Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Moghaddam, Saeed
Doctor of Philosophy - PhD
University of British Columbia
Conventional forms of silicon thin-film, prepared through the use of a plasma, offer a variety of attractive electronic properties but are prone to an instability. Hydrogen atoms are believed to be the source of the instability. Accordingly, experimental collaborators at the National Research Council of Canada employed ultra-high-vacuum evaporation to prepare thin-films of silicon on optical quality fused quartz substrates, which allow for a great deal of atomic species control during the growth process. The optical properties associated with these ultra-high-vacuum prepared forms of silicon thin-film are examined. In particular, through experimental measurements of the specular reflectance spectrum at near-normal incidence and the regular transmittance spectrum at normal incidence, the spectral dependence of the optical functions is resolved for eleven silicon thin- films, deposited at different growth temperatures. Generally, the refractive index increases in response to increases in the growth temperature. The optical absorption spectral dependence is also observed to exhibit a fundamental transition in its behavior with increases in the growth temperature. These observations are related to the changes that occur in the crystalline volume fraction accompanying increases in the growth temperature. A detailed quantitative uncertainty analysis is also performed. Drawing upon X-ray diffraction results, a placement of these silicon thin-films into the overall silicon thin-film continuum is then performed. Raman spectral results are then correlated with the refractive index's spectral dependence. The Raman spectrum of a given silicon thin-film allows for a probe of the order, correlating the Raman results with the optical function results providing one with the opportunity to probe how disorder influences the optical functions. All measures of order suggest that the order increases in response to increases in the growth temperature. Finally, the device implications of these results are explored, with a focus on photovoltaic device applications. It is concluded that this particular form of silicon thin- fil is a promising material for use as the absorbing media within solar cells, offering an enhancement in the absorption which is greater than that offered by conventional plasma prepared silicon thin-films.
The optical response of siliconthin-films grown byultra-high-vacuum evaporationbySaeed MoghaddamB.Sc. Sharif University of Technology, 2014MASc. Simon Fraser University, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe College of Graduate Studies(Electrical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)May 2022© Saeed Moghaddam, 2022The following individuals certify that they have read, and recommend to theCollege of Graduate Studies for acceptance, a dissertation entitled:The optical response of silicon thin-films grown byultra-high-vacuum evaporationsubmitted by Saeed Moghaddam in partial fulfilment of the requirementsof the degree of Doctor of Philosophy.Stephen Karrer O’Leary, School of EngineeringSupervisorJonathan Holzman, School of EngineeringSupervisory Committee MemberChen Feng, School of EngineeringSupervisory Committee MemberGuangrui Xia, Materials EngineeringUniversity ExaminerJayshri Sabarinathan, Western UniversityExternal ExamineriiAbstractConventional forms of silicon thin-film, prepared through the use of aplasma, offer a variety of attractive electronic properties but are prone to aninstability. Hydrogen atoms are believed to be the source of the instability.Accordingly, experimental collaborators at the National Research Councilof Canada employed ultra-high-vacuum evaporation to prepare thin-films ofsilicon on optical quality fused quartz substrates, which allow for a great dealof atomic species control during the growth process.The optical properties associated with these ultra-high-vacuum pre-pared forms of silicon thin-film are examined. In particular, through exper-imental measurements of the specular reflectance spectrum at near-normalincidence and the regular transmittance spectrum at normal incidence, thespectral dependence of the optical functions is resolved for eleven silicon thin-films, deposited at different growth temperatures. Generally, the refractiveiiiindex increases in response to increases in the growth temperature. The opti-cal absorption spectral dependence is also observed to exhibit a fundamentaltransition in its behavior with increases in the growth temperature. Theseobservations are related to the changes that occur in the crystalline vol-ume fraction accompanying increases in the growth temperature. A detailedquantitative uncertainty analysis is also performed.Drawing upon X-ray diffraction results, a placement of these siliconthin-films into the overall silicon thin-film continuum is then performed. Ra-man spectral results are then correlated with the refractive index’s spectraldependence. The Raman spectrum of a given silicon thin-film allows for aprobe of the order, correlating the Raman results with the optical functionresults providing one with the opportunity to probe how disorder influencesthe optical functions. All measures of order suggest that the order increasesin response to increases in the growth temperature.Finally, the device implications of these results are explored, with afocus on photovoltaic device applications. It is concluded that this particularform of silicon thin-film is a promising material for use as the absorbing mediawithin solar cells, offering an enhancement in the absorption which is greaterthan that offered by conventional plasma prepared silicon thin-film.ivKeywords: silicon thin-film, ultra-high vacuum, optical functions, crystallinityand ordervLay SummaryAn examination of the optical response of silicon thin-films, preparedthrough evaporation at very high vacuum levels, is pursued. These thin-films were prepared at a variety of different growth temperatures by researchcollaborators at the National Research Council of Canada, the growth tem-perature being expected to influence the resultant material properties. Bymeasuring the amount of reflection from, and transmission through, thesethin-films of silicon, the optical response of these materials is probed andquantitatively characterized. Drawing upon some previously determined re-sults aimed at characterizing the underlying structure of these thin-films, aconnection between the structural and optical response results is sought. Theimplications of these results for solar cell device applications is examined.viPrefaceLarge parts of the text and many of the figures have been borrowed fromarticles that were published by me and co-authors. Copyright permission, foruse of the text and corresponding figures, was acquired from the publishers.The articles in question include: S. Moghaddam, F. Orapunt, M. Noe¨l, J. C. Zwinkels, J. M. Baribeau, D.J. Lockwood, and S. K. O’Leary, “Influence of the growth temperature onthe spectral dependence of the optical functions associated with thin sili-con films grown by ultra-high-vacuum evaporation on optical quality fusedquartz substrates”, Journal of Materials Science: Materials in Electronics,vol. 31, pp. 13186-13198 (2020). (Chapters 3 and 4) S. Moghaddam, S. H. Cheung, M. Noe¨l, J. C. Zwinkels, J. M. Baribeau,D. J. Lockwood, and S. K. O’Leary, “Thin-film optical function acquisi-tion from experimental measurements of the reflectance and transmittancespectra: a case study”, Journal of Materials Science: Materials in Elec-viitronics, vol. 32, pp. 17033–17060 (2021). (Chapter 3) S. Moghaddam, L. L. Tay, M. Noe¨l, J. C. Zwinkels, J. M. Baribeau, D. J.Lockwood, and S. K. O’Leary, “Crystallinity, order, the thin-film siliconcontinuum, and the spectral dependence of the refractive index in thinsilicon films grown through ultra-high-vacuum evaporation for a range ofgrowth temperatures”, Journal of Non-Crystalline Solids, vol. 559, pp.120657-120666 (2021). (Chapter 4)In addition, additional figures shown in this thesis are from other sources.Copyright permissions were also acquired from the respective copyright hold-ers. The articles in question include: O. Aydin and O. Ucar, “Design for smaller, lighter and faster ICT prod-ucts: technical expertise, infrastructures and processes”, Advances in Sci-ence Technology and Engineering Systems Journal, vol. 2, pp. 1114-1128(2017). (Chapter 2) S. K. O’Leary, “Large area electronics: The future is now!”, University ofRegina, Regina, Saskatchewan, Canada (2005). (Chapter 2) F. Orapunt, L. L. Tay, D. J. Lockwood, J. M. Baribeau, M. Noe¨l, J. C.Zwinkels, and S. K. O’Leary, “An amorphous-to-crystalline phase transi-viiition within thin silicon films grown by ultra-high-vacuum evaporation andits impact on the optical response”, Journal of Applied Physics, vol. 119,pp. 065702-1-13 (2016). (Chapter 4)More details on the contributions of other collaborators are mentioned inSection 2.12.ixTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . lviiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . lixxDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lxChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . 1Chapter 2: Background . . . . . . . . . . . . . . . . . . . . . . 82.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Conventional micro-electronics . . . . . . . . . . . . . . . . . . 102.3 Large area electronics . . . . . . . . . . . . . . . . . . . . . . . 112.4 Developments in large area electronics with a focus on thin-film silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Materials for large area electronics . . . . . . . . . . . . . . . . 172.6 Types of condensed matter . . . . . . . . . . . . . . . . . . . . 192.7 Silicon thin-film preparation . . . . . . . . . . . . . . . . . . . 232.8 Comparing the PECVD and UHV evaporation deposition pro-cesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.9 The optical response and the optical functions . . . . . . . . . 342.10 Disorder and the electronic properties of materials . . . . . . . 392.11 On the uniqueness of the UHV prepared silicon thin-film samples 422.12 Research collaboration . . . . . . . . . . . . . . . . . . . . . . 44Chapter 3: Silicon thin-film optical functions . . . . . . . . . 50xi3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2 UHV silicon thin-film preparation . . . . . . . . . . . . . . . . 563.3 Optical response measurements . . . . . . . . . . . . . . . . . 583.4 Reflectance and transmittance spectra . . . . . . . . . . . . . 653.5 Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . . . 753.6 Analytical framework . . . . . . . . . . . . . . . . . . . . . . . 803.7 Modeling the ambient and the optical quality fused quartzsubstrate optical functions . . . . . . . . . . . . . . . . . . . . 853.8 Inversion process for optical functions . . . . . . . . . . . . . . 943.9 Acquisition and confirmation of the optical functions . . . . . 993.10 Optical functions results . . . . . . . . . . . . . . . . . . . . . 1163.11 Technical achievements . . . . . . . . . . . . . . . . . . . . . . 131Chapter 4: Crystallinity, order, and the silicon thin-film con-tinuum . . . . . . . . . . . . . . . . . . . . . . . . . 1344.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1344.2 Background experimental data . . . . . . . . . . . . . . . . . . 1394.3 Silicon thin-film continuum . . . . . . . . . . . . . . . . . . . . 1504.4 A Raman spectroscopic analysis . . . . . . . . . . . . . . . . . 1544.5 Analysis of refractive index dependence . . . . . . . . . . . . . 168xii4.6 A critical comparative analysis . . . . . . . . . . . . . . . . . . 1794.7 Relationship between the optical absorption spectra and theband structure . . . . . . . . . . . . . . . . . . . . . . . . . . 1854.8 Device implications . . . . . . . . . . . . . . . . . . . . . . . . 1884.9 Technical achievements . . . . . . . . . . . . . . . . . . . . . . 197Chapter 5: Conclusions . . . . . . . . . . . . . . . . . . . . . . 200References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208Appendix A: commercial thin-film optics software analysis . . 236Appendix B: potential future work for material analysis . . . . 239xiiiList of Tables2.1 Commercially available a-Si products in 1989. This table isreproduced from Le Comber et al. [58]. Copyright permissionwas granted to the author. . . . . . . . . . . . . . . . . . . . . 163.1 Growth temperatures, film thicknesses, and crystalline volumefractions for all of the UHV prepared silicon thin-films. Thecrystalline volume fractions are determined through the use ofa Raman peak decomposition process that is further discussedby Orapunt et al. [33]. This table is the same as Table 1of Orapunt et al. [33]. Copyright permission was granted tothe author. An outline of this procedure being provided inSection 4.2. Further details on all of the silicon thin-filmsgrown through UHV are reported upon by Orapunt et al. [33]. 593.2 The Type B standard uncertainty, uCB (T ), for various directtransmittance measurements. . . . . . . . . . . . . . . . . . . 79xiv4.1 The corresponding required thicknesses based on the opticalabsorption coefficient (α) value at 1.5 eV for the various siliconthin-films considered in this analysis. © Saeed Moghaddam,2022. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1934.2 The fraction of incident light absorbed corresponding to thin-films of silicon considered in this analysis. © Saeed Moghad-dam, 2022. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196xvList of Figures2.1 The number of transistors on a representative c-Si-based micro-chip plotted as a function of the year. The data shown in thisfigure is from Figure 4 of Aydin et al. [42]. Copyright permis-sion was granted to the author. . . . . . . . . . . . . . . . . . 122.2 A thin-film deposited over top of an underlying substrate. Thescale of the thin-film has been exaggerated for the purposes ofvisualization. The online version of this figure is depicted incolor. © Saeed Moghaddam, 2022. . . . . . . . . . . . . . . . 182.3 The preparation of c-Si for conventional device applications.This figure is from O’Leary [65]. Copyright permission wasgranted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 20xvi2.4 Two-dimensional schematic representations of the different formsof condensed matter. This figure is after Nguyen et al. [71].The online version of this figure is depicted in color. . . . . . . 222.5 A graphical representation of coordination number disorder [70].The online version of this figure is depicted in color. © SaeedMoghaddam, 2022. . . . . . . . . . . . . . . . . . . . . . . . . 242.6 Schematic of a plasma-enhanced chemical vapor depositionsystem. This image is from O’Leary [65]. Copyright permis-sion was granted to the author. The online version of thisfigure is depicted in color. . . . . . . . . . . . . . . . . . . . . 272.7 A representative profile of the thin-film of silicon grown on ac-Si substrate at 335 ◦C. Copyright permission was granted tothe author. The online version of this figure is depicted in color. 332.8 Without reflection from the surface, the beam exponentiallyattenuates in intensity as it goes through the material [65].Copyright permission was granted to the author. . . . . . . . . 362.9 The optical absorption spectrum associated with a hypothet-ical crystalline semiconductor and that of a disordered coun-terpart [65]. Copyright permission was granted to the author. 37xvii2.10 The impact of disorder on the form of the distribution of elec-tronic states. This image is from O’Leary [65]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . . 413.1 The reflectance and transmittance spectra of an optical qualityfused quartz substrate. This figure was published as Figure 1of Moghaddam et al. [106]. Copyright permission was grantedto the author. The online version of this figure is depicted incolor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.2 The room-temperature reflectance spectra corresponding tothree silicon thin-films grown at 98 ◦C. The experimental datasets are depicted with the solid lines. The film thicknesses cor-responding to each sample are also depicted on this figure. Thereflectance spectrum of a reference optical quality fused quartzsubstrate, without a silicon thin-film, is also depicted. Thisfigure was published as Figure 2a of Moghaddam et al. [106].Copyright permission was granted to the author. The onlineversion of this figure is depicted in color. . . . . . . . . . . . . 68xviii3.3 The room-temperature reflectance spectra corresponding tothe silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256,335, 415, 493, and 572 ◦C. These experimental data sets are de-picted with the solid lines. The room-temperature reflectancespectra corresponding to a reference quartz substrate, withouta silicon film, is also depicted. This figure was published asFigure 2b of Moghaddam et al. [106]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 703.4 The room-temperature transmittance spectra correspondingto three silicon thin-films grown at 98 ◦C. The experimentaldata sets are depicted with the solid lines. The film thick-nesses corresponding to each sample are also depicted on thisfigure. The transmittance spectrum of a reference optical qual-ity fused quartz substrate, without a silicon thin-film, is alsodepicted. This figure was published as Figure 2c of Moghad-dam et al. [106]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color. . 