos θi = √  h1 h2 + k1 k2 + 12 (h1 k2 + h2 k1 ) + (h21 + k12 + h1 k1 +  3a2 2 l )(h22 4c2 1  3a2 l l 4c2 1 2  + k22 + h2 k2 +  3a2 2 l ) 4c2 2  (.)  where a and c are the lattice constants. Reflection XRD requires θi to be smaller than the Bragg angle of the off-axis peak, otherwise the incident or diffracted beam would be behind the sample i.e. transmission XRD. Figure .(a) shows a crosssection of reciprocal space (i.e. an RSM) for A-plane sapphire with Qy axis parallel to the substrate normal and Qx axis oriented in-plane along the direction shown in figure .(c). e two smaller semicircles in the space map denote regions inaccessible by reflection XRD. Some of the off-axis peaks accessible in sapphire and their interplanar angles are provided in appendix C. Analysis of the (030) off-axis peak was performed on the  nm A-plane Nd:sapphire sample shown previously in figure .. To locate that peak, the sample was first rotated in the θ direction to the expected position where the incident beam angle matched the peak Bragg angle: ω = θB − θi for grazing incidence or ω = θB + θi for grazing exit. e latter was chosen for the (030) peak where θB is .◦ and θi is ◦ . Next, a rotation scan about the substrate normal or ϕ scan (refer to fig. .) was done to locate the peak in-plane. Separate ϕ scans were done for the (030) peaks of the substrate and film, where it was determined that both sets of peaks lined up. is result implies that the film has only one in-plane orientation, that of the substrate, which indicates that the film is single crystal. It is common for epitaxial films to consist of multiply oriented domains in-plane while having a single orientation out-of-plane[]. is is not the case for the Nd:sapphire films shown here. e in-plane lattice of the film was analyzed relative to the substrate from a D scan of the Qx –Qy reciprocal space around the substrate (030) peak. Such space maps were done with a channel-cut Ge crystal on the detection arm to minimize   – Structural and optical properties of Nd:sapphire  (2 4 0)  (3 3 0)  (4 2 0)  (a) 10  (1/nm)  (0 5 0)  (1 4 0)  (1 3 0)  (3 2 0)  (2 2 0)  (4 1 0)  (3 1 0)  (5 0 0)  (4 0 0)  (5 -1 0) (6 -2 0)  Q  y  (-2 6 0) (-1 5 0) (0 4 0)  (2 3 0)  (-3 6 0) (-2 5 0)  (0 3 0)  (1 2 0)  (2 1 0)  (5 -2 0) (6 -3 0)  (3 0 0)  5  (-4 6 0)  (1 1 0)  (6 -4 0)  Diffracted beam  Incident beam  below surface  below surface  0 -10  -5  0  Q  (b)  x  5  (1 1 0)  (0 10)  (c)  6.35  6.30  Substrate  (0 0 1)  (1 1 0)  y  (1/nm)  10  (1/nm)  Q  y z Film  x  6.25  -3.70  -3.65  Q  x  -3.60  (1/nm)  Figure .: (a) RSM containing the {110}, {010} and {100} family of peaks of A-plane sapphire. Peaks are specified in units of inverse plane spacing along the in-plane (Qx ) and out-of-plane (Qy ) directions.(b) RSM of the (030) peak showing that the Nd:sapphire film is fully strained to the A-plane sapphire substrate. Analyzing off-axis peaks provides in-plane crystallinity data unavailable from standard θ-θ scans. (c) Sapphire lattice structure oriented in Cartesian space: {110} A-plane ∥ y, {001} Cplane ∥ z, and {¯110} M-plane ∥ x. Hexagonal unit cell shown in red.    – Structural and optical properties of Nd:sapphire dispersion and improve resolution. During the mapping process, the ϕ rotation angle was fixed while the incident beam angle ω and the detector angle θ was varied to probe the different Qx ,Qy points . e transformation to Qx ,Qy , which are the inverse plane spacings in their respective orientations, is given by:  Qx =  } 1{ cos ω − cos(2θ − ω) λ  Qy =  } 1{ sin ω + sin(2θ − ω) λ  (.)  Figure .(b) shows an off-axis space map relating the  nm Nd:sapphire film to its A-plane sapphire substrate. e film peak has a smaller Qy value indicative of a larger vertical lattice spacing and is consistent with the θ-θ scan of figure .(a). e Qx value, which was the goal of the space map, matches that of the substrate. e film is therefore fully strained or pseudomorphic to the substrate in the [¯110] direction shown in figure .(c). In contrast, if the film were not fully strained but fully relaxed, the peak would be located along the diagonal between the substrate peak and the Qx , Qy origin. While the in-plane lattice of A-plane sapphire is not √ isotropic, resembling instead a rectangle with sides 3a and c, it would be fair to assume that the film is also fully strained in the orthogonal [001] direction. e film is strained because of the compressive stress imposed by the smallerlattice substrate. In an attempt to maintain the volume, the film expands in the direction ⊥ to the stress, which is out-of-plane. e vertical lattice spacing of the Nd:sapphire film is therefore larger than a similarly doped, relaxed crystal in isolation (assuming one existed). e stress in a material is related to the strain by a stiffness tensor c comprised of elastic constants. Sapphire has the following rigidity coefficients: c11 = . GPa, c12 = . GPa, c13 = . GPa, c33 = . GPa, c44 = . GPa and c14 = . GPa[]. However the relatively small c14 suggests that sapphire can be approximated as a transversely isotropic material with stress and strain related by[, chap.]:    – Structural and optical properties of Nd:sapphire              σx         σy     σz    =  τyz     τzx    τxy  c11 c12 c13  0  0  0  c12 c11 c13  0  0  0  c13 c12 c11  0  0  0 0  0  0  0  c44  0  0  0  0  0  c44  0  0  0  0  0  0 1 2 (c11  − c12 )              ϵx     ϵy   ϵz    γyz   γzx   γxy  (.)  where σi and τi are the normal and shear stresses while ϵi and γi are their corresponding strains. e x,y,z indices denote the direction, and are consistent with the axes shown in figure .(c). As evaluating the in-plane stresses are impractical, the only useful relation from eqn. . involves the free surface where σy = 0:  c12 ϵx +c11 ϵy + c13 ϵz = 0 ai,film − ai,relaxed where ϵi = ai,relaxed  (.) (.)  With only one equation, further assumptions are necessary: both the c and a lattice constants scale equally with Nd so that ϵz = ϵx ; and that for a low doping level, Nd:sapphire shares the elastic constants of sapphire. Solving for the relaxed lattice constant leads to an overall lattice expansion of . when the Nd-doping level is . at..  .  Optical properties  .. Temperature-dependent emission Emission from Nd:sapphire is dominated by transitions from the upper 4 F3/2 manifold to the 4 I9/2 and 4 I11/2 manifolds, a common property of all Nd-doped solid state laser materials. Transitions from the  energy levels of the upper manifold to the  and  levels in the lower manifolds yield  and  emission lines respectively. Identification of the energy levels was possible by photoluminescence (PL) mea  PL Intensity (arb. units)  – Structural and optical properties of Nd:sapphire T=295 K  (a)  880  T=8 K  890  900  910  920  930  940  950  PL Intensity (arb. units)  Wavelength (nm)  T=295 K  (b)  1070  T=8 K  1080  1090  1100  1110  1120  1130  Wavelength (nm)  Figure .: Comparison of Nd:sapphire PL emission spectra at room temperature and at  K for the (a) 4 F3/2 →4 I9/2 and (b) 4 F3/2 →4 I11/2 transitions. Intensity is in log scale for better display of weaker peaks. e energy levels split by the crystal field are obtained from the peaks still present at low temperature denoted by crosses. Lorentzian peak fits are shown in green. surements at low temperatures that suppressed the emission from the upper level of the upper manifold. A Nd:sapphire sample was loaded into a low-vibration optical cryostat from Advanced Research Systems. e closed cycle helium cryostat was capable of reaching T= K and offered optical access via a .′′ diameter window with a viewing angle corresponding to f/.. e PL setup involved the same components as mentioned in section ., but with a modified layout to conform to the restricted optical access. Measurements were taken at room temperature aer the cryostat pumped down, and approximately  hours later once the sample had been cooled. e  mW power of the  nm diode laser was maintained for both sets of measurements. Figure . compares the emission spectra from a  µm Nd:sapphire film at room temperature and at  K. e peak with the shortest wavelength in the room temperature 4 F3/2 →4 I9/2 spectrum is due to the R2 →Z1 transition, where R2 is the upper   – Structural and optical properties of Nd:sapphire state in the 4 F3/2 manifold and Z1 is the ground state (example in fig. .). e energy level position of R2 is therefore just the reciprocal of that wavelength, which in the wavenumber notation popular among spectroscopists is  cm−1 . At low temperatures, the population of Nd3+ ions in the R2 state waiting for optical decay is suppressed. e distribution of ions in the metastable 4 F3/2 manifold can be described by the temperature-sensitive Boltzmann occupation factors: fR  1 = 1 + exp(− k∆E ) BT  and fR =  exp(− k∆E ) BT 1 + exp(− k∆E ) BT  (.)  where ∆E is the energy difference between R2 and the ground state of the 4 F3/2 manifold, R1 . With the suppression of emission from R2 , the shortest wavelength peak in the low temperature spectrum must correspond to the R1 →Z1 transition thereby placing R1 at an energy level of  cm−1 . Knowing R1 , the other four nonsuppressed peaks in the low temperature spectrum were used to identify the energy level positions of Z2 to Z5 . Likewise for Y1 to Y6 in the 4 I11/2 manifold from the  peaks in figure .(b). e energy level positions determined here are listed in the inset of figure .. Following the identification of the energy level positions, the transitions responsible for the room temperature emission peaks were indexed and are shown in table .. Some of the peaks are due to transitions overlapping in wavelength, as shown in the low temperature emission spectra of figure .. e emission peak linewidths show a temperature dependence consistent with homogeneous broadening, which for an ion in a crystal is due to collisions with lattice phonons[, chap.]. e low temperature narrow peaks were useful for detecting instances of closely spaced peaks and enabled more accurate Lorentzian fits for determining their wavelengths. e low temperature measurements also demonstrate the thermal stability of the emission, where the wavelength shi of the non-suppressed peaks in figure . is barely noticeable. Such stability is an advantage offered by rare-earth-doped crystals over semiconductors, and is particularly suited for high power laser operation. By comparing the occupation of R1 at low vs room temperature, an increase in non-suppressed peak intensity is expected especially when the pump laser power is the same. Instead, the peak intensity drops by a factor of ∼. A likely explana  – Structural and optical properties of Nd:sapphire Table .: Nd3+ states in the 4 F3/2 , 4 I9/2 and 4 I11/2 manifolds responsible for the Nd:sapphire emission peaks near  and  nm. Some peaks are a product of overlapping transitions. Transition  4F 4 3/2 → I9/2  4F 4 3/2 → I11/2  Wavelength (nm) . . . . . . . . . . . . . . .  States involved R2 →Z1 R2 →Z2 , R2 →Z3 R1 →Z1 R1 →Z2 , R1 →Z3 R2 →Z4 , R2 →Z5 R1 →Z4 , R1 →Z5 R2 →Y1 R2 →Y2 R2 →Y3 R1 →Y1 R1 →Y2 R1 →Y3 , R2 →Y4 R2 →Y5 , R2 →Y6 R1 →Y4 R1 →Y5 , R1 →Y6  tion involves weaker 4 I9/2 →4 F5/2 absorption because the  nm diode laser is not matched to any absorption peaks but instead pumps the homogeneously broadened tails that shrink at low temperature. In any case, the change in absorption is not necessary to analyze the suppression of the emission from R2 . e occupation factors in eqn. . can be related to the intensity ratios using the following: IS,Th IN,Tc fR,Tc fR,Th ∆E ( 1 1) )= · = exp( − · fR,Tc fR,Th kB Tc Th IS,Tc IN,Th  (.)  where Tc and Th are the low and room temperatures respectively while IN and IS are the intensities of non-suppressed and suppressed wavelengths. Using the peaks at  nm and  nm and subtracting the background intensities, the suppressed and non-suppressed intensity ratios are  and . respectively. Solving Tc from eqn. . yields . K, which is much higher than the temperature set by the cryostat controller. A likely explanation involves heating by the  mW optical pump, specifically the non-optical transitions in the -level pump/emission scheme. Inci  – Structural and optical properties of Nd:sapphire dentally, tracking the intensities of an emission line from R1 and R2 in Nd-doped crystals may prove useful for temperature monitoring applications.  .. Product of emission cross-section and lifetime Sapphire is anisotropic as explained in section ., and therefore its various properties have directional dependence. e optical symmetry is uniaxial meaning that the refractive index is different along and perpendicular to the optic axis. While both indices are close in sapphire (∼. at  µm[]), the emission spectra polarized along those directions are quite different. Such behaviour is also observed from other uniaxial crystals e.g. Nd:YVO4 . Polarized PL was collected from the  µm Nd:sapphire film analyzed in figure .. A Glan-Taylor calcite prism was added to the detection side of the PL setup for wide wavelength range polarization with a ,: extinction ratio (see fig. .). e asymmetry of the polarizer required that the sample be rotated instead to ensure the optical throughput remain the same between measurements. e  nm pump laser light was unpolarized aer emerging from optical fiber. With the sample facing upwards and rotations only possible about its normal, the optic axis (∥ to crystal c-axis) would have to be in-plane. Among the  available substrate orientations, only two are suitable: A-plane and M-plane, the latter being used for the  µm film. Polarized spectra associated with transitions from the 4 F3/2 manifold to the 4 I9/2 , 4 I11/2 and 4 I13/2 manifolds were collected ∥ and ⊥ to the optic axis. e spectra were then corrected for the optical throughput of the PL setup to get accurate relative strengths of all the peaks. Calibration of the PL setup involved a  V tungsten halogen lamp acting as a  K blackbody source. Knowledge of the entire emission spectrum enables the peak strengths to be quantified. Aull and Jenssen derived a relationship to obtain the emission crosssection from the emission spectrum that was then used to analyze the isotropic crystal Nd:YAG[]. e derivation below is based on theirs but with slight modifications including a change of variable to units of wavelength. From Planck’s spectral energy density in a cavity u(λ, T ) and Einstein’s treatment of light interaction in a two level (i,j) system, the ratio of Einstein’s spontaneous emission coefficient Aji to the stimulated emission coefficient Bji is given by    – Structural and optical properties of Nd:sapphire  u(λ, T ) =  8πhcn3 1 5 hc λ exp( λkT − 1)  therefore  Aji 8πhcn3 = Bji λ5  (.)  where n is the refractive index. e optical gain coefficient in a material, α(λ), can be expressed as a function of the B coefficient, the normalized lineshape g and the population density N as follows: ( ) hn α(λ) = Bji gji (λ)Nj − Bij gij (λ)Ni λ  (.)  from which the emission cross-section σji can be defined σji (λ) = Bji gji (λ)  λ4 hn = Aji gji (λ) λ 8πcn2  (.)  e expression of emission cross-section in terms of spontaneous emission coefficient is also called the Fuchtbauer-Ladenburg equation. e spectral intensity of a PL measurement under low-level excitation (i.e. not saturated) is given by Iji (λ)dλ = GNj Aji gji (λ)  hc dλ λ  (.)  where G is the collection efficiency of the optical setup. e population density of the upper level Nj is simply the product of the Boltzmann occupation factor fj and the total population density of the upper 4 F3/2 manifold NT . Rearranging and integrating over the sum of transitions in eqn. . yields ∫ λ  ∑  ∫ Iji (λ)dλ = hc  GNT  j,i  ∑ j,i    fj Aji gji (λ)dλ  (.)  – Structural and optical properties of Nd:sapphire where the integral is over the entire emission spectrum. e spontaneous emission rate is related to the lifetimes: ∑  fj Aji =  j,i  1 1 η = +W = τR τF τF  (.)  where τR is the radiative lifetime, τF the fluorescent lifetime, W the non-radiative decay rate and η the radiative quantum efficiency. e total spectral intensity is then simplified to ∫ λI(λ)dλ =  ηhc GNT τF  (.)  which is no longer dependent on the lineshape of individual transitions. Returning to eqn. . for substitution with the results of eqn. . and eqn. .,  Iji (λ) =  ] [ ] fj hc [ · GNT · Aji gji (λ) λ  (.)  and factoring in contributions of all transitions to the spectral intensity at λ, σ(λ) =  ∑  fj σji (λ)  (.)  j,i  the emission cross-section as a function of spectral intensity is therefore σ(λ) =  ηλ5 I(λ) ∫ 8πcn2 τF λI(λ)dλ  (.)  For a Nd-doped crystal with suitably low Nd concentration (∼ at.) that is free from concentration quenching effects, the quantum efficiency η is essentially  and τR = τF = τ . While an independent measurement of τ is the final requirement for solving σ(λ) in eqn. ., the σ(λ) · τ product can be evaluated in the interim. In his work on Ti:sapphire, Moulton presented a version of eqn. . suitable for a uniaxial crystal like sapphire that accounted for the polarized emission[]. Essentially there are now  orthogonal orientations producing two unique spectra:   – Structural and optical properties of Nd:sapphire ...  ...  120  11290  R2  11100  R1  2297  Y6  F  optic axis  3/2  100  Polarized  optic axis  -24  ·  80  = 111x10  2  cm s  60  1096 nm  2280 4  2232  I 11/2  .....  -1  )  Polarized  Energy Levels (cm  2045 1978 1937  Y1  510  Z5  489 4  .....  2 -24  Emission Cross Section x Lifetime (x10  cm s)  4  I 9/2  124  40  107 0 -24  ·  = 22x10  Z1  2  cm s  20  0 880  ...  ... 900  920  940  960  1080  1100  1120  1140  1380  1400  1420  1440  Wavelength (nm)  Figure .: Product of emission cross-section σ and lifetime τ for Nd:sapphire derived from the PL emission spectra. e emission is polarized along and perpendicular to the optic axis (c-axis), and shows transitions from the 4F 4 4 4 3/2 manifold to the I9/2 , I11/2 and I13/2 manifolds. e dominant peak at  nm is a lasing candidate. Inset, energy level positions for the states in the 4 F3/2 as well as the two lowest energy manifolds, obtained from the low temperature measurement shown in figure .. one ∥ and two ⊥ to the optic axis. e product of polarized emission cross-section and lifetime is given by 3λ5 Ipol (λ) σpol (λ) · τ = 8πcn2  [∫  ]−1 {I∥ (λ) + 2I⊥ (λ)}λdλ  (.)  where pol is the polarization either ∥ or ⊥ to the optic axis. e spectral intensity Ipol (λ) is obtained by multiplying the measured polarized PL intensity (proportional to photon flux or photons/sec) by the photon energy (∝ 1/λ). A constant refractive index was chosen instead of having it distributed within the integrated intensity as a function of polarization and wavelength. Birefringence in sapphire is almost negligible and the refractive index is basically flat at the infrared wavelengths considered.    2423  Y6  2345 2297 2049 1982 1944  Y1  – Structural and optical properties of Nd:sapphire Figure . shows the σ · τ product from the  µm thick Nd:sapphire sample grown on M-plane sapphire mentioned previously. From an XRD θ-θ scan, the strong film peak coincides with the substrate peak shoulder suggesting that the Nddoping level is low and that η = 1 is valid. As shown in the figure, the Nd:sapphire emission polarized ∥ optic axis is dominant. Such behaviour has also been observed for other uniaxial crystals e.g. Nd:YVO4 and Nd:GdVO4 . e  nm peak of Nd:sapphire has a large σ · τ of ×−24 cm2 s, which is comparable to the ∼×−24 cm2 s produced by the  nm peak of Nd:YVO4 , perhaps the highest among Nd-doped materials[]. For comparison, the  nm peak of Nd:YAG has a σ · τ of ×−24 cm2 s. Uniaxial materials with strong polarized emission tend to have large σ · τ products as shown by the factor of  weighting in eqn. .. e σ · τ product is frequently seen in calculations of laser properties; high values yield low lasing thresholds, high energy storage and better power extraction efficiency[].  .. Lifetime measurement e radiative lifetime of Nd:sapphire was obtained from time-resolved decay measurements of the fluorescence intensity. Alternative methods include frequencydomain measurements[, chap.]. Time-resolved measurements require a pulsed excitaton source with a repetition rate slow enough to observe the fluorescence decay. A pulsed Ti:Sapphire laser, which was the preferred choice, was unavailable. Instead, noting that Nd-doped crystals had lifetimes in the – µs range, the pulsed pump source could be achieved by mechanically chopping a continuouswave laser. A high power Ar+ laser operating at  nm was used to pump the  µm Nd:sapphire sample (as mentioned previously) via a -slit chopping wheel running at  kHz. e Ar+ laser was used instead of the  nm diode laser despite the weaker absorption because of its narrow beam profile and minimal divergence. e beam easily passed through the narrow chopper slit and obviated the need for focusing optics, thus reducing the minimum distance between sample and detector. Measuring the time-resolved intensity of a weak signal such as the luminescence from a thin film requires a fast-response, high gain detector. A Hamamatsu R photomultiplier tube was chosen due to its sensitivity in the near-infrared. e S    Intensity (arb. units)  – Structural and optical properties of Nd:sapphire  (a)  Pump laser scatter Luminescence Fit  -0.2  0.0  0.2  0.4  0.6  Intensity (arb. units)  Time (msec)  Y = A·exp(-t/ 96  s) + C  (b)  -0.10  -0.05  0.00  0.05  0.10  0.15  0.20  0.25  Time (msec)  Figure .: (a) Pulsed luminescence from Nd:sapphire generated by mechanically chopping a continuous wave pump laser at  kHz. (b) Higher resolution scan of (a) with a fit of the exponential decay to obtain the upper metastable state lifetime. photocathode in the tube has a nearly flat radiant sensitivity of ∼ mA/W up to  nm before rapidly falling at higher wavelengths (. mA/W at  nm). Most photomultipliers operate in the visible and offer much higher sensitivity. e R is a wide area detector (x mm2 ) and was exposed directly to the sample without passing a spectrometer to maximize collection efficiency. e entire emission spectra was therefore measured simultaneously albeit weighed heavily towards the 4F 3/2  →4 I9/2 transitions. Since the lifetime essentially describes the depopulation  of the upper manifold, measuring emission to any of the other two manifolds would yield the same result. High levels of thermal noise in the R were suppressed by liquid nitrogen cooling of a cavity placed in contact with the R housing. e housing was sealed with a glass window and purged with nitrogen gas to prevent condensation. Multiple colour glass filters were mounted on the window to eliminate pump laser scatter. e weak current signal from the R was amplified by an electronic circuit that included a Texas Instruments OPA wide bandwidth transimpedance   – Structural and optical properties of Nd:sapphire amplifier[]. e output voltage was then read by a Rigol DS digital storage oscilloscope. Figure . shows the fluorescence response of the Nd:sapphire sample to a pump laser optically chopped at  kHz. e pump signal was measured by replacing the sample with a diffuse scatterer. e figure shows that the pump fall time is long, ∼ µs, a consequence of mechanical chopping. Ignoring the same period in the fluorescence and fitting to the remaining decay yields a single-constant exponential function where τ is  µs. is lifetime is slightly larger than the  µs of Nd:YVO4 , but much less than the  and  µs lifetimes of Nd:YAG and Nd:YLF (Nd:YLiF4 ) respectively[]. e emission cross-section for the  and  nm peaks of Nd:sapphire are then calculated to be . and .