72xix3.5 The room-temperature transmittance spectra correspondingto the silicon thin-films grown at 98 (303 nm), 138, 177, 217,256, 335, 415, 493, and 572 ◦C. These experimental datasets are depicted with the solid lines. The room-temperaturetransmittance spectra corresponding to a reference quartz sub-strate, without a silicon film, is also depicted. This figure waspublished as Figure 2d of Moghaddam et al. [106]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . 743.6 The spectral dependence of the room-temperature reflectanceuncertainty corresponding to the three silicon thin-films grownat 98 ◦C. A logarithmic scale is employed. The experimentaldata sets are depicted with the solid lines. The film thick-nesses corresponding to each sample are also depicted on thisfigure. This figure was published as Figure 1a of Moghaddamet al. [107]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 77xx3.7 The spectral dependence of the room-temperature reflectanceuncertainty corresponding to the silicon thin-films grown at98 (303 nm), 138, 177, 217, 256, 335, 415, 493, and 572 ◦C.A logarithmic scale is employed. This figure was published asFigure 1b of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 783.8 The spectral dependence of the room-temperature transmit-tance uncertainty corresponding to two silicon thin-films grownat 98 ◦C; the room-temperature transmittance uncertaintycorresponding to the other silicon thin-film grown at 98 ◦C,i.e., that grown to a thickness of 303 nm, was not determinedin this analysis. A logarithmic scale is employed. The exper-imental data sets are depicted with the solid lines. The filmthicknesses corresponding to each sample are also depicted onthis figure. This figure was published as Figure 1c of Moghad-dam et al. [107]. Copyright permission was granted to theauthor. The online version of this figure is in color. . . . . . . 81xxi3.9 The spectral dependence of the room-temperature transmit-tance uncertainty corresponding to the silicon thin-films grownat 98 (135 nm), 138, 177, 217, 256, 335, 415, 493, and 572 ◦C;as the transmittance uncertainty silicon corresponding to thethin-film grown at 98 ◦C to a thickness of (303 nm) was not de-termined in this analysis, the 135 nm result was used instead.A logarithmic scale is employed. This figure was published asFigure 1d of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 82xxii3.10 The room-temperature reflectance spectra associated with theuncoated optical quality fused quartz substrate. The experi-mental result is depicted with the solid line. The reflectanceobtained by substituting the nominal values of the refractiveindex, i.e., n0 = 1, n2 = nquartz = 1.49, and k2 = kquartz = 0,into the formalism of Heavens [103], is shown with the dashedline. The reflectance obtained by substituting the 3rd-orderpolynomial fit model for the optical quality fused quartz sub-strate refractive index’s spectral dependence, shown in Fig-ure 3.14, all other optical functions being held at their nominalvalues, is shown with the solid line with the solid points, thesesolid points corresponding to the experimental data points ofPalik [112]. This figure was published as Figure 2a of Moghad-dam et al. [107]. Copyright permission was granted to theauthor. The online version of this figure is in color. . . . . . . 86xxiii3.11 The room-temperature transmittance spectra associated withthe uncoated optical quality fused quartz substrate. The ex-perimental result is depicted with the solid line. The trans-mittance obtained by substituting the nominal values of therefractive index, i.e., n0 = 1, n2 = nquartz = 1.49, and k2 =kquartz = 0, into the formalism of Heavens [103], is shown withthe dashed line. The transmittance obtained by substitut-ing the 3rd-order polynomial fit model for the optical qualityfused quartz substrate refractive index’s spectral dependence,shown in Figure 3.14, all other optical functions being heldat their nominal values, is shown with the solid line with thesolid points, these solid points corresponding to the experi-mental data points of Palik [112]. This figure was publishedas Figure 2c of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 87xxiv3.12 A close-up of the room-temperature reflectance spectra as-sociated with the uncoated optical quality fused quartz sub-strate. The experimental result is depicted with the solid line.The reflectance obtained by substituting the nominal valuesof the refractive index, i.e., n0 = 1, n2 = nquartz = 1.49, andk2 = kquartz = 0, into the formalism of Heavens [103], is shownwith the dashed line. The reflectance obtained by substitut-ing the 3rd-order polynomial fit model for the optical qualityfused quartz substrate refractive index’s spectral dependence,shown in Figure 3.14, all other optical functions being heldat their nominal values, is shown with the solid line with thesolid points, these solid points corresponding to the experi-mental data points of Palik [112]. This figure was publishedas Figure 2b of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 89xxv3.13 A close-up of the room-temperature transmittance spectra as-sociated with the uncoated optical quality fused quartz sub-strate. The experimental result is depicted with the solid line.The transmittance obtained by substituting the nominal val-ues of the refractive index, i.e., n0 = 1, n2 = nquartz = 1.49,and k2 = kquartz = 0, into the formalism of Heavens [103], isshown with the dashed line. The transmittance obtained bysubstituting the 3rd-order polynomial fit model for the opti-cal quality fused quartz substrate refractive index’s spectraldependence, shown in Figure 3.14, all other optical functionsbeing held at their nominal values, is shown with the solidline with the solid points, these solid points corresponding tothe experimental data points of Palik [112]. This figure waspublished as Figure 2d of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . . 90xxvi3.14 The 3rd-order polynomial fit model for the optical qualityfused quartz substrate refractive index’s spectral dependence.The experimental data points of Palik [112] are indicated withthe solid points. The corresponding 3rd-order polynomial fitis indicated with the solid line. The nominal optical qual-ity fused quartz substrate refractive index value, i.e., n2 =nquartz = 1.49, is indicated with the dashed line. This figurewas published as Figure 2e of Moghaddam et al. [107]. Copy-right permission was granted to the author. The online versionof this figure is depicted in color. . . . . . . . . . . . . . . . . 913.15 The solution error of the refractive index as a function of theiteration number for a representative thin-film (grown at 256◦C) for the photon energy set to 1 eV . The solution erroris plotted on a logarithmic scale. The online version of thisfigure is depicted in color. . . . . . . . . . . . . . . . . . . . . 98xxvii3.16 The spectral dependence of the refractive index correspond-ing to the silicon thin-film grown at 256 ◦C. The physical so-lution, and three representative unphysical solutions, are de-picted. This figure was published as Figure 4a of Moghaddamet al. [107]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 1003.17 The spectral dependence of the extinction coefficient corre-sponding to the silicon thin-film grown at 256 ◦C. The physicalsolution, and three representative unphysical solutions, are de-picted. This figure was published as Figure 4b of Moghaddamet al. [107]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 101xxviii3.18 The room-temperature reflectance spectra corresponding tothree silicon thin-films grown at 98 ◦C. The experimental datasets are depicted with the solid lines. The film thicknessescorresponding to each sample are also depicted on this fig-ure. The reflectance spectra obtained, through a substitutionof the acquired optical functions into the formalism of Heav-ens [103], are shown with the dashed lines. A linear scale isemployed. This figure was published as Figure 5a of Moghad-dam et al. [107]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color. . 104xxix3.19 The room-temperature transmittance spectra correspondingto three silicon thin-films grown at 98 ◦C. The film thicknessescorresponding to each sample are also depicted on this figure.The experimental data sets are depicted with the solid lines.The transmittance spectra obtained, through a substitutionof the acquired optical functions into the formalism of Heav-ens [103], are shown with the dashed lines. A linear scale isemployed. This figure was published as Figure 5c of Moghad-dam et al. [107]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color. . 105xxx3.20 The room-temperature transmittance spectra correspondingto three silicon thin-films grown at 98 ◦C. The film thicknessescorresponding to each sample are also depicted on this figure.The experimental data sets are depicted with the solid lines.The transmittance spectra obtained, through a substitutionof the acquired optical functions into the formalism of Heav-ens [103], are shown with the dashed lines. A logarithmicscale is employed. This figure was published as Figure 5d ofMoghaddam et al. [107]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.106xxxi3.21 The room-temperature reflectance spectra corresponding tothe silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256,335, 415, 493, and 572 ◦C. These experimental data sets aredepicted with the solid lines. The reflectance spectra obtained,through a substitution of the acquired optical functions intothe formalism of Heavens [103], are shown with the dashedlines. A linear scale is employed. This figure was published asFigure 5b of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 107xxxii3.22 The room-temperature transmittance spectra correspondingto the silicon thin-films grown at 98 (303 nm), 138, 177, 217,256, 335, 415, 493, and 572 ◦C. These experimental data setsare depicted with the solid lines. The transmittance spec-tra obtained, through a substitution of the acquired opticalfunctions into the formalism of Heavens [103], are shown withthe dashed lines. A linear scale is employed. This figure waspublished as Figure 5e of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . . 108xxxiii3.23 The room-temperature transmittance spectra correspondingto the silicon thin-films grown at 98 (303 nm), 138, 177, 217,256, 335, 415, 493, and 572 ◦C. These experimental data setsare depicted with the solid lines. The transmittance spectraobtained, through a substitution of the acquired optical func-tions into the formalism of Heavens [103], are shown with thedashed lines. A logarithmic scale is employed. This figure waspublished as Figure 5f of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . . 109xxxiv3.24 The spectral dependence of the absolute error associated withthe room-temperature reflectance spectra corresponding to threesilicon thin-films grown at 98 ◦C, where the absolute error cor-responds to the absolute difference between the experimentalresults and those obtained through the substitution of the ac-quired optical functions into the formalism of Heavens [103].The film thicknesses corresponding to each sample are also de-picted on this figure. The data sets are depicted with the solidlines. This figure was published as Figure 6a of Moghaddamet al. [107]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 111xxxv3.25 The spectral dependence of the absolute error associated withthe room-temperature reflectance spectra corresponding to thesilicon thin-films grown at 98 (303 nm), 138, 177, 217, 256, 335,415, 493, and 572 ◦C, where the absolute error corresponds tothe absolute difference between the experimental results andthose obtained through the substitution of the acquired opticalfunctions into the formalism of Heavens [103]. The data setsare depicted with the solid lines. This figure was published asFigure 6b of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 112xxxvi3.26 The spectral dependence of the absolute error associated withthe room-temperature transmittance spectra corresponding tothree silicon thin-films grown at 98 ◦C, where the absolute er-ror corresponds to the absolute difference between the exper-imental results and those obtained through the substitutionof the acquired optical functions into the formalism of Heav-ens [103]. The film thicknesses corresponding to each sampleare also depicted on this figure. The data sets are depictedwith the solid lines. This figure was published as Figure 6c ofMoghaddam et al. [107]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.113xxxvii3.27 The spectral dependence of the absolute error associated withthe room-temperature transmittance spectra corresponding tothe silicon thin-films grown at 98 (303 nm), 138, 177, 217,256, 335, 415, 493, and 572 ◦C, where the absolute error cor-responds to the absolute difference between the experimentalresults and those obtained through the substitution of the ac-quired optical functions into the formalism of Heavens [103].The data sets are depicted with the solid lines. This figure waspublished as Figure 6d of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . . 1143.28 The spectral dependence of the refractive index, n (~ω), corre-sponding to three silicon thin-films grown at 98 ◦C. The exper-imental data sets are depicted with the solid lines. The filmthicknesses corresponding to each sample are also depicted onthis figure. This figure was published as Figure 3a of Moghad-dam et al. [106]. Copyright permission was granted to theauthor. The online version of this figure is in color. . . . . . . 117xxxviii3.29 The spectral dependence of the refractive index, n (~ω), corre-sponding to the silicon thin-films grown at 98 (303 nm), 138,177, 217, 256, 335, 415, 493, and 572 ◦C. The experimentaldata sets are depicted with the solid lines. The film thick-nesses corresponding to each sample are also depicted on thisfigure. This figure was published as Figure 3b of Moghaddamet al. [106]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . 1193.30 The spectral dependence of the extinction coefficient, k (~ω),corresponding to three silicon thin-films grown at 98 ◦C. Theexperimental data sets are depicted with the solid lines. Thefilm thicknesses corresponding to each sample are also de-picted on this figure. This figure was published as Figure 4aof Moghaddam et al. [106]. Copyright permission was grantedto the author. The online version of this figure is depicted incolor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121xxxix3.31 The spectral dependence of the extinction coefficient k (~ω),corresponding to the silicon thin-films grown at 98 (303 nm),138, 177, 217, 256, 335, 415, 493, and 572 ◦C. The experimen-tal data sets are depicted with the solid lines. This figure waspublished as Figure 4b of Moghaddam et al. [106]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . . 1223.32 The spectral dependence of the real part of the dielectric func-tion, 1 (~ω), corresponding to three silicon thin-films grownat 98 ◦C. The experimental data sets are depicted with thesolid lines. The film thicknesses corresponding to each sampleare also depicted on this figure. This figure was published asFigure 5a of Moghaddam et al. [106]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 124xl3.33 The spectral dependence of the real part of the dielectric func-tion, 1 (~ω), corresponding to silicon thin-films grown at 98(303 nm), 138, 177, 217, 256, 335, 415, 493, and 572 ◦C. Thisfigure was published as Figure 5b of Moghaddam et al. [106].Copyright permission was granted to the author. The onlineversion of this figure is depicted in color. . . . . . . . . . . . . 1253.34 The spectral dependence of the imaginary part of the dielec-tric function, 2 (~ω), corresponding to three silicon thin-filmsgrown at 98 ◦C. The experimental data sets are depicted withthe solid lines. The film thicknesses corresponding to eachsample are also depicted on this figure. This figure was pub-lished as Figure 6a of Moghaddam et al. [106]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . . 126xli3.35 The spectral dependence of the imaginary part of the dielectricfunction, 2 (~ω), corresponding to silicon thin-films grown at98 (303 nm), 138, 177, 217, 256, 335, 415, 493, and 572 ◦C.This figure was published as Figure 6b of Moghaddam et al. [106].Copyright permission was granted to the author. The onlineversion of this figure is depicted in color. . . . . . . . . . . . . 1273.36 The spectral dependence of the optical absorption coefficient,α (~ω), corresponding to three silicon thin-films grown at 98 ◦C.The experimental data sets are depicted with the solid lines.The film thicknesses corresponding to each sample are also de-picted on this figure. This figure was published as Figure 7aof Moghaddam et al. [106]. Copyright permission was grantedto the author. The online version of this figure is depicted incolor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129xlii3.37 The spectral dependence of the optical absorption coefficient,α (~ω), corresponding to silicon thin-films grown at 98 (303 nm),138, 177, 217, 256, 335, 415, 493, and 572 ◦C. This figure waspublished as Figure 7b of Moghaddam et al. [106]. Copyrightpermission was granted to the author. The online version ofthis figure is depicted in color. . . . . . . . . . . . . . . . . . 1304.1 GIXRD spectra for a number of silicon thin-films preparedthrough UHV evaporation. A variety of growth temperaturesare employed, the GIXRD spectra corresponding to the highergrowth temperatures exhibiting distinctive peaks representa-tive of the presence of silicon crystallites within the samples.This image is the same as Figure 1 of Orapunt et al. [33].Copyright permission was granted to the author. The onlineversion of this figure is depicted in color. . . . . . . . . . . . . 141xliii4.2 The 415 ◦C UHV prepared silicon thin-film sample Ramanspectrum. The solid black line represents the spectrum itself,the decomposition of this spectrum into its underlying spectralpeaks being represented with the dashed lines. A green lineis used to show the estimated instrumental background, i.e.,the baseline. This image is the same as Figure 2 of Orapuntet al. [33]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 1444.3 The 493 ◦C UHV prepared silicon thin-film sample Ramanspectrum. The solid black line represents the spectrum itself,the decomposition of this spectrum into its underlying spec-tral peaks peaks being represented with the dashed lines. Agreen line is used to show the estimated instrumental back-ground, i.e., the baseline. This image is the same as Figure 3of Orapunt et al. [33]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.145xliv4.4 The 572 ◦C UHV prepared silicon thin-film sample Ramanspectrum. The solid black line represents the spectrum itself,the decomposition of this spectrum into its underlying spec-tral peaks peaks being represented with the dashed lines. Agreen line is used to show the estimated instrumental back-ground, i.e., the baseline. This image is the same as Figure 4of Orapunt et al. [33]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.1464.5 The relationship between the crystalline volume fraction andthe growth temperature for silicon thin-film samples depositedon c-Si, SiO2/c-Si, and optical quality fused quartz substrates.This image is the same as Figure 5a of Orapunt et al. [80].Copyright permission was granted to the author. The onlineversion of this figure is depicted in color. . . . . . . . . . . . . 149xlv4.6 A stylized representation of silicon thin-film’s structural contin-uum. The various types of silicon thin-film, i.e., a-Si, nc-Si, µc-Si,and poly-crystalline Si (poly-Si), are depicted in the top-most row.The grain sizes are depicted in the next row down. The correspond-ing electron and hole mobilities are then depicted in the next tworows. In the final row, the growth temperatures needed in orderto achieve the various types of silicon thin-film, corresponding tothe UHV prepared thin-film form of silicon, are depicted, as willbe seen from the sequence of experimental results that are subse-quently presented. The last rows (in red text and black arrows)correspond to the interpretation of the GIXRD results as to wherethe UHV prepared silicon thin-films are situated on this continuumbased on the GIXRD results. This figure was published as Figure1 of Moghaddam et al. [125]. Copyright permission was granted tothe author. The online version of this figure is depicted in color. . 152xlvi4.7 The Raman spectra associated with the UHV prepared siliconthin-films for the lower growth temperatures. In this plot, theRaman spectra corresponding to the silicon thin-films grownat 98, 138, 335, and 415 ◦C are shown. A benchmark PD-a-SiRaman spectrum is also depicted, this particular Raman spec-trum being acquired from Figure 2 of Sokolov et al. [124]; itcorresponds to curve B of this plot. In order to ease with thevisualization, these Raman spectra have all been offset fromeach other. The nominal locations of the TA, LA, and TOphonon bands are clearly shown. Parts of this figure are incommon with Figure 1a of Tay et al. [32]. Copyright permis-sion was granted to the author. The online version of thisfigure is depicted in color. . . . . . . . . . . . . . . . . . . . . 155xlvii4.8 The Raman spectra associated with the UHV prepared siliconthin-films for the higher growth temperatures. In this plot, theRaman spectra corresponding to the silicon thin-films grownat 415, 493, and 572 ◦C are shown. A benchmark c-Si Ramanspectrum is also depicted, this particular Raman spectrumbeing acquired from an online source. In order to ease with thevisualization, these Raman spectra have all been offset fromeach other. The nominal locations of the TA, LA, and TOphonon bands are clearly shown. This figure was published asFigure 2b of Moghaddam et al. [125]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 156xlviii4.9 The breadth of the TO-peak, ΓTO, plotted as a function of thegrowth temperature for the UHV prepared silicon thin-films.Benchmark temperature dependencies, corresponding to setsof silicon thin-films prepared by Fortner and Lannin [128] andGupta et al. [127], are also depicted. The samples of Fortnerand Lannin [128] were prepared through the use of ion implan-tation of c-Si samples followed by annealing, the temperaturein this case being the annealing temperature. The samples ofGupta et al. [127], however, were prepared through the useof hot-wire deposition, the temperature in this case being thehot-wire deposition temperature. The rms bond angle devi-ation, ∆θ, based on a literal extension of the relationship ofBeeman et al. [129], i.e., ΓTO = 15 + 6∆θ, is shown on theright-axis of this plot. This figure was published as Figure 3of Moghaddam et al. [125]. Copyright permission was grantedto the author. The online version of this figure is depicted incolor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159xlix4.10 The location of the TO-peak, ωTO, plotted as a function ofthe growth temperature for the UHV prepared silicon thin-films. A benchmark temperature dependency, correspondingto the sets of silicon thin-films prepared by Gupta et al. [127],is also depicted; regrettably, Fortner and Lannin [128] did notevaluate ωTO for their silicon thin-films, and thus, a compar-ison, of the form shown in Figure 4.9, was not possible. Forthe purposes of the evaluations performed here, ωTO is set tothe TO-peak position associated with the amorphous phase ofthe UHV prepared silicon thin-films. This position is ascer-tained through the peak decomposition procedure outlined inOrapunt et al. [33]. This figure was published as Figure 4 ofMoghaddam et al. [125]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.165l4.11 The ITA/ITO ratio plotted as a function of the growth tem-perature for the UHV prepared silicon thin-films. BenchmarkITA/ITO temperature dependencies, corresponding to sets ofsilicon thin-films prepared by Fortner and Lannin [128] andGupta et al. [127], are also depicted. The samples of Fort-ner and Lannin [128] were prepared through the use of ionimplantation of c-Si samples followed by annealing, the tem-perature in this case being the annealing temperature. Thesamples of Gupta et al. [127], however, were prepared throughthe use of hot-wire deposition, the temperature in this case be-ing the hot-wire deposition temperature. The intensity ratiosdetermined here are computed through the use of a peak de-composition process, the details which are provided by Tay etal. [32]. This figure was published as Figure 5 of Moghaddamet al. [125]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 167li4.12 The spectral dependence of the refractive index, n (~ω), corre-sponding to the silicon thin-films grown at 98 (303 nm), 138,177, 217, 256, 335, 415, 493, and 572 ◦C. The experimen-tal data sets are depicted with the solid lines. The refractiveindex maxima, associated with each spectrum, is clearly indi-cated. This figure was published as Figure 6 of Moghaddamet al. [125]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 1704.13 The maximum value of the refractive index as a function ofthe growth temperature for the eleven UHV prepared siliconthin-films. Representative PD-a-Si and c-Si refractive indexmaxima values are also depicted. This figure was publishedas Figure 7 of Moghaddam et al. [125]. Copyright permissionwas granted to the author. The online version of this figure isdepicted in color. . . . . . . . . . . . . . . . . . . . . . . . . . 171lii4.14 The maximum refractive index value plotted as a function ofthe Raman TO-peak breadth, ΓTO, for the eleven UHV pre-pared silicon thin-films. This figure was published as Figure 8aof Moghaddam et al. [125]. Copyright permission was grantedto the author. The online version of this figure is depicted incolor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1734.15 The maximum refractive index value plotted as a function ofthe Raman TO-peak position, ωTO, for the eleven UHV pre-pared silicon thin-films. This figure was published as Figure 8bof Moghaddam et al. [125]. Copyright permission was grantedto the author. The online version of this figure is depicted incolor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1764.16 The maximum refractive index value plotted as a function ofthe ITA/ITO ratio for the eleven UHV prepared silicon thin-films. This figure was published as Figure 8c of Moghaddamet al. [125]. Copyright permission was granted to the author.The online version of this figure is depicted in color. . . . . . . 178liii4.17 The spectral dependence of the refractive index corresponding tothe silicon thin-films grown at 138, 335, 415, 493, and 572 ◦C. Theexperimental data is depicted with the solid lines. RepresentativePD-a-Si and c-Si spectral results are also depicted, these spectrabeing depicted with dashed lines. The PD-a-Si spectral dependenceis determined through a fit of the theoretical expression of Forouhiand Bloomer [118] with a representative PD-a-Si experimental dataset; the PD-a-Si data set of Klazes et al. [119] is employed, thesample preparation conditions being consistent with that typicallyemployed for the preparation of conventional PD-a-Si. The c-Sispectral dependence, however, is obtained from a variety of onlinesources and Palik [112]. This figure was published as Figure 8a ofMoghaddam et al. [106]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color. . . . 180liv4.18 The optical absorption spectrum corresponding to the siliconthin-films grown at 138, 335, 415, 493, and 572 ◦C. The exper-imental data is depicted with the solid lines. RepresentativePD-a-Si, SD-a-Si, and c-Si spectral results are also depicted,these spectra being depicted with dashed lines. The PD-a-Sispectral dependence is from Cody et al. [35] while that corre-sponding to SD-a-Si is from Freeman and Paul [6]. The opticalabsorption data corresponding to c-Si is from various onlinesources and Palik [112]. This figure was published as Figure 8bof Moghaddam et al. [106]. Copyright permission was grantedto the author. The online version of this figure is depicted incolor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1834.19 The c-Si band structure associated with the conduction andvalence bands at 300 K, along with different band gap valuesshown in eV. Copyright permission was granted to the author. 1864.20 The 572 ◦C thin-film optical absorption spectrum plotted on alogarithmic scale. The online version of this figure is depictedin color. © Saeed Moghaddam, 2022. . . . . . . . . . . . . . . 187lv4.21 The fraction of light absorbed as a function of the absorbance,i.e., αL. The online version of this figure is depicted in color.© Saeed Moghaddam, 2022. . . . . . . . . . . . . . . . . . . . 1894.22 The air-mass (AM) 1.5G solar spectrum. Copyright permis-sion was granted to the author. The online version of thisfigure is depicted in color. . . . . . . . . . . . . . . . . . . . . 1914.23 The fraction of incident light absorbed plotted as a functionof the growth temperature. The online version of this figureis depicted in color. © Saeed Moghaddam, 2022. . . . . . . . 194lviList of Acronymsa-Se amorphous seleniuma-Si amorphous siliconc-Ge crystalline germaniumc-Si crystalline siliconEFM electrostatic force microscopyGIXRD grazing incidence X-ray diffractionO-H hydroxide ionIR infra-redLA longitudinal acousticMBE molecular beam epitaxync-Si nano-crystalline siliconSiO2/c-Si oxidized crystalline siliconPE Perkin ElmerPD-a-Si plasma-deposited amorphous siliconlviiRMS root mean squareSEM scanning electron microscopeTEM transmission electron microscopyTA transverse acousticTO transverse opticalUHV ultra-high-vacuumUV ultra-violetlviiiAcknowledgementsI would like to thank myself for not giving up despite all the obstacles. Duringmy PhD years, I experienced lots of difficulties which brought me down manytimes, but I always kept going. I will always keep fighting and going forwardas long as I can breath.lixDedicationTo all the people who do not give up until they succeedlxChapter 1IntroductionFueled by their considerable potential for electron device applications,interest in thin-film forms of silicon remains intense [1, 2]. Amorphous silicon(a-Si), a type of silicon thin-film lacking any residue of crystallinity in its“lattice” structure, was the first member of the silicon thin-film family to bethe subject of a prolonged and intense research and development effort [3,4, 5, 6, 7, 8, 9, 10, 11, 12]. During the pioneering days of a-Si, a varietyof different deposition methods were employed for the preparation of thismaterial, including sputtering [5, 8] and evaporation [13, 14, 15, 16, 17].Unfortunately, the resultant materials, being in possession of dangling bondconcentrations of around 1020 cm−3 [18], were found to be of only limitedelectronic utility. Indeed, it was only when the plasma enhanced chemicalvapor deposition (PECVD) technique was introduced that an electronically1useful form of a-Si could be produced. Since then, a-Si has become a stapleof the large area electronics community [10].Contemporary device-quality forms of a-Si are most commonly preparedthrough a plasma decomposition of silane gas, other gases being added tothe plasma as needed [8]. In such a plasma decomposition process, radicalsare generated within the plasma itself. These radicals will then diffuse fromtheir point of genesis, ultimately reacting with the growth surface in orderto produce a thin-film form of a-Si, which will henceforth be referred to asplasma-deposited a-Si (PD-a-Si) [19]. In its purest form, PD-a-Si possessesjust silicon and hydrogen atoms, although in actual device structures, morecomplex forms of this material, hosting a broader diversity of atomic species,are often found, additional atomic species sometimes being deliberately in-troduced for doping and/or alloying purposes. From a device applicationsperspective, the best performing forms of PD-a-Si are found to exhibit hy-drogen contents of around 10 atomic (at.) %.Research has demonstrated that the hydrogen atoms that are residentwithin PD-a-Si passivate the dangling bonds that are present within thismaterial, this being the primary factor responsible for the favorable elec-tronic characteristics exhibited by this material [5, 20]. Hydrogen atoms are2also believed to be responsible for alleviating some of the stress that existswithin the network of silicon atoms that constitutes PD-a-Si [21]. Unfortu-nately, hydrogen is also thought to be responsible for the deterioration in theelectronic properties of PD-a-Si when this material is exposed to light [22].Accordingly, there has been a considerable amount of effort invested into thefabrication of alternate forms of silicon thin-film, which retain the favorableelectronic characteristics of PD-a-Si without this troublesome instability.With the realization that PD-a-Si’s hydrogen atoms are available in muchgreater concentrations than the dangling bond quantities found within un-hydrogenated forms of a-Si, came speculation that perhaps other types ofsilicon thin-film might exist with sufficient hydrogen in order to achieve com-plete dangling bond passivation without PD-a-Si’s instability. In responseto this challenge, a variety of alternate thin-film forms of silicon have beendevised, including that produced through use of hot-wire assisted chemicalvapor deposition [23] and micro-crystalline and nano-crystalline forms of thismaterial [24]. The search for alternative forms of silicon thin-film remains atopic of considerable interest to those within the silicon thin-film community,and this seems likely to remain to be the case for many years to come.Noting that depositions performed under ultra-high-vacuum (UHV) con-3ditions engender significant atomic species control during growth, came thethought that perhaps an UHV preparation of silicon thin-film would offer thecommunity with an improved form of silicon thin-film. Intrigued by this pos-sibility, researchers at the National Research Council of Canada commisionedan UHV molecular beam epitaxy (MBE) chamber to prepare a sequence ofthin-films of silicon and silicon thin-film based superlattices. A variety ofsubstrates, including crystalline silicon (c-Si), oxidized c-Si (SiO2/c-Si), andoptical quality fused quartz, were employed upon which the thin-films of sil-icon were grown. Investigations into the properties of these silicon thin-filmsand superlattices, which have been extensively chronicled within the scien-tific literature [25], have revealed that the silicon thin-film form producedthrough such a growth process offers a myriad of properties that point to itsconsiderable promise, including it having a mass density very close to thatof c-Si and that its hydrogen concentration is significantly lower than thatpossessed by PD-a-Si [26, 27, 28, 29, 30, 31, 32, 33]. This suggests that, forsome applications at least, this particular form of silicon thin-film might beable to perform better