×−18 cm2 respectively. Such high values, especially for the  nm peak, make Nd:sapphire a promising new laser material. For comparison, the primary peak of Nd:YAG and Nd:YVO4 , both at  nm have an emission cross-section of . and .×−18 cm2 respectively[].  .. Absorption cross-section from fluoresence excitation According to Beer’s law, the intensity of a beam passing through a medium decreases exponentially due to absorption: I(z) = Io exp(−σa (λ)N z), where N is the ground state population density and σa (λ) is the absorption cross-section. Nddoped crystals typically have an absorption coefficient σa (λ) · N on the order of  cm−1 , which suggests that detecting the absorption across thin Nd-doped sapphire films (∼ µm thick) would be extremely difficult. In a normal transmissionbased measurement, troughs appearing in the broad spectrum of the transmitted beam would be associated with absorption peaks. e absorption spectrum of Nd:sapphire was instead measured by excitation spectroscopy, an indirect method whereby the sample was pumped at different wavelengths and the resulting emission strength noted. e pump source, a continuous wave Ti:Sapphire laser, was manually tuned in nanometer increments from  to  nm. e PL setup was used to verify the pump peak positions as well as calibrate for spectral variations in power post-measurement. e  µm thick Nd:sapphire sample of the previous sections was used for the measurement, oriented with its optic axis parallel to the pump polarization. As optical edge filters    – Structural and optical properties of Nd:sapphire  4.0  2  833  3.0  Absorption Cross Section (x10  -19  759  cm )  3.5  825  818  2.5  765 752 771  2.0  813 1.5  1.0 910 896 0.5  886  0.0  750  780  810  840  870  900  Wavelength (nm)  Figure .: Room temperature absorption cross-sections of Nd:sapphire measured using excitation spectroscopy. Absorption is polarized ∥ optic axis. Measurements were taken at one nanometer intervals. Peak wavelengths (in nm) are labeled. Crosses indicate fine measurements done to obtain peak heights for use in the reciprocity relation. that isolate the pump from the ∼ nm emission were unavailable, the 4 F3/2 → 4I  13/2  transitions were recorded instead. e signal, although not from the domi-  nant branch, was sufficiently strong. e emission intensity can be simplified to a linear function of the pump intensity, quantum efficiency η and absorption coefficient, as shown by [ ] Iemis (λ) = ηIpump (λ) 1 − exp(−σa (λ)N z) ∼ ηIpump (λ)σa (λ)N z  (.)  which applies when the film is very thin such that σa N z ≪ 1. e quantum efficiency is typically a constant near . e absorption spectrum of Nd:sapphire was therefore plotted in the form of total emission intensity across the 4 I13/2 branch for each pump wavelength, and is shown in figure .. e main absorption peaks   – Structural and optical properties of Nd:sapphire are at  and  nm, which is further in the infrared compared to the  nm peak of both Nd:YAG and Nd:YVO4 . e same trend was observed in the emission spectrum ( vs  nm), suggesting that the Stark-split energy levels are spaced closer in Nd:sapphire. is is likely due to the Nd-doping site: the smaller octahedral (-coordinated) Al site in sapphire compared to the dodecahedral (coordinated) Y site of YAG or YVO4 . In order to approximately quantify the absorption strength, the reciprocity or McCumber method was used to relate the emission and absorption crosssections[]. e relationship originates from the Einstein B coefficient, where transitions between levels i,j have the same probability such that σij = σji . However, when the levels are part of a manifold, Boltzmann occupation factors matter. From a derivation by Payne et. al.[],  σe (λ) =  ∑  fj σji (λ) =  ij  σa (λ) =  ∑  fi σij (λ) =  ∑ exp(−Ej /kT ) ij  Ze  ij  Zg  ∑ exp(−Ei /kT )  ij  σji (λ)  (.)  σij (λ)  (.)  where σe is the emission cross-section. Z is the partition function ∑ m exp(−Em /kT ) calculated for the excited and ground manifolds Ze and Zg respectively. Ej , Ei and the partition functions are relative to the lowest energy level of their particular manifold. e Nd:sapphire energy levels are shown in the inset of figure .. Dividing the two cross-sections and using the substitution  Ej − Ei =  hc − EZL λ  (.)  leads to the reciprocity equation Ze σa (λ) = σe (λ) exp Zg  [(  ) ] hc − EZL /kT λ  (.)  where EZL is the energy level difference between the ground levels of both mani-    – Structural and optical properties of Nd:sapphire folds. σa was calculated for three peaks in the room-temperature 4 F3/2 → 4 I9/2 emission spectrum polarized ∥ to the optic axis (fig. .). Since the absorption spectrum only has nanometer resolution, the heights of those three peaks were measured more accurately and are indicated by the crosses in figure .. e scaling factors between the calculated σa and the three resolved absorption peaks were averaged and applied to the entire absorption spectrum. e best wavelengths for optically pumping Nd:sapphire are therefore at  and  nm, which have absorption cross-sections ∼.×−19 cm2 . is compares to .×−19 cm2 and .×−19 cm2 for Nd:YAG and Nd:YVO4 respectively[]. While the quantum efficiency for non-concentration-quenched Nd-doped crystals is near , another factor, vibronic interactions may cause deviations to the reciprocity relation. Vibronic interactions occur in the form of electron-phonon coupling, where phonons associated with dopant vibrations spread the energy levels into bands. e transitions now consist of a photon-phonon combination leading to a broad optical gain profile suitable for tunable lasers[, chap.]. In the case of Nd, vibronics are typically dismissed because the peaks are not broadened. However, deviations to the reciprocity of Nd:YAG can occur when the phonon energy is comparable to the difference between the Stark-split levels[]. For example, the emission cross-section for the R1 to Z3 transition may be inflated because of vibronic transitions from R1 to Z1 that have an optical R1 to Z3 portion. e reverse vibronic transition, Z1 to R1 is less likely to happen since it requires a phonon excitation from Z1 to Z3 . e effect of vibronics on Nd:sapphire is unclear, but it is possible that the reciprocity relation is not fully accurate.  .  Post-growth annealing  .. Motivation, process and ◦ C anneal Films intended for processing into a waveguide laser device must be decently thick, on the order of microns, depending on the core/cladding index contrast. While the Nd:sapphire films with thicknesses up to ∼ nm were smooth and featured high crystalline quality, extending those growth conditions to make thicker films proved   – Structural and optical properties of Nd:sapphire difficult. e degradation in film quality was observed by reflection high energy electron diffraction (RHEED), where the diffraction streaks/spots would gradually elongate into rings about the specular diffraction spot. at loss of periodicity in the lateral, in-plane direction indicates that the crystal is no longer single crystal but rather turning into an ensemble of multiply oriented crystal grains i.e. a polycrystal. Films with a large polycrystalline portion produced poorer PL and XRD results: emission peaks superimposed on broad backgrounds and weaker Bragg peaks respectively. e degradation might be a result of strain relaxation that increases the level of defects and surface roughness, thus impairing the surface diffusion required for optimal quality. Different growth conditions were tested without significantly dropping the growth rate (i.e. same order of magnitude or more), yet none provided persistent growth of a smooth, single-crystal film with micron-range thickness. A non-ideal workaround was discovered that compromised smoothness for crystal quality, the more important of the two. Following the growth of a smooth, low temperature layer, the growth is interrupted while the temperatures of the substrate as well as Al and Nd cells are raised. When the growth is resumed at the higher temperature and faster rate, the RHEED pattern becomes spotty and lasts for the extended duration. As an example, the  µm Nd:sapphire film on M-plane sapphire analyzed in section . was grown with such an interrupt. e growth temperature was raised from  to ◦ C and the rate from . nm/min to ∼ nm/min. e spotty RHEED pattern persisted for the entire ∼ hours of growth. e film had an RMS roughness of  nm. e partial success of the workaround may be a result of improved surface diffusion at the higher growth temperature. In an attempt to improve the film quality aer growth, samples were annealed in a box furnace in an air environment. e Lindberg  furnace was capable of reaching temperatures up to ◦ C. A thick Nd:sapphire film grown on A-plane sapphire for  hours under similar conditions to those mentioned in the previous paragraph was annealed at two different temperatures: ◦ C for  hours and ◦ C for  hours. e PL emission spectra of the as-grown film was typical of an Nd:sapphire film grown on either A- or M-plane sapphire. PL following the two annealing steps are shown in figure .. For these measurements, a newly purchased pump source was used: an  nm,  W diode laser from Axcel Photon  – Structural and optical properties of Nd:sapphire  12000  (a) 10000  t = 5 ms  8000  PL Intensity (counts)  6000  4000  2000  0  4000  t = 1 s  (b)  3000  2000  1000  0 1060  1080  1100  1120  1140  Wavelength (nm)  Figure .: PL emission spectrum from an Nd:sapphire film aer furnace annealing in air at (a) ◦ C for  hours and (b) ◦ C for  hours. Measurement times are  ms and  s respectively. Annealing at ◦ C broadened the spectrum and weakened the intensity significantly. Intensity comparisons between annealing steps were calibrated using the PL from a reference sample. ics. e laser, which was packaged in a  mm TO-can, was mounted in a orlabs controller with thermo-electric cooling. At typical operating powers of .–. W, the pump laser peak was temperature-tunable between – nm. Pumping the Nd:sapphire samples at the  nm absorption peak with such high powers improved the PL emission significantly, enabling a reduction of exposure times by a factor of a thousand. Aer annealing at ◦ C for  hours, the PL emission spectrum still comprised a collection of sharp, intense emission peaks as shown in figure .(a). Peak widths were also unchanged. ere was a slight difference between the annealed and unannealed spectrum involving the relative peak heights from different polarizations. A comparison of the  nm and  nm peaks, which are polarized ∥ and ⊥ to the optic axis respectively (see fig. .), shows that the post-anneal in-    – Structural and optical properties of Nd:sapphire tensity of the  nm peak increased from . to . relative to the  nm peak. e significance of this ratio stems from its difference between as-grown Nd:sapphire films on A- and M-plane to those on R-plane sapphire. e PL captured from the latter contains stronger ⊥ polarized emission because it has a smaller component of the optic axis in-plane (unpolarized PL is collected along the sample normal). e rise of the : nm ratio aer annealing then suggests a reorientation of the Nd dopants and their local atomic structure from the orientation of A-plane Nd:sapphire towards one where the optic axis is tilted into the substrate. is could happen if Nd segregates to grain boundaries that while not disordered may be tilted instead. It is unclear if an exact tilt can be evaluated based on the peak ratio.  .. Anneal at ◦ C Aer a second annealing step at ◦ C for  hours, the film appearance changed dramatically, becoming a rough white layer that was mostly opaque. e PL emission spectrum also changed dramatically, as shown in figure .(b), featuring very weak Nd:sapphire peaks superimposed on a dominant broad background. Subtracting the background, the relative ratio of the  nm to  nm peak increased further to , which is the ratio observed from unpolarized PL off an R-plane Nd:sapphire film. In order to identify the broad emission background, a lower resolution PL scan was done using the  lines/mm grating instead. e sample was then replaced with a rough aluminum plate and the PL scan repeated. e spectra are shown in figure .(a), where the PL intensity from the Al plate was scaled to match the tail end of the spectrum from the ◦ C annealed sample. e Al plate did not produce emission of its own, but rather scattered the pump laser light. Although the pump peak at  nm was well suppressed by filters placed between the sample and the fiber collection optics, the diode laser also produced broad emission that extended into the region of the Nd:sapphire peaks. at emission could not be filtered out, instead becoming increasingly dominant with sample roughness. e sharp PL rise at ∼ nm was due to a orlabs long pass filter with cut-on wavelength of    – Structural and optical properties of Nd:sapphire o  Nd:Sapphire annealed at 1450 C  (a)  Rough aluminum plate (intensity  PL Intensity (arb. units)  scaled)  Difference of plots in (a)  (b)  1000  Nd-doped polycrystalline alumina (intensity scaled)  1050  1100  1150  1200  1250  1300  1350  Wavelength (nm)  Figure .: PL emission spectra showing the contribution of pump laser scattering and inhomogeneous broadening to the broad spectrum of furnace-annealed Nd:sapphire at ◦ C. (a) Lower resolution, wider range scan from the sample in figure . compared against the measurement produced when the pump laser is scattered off an aluminum plate. (b) e difference of the plots in (a) is a broad emission peak similar to the spectrum from the Nd-doped Al2 O3 film featured in figure .(a).  nm. Taking the difference between the two plots in figure .(a) removed the influence of sample roughness on the PL emission spectrum. e difference, shown in figure .(b), is a broad emission peak centred around  nm similar to the emission spectrum from Nd-doped glass. For comparison, the PL emission spectrum of an Nd-doped Al2 O3 film grown on C-plane sapphire is shown as well. Annealing at ◦ C therefore increases crystal disorder by migrating Nd ions away from their uniformly doped Al sites. at disorder produces the inhomogeneously broadened emission peak. XRD scans (not shown) nevertheless indicate that the film still retained its A-plane orientation, but was now heavily textured (i.e. broken up into crystallites) with a ◦ tilt distribution about the primary orientation. It is likely then that the Nd dopants have segregated to the many grain boundaries   – Structural and optical properties of Nd:sapphire available, which are disordered in contrast to the ◦ C anneal. Since it may be argued that the poor annealing result was due to less than ideal as-grown film quality, a similar anneal at ◦ C was performed on a  nm thin sample with Pendellösung fringes that was part of the set related to figure .. After annealing, an XRD θ-θ scan showed only the substrate peak, while a PL scan produced no detectable emission. is suggests that either the thin film evaporated off, or that the Nd-dopants migrated from the Al sites and became passive optically. e latter is the more likely explanation, since the Nd could have diffused to the surface and formed optically inert Nd2 O3 . In any case, annealing at high temperatures not only fails to improve film surface roughness, but is also counterproductive with regards to crystal and optical emission quality. At the very least, these tests have shown that Nd:sapphire is thermally stable up to ◦ C thus making it suitable for a wide range of applications including high power lasers. If anything, the breakdown at ◦ C indicates that fabrication of Nd:sapphire by bulk methods at the melting point of sapphire is likely to be very difficult, which may explain the non-existence of rare-earth doped bulk sapphire crystals. Furthermore, it appears that the Nd dopants only populate the Al3+ site of the sapphire films when the host is single crystal, preferring instead to segregate to disordered grain boundaries given the opportunity.    4– Epitaxial Nd:Al-Ga-O in the corundum phase e success with Nd:sapphire prompted the search for another new Nd-doped material to be attempted by epitaxial growth. Since the candidate would be grown on sapphire, having a similar crystal structure would improve the film–substrate epitaxial relationship. e candidate should also address the limitation of Nd:sapphire for waveguiding by having a clear refractive index contrast relative to undoped sapphire. For planar waveguides with Nd:sapphire/sapphire core/cladding layers, the index of the core is marginally higher due to the low concentration of dopants. Optical confinement then requires core layers that are tens of microns thick, which is not practical by MBE. e criteria above led to α-Ga2 O3 , a corundum-structure material like sapphire with gallium instead of aluminum ions and with larger lattice constants (tab. C.). e combination of α-Ga2 O3 on a sapphire substrate is appealing as the oxide version of the popular multilayer pair AlAs/GaAs. Unlike the semiconductors, however, the oxides are more difficult to grow in single-phase form due to the variety of other phases that might appear. e growth of α-Ga2 O3 is further complicated by the dominance of β-Ga2 O3 , the stable phase when formed in bulk at/near atmospheric pressure. e growths of both α-Ga2 O3 and β-Ga2 O3 on sapphire have been reported before, but they were geared towards developing wide-bandgap semiconductor devices[, ]. ere are no obvious reports of α-Ga2 O3 used for making solid state lasers, likely because of the difficulty growing bulk samples. In a  Optics Letters article, my colleagues and I reported Nd-doped αGa2 O3 films that were single crystal, and like Nd:sapphire before it, yielded a previously unreported emission spectrum of sharp emission peaks[]. is chapter covers the MBE-growth of Nd:Ga2 O3 and highlights valuable feedback during growth by electron diffraction and thin film reflectometry. e growth conditions required    – Epitaxial Nd:Al-Ga-O in the corundum phase more attention due to issues with metal desorption not experienced when growing sapphire. Using the techniques of chapter , detailed structural and optical properties were obtained. Success with α-Ga2 O3 then motivated the growth of Nd-doped alloys analogous to the popular AlGaAs. e structural and optical properties of these ternary α-(Al1−x Gax )2 O3 films were found to be in-between those of the binary endpoints, and were dependent on composition as well as film strain.  .  Ga2 O3 growth  .. Gallium desorption Ga2 O3 was considerably more difficult to grow than sapphire because gallium adatoms tended to desorb from the sample surface rather than incorporate into the film. Evidence of the desorption was obtained using a residual gas analyzer (RGA) typically used for measuring the partial pressures of growth chamber background gases e.g. H2 , O2 , H2 O, CO2 , etc. e SRS RGA, a mass spectrometer capable of detecting mass-to-charge ratios of up to  a.m.u., was moved to a source port for direct exposure to the sample manipulator. e relocation was necessary because desorbed Ga metal is unlikely to survive multiple collisions with the cold chamber walls like a normal residual gas would to get to the usually obscured RGA. According to Knudsen’s cosine law, the flux at a distance r and angle θ away from the source normal varies as  cos θ . r2  Using this for a source where the total evaporated  mass is Gsource , the evaporated mass arriving at a sample of area Asamp is then given by[, chap.]:  dGsamp =  (G  source Ksource cos θ rs2    ) ( ) · cos φ · dAsamp  (.)  – Epitaxial Nd:Al-Ga-O in the corundum phase  Sample rs  φ φ rt  θ Metal Source  Growth chamber  RGA  Figure .: Schematic showing the RGA detection of desorbed Ga Here Ksource is a geometric factor describing the source:  1 4π  for a point source,  1 π  for a flat surface such as a boat or an effusion cell orifice, etc. e source–sample distance is denoted by rs while φ is the angle between the sample normal and the incident flux: ◦ . Figure . shows the relative orientations of the source, sample and RGA. Source material failing to fully incorporate into the sample will desorb also according to Knudsen’s cosine law. For a sticking coefficient of α, the desorbed mass arriving at the RGA ionizer a distance rt away from the sample will be dGRGA =  (G  samp Ksamp cos φ rt2  )  · dARGA  (.)  where Gsamp is the mass desorbed/evaporated from the sample, and which given the small solid angle captured from the source can be approximated as Gsamp = (1 − α) ·  dGsamp · Asamp dAsamp    (.)  – Epitaxial Nd:Al-Ga-O in the corundum phase Since the sources in the MBE growth chamber are pointed at the sample, θ is effectively zero. e total mass evaporated from the source is not easily known, but the flux arriving at the sample can be measured via the retractable ion gauge. e mass flux  dG dA  arriving at the two locations can then be compared,  dGRGA dARGA  /  dGsamp (1 − α)Ksamp cos φAsamp = dAsamp rt2  (.)  