than more conventional forms of this material.For many of its device applications, the performance of silicon thin-filmmay be directly tied to its optical response. Accordingly, the spectral de-4pendence of the optical functions associated with this material have been thefocus of considerable study over the years, this spectral dependence providinga means whereby this optical response may be quantitatively characterized.Prior to this work, the majority of the work aimed at exploring the opticalresponse of silicon thin-film has been focused on the spectral dependence ofthe optical absorption coefficient; see, for example, Sterenborg et al. [34].It is noted, however, that the optical absorption coefficient is merely oneoptical function, and that the spectral dependence of the other optical func-tions, which also play an important role in determining the performanceof silicon thin-film in many of its envisaged device applications, remainsunder-explored. Accordingly, in order for the true potential of this UHV pre-pared form of silicon thin-film to be identified, in this thesis, drawing upona reservoir of available near-normal reflectance and normal transmittanceexperimental data, acquired by experimental collaborators at the NationalResearch Council of Canada, the spectral dependence of a number of keyoptical functions associated with a sequence of UHV prepared thin-films ofsilicon, prepared at a variety of different growth temperatures, will be de-termined, a transition in the nature of the films, from low-temperature tohigh-temperature, being expected. Resolving how the spectral dependence5of these optical functions is related to the underlying micro-structure of thesethin-films of silicon is another goal of this thesis.At the outset, it is noted that within the scope of this body of work,abundant opportunities for the acquisition of new knowledge are available.First and foremost, an evaluation of the spectral dependence of the opticalfunctions associated with these UHV prepared thin-films of silicon, with aview to assessing the suitability of this particular form of silicon thin-filmfor device applications, is a key goal of this analysis. Second, as will be pre-sented within the body of this thesis, this particular form of silicon thin-filmtraverses the silicon thin-film continuum, i.e. the transition between a-Siand c-Si, in a unique manner, thereby allowing for insights to be gleanedconcerning how disorder shapes the optical response of silicon thin-film thatare not available to many of the other forms of silicon thin-film. Finally, thedetermination of the optical functions from measurements of the reflectanceand transmittance spectra, which is the experimental data that is availablefrom the National Research Council of Canada experimental collaborators,represents a problem of general interest to those within the thin-film commu-nity, relevant beyond the confines of the silicon thin-film community itself.Any improvements that can be offered to the manner in which these optical6functions may be acquired from reflectance and transmittance measurementshas the potential to benefit this broader thin-film community.This thesis is organized in the following manner. In Chapter 2, somebackground material related to this thesis is presented. Then, in Chapter 3,a detailed optical function analysis is laid out. How the spectral dependenceof the optical functions is related to the underlying micro-structure is thenprobed in Chapter 4, the potential of this material for device applicationsalso being considered. Finally, the conclusions of this analysis are drawn inChapter 5, some recommendations for further study being offered.7Chapter 2Background2.1 MotivationSilicon thin-film in its various forms, i.e., the traditional a-Si and more re-cently developed variants of this material, continues to fascinate researchers.At the present time, the a-Si type that is ubiquitous in commercially availablea-Si-based electron devices is that produced through silane gas’s decompo-sition in a plasma, the material produced as a consequence of this processbeing referred to as PD-a-Si [8]. PD-a-Si, a potpourri of silicon, hydrogen,and other atoms, has long been the focus of investigation [3, 6, 35, 36, 37].With other types of silicon in thin-film form now also drawing the attentionof researchers [38, 39], questions delving into silicon thin-film’s fundamentalsseem destined to continue to challenge the silicon thin-film community for8quite some time to come.In this chapter, some of the background material, needed to understandthe results presented within the main body of this thesis, are discussed. InSection 2.2, the manner in which progress has occurred within the field ofconventional micro-electronics is described, the niche field of large area elec-tronics being introduced in Section 2.3. A brief survey if developments thathave occurred in large area electronics, with a focus on thin-film silicon, ispresented in Section 2.4. The materials employed for large area electronicsare then featured in Section 2.5, where these materials fit within the var-ious categories of condensed matter being characterized in Section 2.6. InSection 2.7, the focus shifts to a discussion on the means through which sili-con thin-film may be prepared, some of the newer forms of silicon thin-filmalso being discussed. A contrast between the conventional approach to thedeposition of thin-film silicon and that employed for the fabrication of thesamples examined in this thesis is then presented in Section 2.8. A quan-titative approach to characterizing the optical response of silicon thin-filmis then introduced in Section 2.9. The role that disorder plays in shapingthe electronic properties of materials is then elucidated in Section 2.10. Theuniqueness of the thin-films of silicon prepared through the UHV fabrication9approach, used by the National Research Council of Canada experimentalcollaborators, is then presented in Section 2.11. Finally, the overall organi-zation of the research collaboration that was pursued during the course ofthis work, involving the National Research Council of Canada experimentalcollaborators, is discussed in Section 2.12.2.2 Conventional micro-electronicsWith the genesis of the transistor in 1947, interest in the properties ofsemiconductor materials experienced a dramatic increase. While the initialwork on transistors focused on the crystalline form of germanium (c-Ge) [40],c-Si quickly displaced c-Ge as the primary electronic material of choice withinthe conventional micro-electronics industry, and it has served as the dominantsemiconductor material for over half a century now. Nowadays, transistorsfabricated out of c-Si are widely used for a variety of common micro-electroniccircuit applications, including switching, amplification, and processing. Inlight of the current pre-eminence of c-Si in the electronics world, it seemslikely that c-Si will remain the dominant electronic material upon whichfurther advances in micro-electronics will primarily be based for quite some10time to come.Progress in conventional c-Si-based micro-electronics is typically achievedby making the constituent electron devices, i.e., the transistors, smaller,faster, cheaper, and more reliable. This progress is often characterized interms of a prophecy made by Gordon E. Moore, a key pioneer in conven-tional micro-electronics, who in 1975 noted that, for the previous decade atleast, the number of transistors on a chip had doubled every two years [41].Moore’s law, as this prophecy is now referred to as, has held for the last 55years now, and micro-electronic industry insiders suggest that it will con-tinue to be valid for at least another decade. The number of transistorson a representative c-Si chip, plotted as a function of year, is depicted inFigure 2.1.2.3 Large area electronicsWhile progress in conventional micro-electronics focuses on reduced de-vice dimensions, there are electronic devices that require size in order toeffectively serve their intended application [43]. Scanners and displays, forexample, which serve as the interface between the electronic and physical11Figure 2.1: The number of transistors on a representative c-Si-based micro-chip plotted as a function of the year. The data shown in this figure is fromFigure 4 of Aydin et al. [42]. Copyright permission was granted to the author.12worlds, are two examples of such devices [44]. Solar cells and digital flatpanel X-ray image detectors are two other device applications that requiresize in order to be useful [45]. For this class of device, rather than focusingon sub-micron device features, as in conventional micro-electronics, the focusinstead is on producing devices uniformly over areas of the order of a squaremeter [46]. Such devices are typically referred to as large area electronicdevices.The approach to materials preparation for large area electronics is quitedistinct from that employed for conventional micro-electronics. Indeed, whilethe c-Si used for conventional micro-electronics is prepared from a melt, ma-terials for large area electronics are prepared in the form of thin-films grownon an underlying substrate from the vapor phase [47]. PD-a-Si is one of thedominant materials found in large area electronic device applications. Otherthin-film semiconductor materials, such as amorphous selenium (a-Se), havealso been used in large area electronic device applications [48].Displays are currently the primary application for PD-a-Si. At the presentmoment, these displays are being used in a variety of consumer and industrialapplications, each such application having its own requirements [49]. Thedisplay technologies deployed are customized to the specific requirements that13are pertinent. Variations are found amongst displays with respect to theircolor range, brightness, speed, and other such technical specifications [50, 51,52].PD-a-Si is also still finding applications as a material for photovoltaicdevices, i.e., solar cells. Unfortunately, the prospects for PD-a-Si in the solararena have diminished recently, owing to its lower efficiency when contrastedwith the case of c-Si [53]. Nevertheless, PD-a-Si is expected to make a come-back, either as a solar material in its own right or as a material matchedwith another photovoltaic material. Further discussion about this matter ispresented in the literature [54, 55].2.4 Developments in large area electronics witha focus on thin-film siliconDevelopments within the field of large area electronics have actually oc-curred over more than half a century now. Early applications of thin-filmsemiconductors, for example, include the use of a-Se in early xerographiccopying machines, these being introduced to the market in the 1950s [56].Another significant milestone in the field of large area electronics was the de-14velopment of the aforementioned PD-a-Si-based solar cell; the PD-a-Si-basedphotovoltaic solar cell was introduced to the market in the early 1970s [57].Amorphous forms of thin-film silicon were deployed in consumer electronicproducts by the early 1970s, the solar cells fabricated out of these forms ofthin-film silicon being used to power calculators, watches, and the like. Later,as the light responsive character of this particular form of thin-film siliconcame to recognized, a broader range of applications for this material wasconsidered. In particular, thin-film silicon based products building upon thephoto-responsive character of this material were developed. Later, notingthat thin-film transistors may be easily fabricated out of this material, thethin-film silicon based transistor was developed, this technology underlyingthe performance of many of the earlier generations of large area electronicbased displays. Indeed, the applications of thin-film silicon were quite diverseby the later part of the 1980s, as is seen in Table 2.1.At present, thin-film semiconductors, such as PD-a-Si and a-Se, are beingused in a variety of contemporary device applications [59]. In addition to thepreviously mentioned uses of PD-a-Si, at present, large area electronic mate-rials, such as PD-a-Si, are being used in opto-electronic devices, photorecep-tors, sensors, light emitting diodes, digital X-ray imagers, and scanners [60].15Device ProductPhotovoltaic cell Calculators, watches, battery chargersPhotoreceptor Electrophotography, LED printersPhotoconductorsimage sensorsposition sensitive detectorsColour sensors, light sensorscontact-type image sensorselectronic white boardsspatial light modulatorsHeat control layer Heat reflecting float glassThin-film field-effect transistorsDisplays, televisionslogic circuits for image sensorsHigh-voltage thin-film transistors PrintersTable 2.1: Commercially available a-Si products in 1989. This table is re-produced from Le Comber et al. [58]. Copyright permission was granted tothe author.16New applications for thin-film semiconductors in large area electronic devicesare being devised and commercialized on a yearly basis and this seems likelyto continue apace well into the foreseeable future. Indeed, Reynalds et al. [61]identifies three new potential applications for silicon thin-film , including inmonolithic perovskite/c-Si tandem solar cells, “lab-on-a-chip” systems, andin non-volatile thin-film transistor memory.2.5 Materials for large area electronicsAs has already been mentioned, the materials employed in large areaelectronics are prepared in the form of a thin-film deposited over top of anunderlying substrate, as is shown in Figure 2.2. Early studies of semiconduc-tor thin-films arose directly out of the pioneering studies that were performedon glasses in the 1930s, 1940s, and 1950s [62]. These pioneering studies cen-tered on chalcogenide semiconductors, such as selenium, a-Se based copyingmachines being introduced to the market in the 1950s, as has already beenmentioned [63]. Later, as interest in semiconductor thin-films diversified,silicon thin-film became a focus of attention by the late 1960s [64].The preparation of c-Si for conventional device applications involves the17Figure 2.2: A thin-film deposited over top of an underlying substrate. Thescale of the thin-film has been exaggerated for the purposes of visualization.The online version of this figure is depicted in color. © Saeed Moghaddam,2022.18drawing of a crystal from molten silica; see Figure 2.3. For the materialsused for large area electron device applications, however, thin-films are pre-pared from the vapor phase. Vapor phase deposition, while precluding thepreparation of bulk samples, does allow for the preparation of thin-films uni-formly over large areas, i.e., of the order of a square-meter [66]. This mannerof preparation has served the large area electronics field since its inception.The primary source material for these depositions is silane gas, additionalgases being added to the mix for doping and alloying purposes.2.6 Types of condensed matterThere are three basic forms of condensed matter: (1) crystalline, (2) poly-crystalline, and (3) amorphous. In a crystalline solid, the atoms are dis-tributed in a periodic and ordered fashion. Such a solid is said to possesslong-range order, the environment around any given atom being exactly thesame as every other atom across the entire volume, which ideally extends outinfinitely [67]. In a poly-crystalline solid, however, this long-range order isdisrupted. Instead, crystallites are distributed throughout the material, eachcrystallite being separated from its neighbouring crystallites by grain bound-19Figure 2.3: The preparation of c-Si for conventional device applications. Thisfigure is from O’Leary [65]. Copyright permission was granted to the author.The online version of this figure is depicted in color.20aries. Finally, in an amorphous solid, all residue of crystallinity is absentfrom its “lattice” structure, every atom having a slightly different environ-ment from every other atom. Two-dimensional representations of the threedifferent forms of condensed matter are schematically represented in Fig-ure 2.4. The thin-film semiconductors that are used for large area electronicdevice applications are either poly-crystalline or amorphous in nature [68].Focusing on material forms of condensed matter that are purely comprisedof silicon atoms, c-Si is a tetrahedrally bonded material, each silicon atomwithin this material being bonded to four other silicon atoms, the bondingangle between neighbouring Si-Si bonds being cos−1(−13) ≈ 109.5◦. In itsideal form, the environment about any individual silicon atom is exactly thesame as any other silicon atom, this environment being replicated throughoutthe entire volume of the crystal. This is why c-Si is said to possess long-rangeorder. At the present moment, the largest industrially produced c-Si wafersare 45 cm in diameter, newer and even larger c-Si wafer dimensions beingunder development at the present moment [69].In a-Si, however, the distribution of atoms does not exhibit order over thelong-range. This lack of order manifests itself in a multitude of different ways.While most silicon atoms are bonded to four other silicon atoms, some silicon21Figure 2.4: Two-dimensional schematic representations of the different formsof condensed matter. This figure is after Nguyen et al. [71]. The onlineversion of this figure is depicted in color.22atoms are bonded to three, two, or even one silicon atom; this coordinationnumber disorder is pictorially depicted in Figure 2.5. There are also slightvariations in the Si-Si bond angles and Si-Si bond lengths, these often beinga function of the means through which the a-Si was prepared.As the environment around any particular silicon atom is, on average atleast, similar to that of any other silicon atom, while a-Si may be viewedas having no long-range order, it is found to have a short-range order thatis similar to that of c-Si. As the properties of condensed matter are chieflydetermined by the short-range bonding that occurs, it should come as nosurprise that a-Si shares many properties with c-Si [72].2.7 Silicon thin-film preparationA number of approaches to silicon thin-film deposition have been em-ployed in the past. Traditional approaches for the preparation of siliconthin-film included sputtering and thermal evaporation [73]. Unfortunately,the materials which resulted from such a deposition approach were foundto be of limited electronic utility, primarily owing to their high defect con-centration levels [74], this impeding the ability to dope and draw upon the23Figure 2.5: A graphical representation of coordination number disorder [70].The online version of this figure is depicted in color. © Saeed Moghaddam,2022.24photoconductive potential of these materials. What was needed instead wasa silicon-based thin-film material in which these defects were effectively pas-sivated.In the late 1960s, Chittick et al. [75] employed the plasma decomposi-tion of silane gas in order to prepare an alternate form of silicon thin-film.Experiments performed by Chittick et al. [75] have demonstrated the utilityand practicality of this particular form of silicon thin-film, i.e., they showedthat the defect concentrations were low enough for actual electron deviceapplications, that doping is possible, and that the material exhibits an ap-propriate photo-conductive response. Unfortunately, the work of Chittick etal. [75] remained unrecognized for many years, and it was really only whenLeComber and Spear [58] adopted the approach to deposition suggested byChittick et al. [75] that the true potential of this particular form of siliconthin-film was widely acknowledged by those within the field. While it wasnot recognized at the time by Le Comber and Spear, the ability of hydrogenatoms to passivate the dangling bonds within this particular form of siliconthin-film is the primary reason for this improvement in its electronic proper-ties. For the purposes of this thesis, this particular form of silicon thin-filmis denoted as PD-a-Si.25The deposition chamber within which the preparation of conventionalPD-a-Si may be performed is typically as configured as shown in Figure 2.6.Following the achievement of base pressure, a number of gases are introducedinto the deposition chamber. The primary gas introduced into the deposi-tion chamber is silane, other gases, such as phosphine or diborane, beingintroduced for doping purposes; additional gases may also be added for thepurposes of alloying [76]. When the plasma is excited, many of the atomicspecies within the plasma decompose into a variety of radical species, theseradicals subsequently landing onto a heated substrate [77]. Eventually, athin-film of silicon, growing on this substrate, arises from such a process.Two thin-film forms of silicon, which provide alternatives to conventionalPD-a-Si, are micro-crystalline silicon (µc-Si) and nano-crystalline silicon (nc-Si). These forms of silicon thin-film are essentially comprised of small crys-tallites embedded within an a-Si tissue [78]. The size of the crystallitesdetermines whether or not the form of silicon thin-film is referred to as µc-Si or nc-Si. These forms of silicon thin-film may be prepared through theplasma decomposition of silane gas, as with PD-a-Si [79]. For the prepara-tion of µc-Si and nc-Si, however, hydrogen gas is also introduced into thedeposition chamber, i.e., hydrogen gas dilutes the silane, this dilution lead-26Figure 2.6: Schematic of a plasma-enhanced chemical vapor deposition sys-tem. This image is from O’Leary [65]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.27ing to the presence of the crystallites. The dimensions of the crystallitesdetermines whether or not the material is classified as µc-Si or nc-Si [80].1Further details on this matter are discussed in the scientific literature [81].2.8 Comparing the PECVD and UHV evap-oration deposition processesAs was mentioned earlier, research on thin-film semiconductors aroseout of the body of work that focused on the material properties of glasses.The initial focus of thin-film semiconductor research focused on the chalco-genide semiconductors, such as a-Se. Thin-film silicon was a latecomer tothis area of research, with early thin-films of silicon being prepared eitherthrough sputtering or thermal evaporation. Unfortunately, these materials,while of scientific interest, were characterized by an extremely high defectconcentration, rendering these thin-film forms of silicon useless for electron1Many authors do not discern between µc-Si and nc-Si and simply use these termsinterchangeably. As a consequence, in the absence of experimental evidence that allowsfor the determination of the crystallite sizes, the choice between the use of the termsµc-Si and nc-Si is often more determined by the current fashion as opposed to substance;Orapunt et al. [80] in fact presented this rebranding “as an indisputable example of fashionover substance in the modern practice of science”.28device applications.In the late 1960s, Chittick et al. [75] employed PECVD in order to pre-pare a novel form of thin-film silicon; initially, this technique to depositionwas commonly referred to as glow-discharge deposition, PECVD being morea more common term in modern parlance. In this approach to deposition,SiH4 gas was introduced into a deposition chamber, the gas molecules be-ing dissociated in the electrical plasma that is ignited within the depositionchamber. The thin-films that arose subsequently grew on a heated substratewithin Chittick et al.’s deposition chamber. While the exact details anddesign of modern PECVD deposition chambers have progressed beyond theexact form employed by Chittick et al., the basic principles underlying thisapproach to deposition have remained the same. PECVD deposited forms ofthin-film silicon remain the most common form of thin-film silicon employedin modern device applications.In the absence of a plasma, SiH4 gas naturally will decompose at tem-peratures above 450 ◦C. With plasma excitation, the decomposition of SiH4gas can occur at much lower temperatures, thereby allowing silicon thin-filmto be deposited onto a broader range of substrates. The PECVD deposi-tion chamber depicted in Figure 2.6, is representative of the rf diode type29of substrate, this being the type PECVD system employed commonly today,Chittick et al.’s [75] chamber being slightly different. Most PECVD depo-sitions for the fabrication of silicon thin-film use base pressures of the orderof 10−6 Torr, the pressure during deposition typically ranging between 0.1and 1 Torr; the properties of the resultant thin-films of silicon are not thatsensitive to the exact deposition pressure. A high concentration of impuritiesare found within the resultant thin-film of silicon, hydrogen being found atabout 10 atomic %, trace levels of nitrogen and carbon are also being found.Molecular beam epitaxy found its genesis in the work of Gu¨nther [82] andthe subsequent advances of Cho et al. [83], Panish [84], and Smith et al. [85].This approach to deposition requires the use of a vacuum, the deposition ratetypically being limited to less than 1 nm/s. Evaporation of a heated solidmaterial under this vacuum is the fundamental mechanism underlying growthin molecular beam epitaxy. For the purposes of the growths pursued of thin-film silicon on optical quality fused quartz substrates, an UHV environmentwas used, the base pressure being set to 4 × 10−11 Torr for all of thesedepositions, the pressures experienced within the deposition chamber itselfbeing upper bound by 10−9 Torr throughout the deposition process; UHVis technically defined to be any pressure less than 7.5 × 10−10 Torr, so this30condition applies for most of the growth process. The films grown on opticalquality fused quartz substrate for the purposes of this analysis were all grownat a fixed rate of 0.1 nm/s. Strictly speaking, as the thin-films themselves arenot epitaxial, this requiring the crystal structure of the underlying substrateto be continued into the thin-film itself, one cannot claim that these thin-filmswere prepared through molecular beam, i.e., there is no epitaxy. Accordingly,for the purposes of this thesis at least, the thin-films of silicon are describedas being prepared through the use of UHV evaporation using a molecularbeam epitaxy system.The depositions performed at the National Research Council of Canadawere all performed using a single solid source of ultra-pure silicon. This sourcewas heated in an effusion cell and as a result, the source started to sublime,i.e., evaporate. The silicon atoms in the neighborhood of the heated sourceconstitute a “beam” of molecules, this beam projecting from the source ontoa heated substrate where they eventually condense; this picture of a “beam”of molecules underpins the etymological origins of the term of “molecularbeam epitaxy”. The mean-free path of the gas molecules, i.e., a “beam”,within an UHV environment, is lower bounded by as much as 40 km, i.e.,much larger than the dimensions of the deposition chamber itself. So, unlike31the case of PECVD, collisions between the atoms in such a “beam” are quiterare. Accordingly, this process of deposition is referred to as an example ofa physical vapor deposition process.In spite of the use of UHV evaporation and ultra-pure silicon solid source,impurities still find themselves into the thin-films of silicon. Evidence of thismay be seen from the secondary ion mass spectroscopy results performed onthe thin-films of silicon prepared by the National Research Council of Canadaresearchers. Unfortunately, owing to the delicacy of the samples grown onthe optical quality fused quartz substrates, secondary ion mass spectroscopymeasurements could not be made on these samples. Secondary ion massspectroscopy of thin-film silicon grown on c-Si substrates were able to beacquired, however, a representative impurity profile of such a thin-film ofsilicon grown at 335 ◦C being depicted in Figure 2.7 . It is clearly seen that,in addition to the silicon atoms, a considerable number of hydrogen, carbon,and oxygen atoms are found within the thin-films. The expectation wouldbe that a similar profile would be found for the thin-films of silicon grown onthe optical quality fused quartz substrates.A final point should be made. The thin-film silicon deposition rate typi-cally encountered using PECVD is much higher than that could be obtained32Figure 2.7: A representative profile of the thin-film of silicon grown on a c-Sisubstrate at 335 ◦C. Copyright permission was granted to the author. Theonline version of this figure is depicted in color.33through the use of UHV evaporation. Moreover, PECVD chambers can bearbitrarily scaled to whatever size is required. Molecular beam epitaxy depo-sition chambers, however, are quite small by comparison, and must remain soin order to keep the vacuum levels as required. Accordingly, while molecularbeam epitaxy is excellent at demonstrating possibilities, large scale produc-tion is expensive and difficult. The goal of this study was to point to apossible alternate form of thin-film silicon. How this form of thin-film siliconmay be mass produced, an important consideration for device manufacturingconsiderations, is beyond the scope of this particular thesis.2.9 The optical response and the optical func-tionsThe optical properties of a material play a role in shaping the perfor-mance of the devices that are fabricated from said material. For the casein which light is incident upon a material with an optical absorption coeffi-cient, α, the intensity of the light as it projects through the material may be34described asI (z) = I0 exp (−αz), (2.1)where z denotes the depth into the material, i.e., z = 0 corresponds to thesurface, I0 representing the intensity of the beam in the material at thesurface. The optical absorption coefficient, α, characterizes how rapidly thisattenuation occurs, as shown in Figure 2.8.A spectral variation in the optical absorption coefficient is related to theunderlying physics. Accordingly, insights into this underlying physics maybe gleaned from understanding this spectral dependence. Indeed, withoutdisorder, the optical absorption coefficient will go to zero at the energy gap.With the introduction of disorder, however, the optical absorption coefficientwill extend into the otherwise energy gap region. This softening in the sharp-ness of the optical absorption edge in response to the presence of disorder isa reflection of the re-distribution of electronic states that accompanies suchdisorder, the softening increasing as the amount of disorder is increased.In Figure 2.9, a hypothetical defect-free crystalline semiconductor’s op-tical absorption spectrum is directly contrasted with that of a disordered35Figure 2.8: Without reflection from the surface, the beam exponentiallyattenuates in intensity as it goes through the material [65]. Copyright per-mission was granted to the author.36Figure 2.9: The optical absorption spectrum associated with a hypotheticalcrystalline semiconductor and that of a disordered counterpart [65]. Copy-right permission was granted to the author.37counterpart. For the case of the defect-free crystalline semiconductor, theoptical absorption coefficient terminates at the energy gap. For the disor-dered counterpart, however, three distinct spectral regions are observed. Wellabove the energy gap, i.e., α > 104 cm−1 (region C), an algebraic dependenceof the optical absorption spectrum on the photon energy is observed. Wellbelow the energy gap, i.e., α < 1 cm−1 (region A), a broad exponentialfunction dependence is observed. Finally, between these two extremes, i.e.,1 cm−1 < α < 104 cm−1 (region B), an exponential functional dependence isobserved. Much of the physics of disordered semiconductors is observed fromthis mid-absorption region, and thus, it has been the focus of a considerableamount of attention over the years.The optical absorption coefficient, α, is merely one of many optical func-tions that can be introduced for the quantitative characterization of the op-tical response of a given material. The refractive index and the extinctioncoefficient, n and k, for example, are two other optical functions that may beused to characterize the optical response of materials. The real and imagi-nary parts of the dielectric function, 1 and 2, are two other optical functionsthat may be introduced in order to characterize the optical response of mate-rials. Of course, as will be seen in Chapter 3, many of these optical functions38are in fact related to one another.2.10 Disorder and the electronic propertiesof materialsIn a crystalline semiconductor, the electronic properties may be com-puted through the introduction of Bloch functions modulated by plane waves [86].In a disordered semiconductor, however, the disorder that is present playsa fundamental role in shaping the corresponding electronic properties. As aconsequence, a new approach to determining the electronic properties of thisclass of material must be sought. The study of disorder and its influence onthe properties exhibited by materials represents a broad field of research thathas attracted much attention over the years. This will undoubtedly remainto be the case for many years to come.There are two primary means through which disorder can play a role inshaping the electronic properties:1. the impact on the distribution of electronic states2. the impact on the matrix elements39In terms of the influence of disorder on the distribution of electronicstates, the impact is dramatic. In a disorderless semiconductor, the dis-tribution of electronic states terminates abruptly at the band edges. In adisordered semiconductor, however, the distribution of electronic states en-croaches into the otherwise empty band-gap regions. This arises from theaforementioned re-distribution of electronic states accompanying the pres-ence of disorder. This may be readily demonstrated in Figure 2.10, in whichthe impact of disorder on the form of the distribution of electronic states isvisually represented. Further discussion on this matter is presented in thescientific literature [87].In terms of the quantum mechanical matrix elements, these defining theprobability of transitions between the various electronic states, disorder tendsto soften the spectral dependence of these matrix elements. While the matrixelements associated with a crystalline semiconductor are shaped, in largemeasure, by the ~k-conservation rules, in a disordered semiconductor, these~k-conservation rules are relaxed. It is believed that this relaxation of the ~k-conservation rules is what leads to this softening in the spectral dependenceof these matrix elements. The consequences of this relaxation are furtherdiscussed in the scientific literature [88].40Figure 2.10: The impact of disorder on the form of the distribution of elec-tronic states. This image is from O’Leary [65]. Copyright permission wasgranted to the author. The online version of this figure is depicted in color.412.11 On the uniqueness of the UHV preparedsilicon thin-film samplesThere