which suggests that the RGA flux strength can be improved by increasing the sample size. is was verified by replacing the typical  cm2 samples with a ′′ diameter sapphire substrate. To account for the position of the ion gauge ∼ cm in front of the sample, the flux ratio must be multiplied by rg2 /rs2 where rg is the source–gauge distance. For a Ksamp of π1 , φ of ◦ , rt of  cm and rs of  cm, the flux ratio is approximately (1 − α)/1000. e sensitivity is therefore low, and suggests that the flux of partially desorbed gallium arriving at the RGA will be in the mid −11 to low −10 torr range for typical incident fluxes. e gas species arriving at the RGA are ionized, then discriminated using an electric quadrupole for separation into specific mass/charge ratios. e peaks detected by the RGA therefore not only correspond to cases of single ionization but also include dissociative ionization, isotope differences and multiple ionization[, chap.]. Figure .(a) shows an RGA scan monitoring the desorption of Ga from a ′′ sapphire wafer during deposition under excess molecular oxygen. As an example of the RGA detection capabilities, molecular oxygen produces a number of peaks that form a distinct cracking pattern: a.m.u.  is the dominant (to the point + of saturation) singly ionized O+ 2 , a.m.u  is dissociated O , a.m.u.  is multiply  ionized O2+ and both a.m.u.  and  refer to different isotopes of O+ 2. In the RGA scan of figure .(a), the isotopes of Ga+ (a.m.u.  and ) were detected when the Ga shutter was opened. e metal flux was consistent with the Ga source material and is proof of desorption from the sample surface. Besides the Ga metal, gallium also evaporates in the form of the suboxide Ga2 O. Fully oxidized Ga2 O3 was not detected suggesting that the stable form tended to incorporate while the suboxide was more volatile and had a higher vapour pressure. In figure .(b), an RGA scan of the higher a.m.u. tranche shows that Ga2 O desorbs even without    – Epitaxial Nd:Al-Ga-O in the corundum phase  (a)  Ga cell shutter:  -7  10 OPEN, CLOSED  -8  10  -9  10  69  Ga  -10  Partial Pressure (torr)  10  71  Ga  -11  10  -12  10 10  20  30  40  50  60  (b)  -10  10  70  Ga cell shutter:  69  OPEN, CLOSED  Ga  71  69  Ga  71  Ga  GaO  69  Ga O  -11  2  10  71  Ga O 2  -12  10 70  80  90  100  110  120  130  140  150  160  170  180  190  Mass to charge ratio (a.m.u)  Figure .: RGA scans identifying the desorbed material from a ′′ sapphire wafer heated to ◦ C when the Ga cell shutter is closed/open. e Ga cell is heated to ◦ C yielding a flux of .×−7 torr. Ga that is insufficiently oxidized will desorb in the form of Ga2 O. (a) Scan taken from a.m.u.  to  under oxygen overpressure of ×−6 torr. (b) Scan taken from a.m.u.  to  without an oxygen overpressure an oxygen overpressure. is raises the possibility that Ga2 O evaporates from the source material or that Ga metal reacts with the oxide surface to form the volatile Ga2 O. From experience, Ga etching of the surface has been observed by reflection high energy electron diffraction (RHEED) (returns to the starting pattern) and is even sometimes utilized to effectively “reset” the surface following the growth of a nonideal initial layer. Ga etching has also been effectively used in III-V research to remove the passive Ga2 O3 layer on GaAs substrates prior to growth[]. It is likely    – Epitaxial Nd:Al-Ga-O in the corundum phase  (a)  Oxygen:  6  Ion gauge  On  10  reading  5  10  Off 4  2  (b)  a.m.u 154 smoothed  Pressure (x10  -11  torr)  10  1  8  (c) a.m.u 69  Ga shutter: Open  Closed  6  4  2  500  600  700  800  900  1000  1100  1200  Time (s)  Figure .: Effect of O2 overpressure on Ga and Ga2 O desorption from the ′′ sample: (a) Oxygen overpressure, effectively measured by the growth chamber ion gauge, (b) & (c) Evolution of Ga2 O (a.m.u. ) and Ga (a.m.u. ) desorption respectively. e Ga flux incident on the sample was actuated by shutter control. that some of Ga2 O originates from the source material, which is a non-surprising consequence of operation in an oxygen environment. Ga2 O was also detected when the test was repeated with a ′′ silicon wafer, although it may be argued that the contributing factor was the oxide buildup on the sample manipulator from previous growths. e effect of an oxygen overpressure (i.e. typical growth conditions, except no plasma) on the Ga and Ga2 O desorption is shown in figure .. With the sample at ◦ C, oxygen caused the desorption of less Ga but more Ga2 O, proving that Ga metal does become the volatile suboxide on the sample surface. e elevated background for both a.m.u.  and  under excess oxygen is attributed to a higher noise level. e measurement showed that although oxygen exceeded the Ga flux by almost two orders of magnitude, it was still insufficient to fully oxidize the Ga to the   o  Temperature (x100 C)  – Epitaxial Nd:Al-Ga-O in the corundum phase  Substrate temperature 8  6  4 a.m.u 154 smoothed  4  Pressure (x10  -11  torr)  6  2  a.m.u 69 6  smoothed  4  2  500  1000  1500  2000  2500  3000  3500  Time (s)  Figure .: Similar to figure . showing instead the effect of sample temperature on Ga and Ga2 O desorption. e Ga flux was deposited on the ′′ sample under an O2 overpressure of 2.5 × 10−6 torr. stable form of Ga2 O3 . is observation persisted even when the test was repeated with the in-house plasma source operating across its power range. With oxygen pressure limited for the safety of the heated components, sample temperature became the only option for minimizing desorption and promoting growth. Figure . shows the effect of gradually changing the temperature on the desorption of Ga and Ga2 O. e expected behaviour of higher sticking coefficient at lower temperature is exhibited by Ga metal. In contrast, the Ga2 O level increases suggesting that the extra Ga metal sticking to the surface just desorbs in the form of the volatile oxide. Only at temperatures below ∼◦ C does GaO start to stick, thereby giving it sufficient time to fully oxidize into the stable Ga2 O3 . Re-raising the temperature increased the desorption of Ga as expected, and Ga2 O initially. e minor burst of the suboxide suggests that some of the previously deposited oxide material was desorbing as well. As the temperature ramped up, the amount of    – Epitaxial Nd:Al-Ga-O in the corundum phase Ga metal on the surface continued to decline, eventually deterring the formation and subsequent desorption of Ga2 O. A burst in Ga metal desorption corresponded to that inflection point in the a.m.u.  scan. In essence, for specific conditions of oxygen overpressure and incident gallium flux, there exists a temperature that demarcates a successful growth window. Below this point, gallium can be incorporated into the film in oxide form. Above that, gallium does not incorporate but rather desorbs in the form of either Ga metal or Ga2 O. Furthermore, gallium on the surface might etch the underlying oxide film.  .. Monitoring film quality by RHEED Ga2 O3 films were grown using the same procedure developed for sapphire: aer establishing an oxygen overpressure via the ignited plasma source, growth was started by exposing the Ga source to the heated sapphire substrate. Unlike sapphire, however, the upper range of the growth temperature (> ◦ C) was inaccessible due to Ga desorption. e low end was likewise limited by poorer surface diffusion leading to amorphous or polycrystalline films. Since the onset of growth is indicated by a changing RHEED pattern, higher temperatures were attempted first for better surface diffusion. Failing that, the temperature would be lowered in steps until growth was finally observed. Having demonstrated its value during the growth of sapphire (sect. .), RHEED was used to monitor aspects of Ga2 O3 film quality involving structure and surface roughness. e four available substrate orientations were evaluated and their outcome was similar to sapphire growth where A, M and R-plane yielded one case while C-plane yielded another. Figure . compares the evolution of RHEED patterns for both cases. On an A-plane substrate (likewise for M and R-plane), the initial film produced a RHEED pattern that is consistent with the structure of the underlying substrate. In contrast, the film on C-plane had a different lattice structure right from the beginning. As in the case of sapphire growth, it is likely that weaker diffusion on C-plane promoted the formation of an alternative phase of Ga2 O3 . While Ga2 O3 has five different polymorphs (solid phases), only the β-Ga2 O3 and the corundum-structure α-Ga2 O3 polymorphs are relevant for this work. At ambient pressure, α-Ga2 O3 tends to transform into β-Ga2 O3 at temperatures up-    – Epitaxial Nd:Al-Ga-O in the corundum phase  (a)  t= 0 mins  t= 13 mins  t= 12.3 hours T~ 240 nm  Ga etched t= RESET  t= 0 mins  t= 3 mins  t= 200 mins T~ 60 nm  [0 0 1]  (b)  change flux ratio t= 417 mins T~ 180 nm  t= 123 mins  [0 1 0]  Figure .: Evolution of RHEED patterns during the growth of Ga2 O3 on different sapphire substrate orientations. (a) Film on A-plane sapphire with pattern, and therefore structure matching the substrate. Changing the Ga/O flux ratio led to the appearance of undesirable extra diffraction spots. Ga etching returned the sample close to the starting surface with noticeable Kikuchi (diagonal) lines. Regrowth under a chevron–spotty pattern was stable over a long period. (b) Film on C-plane sapphire with different crystal structure than the substrate, formed almost instantly when growth began. Streaks indicate that the film is smooth. e orientation of the incident beam is noted in both (a) and (b), and shown pictorially in appendix B.    – Epitaxial Nd:Al-Ga-O in the corundum phase wards of ◦ C, meaning that bulk Ga2 O3 (grown from a melt, flame fusion, etc.) will be primarily in the β phase. Bulk crystals of α-Ga2 O3 are difficult to grow, requiring both high temperature and pressure[]. e role of the substrate in thin film growth can then be considered analogous to this high pressure, and coupled with sufficiently high surface diffusion allows for α-Ga2 O3 films with the same structure as the substrate. On C-plane, the adatoms cannot diffuse to the low energy sites, forming instead a thermodynamically stable phase that is likely β-Ga2 O3 . In figure .(b), the RHEED pattern evolves as long hazy streaks indicative of a smooth film, which suggests that the surface diffusion on β-Ga2 O3 is sufficiently high. Since the primary focus is on the corundum-structure films, the RHEED pattern evolution in figure .(a) is extended to highlight the issues influencing αGa2 O3 growth. e initial growth conditions included a substrate temperature of ◦ C, Ga flux ∼×−8 torr (as measured by the MIG) and oxygen overpressure of .×−5 torr with  W net plasma power. e film started out smooth with a dashy–streaky pattern but transitioned early in the growth to a spotty–streaky pattern indicative of elevated surface roughness. is transition is likely a strainrelaxing mechanism that accommodates the larger size of the α-Ga2 O3 lattice. e spotty–streaky pattern was stable, and persisted for over  hours. e growth was then interrupted and the Ga/oxygen ratio increased (Ga at ∼×−8 torr) to test a higher growth rate. While the corundum-structure diffraction spots were still present, the faster rate also produced additional spots that slowly gained prominence. It is possible that the increased adatom density and therefore reduced diffusion led to the nucleation of alternative Ga2 O3 phases. ese undesirable phases were removed by etching the film altogether, which was executed by increasing both Ga flux and substrate temperature. e fully etched surface was approximately similar to the starting surface and was identified by the visible Kikuchi lines (diagonal lines from non-elastic scattering that denote long-range order e.g. from a substrate). Growth was resumed under conditions prior to the etching step but with an increased oxygen overpressure of .×−5 torr. A persistent, stable RHEED pattern of spots with faint outlines of chevrons was obtained. Chevrons typically represent a faceted surface. On another point of interest, the growth rate was similar to the initial slower growth rate although the Ga flux was higher. With oxygen pressure   – Epitaxial Nd:Al-Ga-O in the corundum phase as the only difference, this suggests that extra oxygen can slow down the growth through the formation and subsequent desorption of the volatile gallium suboxide. e RHEED data in this section has shown the influence of growth conditions including substrate orientation on the film structure. Persistent, stable growth of single-phase α-Ga2 O3 is possible although Ga2 O3 is susceptible towards forming other phases. Instant feedback of the film quality by RHEED is invaluable towards achieving this.  .. In-situ characterization by thin film reflectometry Ga2 O3 has a higher refractive index than Al2 O3 , allowing for in-situ characterization of the film by the optical method of thin film reflectometry. During growth, the intensity of the specular reflection oscillates with thickness following the principle of thin film interference, which in this case applies to the contrast between film and substrate. e setup included a  nm Ar+ ion laser light incident on the sample through a windowed source port ◦ off the normal. e light was passed through optical fiber and was therefore unpolarized. Detection was done at a symmetrically opposing windowed port with a UV-enhanced Si photodiode (sensitive from – nm) behind a laser line filter. e incident beam was mechanically chopped, allowing for the amplification of the detected signal by an SRS  lock-inamplifier. In order to restrict the specular reflection signal to the multilayer comprising the film and film–substrate interface, single-side-polished substrates were used. Using the notation of vacuum=, film= and substrate=, the amplitude of the electric field specularly reflected by a two layer dielectric with smooth interfaces as shown in figure . is given by: [ ] r012 = r01 + t01 r12 t10 ei∆ϕ 1 + r10 r12 ei∆ϕ + .... = r01 +  t01 t10 r12 ei∆ϕ 1 − r10 r12 ei∆ϕ  (.) (.)  where ∆ϕ = 2n1 kd cos θ1 is the phase difference between subsequent pairs of reflected rays. Here n1 is the film refractive index, k is the wavevector    2π λ ,  d is  – Epitaxial Nd:Al-Ga-O in the corundum phase  r01  t01r12t10  θ0 0 vacuum t01 1  film θ1 t01r12 substrate  Figure .: Schematic showing thin film reflection from a two layer dielectric the film thickness and θ1 is the refracted incident angle obtained by Snell’s Law. e reflection and transmission coefficients at a smooth interface going from layer i to j are denoted as rij and tij respectively. ese coefficients differ depending on the polarization of the electric field relative to the film, either in-plane or along the plane normal (s or p polarized respectively). e coefficients are obtained from the Fresnel equations[, chap.]: ni cos θi − nj cos θj ni cos θi + nj cos θj ni cos θj − nj cos θi = ni cos θj + nj cos θi 2ni cos θi = ni cos θi + nj cos θj 2ni cos θi = ni cos θj + nj cos θi  rij,s =  (.)  rij,p  (.)  tij,s tij,p  (.) (.)  While the model so far is ideal for smooth layers, the effect of interface roughness must be introduced to account for the evolving growth oscillation peak/trough   – Epitaxial Nd:Al-Ga-O in the corundum phase intensities. From “Scalar Scattering eory”, the reflection at a single rough interface is given by[]:  where Vr ∼ = 2kni cos θi  rij,lossy = rij eiVr f (x)  (.)  f (x) is the deviation in surface height from the mean at point x along the surface and Vr · f (x) the resulting phase shi. Assuming that the heights z = f (x) have a Gaussian distribution with an RMS roughness of σ ≪ λ, then the reflection coefficient can be calculated from the expectation value: ∫ w(z)eiVr z dz /  < rij.lossy > = rij  = rij e−Vr σ  2 2  2 1 where w(z) = √ e−z σ 2π  /  2σ 2  2  (.) (.)  which shows that the reflection coefficient is effectively an attenuated form of its lossless counterpart. A similar approach for lossy transmission yields /  < tij,lossy > = tij e  −Vt2 σ 2 2  where Vt = k(ni cos θi − nj cos θj )  (.)  e lossy reflection/transmission can be incorporated into the model for the two layer dielectric by making two assumptions. Since the substrate is atomically flat, roughness at the film–substrate interface is assumed negligible and instead only present at the film surface. Secondly, the effect of roughness is considered to be purely attenuative, with no contributions to coherent interference. e surface reflection and transmission terms in eqn. . are therefore replaced with their lossy counterparts as follows:  r012,lossy =< r01,lossy > +  < t01,lossy >< t10,lossy > r12 ei∆ϕ 1− < r10,lossy > r12 ei∆ϕ    (.)  – Epitaxial Nd:Al-Ga-O in the corundum phase For an unpolarized incident beam, the measured reflectance intensity contains the amplitudes of both s and p polarizations; e intensity is then related to the reflectance of the vacuum–substrate, which is the starting surface: R012,lossy =  ∗ ∗ r012,s,lossy · r012,s,lossy + r012,p,lossy · r012,p,lossy ∗ ∗ r02,s · r02,s + r02,p · r02,p  (.)  During growth, the specular intensity oscillates with a period corresponding to a film thickness of d =  λ 2ℜ(n1 ) cos θ1 ,  where ℜ(n) is the real part of the complex  refractive index n. Monitoring the time required for each oscillation therefore yields the growth rate. With knowledge of the substrate refractive index, the film index can be determined from the amplitude of the oscillations, which scales with the index contrast and rises over the initial substrate reflection for a higher index film. A perfectly smooth and transparent film will produce uniform oscillations; damping or decay are likely signs of surface roughness or opacity. By monitoring the specular reflectivity oscillations, the factors that influence the growth of Ga2 O3 films can be identified. Figure . shows the oscillations during growths of α-Ga2 O3 on A-plane sapphire that demonstrate the effects of substrate temperature, oxygen overpressure, composition and extended growth duration. In figure .(a), the growth rate is visibly slower at the higher temperature even as the film index (amplitude) and surface roughness (damping) appear similar. Except for the temperature, the two samples were grown under identical conditions including overpressure of oxygen plasma. is result proves that the growth rate is affected by gallium desorption, which in turn is sensitive to substrate temperature. Figure .(b) shows a growth at ◦ C with elevated levels of oxygen in the −5 torr range and plasma ignited. Contrary to the observation from the growth in figure .(a), here the growth rate increased when the oxygen overpressure was raised. e different behaviour might be related to film quality, whereby more gallium incorporates with excess oxygen given certain underlying layer conditions. e weaker oscillation amplitude in figure .(b) than in (a) denotes a lower refractive index and implies lower film density. Furthermore, the RHEED pattern (not shown) featured extraneous spots  mins into the growth signaling the presence of unwanted phases. Ga adatoms arriving on such a porous and mixed-phase underlying    – Epitaxial Nd:Al-Ga-O in the corundum phase  1.8  (a)  Substrate Temp.  1.6  1.4 o  620 C 1.2 o  500 C  1.0  0.8 0  40  80  120  160  200  240  1.8 Oxygen Pressure  (b) 1.6 -5  Intensity (arb. units)  1.4  8.9x10  torr  1.2  -5  1.0  3.3x10  torr  0.8 0  40  80  120  160  200  240  1.8 Ga/Al ratio  (c) 1.6  o  Al cell @ 1030 C  1.4  1.2  o  Al cell @ 1060 C 1.0  0.8 0  1.8  25  50  75  100  125  150  (d) Long Growth  1.6  1.4  1.2 Signal  1.0  loss 0.8 0  200  400  600  800  1000  Time (mins)  Figure .: Specular reflection from Ga2 O3 samples during growth showing the influence of (a) substrate temperature, (b) background oxygen pressure, (c) Ga/Al flux ratio and (d) extended growth duration. Simulated oscillations are shown in green. e optical source is a  nm Ar+ laser.    – Epitaxial Nd:Al-Ga-O in the corundum phase layer may stay on the surface longer with better chances for full oxidation and incorporation. During the second oscillation, the RHEED pattern degenerated further by turning into ring fragments normally associated with polycrystalline samples. Such poor quality films are undesirable, so care must be taken to avoid their formation in the first place. At the laser wavelength, sapphire has an index of ∼.[]. e difficulty in growing bulk α-Ga2 O3 means that data is sparse. e index measured at the sodium D line wavelength of  nm is quoted as . and . in old versions of the CRC Handbook of Chemistry and Physics[, pg. B]. e indices are therefore slightly higher at the laser wavelength. By depositing both Al and Ga simultaneously, mixed Al-Ga-O films with a higher index can be made. e effect of composition is shown in figure .(c), where an identical Ga flux was used for both samples. As expected, the higher Al flux (higher cell temperature) film had a lower index but faster growth rate. Figure .(d) shows the first six specular oscillations from a . µm thick Nddoped α-Ga2 O3 film grown using the same conditions as the post-etch growth of figure .(a). e multiple oscillations enable better modeling of the parameters in eqn. . so a simulated signal is shown in green for comparison. e simulation uses a film refractive index of n ˜ = 2.02 + 0.01i, a substrate index of 1.77 and an RMS roughness that ramps from  to  nm in the first  nm of growth and remains constant thereaer. e growth rate at the beginning is . nm/min with each oscillation accounting for a thickness of . nm. A slow down in growth rate was observed at the  hour mark, which is also shown by the divergence between simulated and measured data. A portion of the measured data was lost due to a soware crash. e film was grown for  hours yielding  oscillations for a total thickness of  nm. e roughness increase used in the simulation is intended to mimic the evolution of the RHEED pattern from dashes–streaks to spots–streaks once growth was started. e pattern then stabilized as α-Ga2 O3 spots–chevrons, which persisted for the remaining growth. is was the motivation for holding the model roughness constant beyond a film thickness of  nm. A useful method for extracting the roughness from the measured oscillation is to gauge the amplitude at the troughs where it is less sensitive to the refractive index. e film index from the model is   – Epitaxial Nd:Al-Ga-O in the corundum phase slightly higher than expected. A likely explanation is that the film is not fully stoichiometric i.e. Ga2 O2.9 instead of Ga2 O3 . As a consequence of the higher metal content, the real part of the refractive index will rise while the imaginary part will become non-zero. at imaginary component is verified by the model, and has the effect of damping the oscillation amplitude. It may be possible to grow better stoichiometry films by adjusting the oxygen level, but care must be given to avoid quality degradation as in figure .(b). Post-growth, the film was characterized using a Filmetrics F analyzer by Wei Li, who measured a thickness of . µm with a surface roughness of  nm. e measurement supports the growth oscillation results, yielding an average growth rate of . nm/min. Wei also measured the refractive index at the laser wavelength to be between . and .. e measurement did not include the imaginary component. Nevertheless, the film was still visibly transparent. In this section, the issues affecting the growth of α-Ga2 O3 were presented. e first difficulty involves gallium desorption, which can be overcome with an optimal growth temperature for both maximal diffusion and minimal desorption. Once gallium can be incorporated into the film, the conditions have to be further refined such that the film structure stays in the α-phase corundum structure. Monitoring RHEED diffraction patterns is a necessary requirement. For long growths, laser reflectometry provides a gauge of the film index and clarity, which could be useful for fine tuning the film stoichiometry by adjusting the elemental fluxes.  .  Structural and optical properties of Nd-doped Ga2 O3  .. β-Ga2 O3 on C-plane sapphire As suggested by the RHEED patterns of figure .(b), gallia grown on C-plane sapphire does not share the substrate structure. e film structure was analyzed in more detail by x-ray diffraction (XRD), and the results are shown in figure .(a) and (b). From a θ-θ scan that measures the periodicity of the out-of-plane lattice, ¯ family of planes of β-Ga2 O3 . No the film yielded peaks associated with the {201} other peaks are present, which implies that the film is single phase and therefore entirely β-Ga2 O3 . e film–substrate orientation in the out-of-plane direction is   Intensity (counts)  – Epitaxial Nd:Al-Ga-O in the corundum phase  5  (a)  (0 0 0 12)  (2 0 -1) -Ga O  4  2  10  (4 0 -2)  3  (6 0 -3)  3  (8 0 -4)  10  2  10 10  20  30  2  Intensity (counts)  Sapphire  (0 0 0 6)  10  6  40  (°)  (b)  -Ga O  10  2  3  (4 0 -3)  Sapphire (1 1 -2 9)  5  10 4  10 3  10 2  10 -270  -210  -150  -90  -30  30  PL Intensity (arb. units)  (°)  (c)  1040  1060  1080  1100  1120  1140  Wavelength (nm)  Figure .: Structural and optical properties of Nd-doped Ga2 O3 grown on Cplane sapphire. (a) XRD θ-θ scan identifying the film as single-phase β-Ga2 O3 with the {20¯1} orientation. (b) Off-axis ϕ scan showing that the film is multiply oriented in-plane with -fold symmetry. (c) photoluminescence (PL) spectrum from a β-Ga2 O3 film featuring a broad central peak and hints of other small peaks in the background. therefore (20¯1) β-Ga2 O3 || (0001) α-Al2 O3 . Using . Å x-rays, the first three film peaks occurred at ., . and .◦ respectively. e corresponding peaks of bulk β-Ga2 O3 were ., . and .◦ , calculated from data in reference [] using the LAZY PULVERIX program described in reference []. e peak location difference describes a film with a slightly larger out-of-plane lattice constant, possibly a consequence of in-plane strain. More XRD data on bulk βGa2 O3 can be found in appendix C.    – Epitaxial Nd:Al-Ga-O in the corundum phase e in-plane orientation of the film was determined by XRD ϕ–rotation (refer to fig. .) scans, which involve detecting off-axis peaks as the sample is rotated about its normal. An off-axis peak represents lattice planes with a direction other than the sample normal, and therefore has an in-plane component useful for identifying the crystal orientation. Prior to the ϕ rotation, the sample and detector must first be tilted to a θ-θ position that satisfies the Bragg diffraction condition for the desired off-axis planes. During the ϕ rotation scan, peaks will occur at angles when that diffraction condition is met i.e. when the in-plane component lies in the plane connecting the source, sample and detector. e film orientation relative to the substrate is obtained by comparing off-axis scans from both. Off-axis scans for β-Ga2 O3 on C-plane sapphire are shown in figure .(b). e ¯ planes points towards A-plane, which appears in-plane component of the (1129) to be -fold symmetric in a hexagonal basis (see fig. A.). Sapphire, however, is a trigonal crystal with -fold symmetry. Nonetheless, when analyzed by XRD, certain planes such as A-plane and M-plane will appear -fold symmetric as discussed in appendix C. For the sake of simplicity then, the  peaks will be grouped into the same (11¯29) plane family. e inconsistent heights of those peaks are due to a limitation where ϕ rotation occurs about the sample holder normal rather than the crystal normal. is creates a wobble-like effect when there is an offset between the two. ¯ film peaks are expectedly weaker but broader and more uniform, pose (403) sibly indicative of structural mosaicity. e (40¯3) peaks are also -fold symmetric ¯ substrate peaks. is is unexand have the same in-plane orientation as the (1129) pected because β-Ga2 O3 has the monoclinic structure shown in figure .(a), and its (20¯1) planes have an in-plane symmetry that is -fold. e in-plane component of the (40¯3) film peak points along the long edge of the (20¯1) rectangle. e -fold symmetry is therefore evidence of rotational domains in the form of crystallites oriented along one of three directions on the hexagonal sapphire lattice. is is shown pictorially in figure .(b). While the poor surface diffusion of C-plane sapphire leads to the nucleation of Ga2 O3 in the thermodynamically stable β-phase, the high symmetry of that surface is responsible for the rotational domains hence their mutual orientation. e β-Ga2 O3 film is therefore not single crystal, just single phase. While the out-of-plane relation is solely (20¯1) β-Ga2 O3 || (0001) α-Al2 O3 , the  in-plane orientations are: [102] β-Ga2 O3 || either [0010], [0100] or [1000] α-Al2 O3 .   – Epitaxial Nd:Al-Ga-O in the corundum phase  (a)  (b) [001]  (201) plane c β  b  [010]  a [100]  β-Ga2O3 unit cell a = 12.214 Å b = 3.0371 Å c = 5.7981 Å β = 103.83°  ¯ plane highlighted. Figure .: (a) Monoclinic unit cell of β-Ga2 O3 with (201) ¯ (b) Plan view of (201) β-Ga2 O3 crystallites on a C-plane sapphire substrate. e three possible orientations produce the -fold symmetric pattern observed in figure .(b). A similar result was demonstrated by Oshima et. al. with β-Ga2 O3 films also grown by MBE[]. Figure .(c) shows the 4 F3/2 →4 I9/2 emission from Nd-doped β-Ga2 O3 on C-plane sapphire excited using the  nm pump laser. e spectrum appears to have a broad background similar to Nd:glass or polycrystalline Nd:Al2 O3 grown on   – Epitaxial Nd:Al-Ga-O in the corundum phase C-plane sapphire (see fig. .(a)). Superimposed on that is a collection of peaks with a main peak at  nm. ese peaks are characteristic of a Nd-doped crystal except broader. ese different emissions can be attributed to the location of the Nd ions relative to the multiply oriented crystallites: the broad background from ions in the disordered boundaries while the peaks are from ions within the crystallites. e broadening of those peaks imply that the local atomic structure around the Nd ions is not perfectly uniform. A possible explanation involves a strain distribution experienced by the crystallites. For the in-plane orientation showed in figure .(b), the lattice mismatch ¯ rectangles and the C-plane hexagons is -. and . across between the (201) the short and long sides respectively. However, according to the ϕ-rotation scan of figure .(b), the broad film peaks imply that the crystallites are not perfectly oriented along one of the three orientations but that there is a slight distribution about each. Each crystallite therefore experiences a slightly different lattice mismatch. e subsequent variation in strain translates to the local atomic structure, thereby broadening the Nd3+ emission peaks. Comparing β-Ga2 O3 to the γ-Al2 O3 film shown in figures . and . gives further evidence that stronger XRD peaks and thus better long-range order (LRO) lead to sharper PL emission spectra. is occurs especially for materials with a large size discrepancy between dopant and substituted host-metal e.g. Nd3+ in Al2 O3 , Ga2 O3 , etc. While Ga3+ is slightly larger than Al3+ (details in sect. ..), it is unclear if the Nd3+ dopants are less likely to segregate away from the ordered Ga3+ sites in favour of the grain boundaries since a proper comparison would require both films to have the same crystal quality. In any case, the emission spectra from Nd-doped β-Ga2 O3 is promising, and if grown homepitaxially with minimal strain on a β-Ga2 O3 substrate, could yield a single-crystal film with sharp emission peaks characteristic of Nd:sapphire, Nd:YAG, etc.  .. α-Ga2 O3 on A-plane sapphire In contrast to growths on C-plane sapphire, Ga2 O3 films grown on R, A and Mplane sapphire had the same α-phase corundum structure as sapphire. at the film matched the substrate phase was also hinted at during growth by the RHEED    – Epitaxial Nd:Al-Ga-O in the corundum phase pattern evolution, as shown earlier in figure .(a). Bulk α-Ga2 O3 shares the same corundum structure and plane orientations as sapphire (shown in figure A.) but with the larger lattice constants of a = . Å and c = . Å. Among the three substrate orientations, A and M-plane films feature an in-plane optic axis preferable for optical applications such as TE-mode waveguide lasers. Of those two, most of the detailed research was done on A-plane sapphire for consistency. Figures .(a-c) show three different XRD data for a  nm thick Nd-doped α-Ga2 O3 film grown on A-plane sapphire. e θ-θ scan shows that film is single phase (no other peaks present) and matches the out-of-plane orientation of the substrate i.e. A-plane α-Ga2 O3 on A-plane sapphire. e film peaks are to the le of the substrate peaks at .◦ and .◦ , which is consistent with having a larger lattice. e peaks are also slightly leward of their corresponding bulk peaks of .◦ and .◦ calculated using LAZY PULVERIX, suggesting that while mostly relaxed, the film has a . larger out-of-plane lattice spacing. is slight lattice expansion could be due to compressive strain from the substrate lattice mismatch or from structural defects within the film. e off-axis ϕ-scan shows that the film is oriented in-plane with the substrate. ere is no evidence of multiple-orientations, as was the case for β-Ga2 O3 on Cplane sapphire, or of a spread about the single orientation as the film peaks do not exceed the substrate width. e film is therefore essentially single crystal. Figure .(c) shows a reciprocal space map (RSM) relating the on-axis (normal to substrate) peaks of both film and substrate. Qx lies in the plane, while Qy is out-of-plane as shown in figure .(c). As usual, Qx and Qy denote inverse plane spacings. e film peak is elongated symmetrically in Qx , denoting the presence of minor mosaicity centred about the substrate orientation. is implies that the orientation of the film is not perfectly normal to the substrate but rather has a small spread about that normal (i.e. texture). Mosaicity is typically evidence of columnar growth, which is not surprising given the large lattice mismatch: . larger in a, . larger in c. In the RSM, there is a vertical streak at Qx =  for both substrate and film. e so called “crystal truncation rod” denotes the presence of a surface as it breaks the translational symmetry of a crystal[, chap.]. To that point, the Fourier transform of a surface is indeed a rod. Truncation rods are indicators of smooth surfaces, and   Intensity (counts)  – Epitaxial Nd:Al-Ga-O in the corundum phase  6  (a)  (c)  10 -Al O  5  2  10  3  (2 2 -4 0)  (1 1 -2 0) 4  10 -Ga O 2  3  4.2  3  10  (1 1 -2 0) 2  10  -Al O 2  3  1  10 10  15  20  25  30  35  40  45  (°)  /2  -1  (b) 4.1  -Al O  5  2  3  (0 3 -3 0)  4  10  (3 0 -3 0)  Q  y  10  (1 1 -2 0)  3  10  -Ga O  -Ga O 2  2  2  3  3  10 1  10 0  10 -150  -100  -50  0  50  100  150  (°)  PL Intensity (arb. units)  Intensity (counts)  6  10  ( nm  )  7  10  4.0  (d)  -0.04  0.00  0.04 -1  Q  x  1040  1060  1080  1100  1120  (nm  )  1140  Wavelength (nm)  Figure .: Structural and optical properties of single-phase Nd-doped αGa2 O3 grown on A-plane sapphire with an orientation matching the substrate. (a) XRD θ-θ scan (b) In-plane orientation ϕ scan (c) Onaxis RSM of the (110) peak with contour heights scaled logarithmically (d) PL spectrum consisting of sharp, narrow emission peaks. are therefore expected from atomically flat substrates. eir presence on a film peak, as in this case, suggests that the film interfaces are smooth. Figure .(d) shows the unpolarized room-temperature PL emission spectrum taken from the  nm thick Nd-doped α-Ga2 O3 film aer excitation by the  nm pump. e collection of sharp peaks are unique but the overall pattern has similarities to that of Nd:sapphire. e sharp peaks indicate that the Nd3+ ions share the same local atomic structure, and thus likely substitute for Ga3+ in the octahedrally coordinated sites. Although the Ga3+ ions are considerably smaller, the high degree    – Epitaxial Nd:Al-Ga-O in the corundum phase Table .: Ionic radii comparison of octahedral (-coordinated) rare-earth dopants and host elements. Data from Shannon[]. Ionic radius (Å) RE-dopants  Bulk sesquioxides New hosts  Nd3+ Er3+ Yb3+ Y3+ Sc3+ Lu3+ Al3+ Ga3+  . . . . . . . .  of crystal perfection (single crystal, lack of disordered grain boundaries, etc.) essentially restrict the dopants to these sites in the host. Table . highlights the ionic radii difference between popular rare earth dopants and the corundum-structure materials of this work. Bulk sesquioxides (A2 O3 , where A = Y, Sc or Lu) that have been successfully doped were also added for comparison[].  .. Emission properties of Nd:α-Ga2 O3 e emission characteristics of Nd:α-Ga2 O3 were evaluated by a comparison between two similarly grown samples: one Nd:α-Ga2 O3 , the other Nd:sapphire. Both films were grown on A-plane sapphire with thicknesses of ∼ nm. ere were changes to the growth and characterization apparatus from those mentioned previously, namely the use of two new pieces of equipment. Following the lackluster performance of the in-house plasma source, a commercial unit was purchased from SVT and Associates that operated at a fixed RF frequency of . MHz. e unit featured an alumina discharge tube and was capable of operating at powers up to  W. e length of the unit was extended for placement closer to the substrate, in order to maximize active oxygen flux at the sample without increasing the background oxygen pressure. Due to its custom length, the unit was not mounted in a standard source port but rather in the optical viewport directly facing the substrate shown in figure .. e new plasma source proved extremely beneficial as it enabled the growth of Ga2 O3 at elevated   – Epitaxial Nd:Al-Ga-O in the corundum phase temperatures (up to ◦ C), likely because the high levels of active oxygen could fully oxidize the Ga adatoms thus preventing desorption. e second piece of equipment was a new pump laser for PL measurements: a  W diode laser in a  mm TO-can package purchased from Axcel Photonics. e laser had a centre wavelength of  nm, which is close to the  nm absorption peak of Nd:sapphire. e laser was operated by a temperature-controlled laser diode mount from orlabs and as such was temperature tunable between – nm at typical operation currents of . A. As opposed to the previous setup where the pump light passed through optical fiber, the new laser was operated in free space and its beam was therefore polarized. Consequently, when measuring polarized PL from the anisotropic corundum-structure films, care had to be given to eliminate the effect of polarization-sensitive absorption. Since the sample was rotated ◦ to access the different polarizations, the PL would be artificially boosted whenever the pump laser polarization coincided with the sample orientation featuring stronger absorption. e sample absorption differences ∥ and ⊥ to the optic axis were accounted for by taking the ratio of the unpolarized PL emission intensities along the two orientations, then applying it as a scaling factor on subsequent polarized measurements. Figure . compares the product of emission cross-section and lifetime for both the Nd-doped sapphire and α-Ga2 O3 films mentioned above, which were grown at ◦ C using the new plasma source. Besides the new pump laser, the rest of the measurement/analysis followed that of section ... At a first glance, the emission from Nd:α-Ga2 O3 is an almost identical yet blue-shied version of the emission from Nd:sapphire. e spectrum ∥ to the optic axis is dominant due to the uniaxial corundum structure, and features a strong emission peak at  nm with a σ · τ of ×−24 cm2 s. e blue-shiing suggests that the Nd3+ ion has the same local atomic structure in both materials except that the Nd-O bond length is larger in Nd:α-Ga2 O3 . e inset of figure . compares the bottom  of the σ · τ spectra of Nd-doped sapphire and α-Ga2 O3 normalized to their respective peaks. e stronger background emission from Nd:α-Ga2 O3 is one reason for its weaker σ · τ compared to Nd:sapphire; another being the wider full width half maximum (FWHM) of the emission peaks. ese differences are due to a higher degree of structural disorder in the α-Ga2 O3 film, and is not surprising given the lattice   – Epitaxial Nd:Al-Ga-O in the corundum phase  120  Polarized  optic axis  Polarized  optic axis  100  Nd:  -Ga O  Nd:  -Al O  80  2  (%)  10  Normalized  cm s)  2 -24  Emission Cross Section x Lifetime (x10  ...  ...  140  5  0 1070  3  1090  1110  1130 nm  60  40  2  3  20  0  ... 890  910  930  950  ... 1070  1090  1110  1130  1380  1400  1420  1440  Wavelength (nm)  Figure .: Product of emission cross-section σ and lifetime τ for Nd-doped α-Ga2 O3 and α-Al2 O3 films grown on A-plane sapphire. e spectra are due to Nd3+ transitions from the 4 F3/2 manifold to the 4 I9/2 , 4 I11/2 and 4 I13/2 manifolds respectively. Inset: Magnified plot of normalized σ · τ for emission polarized ∥ optic axis. mismatch for the heteroepitaxial growth on sapphire. However, given a film comparable in quality to Nd:sapphire, σ · τ would still be weaker due to the n2 dependency shown in eqn. .. Although weaker than Nd:sapphire, the  nm peak of Nd:α-Ga2 O3 is still suitable as a laser material. For comparison, the  nm peak of Nd:YAG has a σ · τ of ×−24 cm2 s[]. While numerous Nd-doped α-Ga2 O3 films were grown during the course of this research, thick films (> µm) with sufficiently high Nd-doping levels ( ) were not among them (including the film from fig. .(d)). Consequently, additional optical properties such as the absorption spectrum from fluorescence excitation, lifetime and energy levels from cryo-PL were not experimentally obtained. While measuring the PL however, the maximum emission intensity was obtained when the tunable pump laser was set to  nm, which is a blue-shi of the  nm absorption peak of Nd:sapphire. A summary of the laser properties of Nd-doped α-Ga2 O3 , with a comparison to Nd:sapphire and two popular bulk laser crystals is shown in table .. While Nd:sapphire offers stronger emis-    – Epitaxial Nd:Al-Ga-O in the corundum phase Table .: Comparison of the Nd-doped corundum-structure materials to popular bulk crystals. For thin epitaxially grown films, the thermal conductivity is determined primarily by the substrate material. Data from [, , thermal cond.], [, abs. cross sect.] and [, optical].  Primary emission peak (nm) Product of σ · τ (×−24 cm2 s) Lifetime (µs) Primary absorption peak (nm) Absorption cross-section (×−19 cm2 ) Refractive index @  µm ermal conductivity (Wm−1 K−1 )  α-Ga2 O3  α-Al2 O3  Y3 Al5 O12 (YAG)  YVO4         . .  (subs)      . .       . .    .  (subs)  sion, Nd:α-Ga2 O3 is better suited for making waveguide lasers because the larger refractive index contrast reduces the film thickness necessary for optical confinement. For example, a  µm thick core with sapphire cladding would be sufficient to confine  of the fundamental TE-mode.  .  