are three unique features associated with these UHV preparedsilicon thin-films when contrasted with those prepared through other means.First, the mass density of the UHV prepared form of silicon thin-film is foundto be more than 98 % that of c-Si [26], which is higher than that associatedwith the more common forms of silicon thin-film; the differences in the massdensity, while seemingly small, are in fact significant, the mass density of c-Siprobably forming an upper bound on the mass density of silicon thin-film.Second, infrared and secondary ion mass spectroscopic measurements, per-formed on similarly prepared thin-films, have demonstrated that there areonly small amounts of hydrogen present within this form of silicon thin-film,i.e., between 0.1 and 1 at. % [32], this contrasting dramatically with the caseof conventional PD-a-Si, meaning that this new form of UHV prepared siliconthin-film might be expected to be less susceptible to the Staebler-Wronskieffect than more conventional forms of this material [90, 91];2 the hydrogen2The suitability of these silicon thin-films for photovoltaic device applications has yetto be fully probed. While the electron spin resonance work of Akbari-Sharbaf et al. [90] andthe carrier dynamic work of Titova et al. [91] has shown that similarly prepared thin-films42distributions, found within similarly prepared silicon thin-film samples de-posited on c-Si substrates, are presented in Baribeau et al. [29] and Tay etal. [31], these results being acquired through the use of secondary ion massspectrometry, see Figure 2.7 for a representative impurity profile. Finally,the nature of the growth process itself is quite distinct.The preparation of conventional forms of nc-Si, i.e., through the use ofhydrogen dilution within the framework of a plasma deposition process [39],initially involves the deposition of an amorphous layer [92]. When the ac-cumulated growth exceeds a certain thickness, crystallite nucleation withinthis amorphous phase will occur. Eventually, with further film growth, amixed amorphous/crystalline phase will develop, the crystallite regions ul-timately coalescing into a single crystalline phase. In the UHV depositionprocess, however, the order of the deposition is different. Transmission elec-tron microscopic analyzes, performed on similarly prepared silicon thin-filmsdeposited on c-Si and oxidized c-Si substrates, suggests that the growth startsout more crystalline in nature [29, 31]. Beyond a certain thickness, however,this crystallinity degenerates, ultimately deteriorating into an amorphousof silicon are promising for photovoltaic device applications, light soaking experiments,and other photovoltaic-specific analyzes, have yet to be pursued. These will have to beperformed in the future if the photovoltaic potential of this material is to be fully realized.43phase. While a TEM analysis was not performed for the case of the sili-con thin-films grown on the optical quality fused quartz substrates owing totheir delicacy, it is felt that something similar happens; the growth imme-diately above the substrate is probably initially proto-crystalline in nature,then transitioning into a crystalline phase as the growth further proceeds.2.12 Research collaborationThe results presented within the body of this thesis represent the latestresults associated with a long-term research collaboration that has been pur-sued by my supervisor, Dr. Stephen O’Leary, and researchers at the NationalResearch Council of Canada. Motivated by the need to find an alternate formof silicon thin-film with properties that are improved over those associatedwith more conventional forms of this material, using an UHV MBE deposi-tion system, thin-films of silicon were prepared at a variety of different growthtemperatures. A variety of substrates were employed for these depositions,including c-Si, oxidized c-Si, and optical quality fused quartz. Grazing in-cidence X-ray diffraction (GIXRD) and Raman spectroscopies were pursuedfor all of the deposited thin-films of silicon. Measurements of the reflectance44and transmittance spectra were also pursued, these being performed throughthe use of a number of spectrophotometers for the thin-films of silicon de-posited onto optical quality fused quartz substrates, the opacity of a c-Sisubstrate not allowing for measurements of the transmittance for the thin-films of silicon deposited on the c-Si and oxidized c-Si substrates.There have been a number of publications that have arisen from thisongoing research collaboration. Publications that have stemmed directlyfrom work that was performed in Dr. O’Leary’s group, not including thatperformed with me, listed in chronological order, include:1. D.J. Lockwood, J.-M. Baribeau, M. Noe¨l, J.C. Zwinkels, B.J. Fogal,and S.K. O’Leary, Molecular beam epitaxially deposited amorphous sil-icon, Materials Research Symposium Proceedings, Volume 609,pages A5.1.1-A5.1.6, 2000. [93]2. B.J. Fogal, S.K. O’Leary, D.J. Lockwood, J.-M. Baribeau, M. Noe¨l,and J.C. Zwinkels, Disorder and the optical properties of amorphoussilicon grown by molecular beam epitaxy, Solid State Communica-tions, Volume 120, pages 429-434, 2001. [26]3. S.K. O’Leary, B.J. Fogal, D. J. Lockwood, J.-M. Baribeau, M. Noe¨l,45and J. C. Zwinkels, Optical dispersion relationships in amorphous sil-icon grown by molecular beam epitaxy, Journal of Non-CrystallineSolids, Volume 290, pages 57-63, 2001. [27]4. D.J. Lockwood, J.-M. Baribeau, M. Noe¨l, J.C. Zwinkels, B.J. Fogal,and S.K. O’Leary, Optical absorption in an amorphous silicon superlat-tice grown by molecular beam epitaxy, Solid State Communications,Volume 122, pages 271-275, 2002. [28]5. D.J. Lockwood, J.-M. Baribeau, M. Noe¨l, J.C. Zwinkels, B.J. Fogal,F. Orapunt, and S.K. O’Leary, Amorphous silicon films and superlat-tices grown by molecular beam epitaxy: an optical analysis, MaterialsResearch Symposium Proceedings, Volume 715, pages A19.1.1-A19.1.6, 2002. [94]6. L.-L. Tay, D.J. Lockwood, J.-M. Baribeau, M. Noe¨l, J.C. Zwinkels, F.Orapunt, and S.K. O’Leary, Influence of growth temperature on orderwithin silicon films grown by ultrahigh-vacuum evaporation on silica,Applied Physics Letters, Volume 88, pages 121920-1-3, 2006. [32]7. F. Orapunt, L.-L. Tay, D. J. Lockwood, J.-M. Baribeau, J.C. Zwinkels,M. Noe¨l, and S.K. O’Leary, An amorphous-to-crystalline phase transi-46tion within thin silicon films grown through ultra-high-vacuum evapora-tion on fused quartz substrates, MRS Advances, DOI: 10.1557/adv.2016.244, 2016. [80]8. F. Orapunt, L.-L. Tay, D.J. Lockwood, J.-M. Baribeau, M. Noe¨l, J.C.Zwinkels, and S.K. O’Leary, An amorphous-to-crystalline phase tran-sition within thin silicon films grown by ultrahigh-vacuum evaporationand its impact on the optical response, Journal of Applied Physics,Volume 119, pages 065702-1-12, 2016. [33]In these publications, GIXRD, Raman, near-normal reflectance, and nor-mal transmittance spectral results, acquired by the experimental collabo-rators at the National Research Council of Canada, were drawn upon inorder characterize the properties of some of these UHV prepared thin-filmsof silicon. Complementary results, related to these UHV prepared thin-filmsof silicon, were reported upon in other publications authored by these Na-tional Research Council of Canada experimental collaborators; these addi-tional publications were not co-authored with members of Dr. O’Leary’sresearch group.At the present time, what remains unknown is how the growth temper-ature influences the spectral dependence of the optical functions and how47the micro-structure exhibited by these thin-films of silicon is related to thespectral dependencies of the corresponding optical functions.3 It is a maingoal of this analysis to address both of these issues within the scope of thisthesis.Before drawing this section to a close, I would be remiss not to pointout the individual contributions to this body of work from the individualNational Research Council of Canada experimental collaborators.Joanne C. Zwinkels and Mario Noe¨l: Dr. Zwinkels is an expert in op-tical characterizations and her state-of-the-art laboratory was employed forthe purposes of this analysis. Mr. Noe¨l performed the experimental mea-surements under Dr. Zwinkel’s supervision.Jean-Marc Baribeau: Dr. Baribeau prepared the UHV grown thin-filmsof silicon along with performing the GIXRD measurements.3While there has been work performed on how the spectral dependence of the opticalabsorption coefficient is related to the underlying micro-structure of these thin-films ofsilicon, the optical absorption coefficient is merely one of many optical functions. In thiswork, the spectral dependence of the entire collection of optical functions, i.e., the refrac-tive index, the extinction coefficient, the real and imaginary components of the dielectricfunction, and the optical absorption coefficient, are considered, many of these opticalfunctions being related with each other. Based on these results, the device implicationsof these UHV prepared forms of silicon thin-film will be explored. It is these matters thatare going to be the focus of this body of work.48David J. Lockwood and L.-L. Tay: Dr. Lockwood suggested the exper-iment. He also supervised the Raman spectral measurements for each andevery UHV prepared thin-film of silicon. Dr. Tay performed many of thesemeasurements under Dr. Lockwood’s supervision.49Chapter 3Silicon thin-film opticalfunctions3.1 IntroductionThin-films of silicon, which range the gamut from the traditional a-Si to more recently developed forms of this material, such as µc-Si andnc-Si, continue to attract the attention of the materials research commu-nity [1, 2, 95]. This fascination with the silicon thin-film genome undoubt-edly stems from the plethora of electron device configurations that employit [8, 10]. At present, the silicon thin-film form that is commonly deployedin commercial products is that fabricated through silane’s decomposition ina plasma [19]. The resultant material, PD-a-Si, is a jumble of silicon, hy-50drogen, and other atoms, the disorder present within this distribution ofatoms playing a decisive role in shaping its corresponding electronic prop-erties. Much research has been pursued aimed at resolving the materialproperties of PD-a-Si, and in exploring the electron device potential of PD-a-Si [3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. With more recently developed forms ofsilicon thin-film still being actively explored, interest in silicon thin-film isexpected to continue apace for many years to come.The role that hydrogen atoms play in defining PD-a-Si’s character haslong been the subject of investigation [96, 97, 98, 99, 100]. It is now wellrecognized that PD-a-Si’s resident hydrogen atoms are responsible for passi-vating dangling bonds, and that this leads to PD-a-Si’s device-friendly elec-tronic properties [5, 20]. Light and mobile, hydrogen is also held responsiblefor alleviating some of the stress that exists within PD-a-Si, i.e., that the hy-drogen atoms are able to contort themselves into bonding configurations thatwould not typically occur with only silicon atoms present. Unfortunately, aninstability that bedevils PD-a-Si, a light exposure induced deterioration in itselectronic properties over time, has also been recognized as being hydrogen-related [22, 101, 102]. So, with respect to PD-a-Si, hydrogen atoms play bothbeneficial and detrimental roles.51With the realization that PD-a-Si’s hydrogen atoms are available in muchgreater concentrations than the dangling bond quantities found within un-hydrogenated forms of a-Si, came speculation that perhaps other types ofsilicon thin-film might exist with sufficient hydrogen in order to achieve com-plete dangling bond passivation without PD-a-Si’s instability. In responseto this challenge, a variety of alternate thin-film forms of silicon have beendevised [23, 24]. Noting that depositions performed under UHV conditionsengender significant atomic species control during growth, came the thoughtthat perhaps an UHV preparation of silicon thin-film would offer the com-munity with an improved form of silicon thin-film. Accordingly, an UHVMBE chamber was used to prepare a sequence of thin-films of silicon and sil-icon thin-film based superlattices. Investigations into the properties of thesesilicon thin-films and superlattices, which have been extensively chronicledwithin the scientific literature, have revealed that the silicon thin-film formproduced through such a growth process offers a myriad of properties thatpoint to its considerable promise, including it having a mass density veryclose to that of c-Si and that its hydrogen concentration is significantly lowerthan that possessed by PD-a-Si [26, 27, 28, 29, 31, 32, 33].In order to make projections regarding the device performance of this52UHV prepared silicon thin-film form, the spectral dependence of a numberof the optical functions associated with this material must be acquired. Ac-cordingly, for the purposes of this investigation, a number of silicon thin-filmsamples were prepared through UHV evaporation on optical quality fusedquartz substrates; these growths were performed by experimental collabora-tors at the National Research Council of Canada. The growth temperaturesused for these depositions ranged between 98 and 572 ◦C, this spanning asufficient range in order to expect a transition in the nature of the material,from purely a-Si at the lower growth temperatures to a more crystalline-like form for the higher growth temperatures. Specular reflectance spectralmeasurements at near-normal incidence and regular transmittance spectralmeasurements at normal incidence provided the experimental basis for thisanalysis. An inversion analysis, performed within the analytical frameworkprescribed by Heavens [103], will be used for the silicon thin-film optical func-tion acquisitions. The optical functions that are considered in this analysisinclude the refractive index, the extinction coefficient, the real and imaginaryparts of the dielectric function, and the optical absorption coefficient, manyof these optical functions being related to one another.The UHV growths of the silicon thin-films were performed on underly-53ing transparent substrates, i.e., the optical quality fused quartz substrates.Silicon thin-film optical function acquisition was pursued using experimentaldata gleaned from measurements performed on overall thin-film/substratesystems by researchers at the National Research Council of Canada. Thethin-film optical problem pursued here represents one of general interest tothose within the thin-film community, this interest extending far beyond theconfines of just the silicon thin-film community itself. Accordingly, in thisstudy, a number of important details, employed in this silicon thin-film op-tical function acquisition analysis, are chronicled. In particular, many ofthe analytical details that were commissioned in the current optical functionanalysis, but not explicitly previously discussed in the scientific literature,are presented. The focus of this discussion is on means of determining theoptical functions themselves from the experimental reflectance and transmit-tance data, this study of the UHV prepared thin-films of silicon providinga case study on the issues and challenges involved. It is hoped that thereaders within the broader community of thin-film researchers will find thisdiscussion of use.This chapter is organized in the following manner. In Section 3.2, theUHV deposition technique that is used for the preparation of the thin-films54of silicon, employed for the purposes of this analysis, is discussed. The ex-perimental means, through which the reflectance and transmittance spectraare obtained, are then presented in Section 3.3. The reflectance and trans-mittance spectra, acquired from the National Research Council of Canadaexperimental collaborators, are then presented in Section 3.4. An uncer-tainty analysis, corresponding to these experimental results, is then featuredin Section 3.5. The analytical framework, within which the thin-film opticalfunctions are acquired, is then discussed in Section 3.6, Section 3.7 detail-ing the approach that is adopted for the purposes of modeling the opticalfunctions associated with the ambient and the optical quality fused quartzsubstrates. How inversion was employed in order to determine the opticalfunctions is then commented upon in Section 3.8. Means of confirming theaccuracy of these optical function results are elucidated upon in Section 3.9,the acquired silicon thin-film optical function results being presented in Sec-tion 3.10. Finally, a summary of the technical achievements, reported uponin this chapter of the thesis, is provided in Section 3.11.553.2 UHV silicon thin-film preparationThe thin-films of silicon that are studied for the purposes of this analysiswere prepared by researchers at the National Research Council of Canada.UHV evaporation was used for the silicon thin-film growths, a Vacuum Gen-erators Semicon V80 MBE deposition chamber being employed for this pur-pose. All of the UHV growths occurred through depositions onto opticalquality fused quartz substrates, these substrates being acquired from ESCOOptics; the experimental optical response measurements were performed onthin-film/substrate systems, and hence, a substrate, of great transparency,was required. Each substrate was 50 mm in diameter and 116of an inch inthickness, i.e., about 1.60 mm thick. These substrates had both sides pol-ished and it was determined that both sides had an RMS surface roughnessof less than 0.5 nm. Before each deposition, the particular substrate involvedwas ultrasonically degreased using isopropanol alcohol for about 60 s, an N2gun being used to dry the substrate following this particular cleaning step.In the reactor, for each growth, the substrate surface was placed facedown. It was held approximately 30 cm away from the evaporation source,the source being 27◦ off the wafer normal. Through the controlled e-beamevaporation of a high-purity silicon source, source material for the growths56was supplied to the deposition chamber. Growth temperatures, ranging from98 to 572 ◦C, were employed for the silicon thin-film growths, this temper-ature being kept constant for any given growth. A thermo-couple was usedto ascertain the growth temperature in the deposition chamber, the thermo-couple’s temperature response being calibrated with respect to indium, tin,and lead’s melting points, the experimental error in the measured growthtemperature being ± 25 ◦C. The rate of film growth was monitored and reg-ulated continuously during each deposition using a quartz microbalance andan electron impact ionization spectrometer (an Inficon Sentinel III), a fixed0.1 nm/s growth rate being used for each deposition; the quartz microbal-ance was used to calibrate the Inficon gain and also provide an estimate forthe total amount deposited at the end of any given run while the spectrom-eter was used to monitor and stabilize the rate during the deposition.4 The4A sequence of complementary UHV silicon thin-film growths, performed on c-Si andoxidized c-Si substrates, were also prepared, the growth rate for these growths being set to0.2 nm/s for all cases. The optical responses of these silicon thin-films could not be exploredowing to the opacity of c-Si, i.e., joint determinations of the reflectance and transmittancespectra are required in order to determine the spectral dependence of the silicon thin-filmoptical functions. That is why the silicon thin-films grown for the purposes of this opticalfunction analysis were grown on optical quality fused quartz substrates, which are highlytransparent.57signal from this rate monitor was continuously fed back to the e-gun powersupply in order to ensure that the growth rate was held constant. The sen-sor signal was rather noisy, so there were instantaneous residual growth ratefluctuations, of the order of ± 10 %, about this set growth rate. In parallel,the quartz oscillator measured the integrated amount of material deposited.The growth temperatures used and the resultant thin-film thicknesses, cor-responding to the eleven UHV prepared silicon thin-films considered in thisanalysis, are tabulated in Table 3.1.3.3 Optical response measurementsThe experimental basis for this analysis is provided from data ac-quired from the eleven UHV prepared silicon thin-film/substrate samplesthrough near-normal incidence specular reflectance and normal incidence reg-ular transmittance measurements. These experimental measurements wereperformed by researchers at the National Research Council of Canada. Com-plementary experimental measurements were also performed on an uncoatedreference substrate, also by the same National Research Council of Canadaresearchers. From these reflectance and transmittance spectra, through the58Growth temperature(◦C) Film thickness(nm)Crystalline volumefraction98 135 098 303 098 605 0138 132 0177 125 0217 207 0256 106 0335 180 0415 190 0.0084493 170 0.57572 180 0.83Table 3.1: Growth temperatures, film thicknesses, and crystalline volumefractions for all of the UHV prepared silicon thin-films. The crystalline vol-ume fractions are determined through the use of a Raman peak decomposi-tion process that is further discussed by Orapunt et al. [33]. This table is thesame as Table 1 of Orapunt et al. [33]. Copyright permission was granted tothe author. An outline of this procedure being provided in Section 4.2. Fur-ther details on all of the silicon thin-films grown through UHV are reportedupon by Orapunt et al. [33].59use of the formalism of Heavens [103], the silicon thin-film optical functionswere acquired. Details, related to these reflectance and transmittance mea-surements, are now provided.5The reflectance measurements are discussed first. For the absolute spec-ular reflectance measurements of thin-film-silicon with a substrate, a PerkinElmer (PE)-900 UV/VIS/NIR spectrophotometer was used, this apparatusbeing equipped with a PELA-1029 absolute specular reflectance accessory.For the uncoated reference substrate absolute specular reflectance measure-ments, a PE-9 UV/VIS/NIR spectrophotometer, equipped with a PE dual-beam V-W absolute specular reflectance accessory, was employed. For bothspectrophotometers, the acquisition of the square of the absolute specular re-flectance was performed through the use of the “V-W” optical configuration,the angle of incidence being set to 7.5 ± 0.5 ◦ for all cases. The advan-tage of the PE dual-beam V-W reflectance accessory is that it allows forthe use of a National Research Council of Canada developed compensationprocedure that improves the accuracy of the specular reflectance measure-ments for low reflecting samples, such as the reference uncoated substrate,5It is common to describe the experimental set-up used for these optical property mea-surements as configuring the spectrophotometer in the reflection mode or the transmissionmode for the reflectance and transmittance measurements, respectively.60compared with the use of the more conventional V-W method [104]. In thiscompensation procedure, the reflectance of the optical quality fused quartzsubstrate was measured in combination with a National Research Council ofCanada high reflectance mirror; in this case, the Al alloy 6061 “C” was used,this compensating for the reference substrate’s low reflectance. Three sep-arate measurement steps were employed, the sample and the compensationmirror’s positions being interchanged at each measurement step, an absolutemeasurement of the compensation mirror’s reflectance being pursued usingthe traditional V-W method. A well-collimated measurement beam was em-ployed for these measurements, the maximum angle of divergence from theangles of incidence and reflection being ± 0.5 ◦. The irradiated sample areaswere approximately 5 mm × 6 mm for the first reflection and about 6 mm× 7 mm for the second. The reflectance spectral data was recorded at anambient temperature of 23 ± 1 ◦C, the relative humidity being found to be40 ± 10%. The measurements were performed on the PE-900 over the wave-length range 190 to 1500 nm for 5 nm intervals for eight of the samples (thosegrown at less than 400 ◦C) and for 2 nm intervals for the remaining threesamples (those grown above 400 ◦C). The uncoated reference substrate’s re-flectance was measured for 1 nm intervals over the same wavelength range61on the PE-9 spectrophotometer. Both instruments used a tungsten-halogensource (320 to 1500 nm) in combination with either a photomultiplier de-tector (190 to 860 nm) or a PbS detector (860 to 1500 nm). The samplecompartment of the PE-900 spectrophotometer was purged with nitrogengas (UHP grade) during the measurements; the sample compartment of thePE-9 spectrophotometer could not be purged owing to a technical reason.6The validation of the National Research Council of Canada calibration re-sults was based on a number of surface specular reflectance standards, andreflectance results corresponding to three high reflectance dielectric laser mir-rors, optimized for the 694, 1235, and 2010 nm wave-lengths, respectively.For all of the samples considered, a minimum of three independent mea-surements was performed. The scale for the reflectance measurements ranthe gamut from zero to unity, where unity corresponds to 100 % absolutereflectance.6The PE-900 spectrophotometer could not accommodate the dual V-W accessory withthe sample mounted in the horizontal plane, this particular geometry being required inorder for the aforementioned three-step National Research Council of Canada compensa-tion method with a high reflectance standard to be performed. Hence, the need to use thePE-9 spectrophotometer for these measurements. Unfortunately, when configured in thisparticular geometry, the PE-9 spectrophotometer did not allow for a purge of the samplecompartment.62Now, details related to to the transmittance measurements are discussed.For the regular thin-film-silicon/substrate transmittance measurements, aPE-900 spectrophotometer or a PE-Lambda-19 spectrophotometer was em-ployed. In an effort to improve the measurement accuracy, a reference beamattenuation technique was used for the silicon thin-films that were deemedto be highly absorbing. The regular transmittance mode geometry was em-ployed for these measurements, the sample being positioned normal to thebeam for all cases. A well-collimated measurement beam was employed forthese measurements, the maximum angle of divergence being ± 4 ◦. Theirradiated sample area was approximately 10 mm × 5 mm. The transmit-tance measurements were made relative to air at an ambient temperature of23± 1 ◦C, the relative humidity being found to be 40 ± 10%. The measure-ments were performed on the PE-900 and PE-Lambda-19 spectrophotome-ters over the wave-length range 190 to 1500 nm for a spectral bandwidthof 5 nm. The sample compartments of the PE-900 and the PE-Lambda-19spectrophotometers were purged with nitrogen gas (UHP grade) during themeasurements. So as to enhance the accuracy of the measurements, for casesin which highly absorbing filters were used, i.e., optical transmission den-sities that exceed unity, a reference beam attenuation technique was used.63The true transmittance of the test sample is calculated from the measuredtransmittance multiplied by the known transmittance of the reference beamattenuator. For most of the samples considered, a minimum of three in-dependent measurements was performed, these results then being averaged;single transmittance measurements were performed for the thin-films of sili-con grown at 98 ◦C to a thickness of 303 nm and that prepared at 177 ◦C.For the transmittance measurements, the scale ran the gamut from zero tounity, unity corresponding to 100 % absolute transmittance through the air.From the aforementioned measurements of the reflectance and transmit-tance spectra, one can acquire the silicon thin-film optical functions. Thiswas done through a process of inversion and confirmation, the details of whichare further discussed in Sections 3.5, 3.6, 3.7, 3.8, and 3.9. Further details,related to these experimental measurements, are presented elsewhere in thescientific literature [26, 27, 28, 32, 33, 105].77While measurements of the reflectance and transmittance spectra are often used inorder to determine the optical functions of thin-films deposited onto an underlying sub-strate, ellipsometry can also be used for such an application. A discussion on the strengthsand weaknesses of these approaches is provided by Poelman and Smet [105].643.4 Reflectance and transmittance spectraThe reflectance and transmittance spectral measurements are performedon silicon thin-film/substrate systems. Prior to teasing out the optical func-tions of the silicon thin-film samples, it is instructive to benchmark theseresults with an analysis of the reflectance and transmittance results corre-sponding to a reference bare optical quality fused quartz substrate, bereft ofany thin-film coating. The resultant reflectance and transmittance spectralresults are depicted in Figure 3.1. Two observations may be made from thisset of experimental results. First, it is noted that the spectral dependenceof the reflectance and transmittance spectra are more or less flat and fea-tureless, with the exception of a slight increase in the reflectance spectrumand a corresponding decrease in the transmittance spectrum as the photonenergies start to exceed 6 eV, this undoubtedly being related to the finiteabsorption associated with the optical quality fused quartz substrate itself.Second, notches are found in the reflectance and transmittance spectra inand around 0.89 eV; the notch is observed to be particularly noticeable forthe case of the transmittance spectrum, a minor corresponding notch beingfound in the reflectance spectrum. These notches are believed to be relatedto the presence of hydroxide ion (O-H) impurities.65Figure 3.1: The reflectance and transmittance spectra of an optical qualityfused quartz substrate. This figure was published as Figure 1 of Moghaddamet al. [106]. Copyright permission was granted to the author. The onlineversion of this figure is depicted in color.66The analysis is now continued with an examination of the experimen-tally acquired reflectance spectra results corresponding to the silicon thin-film/substrate systems. In order to ease with the visualization, the threesilicon thin-films grown at 98 ◦C are first considered, the film thicknesses be-ing 135, 303, and 605 nm. The corresponding reflectance spectra are depictedin Figure 3.2. The result, corresponding to the uncoated reference opticalquality fused quartz substrate, is also depicted. It is noted that for thelower photon energies these reflectance spectra exhibit oscillations related tothe constructive and destructive interference that occurs. The difference be-tween these minima and maxima is mostly consistent with the correspondingthin-film thicknesses (recall Table 3.1) [108]. At the higher photon energies,however, the optical absorption within the thin-films becomes so large thatthese interference patterns subside, i.e., for these photon energies, the lightreflected from the back of the thin-film is sufficiently weak (it will have at-tenuated by propagating back and forth through the thin-film itself) that itwill not interfere with the light incident into the thin-film. Accordingly, thevarious reflectance spectra converge towards a single curve representative ofsilicon thin-film deposited at 98 ◦C; the small differences in these reflectancespectra are large enough in order to meaningfully resolve the differences in67Figure 3.2: The room-temperature reflectance spectra corresponding to threesilicon thin-films grown at 98 ◦C. The experimental data sets are depictedwith the solid lines. The film thicknesses corresponding to each sample arealso depicted on this figure. The reflectance spectrum of a reference opticalquality fused quartz substrate, without a silicon thin-film, is also depicted.This figure was published as Figure 2a of Moghaddam et al. [106]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.68the corresponding refractive index spectral dependencies.The impact of the growth temperature on the reflectance spectra is nowconsidered. The experimentally acquired reflectance spectra results, corre-sponding to nine of the silicon thin-films grown at the different temperaturesconsidered in this analysis, are plotted in Figure 3.3. In particular, the re-flectance spectra corresponding to the silicon thin-films grown at 98 (onlythe result corresponding to silicon thin-film grown at 98 ◦C to a thicknessof 303 nm is depicted), 138, 177, 217, 256, 335, 415, 493, and 572 ◦C areshown in this figure; only the reflectance spectra corresponding to the 135and 605 nm thick silicon thin-films grown at 98 ◦C are not shown in thisplot. These experimental results, which correspond to measurements per-formed on the thin-film-silicon/substrate systems, are also contrasted withthose of an uncoated optical quality fused quartz substrate. For these sam-ples, i.e., those grown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493,and 572 ◦C, the film thicknesses are 303, 132, 125, 207, 106, 180, 190, 170,and 180 nm, respectively, the optical quality fused quartz substrates beingabout 1.60 mm thick for all cases. The plotted experimental results exhibitfunctional forms that are expected of the silicon thin-film reflectance spec-tra, the characteristic oscillations found in these spectra being found in most69Figure 3.3: The room-temperature reflectance spectra corresponding to thesilicon thin-films grown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493, and572 ◦C. These experimental data sets are depicted with the solid lines. Theroom-temperature reflectance spectra corresponding to a reference quartzsubstrate, without a silicon film, is also depicted. This figure was publishedas Figure 2b of Moghaddam et al. [106]. Copyright permission was grantedto the author. The online version of this figure is depicted in color.70silicon thin-film reflectance spectra. Note that the reflectance spectra asso-ciated with some of the silicon thin-films goes slightly below that associatedwith the bare optical quality fused quartz substrate result over some smallregions of the spectrum owing to the anti-reflective nature of these siliconthin-film/substrate systems.8The analysis is continued with an examination of the experimentallyacquired transmittance spectra results corresponding to the silicon thin-film/substrate systems. As with the reflectance analysis, the results for threesilicon thin-films grown at 98 ◦C of film thicknesses 135, 303, and 605 nm areconsidered first. The corresponding transmittance spectra, including that ofan uncoated reference optical quality fused quartz substrate, are depicted inFigure 3.4. As with the reflectance results, it is noted that for the lower pho-ton energies these transmittance spectra exhibit oscillations