Nd-doped α-(Al1−x Gax )2 O3 alloys  .. Composition and density e structural and optical similarity between the α-Ga2 O3 and α-Al2 O3 isomorphs provided a compelling case to make Nd-doped alloys of both materials. ese oxide alloys would be analogous to the popular III-V semiconductor alloy AlGaAs, which is also grown epitaxially for making devices such as diode lasers and high speed transistors. A set of Nd-doped α-(Al1−x Gax )2 O3 films were grown at ◦ C on Aplane sapphire with varying Ga/Al ratios. Active oxygen was supplied by the SVTA plasma source. e composition was controlled by fixing the Ga flux throughout the set and varying the Al fluxes under an oxygen overpressure. As such, the film thicknesses were not uniform but instead ranged from  to  nm. e Ga/Al ratio was measured post-growth using x-ray photoelectron spectroscopy (XPS), a technique that identifies the relative concentration of elements in a sample from the photoelectrons emitted as a result of x-ray excitation. e technique is surface  – Epitaxial Nd:Al-Ga-O in the corundum phase  Ga O 1s Al  =  Ga 3p Al 2p  x  0.229 1.08  Intensity (arb. units)  Al 2s Ga LMM  Ga 3p  Al 2p  Ga 3d  Ga 3s  C 1s  600  500  400  300  200  100  0  Binding energy (eV)  Figure .: XPS spectrum used to identify the Ga/Al ratio of a mixed Nddoped α-(Al1−x Gax )2 O3 film. e ratio was measured from the areas of the Ga p and Al p peaks, which were corrected for instrument sensitivity. Scan by Ken Wong, UBC. sensitive, so unless etching is employed, a typical survey scan will only probe the top – nm of the sample. e XPS scans were done by Ken Wong at the UBC Interfacial Analysis & Reactivity Laboratory, using x-rays generated from an Al target. Figure . shows the result of an XPS survey scan of a Nd-doped α-(Al1−x Gax )2 O3 (i.e. Al-Ga-O) film, with peak labels identifying the electronic configuration and associated element of the photoelectrons (e.g. Al s). Neodymium could not be detected due to its low concentration. Besides Al and Ga, the scan also detected oxygen and carbon, but these are likely affected by surface contamination upon removal from vacuum post-growth and are therefore unsuitable for composition analysis (e.g. Al/O ratio). Since it is unlikely that the sample surface was covered by Al or Ga outside the MBE system, and also unlikely that the growth fluxes deviated during the growth, the XPS ratio of Ga/Al from the sample surface is therefore an accurate representation of the Ga/Al ratio of the entire film. e Ga/Al ratio was calculated from the integrated intensities of the Al p and Ga p peaks using the equation in the inset of figure .. During his initial analysis of the sample, Ken Wong used the Ga d peak to estimate the ratio, which led to an artificially higher Ga/Al ratio because of an overlap of the Ga d and O s peaks. e overlap is a common problem for   – Epitaxial Nd:Al-Ga-O in the corundum phase  3  Ga ) O  1-x  x 2  3  ,  Density (g/cm )  Intensity (arb. units)  (Al  x=1  ,  = 6.4  x=1  ,  = 5.95  x=0.87,  = 5.85  x=0.74,  = 5.6  x=0.57,  = 5.3  x=0.49,  = 5.1  x=0.39,  = 4.9  0.2  0.4  0.6  0.8  (°)  Figure .: Density and thickness of a set of mixed Nd-doped α(Al1−x Gax )2 O3 films obtained using XRR. e critical angle determines density while the spacing of the Kiessig fringes yields thickness. survey scans of gallium oxide samples[]. As shown in figure ., x-ray reflectivity (XRR) scans of the Nd-doped Al-GaO alloys were used to determine the film thicknesses and densities. e respective parameters for each film were obtained by a comparison to a simulated model that matched the Kiessig fringes and critical angle (see sect...). e density of the alloys increased with Ga concentration, which is expected because bulk α-Ga2 O3 has a much higher density than sapphire (. vs . g cm−3 []). When compared to a linear interpolation of the two bulk densities (Vegard’s law), the film densities deviate from the trend at higher levels of Ga. ese details are provided in table .. A possible explanation for the density deviation may be deduced from a comparison of the two α-Ga2 O3 (x=) films. e  nm thick film is less dense than its  nm counterpart, and is consistent with the non-linear trend of larger density deviations at higher Ga levels. is suggests that while thinner films grow with almost    – Epitaxial Nd:Al-Ga-O in the corundum phase Table .: Density comparison between the set of α-(Al1−x Gax )2 O3 films with those expected from bulk sapphire, α-Ga2 O3 or a linear interpolation of the two. Bulk data from []. x in (Al1−x Gax )2 O3  ickness (nm)  Film density (gcm−3 )  Bulk or Vegard density (gcm−3 )    . . . . .            . . . . . . . .  . . . . . . . .  bulk-like density, structural relaxation is eventually necessary to compensate for the large lattice mismatch. e relaxation mechanism remains to be investigated (could be defects), but the consequence is a reduced film density. e higher Al level films shown here are therefore more likely to have a higher density because the smaller lattice mismatch suggests a thicker “critical thickness” before relaxation occurs. An interesting focus of future work could be the effect of alloy composition on the critical thickness.  .. Structure and emission e set of Nd-doped Al-Ga-O films were nonetheless single crystal and oriented with the sapphire substrate. Figure . shows the effect of Ga concentration on both the dominant polarized PL emission peak as well as the XRD θ-θ film peak ¯ planes. e polarized PL peak shis from the  nm corresponding to the (1120) of Nd:α-Ga2 O3 to the  nm peak of Nd:sapphire with increasing Al, thereby introducing the option of compositionally tuned devices for wavelength-specific applications in that range. e trend with composition is not linear, however, since the shi toward  nm occurs much faster at higher Al levels. An explanation of this will be provided later, and involves strain. e emission peaks of the alloys are noticeably wider than their non-alloy counterparts as a consequence of inhomogeneous broadening. e crystal field on the   – Epitaxial Nd:Al-Ga-O in the corundum phase  ( Al  (a)  Ga  1-x  x  ) O 2  (b)  3  x=0  x=0.39  x=0.49  x=0.57  x=0.74  x=0.87  x=1  1085  1095  1105  1115  1125  Wavelength (nm)  18  19  /2  (°)  Figure .: Varying the Ga/Al ratio of Nd-doped α-(Al1−x Gax )2 O3 has the following effects: (a) the polarized strong emission peak is tuned from  to  nm, and (b) the (110) XRD film peak is shied closer to the A-plane sapphire substrate peak. Nd3+ ion is no longer perfectly uniform, but rather has a distribution that reflects the multiple configurations possible due to the mixed occupancy of Ga3+ and Al3+ ions on the octahedral site. Similar instances of peak broadening have been observed from alloys of bulk solid state laser crystals e.g. Nd:YGAG[]. e difference between the films and bulk crystals is that here the widest peaks are not from alloys with x near ., but rather from those that are Al-rich. A likely explanation here also involves strain. While a broader emission profile may offer less efficient laser performance, possible benefits include more lasing wavelengths, better pulsed mode operation and a broader absorption peak for easier diode laser pumping. In figure .(b), the XRD θ-θ film peak shis from α-Ga2 O3 to sapphire with increasing Al, but the shi becomes incrementally smaller for Al-rich films. e out-of-plane lattice therefore remains larger, which represents an expansion typically associated with in-plane compressive strain. For ideal epitaxial growth on a lattice mismatched substrate, the film should have the same in-plane lattice constants as the substrate while its out-of-plane lattice distorts elastically to accommodate the strain. With the aim of gauging the in-plane lattice, the RSMs of figure . show that the Al-rich films are compressively strained in-plane to match the lattice constant of the sapphire substrate up to a critical Ga content of x=.. For higher Ga contents the lattice constant of the film expands in both the in-plane and out  – Epitaxial Nd:Al-Ga-O in the corundum phase  6.35 (1 1 0)  (1 0 0)  y 6.30  6.25  z  x  x=0  (0 0 1) (1 1 0)  x=0.39  6.20  -1  (Al  Ga ) O  1-x  x 2  3  6.15  Q  y  (nm  )  (300)  x=0.49 6.10 x=0.57  x=0.74 5000 Log Scale  6.05  x=0.87  1880 707.1 6.00  265.9 x=1 100.0  3.40  3.45  3.50  3.55  3.60  3.65  -1  Q  x  (nm  )  Figure .: RSM showing the off-axis () peaks for Nd-doped α(Al1−x Gax )2 O3 films grown on A-plane sapphire. Changing the composition shis the film peaks from α-Ga2 O3 to α-Al2 O3 in Qx and Qy , which are the inverse plane spacings along the [1¯10] and [110] (in-plane and out-of-plane) directions respectively. Al-rich films that deviate from the expected linear trend are compressively strained by the substrate. Inset: hexagonal lattice structure of corundum (unit cell in red) showing the orientations of the x, z (in-plane) and y (out-of-plane) directions with respect to the crystal unit cell.    – Epitaxial Nd:Al-Ga-O in the corundum phase Table .: Plane spacings of α-(Al1−x Gax )2 O3 alloys along the orientations x, y and z (shown in fig. .) that enable the calculation of the alloy unit cell volume. e corresponding dominant PL emission peak is also provided. x in (Al1−x Gax )2 O3  d300,x (nm)  d300,y (nm)  d22¯6,z (nm)  cell volume (nm3 )  PL peak (nm)   (bulk)  (film) . . . . .   . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . .  of-plane direction. e in-plane expansion is a relaxation mechanism presumably associated with the formation of bulk or interfacial structural defects in the film. e PL emission peak is therefore dependent on film strain, as demonstrated by the strained Al-rich films with peaks near the  nm peak of Nd:sapphire. As such, associating the PL emission peak with composition may not be entirely accurate because the strain could vary. For example, a much thicker film with the critical Ga content of x=. mentioned earlier might actually relax, leading to larger in-plane constants and a blue-shied PL emission peak. Since the lattice structure reflects the effects of both Ga/Al ratio and film strain, it could be the main factor influencing the PL emission peak location. A single parameter suitable for representing the lattice is the unit cell volume, which was obtained from RSMs of the (300) and (22¯6) off-axis peaks. Both orientations were necessary because the in-plane lattice of A-plane corundum is rectangular, and responds anisotropically when strained. e x and y plane spacings were taken from the (300) RSMs of figure ., where the location of the (300) peak in A-plane reciprocal space was shown earlier in figure .(a). e (22¯6) peak exists outside of that plane and enables access to the lattice constants in the z direction (see inset ¯ RSMs (not shown) displayed the same of fig. . for the orientations). e (226) trend as the (300) RSMs but with different amounts of strain. Table . shows the measured plane spacings (and therefore lattice constants)    – Epitaxial Nd:Al-Ga-O in the corundum phase 3  Unit cell volume (nm ) 0.26  0.27  0.28  0.29  Emission peak (nm)  1096  1094  1092  1090  0.0  0.2  0.4  0.6  (Al  0.8  1.0  Ga ) O  1-x  x 2  3  Figure .: Effect of composition and unit cell volume of Nd-doped α(Al1−x Gax )2 O3 films on emission peak wavelength. along the  orientations, and the overall unit cell volume as calculated from V = 1 6,z ). 2 (3d300,x )(3d300,y )(6d22¯  e unit cell was highlighted in the inset of fig-  ure .. e corresponding PL emission peaks are also shown in the table, and then plotted in figure . to show the linear correlation between the wavelength and unit cell volume. A similar effect has been shown by bulk laser crystals compressed under hydrostatic pressure, e.g. Nd:YVO4 with a bulk strain influence on wavelength of almost a factor of two smaller[]. e films reported here may be the first instance where the strain is anisotropic (compressive in-plane, tensile outof-plane) yet still producing the linear dependence. Physically this suggests that the change in pressure of the oxygen cage coordinating the rare-earth ion is ultimately the reason for the composition dependence of the emission wavelength. Nd-doped α-(Al1−x Gax )2 O3 is a rare-earth doped binary oxide alloy useful for making compositionally tuned lasers. A wavelength range of – nm is accessible by compositional control of the unit cell volume. Single-phase laser alloys typically involve ternary oxides such as the Y3 (Gax Al1−x )5 O12 garnets[] and the (Yx Gd1−x )VO4 vanadates[]. e strong  nm peak of the former does not shi but is instead split up while the latter has a negligible tuning range because   – Epitaxial Nd:Al-Ga-O in the corundum phase the peaks of both vanadates are at  nm. Binary oxides are simpler to grow but the alloys must be single phase. As a counter-example, alloying Y2 O3 and Al2 O3 leads to a variety of different phases (e.g. YAG) with different crystal structures and refractive indices, and different emission spectra for each phase. e ability to continuously tune the composition and properties of the α(Al1−x Gax )2 O3 during MBE growth without phase changes makes this material well-suited for making graded-index layers. A waveguide laser using a symmetrically graded core layer with Nd:α-Ga2 O3 at the centre and Nd:α-Al2 O3 at the edges would have a – nm broad gain profile useful for a tunable laser. Grading the core–cladding interface on either side of the high-index Nd:α-Ga2 O3 core would be useful for minimizing the scattering losses due to interfacial roughness. is would offer a significant improvement over the typical losses of  dB/cm observed from other growth methods[].    5– Epitaxial films of the popular Y-Al-O system Before the work on corundum-structure films, the initial focus of oxide research at the UBC MBE lab involved yttrium oxide. As a proven laser host crystal with a simple binary composition, Y2 O3 was an ideal starting point for a new research campaign. Success with this material would be supportive of a broader research scope that included the ternary Y-Al-O materials, of which there are  primary phases: yttrium aluminum garnet or Y3 Al5 O12 (YAG), ytrrium aluminum perovskite or YAlO3 (YAP) and yttrium aluminum monoclinic or Y4 Al2 O9 (YAM). YAG and YAP are popular laser hosts, and in fact Nd:YAG is the industry choice for high power emission near  µm. When I joined the research at the MBE lab, Y2 O3 films were being grown by Ivan Christophe-Robin on sapphire and silicon substrates. e films were crystalline and could be doped with Nd. e crystal structure was analyzed by Shawn Penson and Ivan while the optical properties were analyzed by me. Scott Webster continued the research on Y2 O3 growth aer Ivan’s departure. My research focus then shied to the growth of the ternary Y-Al-O materials.  .  Nd-doped Y2 O3  For an Nd:Y2 O3 film to become a waveguide, its cladding material must have a lower refractive index. As silicon substrates were unsuitable for this purpose, most of the detailed research was done using films grown on sapphire. High growth temperatures were necessary (∼◦ C) for surface diffusion of the yttrium atoms on the sapphire substrate. is was not surprising given that a high-temperature effusion cell was needed to evaporate yttrium. Typical cell temperatures ranged between –◦ C. It was determined that oxygen plasma was unnecessary, and that molecular oxygen was sufficient for oxidizing the yttrium adatoms to form crys  – Epitaxial films of the popular Y-Al-O system  4  F  4  I  3/2  J,9/2  9/2  ~ 48% 4  4  PL Intensity (arb. units)  F  I  3/2  11/2  J,11/2  ~ 44%  4  4  F  I  3/2  13/2  J,13/2  900  950  1050  1100  ~ 8%  1350  Wavelength (nm)  Figure .: PL spectra from a  µm thick Nd:Y2 O3 film grown on C-plane sapphire. Nd-doping level is approximately  at. . e spectra corresponds to transitions from the 4 F3/2 manifold to the 4 I9/2 , 4 I11/2 and 4 I13/2 manifolds respectively. e branching ratios βj of each manifold are indicated. talline Y2 O3 . e photoluminescence (PL) emission spectra from the Nd:Y2 O3 films were collected using the setup of section . (shown in fig. .), where unpolarized  nm light was used for excitation. As Y2 O3 is optically isotropic, its emission is not polarization-dependent. In figure ., the unpolarized emission from a Nd:Y2 O3 film grown on C-plane sapphire features a collection of sharp peaks matching those from bulk Nd:Y2 O3 crystals[]. e relative strength of the transitions from the upper 4 F3/2 manifold to one of the lower 4 I9/2 , 4 I11/2 and 4 I13/2 manifolds is given by the branching ratio βj , which was calculated by comparing the photon counts from one intermanifold transition (e.g. 4 F3/2 →4 I11/2 ) to the counts of the overall spectrum. e branching ratios from the Nd:Y2 O3 film were comparable to those of their bulk counterparts: ,  and  compared to ,  and  for the three manifolds respectively[]. e branching ratio of Nd:Y2 O3 is strongest for 4 F3/2 →4 I9/2 instead of    1400  – Epitaxial films of the popular Y-Al-O system 1.0 Data points Fit  PL Intensity (arb. units)  0.8  0.6  0.4  0.2  0.0 1  3  5  7  9  Nd concentration (atomic %)  Figure .: PL intensity of the 4 F3/2 →4 I11/2 transitions for varying concentrations of Nd:Y2 O3 grown on C-plane sapphire. e solid line is the expected concentration dependence for the quenching effect discussed in the text. 4F 4 3/2 → I11/2 ,  which is atypical for an Nd-doped crystal⁵. However, the lack of  a single dominant peak from either intermanifold transition suggests that Nd:Y2 O3 is not optimal for laser emission in the  nm as well as  nm range. In any case, the growth of films with the same optical emission as bulk Nd:Y2 O3 proves that MBE is a viable technique for growing solid state laser materials. To study the effect of PL intensity on Nd concentration, Ivan and I grew a set of eight  nm thick Nd:Y2 O3 films on sapphire using similar growth conditions with the exception of the Nd/Y flux ratio. e Nd concentration was deduced from this flux ratio assuming complete Nd incorporation. e fluxes were measured by the monitoring ion gauge (MIG) before and aer each film growth and the average value used. At higher Nd fluxes, however, larger pre- and post-growth differences increased the uncertainty in the measurement. e quartz crystal microbalance (QCM) was unavailable at that time. As shown in figure ., at low Nd concentrations the PL intensity increases with ⁵e emission from the 4 F3/2 →4 I15/2 transitions were not collected due to detector insensitivity, but are typically weak (βj < 1) for Nd-doped crystals and can be ignored[].    – Epitaxial films of the popular Y-Al-O system concentration to a peak value around  at., but decreases with further increases in concentration. is quenching effect is due to cross-relaxation interactions between Nd ions. A specific example involves a (non-radiative) 4 F3/2 →4 I15/2 transition that excites an adjacent Nd3+ ion from the ground level to the 4 I15/2 manifold, which for Nd is near the midpoint between the upper metastable and ground levels. Both Nd3+ ions then relax non-radiatively to the ground level. Assuming an N2 dependence on the non-radiative relaxation rate, the fluorescence efficiency can be expressed as 1/(1 + AN 2 ) where N is the Nd concentration[]. Factoring in absorption, the total PL emission can be fitted to the form BN /(1 + AN 2 ), where A and B are fitting parameters. Using this model, the optimal dopant concentration was determined to be  at. (Nd/Y ratio), which is similar to the concentration for maximum PL intensity in Nd:YAG[].  .  Mixed Y-Al-O growth considerations  .. Al desorption Films of the mixed yttrium-aluminum-oxides were attempted using the same growth conditions as Nd-doped Y2 O3 with the addition of Al fluxes from an elemental effusion cell. At the high growth temperatures above ◦ C, Al adatoms do not fully incorporate and tend to desorb. Using the same residual gas analyzer (RGA) method of section .., evidence of Al desorption is presented in figure .. In the (a) subfigure, an oxide-coated molybdenum plate was heated to ◦ C and exposed to an Al flux of ×−7 torr as measured by the monitoring ion gauge (MIG). e flux of desorbed Al measured at the RGA was .×−10 torr, which is consistent with the three orders of magnitude reduction in flux. Al2 O was also detected by the RGA but at more than an order of magnitude less than Al. is contrasts with the desorption of gallium discussed earlier in section .. where the relative Ga2 O level was higher (see fig. .(b)). While the different suboxide desorption in the two cases may be due to substrate choice (Mo vs sapphire), it was observed in subsequent oxide growths that the rapid desorption of Al2 O did not occur to the extent that fully oxidized Al2 O3 films were unreachable. Al therefore oxidizes more easily than Ga.   – Epitaxial films of the popular Y-Al-O system  RGA partial pressure (torr)  -7  10 -8  10  (a)  Background  Al  Al shutter opened  -9  Al O  10  2  -10  10 -11  10 -12  10 -13  10 5  10  15  20  25  30  35  40  45  50  55  60  65  70  o  = 1140 C  o  1150 C  o  1170 C  o  1180 C  o  1190 C  8 -7  1160 C  6  6  Shutter:  (b)  opened  closed  4  4  2  2  0  0 0  torr)  T  5  10  15  20  25  30  Time (mins)  Figure .: (a) RGA scan analyzing the desorbed material from a heated molybdenum plate before and during exposure to an Al cell at ◦ C. (b) RGA scan tracking the pressure of Al desorbing from a ′′ sapphire wafer as the cell shutter is opened/closed. e cell temperature is raised aer each test. Direct flux gauge measurements at  temperatures are shown for comparison. In figure .(b), the desorption of Al metal (a.m.u. ) off a sapphire wafer at ◦ C is tracked by the RGA for varying Al cell temperatures/fluxes. To extend the life of the Al cell, operation above ◦ C was avoided. Increasing the cell temperature from ◦ C to this maximum yielded respective increases in the flux of desorbed Al. e flux incident on the substrate was measured by the MIG at three of the analyzed cell temperatures and showed a linear correlation to the RGA fluxes. is suggests that the ratio of Al desorbing remains the same for the range of cell temperatures. e most likely value for the Al sticking coefficient α is then zero. e ratio of the RGA to MIG fluxes at TAl =◦ C is .×−3 while the theoretical ratio from section .. assuming α = is .×−3 . is slight discrepancy is unlikely a result of a non-zero α but rather due to geometric factors or to the un  35  Flux gauge reading (x10  o  8  Al  RGA partial pressure (x10  -10  torr)  Mass (a.m.u)  – Epitaxial films of the popular Y-Al-O system Table .: MBE growth conditions for single-phase Y-Al-O films. Material Nd:Y2 O3 Nd:Y4 Al2 O9 Nd:YAlO3 Nd:Y3 Al5 O12  Substrate R-sapph. C-sapph. R-sapph. C-sapph.  MIG Flux (×−7 torr) Y  Al  O2  . . . .  . . . .       Temperature ◦ C ◦ C ◦ C ◦ C  tracked desorption of aluminum in the form of the Al2 O suboxide. e evidence therefore indicates that Al by itself does not stick on a sapphire substrate at ◦ C.  .. Single-phase Y-Al-O films Yttrium-aluminum oxide films were grown by MBE at temperatures near ◦ C despite the poor Al sticking coefficient, suggesting that Al incorporation is influenced by yttrium and oxygen in addition to the growth temperature. Y-Al-O films with different Al/Y ratios were therefore accessible by controlling these four growth parameters: temperature as well as yttrium, aluminum and oxygen fluxes. e  stable phases in the Y-Al-O system are Y4 Al2 O9 , YAlO3 and Y3 Al5 O12 , which are stoichiometric for Al/Y ratios of ., , and . respectively. According to the bulk crystal phase diagram, nonstoichiometric Y-Al-O (e.g. Y3 Al4 O12 ) will consist of mixtures of stoichiometric phases (e.g. YAlO3 + Y3 Al5 O12 )[]. Table . lists the growth conditions for Y-Al-O films on sapphire that reproduce all three stable phases. e growths were less sensitive to choice of substrate orientation, as both (most of the work was done on R and C-plane sapphire) orientations were successfully used to grow all three Y-Al-O phases. However, to achieve films with better crystallinity, a particular substrate may be preferable if it offers a closer lattice match to a specific Y-Al-O orientation. Figure . shows the PL emission spectra from the films of table ., which were excited by  nm light from a diode laser. e film PL spectra matched those of its bulk counterparts where available (Nd:YAP[] and Nd:YAG[]). ere is currently no record of bulk crystal Nd:YAM but the growth of nanocrystals using a solgel method has been reported[]. e emission from the nanocrystals and MBE  – Epitaxial films of the popular Y-Al-O system  Nd: Y O 2  3  PL Intensity (arb. units)  Nd: Y Al O 4  2  9  (YAM)  Nd: YAlO  3  (YAP)  Nd: Y Al O 3  5  12  (YAG)  1020  1040  1060  1080  1100  1120  Wavelength (nm)  Figure .: PL spectra of the 4 F3/2 → 4 I11/2 transition from Nd-doped Y2 O3 , Y4 Al2 O9 , YAlO3 and Y3 Al5 O12 films grown on sapphire. e collection of emission peaks is unique for each material. grown films were similar except that the – nm peaks of the nanocrystals were stronger when normalized to the  nm peak. Since the Y-Al-O phases have different crystal structures (monoclinic, perovskite, garnet) with correspondingly different local atomic structures, the collection of Nd3+ peaks observed in the PL emission spectra was unique and provided a structural fingerprint for identifying the phase of the Y-Al-O films.  .. Parameters affecting film Y-Al-O phase e growth conditions leading to a particular Y-Al-O phase were investigated via sets of growths that involved changing a single parameter per set. Among the nu  – Epitaxial films of the popular Y-Al-O system Table .: Growth sets investigating the effect of single parameter variations on the Y-Al-O film phase. Elemental fluxes were independently measured by a MIG. e Al/Y ratio is an atomic flux ratio obtained using QCM calibration data, while the O2 /Y ratio is simply the ratio of MIG fluxes (O2 fluxes are not measurable with a QCM). Parameter  Yttrium  Oxygen  Aluminum Plasma  MIG Flux (×−7 torr)  Flux ratio  Al  Y  O2  Al/Y  O2 /Y  . . . . . . . . . . .  . . . . . . . . . . .  . . . . .  . . . .( W) .( W)  . . . . . . . . . . .  . . . . . . . . . . .  Phase YAP YAP + YAM YAM + YAP YAG YAP YAM Yttria Yttria + YAP YAP YAP YAM  merous parameters affecting film phase, only those pertaining to the fluxes were evaluated, of which there are four: yttrium flux, aluminum flux, oxygen overpressure and oxygen plasma power (in-house source). Other influential parameters including growth temperature and substrate type were fixed as all the films were grown at ◦ C on R-plane sapphire substrates. e PL emission spectra was used to identify the film phase, or the phases present if the film was not single phase. e films were not necessarily stoichiometric, so the phase results were primarily used for tracking the dependence of the film Al/Y ratio on a particular growth parameter. For example, if increasing parameter x yielded a YAG film instead of a YAP film, it was then assumed that the film Al/Y ratio increased with x. Table . shows the parameters varied in each growth set and the resulting phase outcome. Films that are not single phase have PL emission spectra that are a superposition of the unique spectra from each of the phases present. While the relative PL intensity of the individual phases should denote the portion of the film in a particular phase, differences in absorption/emission cross-sections make it difficult   – Epitaxial films of the popular Y-Al-O system to quantify the relative proportions. Since the multiphase films were observed to consist primarily of two phases, the phase producing the stronger PL intensity was deemed as the dominant portion. e trend of the film Al/Y ratio within the growth set was then identified by changes to the dominant phase. e multiphase films in the table are listed beginning with the dominant phase. e growth set variables are shown in the flux columns of table .. Each flux was measured independently by the MIG in units of pressure. e following trends were observed: film Al/Y ratio increases with higher Al flux, Y flux, oxygen plasma power as well as lower molecular oxygen flux. e Al flux dependence is not surprising because the Al sticking coefficient is likely constant when the remaining parameters are fixed. Higher levels of molecular oxygen unexpectedly promoted Al desorption in the form of volatile Al2 O or AlO suboxides rather than helping oxidize Al adatoms into stable Y-Al-O compounds. In contrast, plasma power improved Al incorporation because of the higher flux of active oxygen. e plasma power set involved two different plasma powers discharged on the same initial O2 flux, which dropped slightly with power as shown in the table. e MIG flux, even with plasma activated, is still largely comprised of molecular oxygen due to the poor dissociation of the in-house-designed source (as analyzed by Shawn Penson[]). e minor O2 flux change is unlikely to have influenced the film phase as much as the active oxygen flux generated by the plasma, small though it may be. e effect of yttrium flux was another counterintuitive result, where the film Al/Y ratio increased with Y flux given a fixed Al flux. One possible explanation is that yttrium desorbs from the substrate, but this is very unlikely considering the large temperature difference between the Y cell and the sample (◦ C vs. ◦ C), which instead suggests that all the Y adatoms incorporate fully into the film. For comparison, the Al cell temperature of ∼◦ C is much closer to that of the substrate. A more plausible explanation is that yttrium acts as a catalyst for aluminum incorporation. While the bonding energies between the metal ( Y and Al ) adatoms with oxygen on a crystalline oxide surface is not available, some insight may be gained from the dissociation energies of gaseous diatomic molecules. In units of kJ mol−1 , the energies for the following bonds are: . for O–O, . for Al–O and . for Y–O (another pair of interest is  for Ga–O)[]. e stronger Y–O bond implies that Y is more reactive with molecular oxygen compared to Al, and   – Epitaxial films of the popular Y-Al-O system 230  YAM  Vary Y Vary O  220  2  Vary Al O  plasma, vary power  YAP  50  YAM + YAP  40  2  O /Y MIG Flux Ratio  2  30 YAP + YAM YAM, Low power YAG  20  YAP, High power  YAP  ri tt Y  a  ri tt Y  a  +  A Y  P  A Y  P  10 1.0  1.5  2.0  2.5  3.0  3.5  4.0  Al/Y Atomic Flux Ratio  Figure .: Map showing the phase of Nd-doped Y-Al-O films grown on sapphire at ◦ C under different growth conditions. Each growth set involves the variation of a single parameter (Y and Al fluxes, O2 pressure and plasma power), leading to a specific trend for Al incorporation. Film phase is determined from the PL spectrum. Films with mixed phases are denoted with dominant phase first. therefore enhances O2 dissociation on the sample surface. In Y-Al-O compounds, the Y atoms are coordinated to  or  oxygen atoms that in turn are each coordinated to a mixture of  or  metal ions (Y or Al) depending on the compound[]. Catalysis of Al incorporation occurs when Y adatoms dissociate O2 molecules thereby creating a number of dangling Y–O– bonds receptive towards Al adatoms. While the yttrium growth set showed that each additional Y adatom promoted the incorporation of multiple Al adatoms, a general observation for all the high temperature growths at ◦ C was that yttrium was necessary for any noticeable aluminum incorporation. Otherwise, the reflection high energy electron diffraction (RHEED) pattern would remain unchanged and the post-growth film would be undetectable by PL or x-ray diffraction (XRD). In an attempt to simplify the influence of the various growth parameters for visualization purposes while empha  – Epitaxial films of the popular Y-Al-O system sizing the key role of yttrium, the film phase outcomes were shown in the D phase map of figure . where both axes were related to the yttrium flux. e Al/Y ratio is in terms of atomic fluxes, obtained by converting the MIG fluxes using calibration data obtained from quartz crystal microbalance (QCM) flux measurements. As O2 is not measurable by the QCM, no such calibration data was available for O2 /Y so the MIG ratios were used instead. e figure clearly shows the phase trend of the films of each growth set as discussed earlier in this section. e overlapped sets, however, do not produce regions on the map unique to the specific phases, suggesting that the flux ratios alone do not predict the phase outcome. A candidate explanation is that the amount of Al adatoms incorporated per Y catalyst is dependent on the individual flux levels and not just the ratios. Going forward, more growths are needed to better resolve the growth parameter effects on film phase.  .  Emission spectra dependence on phase stoichiometry  In the previous section, the PL emission spectra was used to evaluate the trend of the film Al/Y ratio, where the film phase was identified by the unique collection of emission peaks. e spectra, while single phase, varies between films and are not necessarily identical to the spectra from bulk crystals. ese deviations were due to differences in the film Al/Y ratio, and worth further investigation. For more accurate film composition data, a set of single-phase Nd-doped YAG samples were sent for xray photoelectron spectroscopy (XPS) analysis. Figure . shows the various Y and Al peaks detected by an XPS survey scan on one of the samples. By comparing the Y d and Al p peak strengths, an Al/Y ratio of . was obtained. e measurement error is likely ∼ ± as a similarly analyzed YAG substrate yielded a ratio of . rather than .. e XPS scan also detected silicon on the sample surface, which was likely deposited during growth rather than a consequence of post-growth atmospheric exposure (the case for carbon). e SiC heater is the most probable source because the main product of SiC evaporation is elemental Si, which has a vapour pressure of ∼×−8 torr at a heater temperature of ◦ C (corresponding to the ◦ C growth temperature)[]. e silicon flux is on the same order of magnitude as the yttrium flux and has a chance of reaching the sample surface via the four mounting    – Epitaxial films of the popular Y-Al-O system  Intensity (arb. units)  O 1s  600  Name  At %  Y 3d  10.16  Al 2p  19.83  O 1s  48.95  C 1s  18.5  Si 2p  2.562  Y 3d Si 2s Al 2s  Y 3p 3/2  Si 2p Y 3p 1/2  Al 2p Y 4s Y 3s  C 1s Y 4p  400  200  0  Binding energy (eV)  Figure .: XPS survey scan showing the surface composition of an Nd:YAG film grown on sapphire. e Al/Y ratio is obtained by comparing the integrated intensity of the Y d and Al p peaks corrected for sensitivity (see table inset). Measurement performed by Ken Wong at UBC AMPEL. holes that pass through the substrate holder. In figure ., the PL emission spectra from the set of Nd:YAG films grown at ◦ C is compared to show the effect of film Al/Y ratio.  A YAG substrate with slight  Nd doping was also analyzed to gauge the XPS accuracy as well as provide a bulk crystal reference for the PL emission. Compared to the growth sets of the previous section, the films in this set were produced using the same range of Y, Al and oxygen fluxes but at the lower growth temperature. is difference appears to have increased the likelihood of obtaining YAG phase films, possibly by reducing the aluminum suboxide desorption. e tiles in the figure show films sorted in increasing Al/Y film ratio with the bulk YAG at the bottom. It is surprising that the film with a ratio of . is in the YAG phase instead of the closer YAP phase (. vs .). While the PL emission peaks are not well defined, the overall spectrum outline nevertheless matches that of Nd:YAG and does not include evidence of other Nd:Y-Al-O phases. When comparing the four films, the similarity of the emission spectra to that of bulk Nd:YAG is dependent on the closeness of the film Al/Y ratio relative to bulk. Deviations from the stoichiometric bulk ratio cause peak broadening as well as alter the relative peak heights. However, in contrast to the compositional effect of the Al-Ga-O films, the peak wavelengths here remain unchanged. is suggests that   – Epitaxial films of the popular Y-Al-O system  XPS Al/Y Ratio  1.08  PL Intensity (arb. units)  1.26  1.95  2.07  1.75 Bulk Nd:YAG  1020  1040  1060  1080  1100  1120  Wavelength (nm)  Figure .: PL spectra from Nd-doped Yx Aly O films grown on sapphire with varying Al/Y ratios as measured by XPS. e spectra are consistent with Nd:YAG phase films and feature improving peak sharpness as film stoichiometry approaches the Al/Y ratio of bulk Nd:YAG. the local atomic structure about the Nd dopant does not vary significantly, a likely possibility given that the Nd dopant sits on the yttrium sites and assuming that distortions to the unit cell due to a non-stoichiometric Al/Y ratio primarily affect the Al sites.  .  Effect of growth temperature on phase stoichiometry  From previous work on Y2 O3 by I.C. Robin and S. Webster, a growth temperature window of between –◦ C was necessary for crystalline Y2 O3 film growth at rates in the nm/min range while avoiding damage risk to the sample heater. Various   – Epitaxial films of the popular Y-Al-O system  (a) Specular reflection during growth of YAG  o  T = 920 C o  T = 870 C o  Intensity (arb. units)  T = 820 C  o  T = 720 C (b) Substrate temperature variation  n  n = 1.86  = 1.85  3  1  n = 1.88 2  (c) Refractive index model  (d) Specular reflection model  0  20  40  60  80  100  120  140  160  180  200  Time (mins)  Figure .: Effect of substrate temperature on Al incorporation during the growth of a YAG film on sapphire. e refractive index of YAG decreases with Al/Y ratio. (a) in film reflection showing amplitude variations with (b) substrate temperature. (c) Model of a multilayer with different refractive indices and its (d) calculated specular reflection that match the measured data. Y-Al-O films were grown within this temperature window, but not in a sequence under identical conditions that could be analyzed as a growth set. Some of the growth temperature effects, however, can be derived from the growth of a single film with variable temperature. Figures .(a) and (b) show the thin film reflectometry oscillations and corresponding temperature during the growth of a Nd:YAG film. e Y, Al and O2 fluxes were .×−7 , .×−7 and .×−5 torr respectively and a  W plasma was used. e film segment shown was grown on top of a  nm Nd:YAG layer grown with similar fluxes but with a fixed sample temperature of ◦ C.   – Epitaxial films of the popular Y-Al-O system In figs. .(a) and (b), each growth temperature step was held for the duration of two specular reflection oscillations. e amplitudes at ◦ C and ◦ C were similar, but noticeably increased at ◦ C. Lowering the temperature to ◦ C produced an intermediate amplitude. Figures .(c) and (d) show the simulated oscillations for a changing refractive index, obtained from the model described in section .. but ignoring the effects of roughness and absorption. Using the bulk refractive index of YAG for comparison (. at the  nm laser wavelength []), the simulated indices may help gauge the divergence of the film Al/Y ratio away from bulk. For example, the ◦ C layer has a higher index, which is consistent with a smaller Al/Y ratio caused by higher levels of Al desorption with increasing temperature. Although the film stays in the YAG phase, the refractive index depends on the Al/Y ratio, which when reduced, should deviate towards the index of YAP that is larger than YAG[]. In contrast, a larger Al/Y ratio would lower the index towards that of Al2 O3 . An interesting observation from the reflection oscillations shown in figure .(a) is that the film refractive index is not solely temperature dependent but is also affected by the index of underlying layers. e layer grown at ◦ C has a higher index than the ◦ C layer likely because of a residual influence from the high index ◦ C layer that attempts to retain the prevailing structure despite changing conditions. As another example, the effect on refractive index was not distinguishable at ◦ C, and only became noticeable with the second temperature increase to ◦ C when the Al desorption levels were high enough to affect the structure. e underlying layer effect can be extrapolated to the start of growth where it appears that the initial film has a significant role in establishing the phase and film composition. It is likely for this reason that the film in figure .(a) stayed in the Nd:YAG phase. Due to the difficulty of starting a growth with the perfect Al/Y stoichiometry because of the sensitivity to the various growth parameters, an in-situ monitoring technique like thin film reflectometry may be useful for optimizing the refractive index and therefore Al/Y ratio. One limitation of this technique is the relatively long wait for feedback, as at least a single oscillation is required.    – Epitaxial films of the popular Y-Al-O system  .  Nd-doped YAP film with high degree of crystallinity  e importance of the starting growth layer was demonstrated by a Nd:YAP film produced under unusual circumstances, and which has not been reproduced since. e  nm film was started on an R-plane sapphire substrate at ◦ C using Al, Y and oxygen fluxes of .×−7 , .×−7 and .×−6 torr respectively. e oxygen flux may appear uncharacteristically low, but that was because the active plasma produced was intensely bright and spread outwards on the back end of the quartz discharge tube. e plasma power could not be accurately measured as the forward power reading exceeded the limits of the Bird wattmeter (> W forward,  W reflected). Midway during the – nm/min growth, the plasma switched to a less intense and more typical mode of operation with  W forward,  W reflected powers and an oxygen pressure of .×−5 torr but with the same oxygen gas pressure/flow controller (PFC) setting. e film was characterized by both PL and XRD post-growth, the results of which are shown in figure .. e PL emission spectra (fig. .(c)) featured a collection of peaks that identified the film as single-phase Nd-doped YAP. While the peak wavelengths match those of other Nd:YAP films as shown in ., the relative peak heights are different because Nd:YAP is optically anisotropic and its emission depends on the crystal orientation. YAP has an orthorhombic structure with the lattice constants a=. Å, b=. Å and c=. Å []. Although the PL collected was unpolarized, a comparison to anisotropic spectra measured by Dischler and Ennen showed that the emission was dominantly polarized along the a axis [, note the different lattice notation]. In contrast, the emission from the other Nd:YAP films was b-dominant. A more detailed analysis of the crystal structure and orientation of the high quality Nd:YAP film was accomplished by XRD as shown in figs. .(a) and (b). e θ-θ scan confirmed that the film was single-phase YAP, and had the sole out-of¯ α-Al2 O3 relative to the R-plane sapphire plane orientation (001) YAlO3 ∥ (0112) substrate. e full width half maximum (FWHM) of the YAlO3 (002) peak was .◦ in the θ-θ direction and ◦ in the ω direction, where the latter was obtained from a reciprocal space map (not shown). As suggested by the anisotropic PL, the other Nd:YAP films grown on the same type of substrate were oriented differently as shown in figure ., which will be discussed in detail later. e θ-θ scan there    XRD Intensity (arb. units)  – Epitaxial films of the popular Y-Al-O system  (a) (0 1 -1 2)  (002)  10  15  Al O  (0 2 -2 4)  2  YAlO  (004)  20  (0 3 -3 6)  3  (006)  3  25  30  35  40  XRD Intensity (arb. units)  (°) (b)  YAlO  YAlO  (206)  3  Sapphire substrate (0 3 -3 0)  -90  PL Intensity (arb. units)  (116)  3  -45  0  45  90  (°) (c)  1040  Nd:YAlO 3  1050  1060  1070  1080  1090  1100  1110  Wavelength (nm)  Figure .: Structural and emission properties of a high quality Nd:YAlO3 film grown on R-plane sapphire:(a) High resolution XRD θ-θ scan (b) XRD ϕ scans of the YAlO3 (116) and (206) peaks showing in-plane orientation relative to the substrate (c) PL emission spectra involving 4 F3/2 →4 I11/2 transitions of Nd3+ . reveals an out-of-plane orientation of (112) YAlO3 ∥ (01¯12) α-Al2 O3 instead, as well as instances of other orientations that imply poorer overall crystallinity (refer to app. C for XRD data). e in-plane orientation of the high quality Nd:YAP film was determined by ϕ scans (fig. .(b)), which involve finding off-axis peaks via sample rotations about its normal, then relating the peaks from both film and substrate. e (116) and (206) YAP peaks have in-plane projections along the [110] and [100] in-plane directions    – Epitaxial films of the popular Y-Al-O system ¯ sapphire peak has an in-plane projection along the respectively while the (0330) ¯ direction, which is along the long end of the R-plane sapphire rectangle (see [1¯21] fig.B. in the appendix). e Nd:YAP film was therefore preferentially oriented such ¯ α-Al2 O3 and [010] YAlO3 ∥ [1¯21] ¯ α-Al2 O3 . e figure also that [100] YAlO3 ∥ [010] shows a weak YAP (206) peak coincident with the sapphire (03¯30) peak, implying that parts of the film have the in-plane orientation of [100] YAlO3 ∥ [¯1¯21] α-Al2 O3 , which is a ◦ in-plane rotation of the main orientation. is alternative orientation likely occurs because of the similarity between the a and b lattice constants. When the [100] YAlO3 a-axis is parallel to [0¯10] α-Al2 O3 , the lattice mismatch is .. Along the [010] YAlO3 b-axis, a supercell of three YAP lattice units has a mismatch of .. For domains with the alternative orientation, the lattice mismatches are . and . for the three lattice supercells along the a direction and the b direction respectively. e minimum mismatch of . vs . could explain the preference for the [100] YAlO3 ∥ [0¯10] α-Al2 O3 in-plane orientation. e overall large lattice mismatches might be the reason for the broad XRD ω FWHM, where strain relaxation causes the YAP (001) axis to be multiply tilted (i.e. mosaic spread) relative to the substrate normal.  .  Crystallinity of Y-Al-O films and effects of post-growth annealing  e Nd:YAP film in the previous section was deemed to be of high quality for its single-phase YAP composition, its single out-of-plane orientation with strong θ-θ peaks and its predominant in-plane orientation. Most of the other Y-Al-O films fall short against this benchmark because they consist of crystallites with different out-of-plane orientations. As an example, figure . shows θ-θ scans of two asgrown Nd:YAG and Nd:YAP films. e YAG film, while dominant in the {400} orientation, also has a small percentage of crystallites with the {420} and {532} orientations. Likewise, the {112}-dominant YAP film also includes the orientations {002}, {111}, {113}, {114} and {312}. YAG films on C-plane (shown) or A-plane sapphire tend to be dominant in the {400} orientation while films on R-plane are a mixed composite of {400} and {420}. e preference for these orientations suggest partial independence from substrate orientation and possibly greater dependence   – Epitaxial films of the popular Y-Al-O system  As-grown  Nd:YAG  (a)  Post anneal YAG (400) Sapphire (0006)  XRD Intensity (arb. units)  YAG (800)  Nd:YAP  Sapphire (0 1 -1 2)  Sapphire (0 2 -2 4)  YAP (112)  Nd:Y O  Sapphire (0 1 -1 2)  2  3  Sapphire (0 2 -2 4)  Peak labels in red are YAG (420) (321)  (400)  15  (422)  (521)  20  25  /2  PL Intensity (arb. units)  (640)  (532)  (642)  (800)  30  (°)  (b) Post anneal  1060  1080  1100  1120  Wavelength (nm)  Figure .: Effect of a  hr, ◦ C furnace-anneal on Nd-doped YAG, YAP and Y2 O3 films grown on sapphire. (a) XRD θ-2θ scans of the samples before and aer annealing. An as-grown measurement of the Nd:Y2 O3 sample was not performed. All  samples are converted to the YAGphase. (b) Nd:YAG PL spectrum with sharp peaks produced by all  samples post-anneal. e as-grown emission spectra matched the materialspecific spectra shown in figure .. on the initial growth conditions. Unfortunately, concrete evidence is lacking as YAP films were only grown on R-plane sapphire, and aside from the high quality film mentioned previously all were {112} dominant. Unlike the Nd-doped sapphire and Al-Ga-O films, a Y-Al-O film with multiple orientations can still produce the unique emission spectra associated with its   – Epitaxial films of the popular Y-Al-O system particular phase (e.g. YAP). is was demonstrated by comparing the PL emission spectra between the high quality and typical versions of Nd:YAP in figures . and . respectively. Aside from the difference due to anisotropy, the sharpness of the peaks are similar and match their bulk crystal counterparts[]. In the case of Y-AlO then, the majority of Nd dopants still migrate to the Y site in the host instead of the disordered boundaries between crystallites. Nevertheless, films with excellent crystalline long-range order (LRO) (i.e. singly oriented) are preferable for making laser devices because the boundaries between crystallites may induce scattering losses. LRO is also important for devices that exploit crystal anisotropy, for example a laser with linearly polarized emission and lower thermally induced birefringence, of which YAP is a good host candidate[]. In an attempt to improve the crystalline LRO, Y-Al-O films were annealed in air inside a furnace at temperatures of up to ◦ C. As a first step, the three films grown under varying oxygen pressures in figure . were annealed at ◦ C for  hours. Analysis by XRD revealed that the YAM film underwent a transition from YAM {023} to a mixture of YAG {420} and YAG {400}; the YAP film from YAP {112} to a mixture of YAP {112}, YAG {420} and YAG {400}; and the YAG film remained unchanged with both YAG {400} and {420}. It is important to note that all the films had multiple orientations both before and aer annealing. A second experiment involved another set of Y-Al-O films annealed at ◦ C for  hours, the XRD θ-θ scans of which are shown in figure .(a). e general observation was that annealing failed to improve the LRO by recrystallizing the film into a single orientation. Annealing did, however, yield some interesting results. It showed that the YAl-O phases all evolve into YAG, likely a consequence of substrate–film interlayer diffusion that enriches the film Al content and therefore promotes the formation of YAG as the stable phase. In figure ., the as-grown, non-YAG films were converted entirely into YAG, which was predicted earlier by the ◦ C anneal experiment. Aer the ◦ C anneal, both Nd:YAP and Nd:Y2 O3 films featured the same collection of polycrystalline YAG peaks. In the case of the as-grown YAG film, the crystal orientations remained the same but their diffraction peaks were stronger and slightly shied to positions associated with the lattice constants of bulk YAG. e PL emission spectra from all three films were identical and represented single-phase   – Epitaxial films of the popular Y-Al-O system Nd:YAG as shown by figure .(b). e peak sharpness was comparable to that of bulk crystals, and is an improvement over typical Nd:YAG films. Annealing is therefore useful for making Nd:YAG from Y-Al-O films regardless of composition. However, to ensure the best LRO, the starting material should be in the Nd:YAG phase to avoid the formation of polycrystalline YAG. As shown by the YAG film of figure ., the existing orientations remain but the lattice is modified to match bulk YAG. e improvement is likely made by fixing the stoichiometry either for the oxygen or the Al/Y ratio e.g. Y3 Al5 O11.98 , Y3 Al6 O12 respectively. It is unclear what happens post-anneal to the excess Al in as-grown films with an Al/Y ratio greater than the YAG stoichiometric ratio.    6– Conclusions and future work Light-emitting rare-earth (RE)-doped materials are popular for a variety of optical applications involving display, lighting, etc. Each application will have specific criteria for the choice of dopant, host as well as crystallinity of the overall material. For intense light sources such as fixed-wavelength lasers, a crystalline material with short-range order (SRO) is preferable for its sharp RE emission peaks. e dopant and host combination should then be chosen based on the availability of a dominant emission peak with strong optical gain at the desired wavelength. Laser gain media are typically single crystals grown in bulk form because aside from SRO, their long-range order (LRO) helps to minimize propagation losses within the media that impair lasing. Recent progress with sintered nanocrystals offers an easier alternative for making isotropic laser crystals, but anisotropic crystals are still desirable because they include some of the strongest gain materials (e.g. Nd:YVO4 ) and are thus still grown as bulk single crystals. Single crystals grown in thin-film form combine the manufacturing advantages of thin film media with the optical properties of single crystals. Furthermore, their reduced geometry improves laser devices by offering better heat extraction, compact design and wider functionality. Planar waveguide lasers (PWLs) are a promising class of thin film devices where optical confinement from planar multilayer structures allows single crystals to acquire the benefits of optical fiber such as efficient laser operation and low lasing thresholds. e research presented in this thesis was motivated by the goal of making PWL gain media using molecular beam epitaxy (MBE). While various thin film growth methods have been used to make PWLs, MBE offers a number of unique advantages related to its ability to grow anisotropic single-crystal films that are oriented with the underlying substrate. Film composition can be controlled for each atomic layer deposited successively, allowing for complex multilayer structures with precise thickness control. Furthermore, the low growth temperature compared to the melt-    – Conclusions and future work ing point where typical bulk growth occurs permits the creation of new metastable materials such as Nd-doped sapphire.  .  Comparison of Y-Al-O and Al-Ga-O films  Since the work in this thesis constituted the early steps of a larger campaign targeting PWLs by MBE, much of the focus was on material growth and characterization. Using Nd solely as the RE dopant, films from the Y-Al-O and Al-Ga-O material systems (including binary phases) were grown on sapphire substrates with the C, R, A and M-plane orientations. Sapphire was chosen for various reasons including advantageous thermal and optical properties: high thermal conductivity for better heat extraction; wide transparency window compatible with assorted pump wavelengths and configurations; and refractive index lower than popular laser materials making it an attractive cladding material. e films were probed during growth using in-situ techniques such as reflection high energy electron diffraction (RHEED) and thin film reflectometry, and analyzed in more detail post-growth chiefly by photoluminescence (PL) and x-ray diffraction (XRD). e PL emission spectrum from an ensemble of Nd3+ dopants is a useful gauge of SRO, where sharp/narrow peaks indicate a uniform local structure. e distinct pattern formed by the collection of these peaks is unique to the local structure and likely the overall structure as well, making it useful for phase identification. XRD complements PL by resolving the LRO, where strong peaks denote a crystalline film. From XRD scans along various orientations, the film can be identified as single crystal or composed of crystallites, its lattice constants measured, and both its out-of-plane and in-plane orientation relative to the substrate determined. e Y-Al-O system has three ternary phases: Y3 Al5 O12 (YAG), YAlO3 (YAP) and Y4 Al2 O9 (YAM), here listed with decreasing Al/Y ratio. Nd:YAG is a popular laser material with strong gain at  nm and was the motivation for growing Y-AlO films. Single-phase films of each of the Y-Al-O phases were grown, as verified by PL emission spectra unique to their respective crystal structures. e Nd:YAG and Nd:YAP spectra were the best with sharp and well-defined peaks similar to those from their bulk crystal counterparts. Bulk Nd:YAM was unavailable for comparison, but the film emission approximated that of nanocrystals grown by sol-gel. XRD    – Conclusions and future work scans showed that most of the Y-Al-O films had weak LRO because they were composed of crystallites with multiple out-of-plane orientations. An exception was the high quality Nd:YAP film that was almost single crystal save for slight in-plane twinning. Its PL emission, however, was not superior (e.g. sharper peaks) to those from other Nd:YAP films but matched that of bulk Nd:YAP crystals as well. Unlike the Y-Al-O system, the focus on the Al-Ga-O system primarily involved the two binary-phase endpoints α-Al2 O3 and α-Ga2 O3 . Both shared the same corundum structure as the substrate, so a better film–substrate epitaxial match was anticipated. More importantly, Nd3+ emission with SRO had not been reported for either material. e Nd:sapphire and Nd:α-Ga2 O3 films grown were single crystal and oriented with the substrate both in- and out-of-plane. eir previously unreported emission spectra were distinct, with dominant emission peaks at  and  nm for Nd:sapphire and Nd:α-Ga2 O3 respectively. ese new spectra are a result of SRO at the Nd-occupied Al or Ga sites, which could be difficult to achieve using bulk methods because the Nd3+ ions are much larger than both the Al3+ and Ga3+ ions. e emission spectrum of Nd:α-Ga2 O3 appears to be an almost identical but blue-shied version of the Nd:sapphire spectrum. is is consistent with the idea that the oxygen cage around the dopants is similarly shaped in both cases, but with different sizes since α-Ga2 O3 has larger lattice constants. When alloys of the two materials are made, the emission spectrum shis between the two binary endpoints depending on Ga/Al ratio as well as film strain, which was observed in Al-rich films. e effects of both factors could be aggregated using the unit cell volume, which in turn showed a linear effect on emission shi. e unit cell volume thus became a macroscopic gauge of the changes to the oxygen cage. Unlike Al-Ga-O, changing the Al/Y ratio in Y-Al-O films does not shi the emission spectrum but rather affects the sharpness of its peaks i.e. more local disorder. is suggests that the size of the oxygen cage around the Nd-occupied Y site is less sensitive to variations in Al concentration. Applications involving compositional tuning are thus better served using Al-Ga-O instead of Y-Al-O films. Narrow emission lines are obtained when the metal ratio approaches a stoichiometric phase: one of the ternary phases for Y-Al-O and one of the binary endpoints for Al-Ga-O. Since the SRO for either of the Y-Al-O phases is easily achieved, control of the overall film   – Conclusions and future work stoichiometry is necessary to avoid the formation of unwanted phases. Film structure rather than stoichiometry is the critical factor for Al-Ga-O, where films not single crystal and oriented with the substrate (i.e. limited LRO) tend to form in thermodynamically stable alternative phases. e larger-sized Nd3+ dopants then segregate to disordered grain boundaries producing Nd:glass-like emission. In general, the best Al-Ga-O and Y-Al-O emission are obtained from films with the best crystalline quality. During the course of this research, varying levels of film quality were observed. ey are listed below in order of declining quality together with their notable properties: Strained single crystal — Orientation: with the substrate; Density: comparable to bulk; RHEED: streaks/dashes; XRD thickness fringes; PL: anisotropic emission with sharp peaks. E.g. thin Nd:sapphire or α-Ga2 O3 films. Relaxed single crystal — Orientation: with the substrate, with some texture/mosaicity; Density: lower than bulk version; RHEED: spots/chevrons; PL: anisotropic emission with sharp peaks.  E.g.  thick (few hundred nm)  Nd:sapphire or α-Ga2 O3 Single phase, few orientations — Orientation(s): One out-of-plane, few in-plane; RHEED: crystalline pattern of spots/streaks; PL: sharp emission peaks (highquality Nd:YAP), or broad spectrum (Nd:β-Ga2 O3 or Nd:Al2 O3 on C-plane sapphire). Single phase, polycrystalline — Orientation(s): Many, both out-of and in-plane; Weak, single-phase XRD θ-θ peaks from multiple orientations; RHEED: rings or ring fragments; PL: distinct peaks from only one phase (most Nd:YAl-O films). Multi-phase, polycrystalline — Orientation(s): Many, XRD θ-θ peaks from more than one phase; RHEED: rings or ring fragments; PL: distinct peaks from more than one phase (some Nd:Y-Al-O films). Amorphous — No XRD θ-θ peaks; No RHEED pattern; PL: broad emission similar to Nd:glass. E.g. low temperature Al2 O3 , Ga2 O3 or Y-Al-O films.    – Conclusions and future work Table .: Comparison of the Nd-doped corundum-structure materials to bulk Nd:YAG and Nd:YVO4 , repeated from table . (where data references are provided).  Primary emission peak (nm) Product of σ · τ (×−24 cm2 s) Primary absorption peak (nm) Refractive index @  µm ermal conductivity (Wm−1 K−1 )  .  α-Ga2 O3  α-Al2 O3  Y3 Al5 O12 (YAG)  YVO4     .  (subs)     .  (subs)     .      .   Comparison of laser properties  For a comparison of the laser figures-of-merit between Nd:sapphire, Nd:α-Ga2 O3 and the popular bulk laser crystals Nd:YAG and Nd:YVO4 , part of table . is reviewed again here in table .. At a first glance, both the primary emission and absorption peaks of the Nd-doped corundum-structure materials are further in the infrared compared to their YAG and YVO4 counterparts. is is likely a consequence of the smaller O2 cage (also coordination number) around the Nd dopant. e new emission wavelengths may be desirable for some applications, including those requiring frequency doubling. e  nm peak of Nd:sapphire has strong gain with a product of emission cross-section and lifetime (σ · τ ) higher than the  nm peak of Nd:YVO4 , which is one of the highest available. e  nm peak of Nd:α-Ga2 O3 is likewise comparable to the  nm peak of Nd:YAG, but it could be higher at levels ∼ less than the Nd:sapphire peak given better film quality. at -less limit occurs because Nd:α-Ga2 O3 has a higher refractive index. Nd:YVO4 is a popular choice for low power laser devices due to its strong gain and thus high efficiency. Its low thermal conductivity is less desirable for high power operation, however, causing the lower-gain Nd:YAG to be preferred instead. e corundum-structure materials on sapphire substrates have both high gain and high thermal conductivity, making them ideal for efficient and power-scalable devices. While sapphire substrates could also be used for the growth of Nd:YAG and Nd:YVO4 films, the epitaxial match would be better with the corundum-structure    – Conclusions and future work materials thus ensuring films with better crystal quality. is includes corundumstructure alloys that are promising for graded-index waveguide devices.  .  Comparison of growth conditions  While the properties of the Al-Ga-O and Y-Al-O films are the highlight of this work, much can be gleaned from the MBE growth conditions used to produce those films. Each of the various parameters has an effect, some more interesting than others. e following is a list of issues affecting growth: Metal desorption — Metal adatoms desorb from the substrate with increasing temperature either in metal (e.g. Al) or suboxide (e.g. Al2 O) form. e oxygen overpressure is also a factor, but varies with metal species. More gallium desorbs under excess O2 than without O2 because of the high Ga2 O vapour pressure at typical growth temperatures. is contrasts with aluminum where Al2 O remains longer on the substrate than Al metal, increasing the likelihood of full oxidation and thus incorporation. Yttrium desorption was not observed, probably because of the large substrate–cell temperature difference. Oxidation — Oxygen plasma was required to grow sapphire as molecular oxygen would yield polycrystalline alumina films at best. is suggests a contribution by the in-house plasma source involving better diffusion. During the growth of Y-Al-O films, plasma power affected Al incorporation and thus film phase. However, with limited impact on the Ga sticking coefficient, the source was replaced with an SVTA source capable of higher active oxygen levels. is led to the full oxidation and thus incorporation of Ga at higher growth temperatures. Reattempting the Y-Al-O growths with this source may yield interesting results. Growth temperature — With the in-house plasma source, α-Ga2 O3 and sapphire films could be grown at temperatures around ∼◦ C for ∼ nm before the film quality started to degrade. If continued, the resulting thick film (∼ µm) would have poor crystal quality. is may be in part due to disordered low-temperature film relaxation. For good quality thick films, the growths were transitioned into a stable mode denoted by unchanging RHEED   – Conclusions and future work spots/chevrons. is typically involved raising the growth temperature to ∼◦ C and increasing the metal fluxes at the first sign of degradation. ick films with the SVTA source have not been attempted, so it is unclear if a similar step is required. Although the new source widened the growth temperature window for α-Ga2 O3 , at growths above ◦ C crystallites of the more stable β-Ga2 O3 phase started to appear. Y-Al-O films generally require a growth temperature above ∼◦ C for the best quality, though high levels of active oxygen may lower this requirement. Substrate orientation — Epitaxial Al-Ga-O films matching the substrate were grown on R, A and M-plane sapphire. On C-plane sapphire, the films were the thermodynamically stable phases instead. Weak diffusion on C-plane is the likely reason, which may be overcome possibly by increasing the growth temperature or active oxygen flux. e Y-Al-O films were generally insensitive to the substrate orientation since they consisted of multiply oriented crystallites. However, the almost-single-crystal high-quality Nd:YAP film had a unique orientation with the substrate that minimized the lattice mismatch. Post-growth annealing — High temperature annealing (above ◦ C) in an air environment weakens the intensity and reduces the anisotropy of the emission from the Nd-doped Al-Ga-O films. e effect becomes worse the higher the anneal temperature. is metastability explains why the material is inaccessible by bulk growth methods using the melting point, but is also an indication that the material is stable enough for high power laser operation. Annealing at ◦ C also did not benefit Y-Al-O films unless YAG was desired, since all the films regardless of phase began changing into YAG. e Nd:Y-Al-O films annealed at ◦ C ended up as stoichiometric YAG with sharp emission peaks similar to bulk Nd:YAG.  .  Ideas for future work  Alloys of α-Al2 O3 and α-Ga2 O3 , when doped with neodymium, have compositiondependent optical properties ideal for making waveguide lasers with advanced new configurations. With low threshold powers and excellent heat extraction via the pla  – Conclusions and future work nar multilayer structure on a sapphire substrate, they could supplant both Nd:YVO4 (high gain but low power) and its alternative Nd:YAG (higher power but lower gain) as the Nd-doped laser of choice. Laser devices should be fabricated by first depositing planar waveguide layers epitaxially onto a sapphire substrate, followed by polishing and mirror coating the ends to form the resonator cavity. Lasing action could be demonstrated by optically pumping the samples with a diode laser array. While coupling optics might be used during the initial stages, efforts to commercialize these devices should include incorporating both diode pump and solid state laser into a compact monolithic device. Adding a non-linear crystal for second harmonic generation will yield high power, low cost visible lasers for such applications as projection displays and flow cytometry. Once optimal laser structures can be fabricated, novel waveguide designs should be implemented by customizing the core/cladding layer materials. Waveguide layers with a sharp index contrast produce high scattering losses (∼  dB/cm) when roughness is present at the interfaces. Using the Al-Ga-O alloys, graded-index waveguides with minimal scattering loss and better laser efficiency can be made. is would be the first instance of a crystalline solid state waveguide laser with a graded index. e waveguide will feature a Nd-doped α-Ga2 O3 high index core and α(Al1−x Gax )2 O3 cladding layers with a Ga/Al ratio varying from  to  towards the core. e smooth index gradient is possible because the multilayer maintains its single-phase corundum structure. Other novel designs can be achieved by using Nd-doped Al-Ga-O alloys as the active core layer. By specifying the Ga/Al ratio, the dominant Nd emission peak can be compositionally tuned between – nm. Alternatively, a graded-index core can be implemented with a symmetric Nd-doped α-(Al1−x Gax )2 O3 layer that produces a broad gain profile of – nm suitable for making tunable lasers. Tailoring the waveguide composition profile may lead to a flat-top gain profile. Aer successfully demonstrating a waveguide laser device, other new laser materials with the same corundum structure should be pursued. Candidates for Nd doping include the α-phases of Ti2 O3 , Cr2 O3 , V2 O3 , and Fe2 O3 . ese materials have a larger unit cell than sapphire and Ga2 O3 , suggesting that their dominant Nd emission peak will have a wavelength shorter than  nm. Assuming the same   – Conclusions and future work  1096  (Al  1-x  Ga ) O x 2  3  Emission peak (nm)  1094  1092  1090 Cr O 2  1088  3  V O 2  3  Fe O 2  3  1086  Ti O 2  1084  0.25  0.26  0.27  0.28  0.29  3  0.30  0.31  3  Volume (nm )  Figure .: Estimated wavelength of the dominant PL peak for the other candidate corundum-structure oxides. linear dependence observed from Al-Ga-O films, their dominant peaks can be expected at the wavelengths shown in figure .. Once single-phase oxides with sharp emission lines characteristic of Nd can be grown, sapphire alloys should be attempted. Graded-index laser devices similar to those mentioned above will then be fabricated to benefit from the extended tuning range and higher refractive index. Aside from working on new laser hosts, candidates for new laser emission peaks may be discovered by doping all the corundumstructure materials with other rare-earths e.g. Yb, Er, Ho, and Ce. e sharp emission peaks will be unique for each crystal and is expected to be red-shied compared to typical hosts doped with the same rare-earth. New applications could arise for these emission peaks. Graded-index layers have played a significant role in the advancement of optical fiber and compound semiconductor technology. e development of corundumstructure alloys will be an opportunity to demonstrate a similar breakthrough in the area of crystalline solid state laser materials.    Bibliography [] Bilbao Crystallographic Server. http://www.cryst.ehu.es. 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Spectroscopic characterization of Nd:Y2 O3 : application toward a differential absorption lidar system for remote sensing of ozone. Journal of the Optical Society of America B, (): –, Dec . doi:./JOSAB... URL http://josab.osa.org/abstract.cfm?URI=josab---. Last visited: --. → pages ,  [] G. Wang, O. Marty, C. Garapon, A. Pillonnet, and W. Zhang. Rare earth doped α-alumina thin films prepared by pulsed laser deposition: structural and optical properties. Applied Physics A: Materials Science & Processing, :–, . doi:./s---. → pages  [] J. Wang, W. Brocklesby, J. Lincoln, J. Townsend, and D. Payne. Local structures of rare-earth ions in glasses: the ‘crystal-chemistry’ approach. Journal of Non-Crystalline Solids, (): – , . ISSN -. URL http://dx.doi.org/./-()-K. Last visited: --. → pages ,  [] Z. R. Wasilewski, J.-M. Baribeau, M. Beaulieu, X. Wu, and G. I. Sproule. Studies of oxide desorption from GaAs substrates via Ga2 O3 to Ga2 O conversion by exposure to Ga flux. Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, (): –, . URL http://dx.doi.org/./.. Last visited: --. → pages  [] R. Weast, editor. CRC handbook of chemistry and physics: a ready-reference book of chemical and physical data. CRC handbook series. CRC Press, th edition, . ISBN . → pages , ,  [] J. Weaver, C. Kraa, D. Lynch, and E. Koch. Physics Data: Optical Properties of Metals, volume : e Transition Metals. Fachinformationszentrum Energie Physik Mathematik GmbH, . → pages  [] M. J. Weber and T. E. Varitimos. Optical Spectra and Intensities of Nd3+ in YAlO3 . Journal of Applied Physics, ():–, . doi:http://dx.doi.org/./.. Last visited: --. → pages  [] S. Webster, R. Kumaran, S. Penson, and T. Tiedje. Structural analysis of thin epitaxial Y2 O3 films on sapphire. Journal of Vacuum Science & Technology B, ():CA–CA, . doi:http://dx.doi.org/./.. Last visited: --. → pages  [] M. Wilding. Aluminates. In J. Shackelford and R. Doremus, editors, Ceramic and glass materials: structure, properties and processing. Springer, . URL http://books.google.ca/books?id=ASIYuNCpYC. Last visited: --. → pages  [] J.-F. Wyart, A. Meah, A. Bachelier, J. Sinzelle, W.-. L. Tchang-Brillet, N. Champion, N. Spector, and J. Sugar. Energy levels of f3 in the Nd3+ free ion from emission spectra.  Bibliography Journal of Physics B: Atomic, Molecular and Optical Physics, ():L, . URL http://stacks.iop.org/-//i=/a=L. Last visited: --. → pages  [] Y. Yu, J. Wang, H. Zhang, H. Yu, Z. Wang, M. Jiang, H. Xia, and R. I. Boughton. Growth and characterization of Nd:Yx Gd1−x VO4 series laser crystals. Journal of the Optical Society of America B, ():–, . URL http://josab.osa.org/abstract.cfm?URI=josab---. Last visited: --. → pages  [] K. Yvon, W. Jeitschko, and E. Parthé. LAZY PULVERIX, a computer program, for calculating X-ray and neutron diffraction powder patterns. Journal of Applied Crystallography, (): –, Feb . URL http://dx.doi.org/./S. Last visited: --. → pages  [] N. Zangenberg, D. A. Beaton, T. Tiedje, S. Tixier, M. Adamcyk, R. Kumaran, J. A. MacKenzie, E. Nodwell, E. C. Young, and G. I. Sproule. Molecular beam epitaxy growth of the dilute nitride GaAs1−x Nx with a helical resonator plasma source. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, ():–, . URL http://dx.doi.org/./.. Last visited: --. → pages  [] D. E. Zelmon, D. L. Small, and R. Page. Refractive-Index Measurements of Undoped Yttrium Aluminum Garnet from . to . µm. Applied Optics, ():–, Jul . URL http://dx.doi.org/./AO... Last visited: --. → pages   A– Sapphire lattice A crystal may have  of  point group symmetries, each representing a set of rotation, reflection and roto-inversion operations that leave the crystal invariant about a point. Finding the point group usually involves observing the external symmetry of a perfect bulk crystal piece. e point group of sapphire (α-Al2 O3 ) is denoted as ¯3m in international notation (or D3d in Schönflies notation), representing  roto-inversion axes and a mirror plane. Knowing the point group, a crystal can be grouped with others of similar symmetry (exceptions exist) into  of  crystal systems: cubic, hexagonal, trigonal, tetragonal, orthorhombic, monoclinic and triclinic. As point groups do not include translation symmetry, a lattice system based on repeating unit cells is used to express how the crystal translates in space. ere are  lattice systems: cubic, hexagonal, rhombohedral, tetragonal, orthorhombic, monoclinic and triclinic; and crystals belonging to one usually belong to the crystal system of the same name. e trigonal crystal system is different, however, as it includes crystals from either the rhombohedral or hexagonal lattice system. e  lattice systems can be refined further into  Bravais lattices by distinguishing different arrangements within the unit cell e.g. cubic → primitive-, body- and facecentreing. Rhombohedral and hexagonal lattices only have primitive centreing. Sapphire is a trigonal crystal that has a rhombohedral lattice with unit cell parameters: a = 5.128 Å and α = 55.3◦ . However, it has become customary to use the hexagonal basis to maintain consistency with hexagonal-lattice materials in the same crystal family. Furthermore, the distorted cube appearance of rhombohedral lattices is more difficult to visualize. To accomodate the lattice differences, the hexagonal unit cell is three times the size of the rhombohedral unit cell. More details on the conversion between lattices or their mutual orientations can be found in the appendix of reference []. In the hexagonal basis, sapphire has a unit cell with lattice constants a = 4.759 Å and c = 12.991 Å, as shown in figure A.. Planes    A– Sapphire lattice  [0001] or [001]  c  [0010 ] or [11 0  [1000] or [100] ]  R-plane (0112) or (012)  A-plane (1120) or (110)  M-plane (1010) or (100)  Hexagonal Unit Cell  [0100] or [010] a3 a1  a2  C-plane (0001) or (001) a1 = a2 = a3 = 4.759 Å c = 12.991 Å  Figure A.: Hexagonal lattice of sapphire showing the  most popular substrate orientations C, R, A and M. e unit cell (/ the hexagon) contains  Al2 O3 formula units. Plane () and vector [] orientations are given in both  and  coordinate descriptions.  A– Sapphire lattice Table A.: Equivalent planes in sapphire Orientation C R A M  Type Basal Morphological rhombohedral Prismatic Prismatic  Equivalent planes {0001} ¯ {1012}, {01¯12}, {1¯102} {1¯210}, {11¯20}, {¯2110} {10¯10}, {¯1100}, {0¯110}  and directions are indexed in either  or  coordinate notations, with planes having the simpler conversion (hkil) = (hkl) since i is redundant and merely −(h + k). Directions are slightly more complicated since every coordinate vector of the particular notation must be utilized. e figure also shows the four sapphire substrate orientations used in the thesis, chosen mostly because they were commonly available. Although each orientation is highlighted by a single plane, other crystallographically equivalent planes may exist due to symmetry. ese planes are listed in table A., where it should be noted that orientations like R-, A- and M-plane sapphire have the -fold symmetry of trigonal crystals rather than the -fold symmetry of hexagonal crystals. In appendix C however, a case is made for apparent -fold symmetry for some of those planes during XRD analysis.  B– Simulated TEM patterns for RHEED Prior to film growth, the substrate is rotated about its normal until a suitable RHEED diffraction pattern can be found. e best pattern should feature numerous reciprocal lattice points that can be tracked during the growth to evaluate the film quality. Using diffraction patterns simulated for electron transmission, the observed RHEED pattern can be associated with an azimuthal direction along the substrate surface and its reciprocal lattice points indexed. Compared to electron transmission, the reduced geometry sampled by RHEED leads to elongated reciprocal lattice points such as streaks and dashes. Identification of the out-of-plane lattice periodicities are therefore more difficult compared to those in the lateral direction. Nevertheless, the similarities between the matching RHEED and transmission electron microscopy (TEM) patterns are easily recognizable. e electron transmission patterns were simulated using the SingleCrystal program in the CrystalMaker soware package. Useful patterns for the four popular sapphire substrate orientations are shown in figures B. and B..    B– Simulated TEM patterns for RHEED  [0 0 1]  A-plane  [-1 1 0]  1 [0 0  ]  [-1 1  [0 1 0]  C-plane  0]  [-2 -1 0]  [-2 -1 0]  [0 1 0]  Figure B.: Simulated TEM patterns produced using an electron beam directed towards different sapphire substrate orientations along the denoted azimuths. e patterns are similar to those observed by RHEED and serve to identify lattice planes from diffraction spots.  B– Simulated TEM patterns for RHEED  [0 0 1]  M-plane  [0 1 0]  [0 0 1] [0 1 0]  [-1 0 0]  R-plane  [-1 -2 1]  [-1 -2 1]  [-1 0 0]  Figure B.: Continuation of fig. B. showing M and R-plane sapphire.  C– X-ray diffraction data X-ray diffraction (XRD) occurs when x-rays incident on a crystal are coherently scattered by successive crystal planes satisfying the Bragg condition of 2d sin θ = λ. Here d is the plane spacing, θ the incident angle and λ the x-ray wavelength. Since each crystal tends to have a unique lattice geometry (combination of Bravais lattice and unit cell parameters), XRD peaks associated with the plane spacings in that crystal would become a signature for its presence in a given sample. As an example, a scan yielding a collection of peaks may denote a polycrystalline sample (i.e. multiple orientations of the same crystal), multiple phases of a ternary material system (e.g. Y3 Al5 O12 , Y4 Al2 O9 , YAlO3 ), or a single crystal with multiple plane spacings from the same plane family (e.g. {111} = (111), (222), (333)). Single-crystal status should be verified by analyzing the structure in more than one direction. e characteristic XRD data for the Al-Ga-O and Y-Al-O phases researched for this thesis are shown in table C. onwards. Each table covers one material, listing a selection of its observable planes in Miller index notation together with properties such as plane spacing d, incident angle θ and intensity. To calculate d, an equation corresponding to the specific lattice system is used; the complete set can be found in the appendix of reference []. For example, hexagonal lattice spacings can be calculated from eqn. .. e respective θ angles were then calculated from the Bragg law above using an x-ray wavelength of . Å. e intensity of a peak is proportional to the squared-magnitude of its structure fac∑ tor F = j fj exp[2πi(hxj + kyj + lzj )], which essentially tallies the scattering contribution of each atom (with atomic scattering factor f ) in the unit cell based on their position (x, y, z) and the plane (hkl) to be reflected off. e tabulated intensities were computed by the LAZY PULVERIX program available from the Inorganic Crystal Structure Database[]. e structure factor equation suggests that reflections from certain (hkl) planes will be extinguished by destructive interference. ese planes are systematically ab-    C– X-ray diffraction data sent because the atom positions that they depend on have infinite variations via translation symmetry. Knowing the translation symmetry elements present in a crystal then allows its systematic absences to be identified. However, the full symmetry of a crystal contains translation elements outside those of the standard Bravais lattice. Denoted by  of  space groups, the full symmetry is formed by combining the symmetries of both the point group ( of ) and the Bravais lattice ( of ), which were introduced in appendix A. e combination adds two new mixed symmetry elements: screw axes (rotation + translation) and glide planes (mirror + translation)[, chap.]. Table C. shows the space groups of the materials grown for this thesis and their conditions for allowed reflections (Conditions from [, chap.] and []). As an ¯ space group where R denotes the rhombohedral example, sapphire has the R3c lattice, ¯3 the rotoinversion about the hexagonal c axis, and c the glide planes parallel also to that axis. e diffraction conditions are expressed in the hexagonal basis, and the first, −h + k + l = 3n, satisfies the rhombohedral lattice requirement for fitting three unit cells into a hexagonal unit cell[, App.]. e next two conditions are variations of the first. e fourth condition is due to the c glide planes, and the last two are special cases of them as well[, chap.]. When analyzing a sapphire film or substrate, these conditions determine the observable planes for a given orientation (or plane family). is narrows the choice of planes given in table A. such that the first observable peaks now correspond to ¯ for M-plane sapphire. R-plane and A-plane sapphire (0006) for C-plane and (3030) are not affected, but the common practice of denoting R-plane as (10¯12), one of the equivalent -fold rotations in the hexagonal lattice, has been exposed as a fallacy since that plane and its -fold-rotated variants violate the rhombohedral condition −h + k + l = 3n. Given an unknown crystal, the diffraction pattern from a powder (heavily polycrystalline) sample could shortlist or identify the space group. If the conditions of ¯ space group[, sapphire were obtained, the choice would be either the R3c or R3c chap.]. is is because XRD is not capable of distinguishing systematic absences due to finite symmetry elements such as rotations. Here 3 is a -fold rotation and ¯3 a -fold rotation plus inversion. In contrast to the R-plane (10¯12) fallacy, planes non-equivalent rotationally may appear to be symmetrically equivalent by XRD as  C– X-ray diffraction data long as the diffraction conditions are satisfied. As an example, the A-plane orienta¯ can not be distinguished from the (¯12¯10) plane rotated by ◦ about the tion (1120) hexagonal c-axis. is leads to an appearance of -fold symmetry when doing inplane orientation ϕ scans, as shown in figure .. A similar occurrence for M-plane sapphire involves the (03¯30) plane, as shown in figure .. Off-axis planes are necessary for investigating the in-plane structure of a sample, for example when tracked during a ϕ scan looking for the in-plane orientation of crystallites. An off-axis plane is deemed suitable when the interplanar angle between it and the substrate/film plane is less than its x-ray Bragg angle θ. Failing that, the plane will not be accessible by the diffractometer as the incident/reflected beam will be behind the sample. Figure . is an example showing accessible off-axis planes in reciprocal space. e interplanar angles are calculated from equations specific to the lattice system; hexagonal lattices are given by equation . while the full set is available in reference [, App.]. Some of the tables from table C. onwards list a selection of off-axis planes suitable for frequently used film/substrate orientations along with their interplanar angles.  C– X-ray diffraction data Table C.: Relevant Y-Al-O and Al-Ga-O space groups and their allowed XRD reflections. Subsequent conditions override previous ones when indices overlap. Note that the YAlO3 space group Pbnm defines lattice constants differently than the conventional form of space group  (Pnma), where (a,b,c)Pbnm → (c,a,b)Pnma. Crystal  α-Al2 O3  γ-Al2 O3  Space group, No.  Index  Conditions  R-c,   hkil hki hh(-h)l h-hl l h-h  -h+k+l=n -h+k=n l=n h+l=n, l=n l=n h=n  Fd-m,   hkl kl hhl h  h+k=n, h+l,k+l=n k+l=n, k,l=n h+l=n h=n  α-Ga2 O3  β-Ga2 O3  Y2 O3  Y4 Al2 O9  YAlO3  Y3 Al5 O12  XRD reflection conditions  same as α-Al2 O3  C/m,   hkl hl kl hk k h  h+k=n h=n k=n h+k=n k=n h=n  Ia-,   hkl kl hhl h  h+k+l=n k,l=n l=n h=n  P1 /c,   hkl hl k l  any l=n k=n l=n  Pbnm, *  hkl kl hl h k l  any k=n h+l=n h=n k=n l=n  Ia-d,   hkl kl hhl h  h+k+l=n k,l=n h+l=n h=n  C– X-ray diffraction data Table C.: Partial list of sapphire diffraction data, calculated using a hexagonal lattice with a = 4.759 Å, c = 12.991 Å h  k  l  d (Å)  θ (◦ )  Intensity                                                                                               -    -  -  -  -   -     - -     -  -  -  -     -  -  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Accessible interplanar angles (◦ ) () () () ()  . .  .  . . . .  .  . .  .  . . . . .  .  . .  .  . .  . .  . . . . . .  . . . .  .  . . . .  . . . . .  . .  C– X-ray diffraction data  Table C.: Partial list of γ-Al2 O3 diffraction data, calculated using a cubic lattice with a = 7.914 Å. h  k  l  d (Å)  θ (◦ )  Intensity                                                                                            . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  C– X-ray diffraction data Table C.: Partial list of α-Ga2 O3 diffraction data, calculated using a hexagonal lattice with a = 4.9825 Å and c = 13.433 Å. h  k  l  d (Å)  θ (◦ )  Intensity                                                                                               -    -  -  -  -   -     -  -    -  -  -  -    -   -  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Accessible interplanar angles (◦ ) () () () ()  . .  .  . . . .  .  . .  .  . . . . . . .  . . .  . .  . . .  .  . . . . . .  . . . .  .  . . . . .  . .  C– X-ray diffraction data Table C.: Partial list of β-Ga2 O3 diffraction data, calculated using a using monoclinic lattice with a = 12.2140 Å, b = 3.0371 Å, c = 5.7981 Å and β = 103.83◦ . h  k  l  d (Å)  θ (◦ )  Intensity                                                                                            -    - -  -    - -   - - -   - -   -  -  -    - - -  -  -    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Accessible interplanar angles (◦ ) (  -)  .  .  . .  .  C– X-ray diffraction data Table C.: Partial list of Y2 O3 diffraction data, calculated using a cubic lattice with a = 10.6056 Å. h  k  l  d (Å)  θ (◦ )  Intensity                                                                                                                                   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Accessible interplanar angles (◦ ) () ()  . .  . . . . . .  . .  . .  .  .  . . . . .  .  . .  . . . . . . . . . . . . .  . . .  . . . . .  C– X-ray diffraction data Table C.: Partial list of Y4 Al2 O9 diffraction data, calculated using a using monoclinic lattice with a = 7.4579 Å, b = 10.531 Å, c = 11.1498 Å and β = 108.806◦ . h  k  l  d (Å)  θ (◦ )  Intensity                                                                                           -   -    -  -    -  - -  -    -  - -  -     - -  - -  -  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  C– X-ray diffraction data Table C.: Partial list of YAlO3 diffraction data, calculated using an orthorhombic lattice with a = 5.17901 Å, b = 5.32663 Å and c = 7.36971 Å. h  k  l  d (Å)  θ (◦ )  Intensity                                                                                                                                   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Accessible interplanar angles (◦ ) () ()  .  .  . . . .  .  . . . . . . . .  . . . . . .  . . . . . .  . . . . . . . . . . . . . . .  C– X-ray diffraction data Table C.: Partial list of Y3 Al5 O12 diffraction data, calculated using a cubic lattice with a = 12.016 Å. h  k  l  d (Å)  theta (◦ )  Intensity                                                                                                                                      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Accessible interplanar angles (◦ ) ()  .  . .  .  . . . . .  .  . . . . .  D– Artwork I designed a logo to help promote my work on epitaxial growth at conferences, etc. “Vorsprung durch Epitaxie”, from the German meaning “Progress through epitaxy” was inspired by (without infringing) the logo of the German carmaker Audi and features  linked atoms in a single epitaxial layer. Below the logo is a word cloud highlighting the most frequently used terms in this thesis.  Vorsprung durch Epitaxie    

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