related to theconstructive and destructive interference that occurs. The differences be-8The apparently anomalous behavior observed in the reflectance spectra, where themeasured reflectance of the silicon thin-film coating is less than that associated with thebare optical quality fused quartz substrate, can be explained if the optical thickness of thethin films at these particular wavelengths is such that destructive interference occurs. Inthis situation, the thin-film behaves like an anti-reflection coating, where the reflectanceis diminished and the throughput (transmittance) is increased compared with the bareoptical quality fused quartz substrate.71Figure 3.4: The room-temperature transmittance spectra corresponding tothree silicon thin-films grown at 98 ◦C. The experimental data sets are de-picted with the solid lines. The film thicknesses corresponding to each sampleare also depicted on this figure. The transmittance spectrum of a referenceoptical quality fused quartz substrate, without a silicon thin-film, is also de-picted. This figure was published as Figure 2c of Moghaddam et al. [106].Copyright permission was granted to the author. The online version of thisfigure is depicted in color.72tween these minima and maxima are mostly consistent with the correspond-ing thin-film thicknesses (recall Table 3.1). At the higher photon energies,however, the optical absorption within the thin-films becomes sufficientlygreat that these interference patters subside, as with the reflectance case.The impact of growth temperature on the transmittance spectra is nowconsidered. The experimentally acquired transmittance spectra results, cor-responding to nine of the silicon thin-films grown at different temperatures,are plotted in Figure 3.5. In particular, the transmittance spectra corre-sponding to the silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256,335, 415, 493, and 572 ◦C are depicted. These results, corresponding to thesesamples with thin-film and optical quality fused quartz substrate included,are contrasted with those of the uncoated optical quality fused quartz sub-strate. It is observed that the transmittance associated with some of thesilicon thin-films goes above the result associated with the uncoated refer-ence optical quality fused quartz substrate over some small regions of photonenergy owing to the anti-reflective nature of these thin-silicon-film/substratesystems; recall footnote 8. It is noted that each of these transmittance spec-tra starts to attenuate just beyond the corresponding optical gap.73Figure 3.5: The room-temperature transmittance spectra corresponding tothe silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493,and 572 ◦C. These experimental data sets are depicted with the solid lines.The room-temperature transmittance spectra corresponding to a referencequartz substrate, without a silicon film, is also depicted. This figure waspublished as Figure 2d of Moghaddam et al. [106]. Copyright permission wasgranted to the author. The online version of this figure is depicted in color.743.5 Uncertainty analysisPrior to presenting the silicon thin-film optical function results, somecomments related to the uncertainty in these experimental measurements arecalled for. The Type B standard uncertainty, uCB (R), of the National Re-search Council of Canada absolute specular reflectance scale over the 190 to1500 nm wave-length range is estimated to be upper bounded by ± 0.12 % ofthe reflectance value. The Type A standard uncertainty, uCA (R), may be de-termined through the standard deviation corresponding to the independentsample measurements that were performed on each of the UHV preparedsilicon thin-film/substrate samples. The wave-length scale standard uncer-tainty, uλ (R), is estimated to be ± 0.1 nm for wave-lengths between 190 to860 nm and ± 0.2 nm for wave-lengths between 860 to 1500 nm. The com-bined standard uncertainty, uC (R), may be computed through combining,in quadrature, the uncertainty in the reflectance scale, uCB (R), the Type Astandard uncertainty, uCA (R), and an additional term, uλ (R), related to thewave-length scale uncertainty. The expanded uncertainty may be expressedasUNRC (R) = 2uC (R) = k√u2CB (R) + u2CA (R) + u2λ (R), (3.1)75where k denotes the coverage factor. Assuming a normal distribution, forthe selection of k = 2, a 95 % confidence level may be achieved. For theUHV prepared thin-film-silicon/substrate samples grown at 98 ◦C, the spec-tral dependence of the reflectance measurement uncertainty are as depictedin Figure 3.6. For the UHV prepared thin-film-silicon/substrate samplesprepared at the other growth temperatures, the spectral dependence of thereflectance measurement uncertainties are depicted in Figure 3.7, one of the98 ◦C results being retained for benchmarking purposes, i.e., the thin-film-silicon/substrate sample grown at 98 ◦C to a 303 nm thickness.For the transmittance results, a similar approach to the uncertainty eval-uation is adopted. The Type B standard uncertainty, uCB (T ), of the NRCtransmittance scale depends on the photometric range and on whether ornot reference beam attenuation is used. The Type B standard uncertaintiesfor direct transmittance measurements are as shown in Table 3.2. The TypeA standard uncertainty, uCA (T ), may be determined through the standarddeviation corresponding to the independent sample measurements that areperformed for each of the UHV prepared silicon thin-film/substrate samples.The wave-length scale standard uncertainty, uλ (T ), is ± 0.1 nm for the 190to 860 nm wave-length range and ± 0.2 nm for the 860 to 1500 nm wave-76Figure 3.6: The spectral dependence of the room-temperature reflectanceuncertainty corresponding to the three silicon thin-films grown at 98 ◦C. Alogarithmic scale is employed. The experimental data sets are depicted withthe solid lines. The film thicknesses corresponding to each sample are alsodepicted on this figure. This figure was published as Figure 1a of Moghaddamet al. [107]. Copyright permission was granted to the author. The onlineversion of this figure is depicted in color.77Figure 3.7: The spectral dependence of the room-temperature reflectanceuncertainty corresponding to the silicon thin-films grown at 98 (303 nm), 138,177, 217, 256, 335, 415, 493, and 572 ◦C. A logarithmic scale is employed.This figure was published as Figure 1b of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.78Photometric range(transmittance unit)Type B standard uncertaintyuCB (T )0.1 to 1.0 ± 0.1 % of the transmittance value0.01 to 0.1 ± 0.35 % of the transmittance value0.001 to 0.01 ± 0.5 % of the transmittance value0.0001 to 0.001 ± 1.0 % of the transmittance valueTable 3.2: The Type B standard uncertainty, uCB (T ), for various directtransmittance measurements.length range. The combined standard uncertainty, uC (T ), may be computedthrough combining, in quadrature, the uncertainty in the absolute spectraltransmittance scale, u2C (T ), the Type A standard uncertainty, u2CA (T ), andan additional term, µλ (T ), related to the wave-length scale uncertainties.The expanded uncertainty may be expressed asUNRC (T ) = 2uC (T ) = k√u2CB (T ) + u2CA (T ) + u2λ (T ), (3.2)where k represents the coverage factor. Assuming a normal distribution,for the selection of k = 2, a 95 % confidence level may be achieved. For79the UHV prepared thin-film-silicon/substrate samples grown at 98 ◦C, thespectral dependence of the transmittance measurement uncertainties are de-picted in Figure 3.8. For the UHV prepared thin-film-silicon/substrate sam-ples prepared at the other growth temperatures, the spectral dependenceof the transmittance measurement uncertainties are depicted in Figure 3.9,one of the 98 ◦C results being retained for benchmarking purposes, i.e., thethin-film-silicon/substrate sample grown at 98 ◦C to a 135 nm thickness; the98 ◦C 303 nm thin-film transmittance uncertainty was not available owing tothe fact that only a single measurement of this spectrum was taken, as wasmentioned before.3.6 Analytical frameworkHeavens’ [103] thin-film formalism forms the theoretical underpinningfor this analysis. In this formalism, for the problem of light normally inci-dent upon a thin-film overlaying a substrate, expressions for the reflectanceand transmittance spectra, R and T , respectively, are developed in terms ofthe optical functions associated with the three different media involved, i.e.,(1) the non-absorbing ambient (medium of incidence - medium 0), (2) the80Figure 3.8: The spectral dependence of the room-temperature transmittanceuncertainty corresponding to two silicon thin-films grown at 98 ◦C; the room-temperature transmittance uncertainty corresponding to the other siliconthin-film grown at 98 ◦C, i.e., that grown to a thickness of 303 nm, wasnot determined in this analysis. A logarithmic scale is employed. The ex-perimental data sets are depicted with the solid lines. The film thicknessescorresponding to each sample are also depicted on this figure. This figurewas published as Figure 1c of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure is in color.81Figure 3.9: The spectral dependence of the room-temperature transmittanceuncertainty corresponding to the silicon thin-films grown at 98 (135 nm),138, 177, 217, 256, 335, 415, 493, and 572 ◦C; as the transmittance uncer-tainty silicon corresponding to the thin-film grown at 98 ◦C to a thicknessof (303 nm) was not determined in this analysis, the 135 nm result was usedinstead. A logarithmic scale is employed. This figure was published as Fig-ure 1d of Moghaddam et al. [107]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color.82thin-film itself (medium 1), and (3) the underlying substrate (medium 2).In order to simply matters, it is instructive to cast the expressions of Heav-ens [103] into the form suggested by Denton et al. [109], noting that theexpressions for 1+RTand 1−RTare less mathematically cumbersome than thoseassociated with R and T themselves. Specifically, denoting the refractiveindices associated with the different media involved to be n0 (medium 0),n1 (medium 1), and n2 (medium 2), i.e., the ambient, the thin-film, andthe substrate, respectively, k0, k1, and k2 being the corresponding extinctioncoefficients (as the ambient is non-absorbing, k0 = 0, of course, by defini-tion), for light normally incident upon the thin-film from the ambient, if thethin-film thickness is d, then Denton et al. [109] concluded that1 +RT=14n0n2 (n21 + k21)[(n20 + n21 + k21){ (n21 + n22 + k21 + k22)cosh(4pik1dλ)+2 (n1n2 + k1k2) sinh(4pik1dλ)}+(n20 − n21 − k21){ (n21 − n22 + k21 − k22)cos(4pin1dλ)+2 (n1k2 − n2k1) sin(4pin1dλ)}],(3.3)83and that1−RT=12n2 (n21 + k21)[n1{(n21 + n22 + k21 + k22)sinh(4pik1dλ)+2 (n1n2 + k1k2) cosh(4pik1dλ)}+k1{(n21 − n22 + k21 − k22)sin(4pin1dλ)−2 (n1k2 − n2k1) cos(4pin1dλ)}],(3.4)where λ is the wave-length of the light; the expressions presented in Eqs. (3.3)and (3.4) contain the same physical content as those presented in Denton etal.’s [109] Eqs. (1) and (2), the thin-film’s optical functions being n1 and k1;k2 is retained in the formalism of Heavens [103] and Denton et al. [109] for thepurposes of generalization, in spite of the fact that it is ultimately assumedthat the underlying substrate is transparent, i.e., that k2 = 0. Denton etal. [109] developed these expressions directly from those of Heavens [103], aswas shown by Tomlin [110].843.7 Modeling the ambient and the optical qual-ity fused quartz substrate optical func-tionsResolving the UHV prepared silicon thin-film optical function spectraldependencies is the primary focus of this analysis. In order to realize thisambition, optical function models for the medium of incidence (ambient),i.e., n0, and the underlying substrate, n2 and k2, must be devised. As afirst-order approach, one can simply assume that the medium of incidence(ambient) has a unity refractive index and that the optical quality fusedquartz substrate is non-absorbing, i.e., that k2 = 0, and that it has a re-fractive index, n2, that is constant, i.e., wave-length invariant. Specifically,these optical functions maybe simply set to nominal reference values, i.e.,n0 = nair = 1, n2 = nquartz = 1.49, and k2 = kquartz = 0, the 1.49 refractiveindex value for the substrate being a reference value commonly employedin the scientific literature [111]. The reflectance and transmittance spectra,obtained through the substitution of these nominal optical function resultsinto the formalism of Heavens [103], for the specific case of an uncoated sub-strate, are shown in Figures 3.10 and 3.11, respectively, the corresponding85Figure 3.10: The room-temperature reflectance spectra associated with theuncoated optical quality fused quartz substrate. The experimental result isdepicted with the solid line. The reflectance obtained by substituting thenominal values of the refractive index, i.e., n0 = 1, n2 = nquartz = 1.49, andk2 = kquartz = 0, into the formalism of Heavens [103], is shown with the dashedline. The reflectance obtained by substituting the 3rd-order polynomial fitmodel for the optical quality fused quartz substrate refractive index’s spectraldependence, shown in Figure 3.14, all other optical functions being held attheir nominal values, is shown with the solid line with the solid points, thesesolid points corresponding to the experimental data points of Palik [112].This figure was published as Figure 2a of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version of this figure is incolor.86Figure 3.11: The room-temperature transmittance spectra associated withthe uncoated optical quality fused quartz substrate. The experimental resultis depicted with the solid line. The transmittance obtained by substitutingthe nominal values of the refractive index, i.e., n0 = 1, n2 = nquartz = 1.49,and k2 = kquartz = 0, into the formalism of Heavens [103], is shown withthe dashed line. The transmittance obtained by substituting the 3rd-orderpolynomial fit model for the optical quality fused quartz substrate refractiveindex’s spectral dependence, shown in Figure 3.14, all other optical functionsbeing held at their nominal values, is shown with the solid line with the solidpoints, these solid points corresponding to the experimental data points ofPalik [112]. This figure was published as Figure 2c of Moghaddam et al. [107].Copyright permission was granted to the author. The online version of thisfigure is depicted in color.87experimental results also being depicted; these results can be computed ei-ther by setting d = 0 or by setting n1 = nair = 1 and k1 = 0.9 Close-ups ofthese results, for the reflectance and transmittance spectra, are depicted inFigures 3.12 and 3.13, respectively. It is noted that the essence of the ex-perimental results is captured with these elementary optical function modelswith reasonable accuracy up until the photon energy approaches 5.5 eV, be-yond which absorption processes within the optical quality fused quartz itselfstart to influence the results.A more accurate modeling of the optical quality fused quartz substrate’srefractive index spectral dependence may be pursued, but this is found tomerely complicate the analysis without having much of an impact on theresults. In Figure 3.14, for example, the optical quality fused quartz re-fractive index’s spectral dependence is depicted, these results being from a9The broad absorption feature that is observed in the transmittance spectrum of theoptical quality fused quartz substrate is most probably due to absorption from O-H impu-rities; UV-grade fused silica has a dip in its transmittance centered at about 1.4 microns(0.89 eV) whereas IR-grade fused silica does not exhibit this dip. The sharp narrow fea-tures that are observed superimposed on this 0.89 eV feature in the unpurged reflectancespectrum of the bare (uncoated) optical quality fused quartz substrate is most likely dueto atmospheric water vapor absorption (H-bonding) related to the intrinsic hydroxide ionimpurities. The residual features associated with these absorption features are also foundin the other spectra, albeit to a lesser degree.88Figure 3.12: A close-up of the room-temperature reflectance spectra asso-ciated with the uncoated optical quality fused quartz substrate. The ex-perimental result is depicted with the solid line. The reflectance obtainedby substituting the nominal values of the refractive index, i.e., n0 = 1,n2 = nquartz = 1.49, and k2 = kquartz = 0, into the formalism of Heavens [103],is shown with the dashed line. The reflectance obtained by substituting the3rd-order polynomial fit model for the optical quality fused quartz substraterefractive index’s spectral dependence, shown in Figure 3.14, all other opticalfunctions being held at their nominal values, is shown with the solid line withthe solid points, these solid points corresponding to the experimental datapoints of Palik [112]. This figure was published as Figure 2b of Moghaddamet al. [107]. Copyright permission was granted to the author. The onlineversion of this figure is depicted in color.89Figure 3.13: A close-up of the room-temperature transmittance spectra asso-ciated with the uncoated optical quality fused quartz substrate. The experi-mental result is depicted with the solid line. The transmittance obtainedby substituting the nominal values of the refractive index, i.e., n0 = 1,n2 = nquartz = 1.49, and k2 = kquartz = 0, into the formalism of Heavens [103],is shown with the dashed line. The transmittance obtained by substitut-ing the 3rd-order polynomial fit model for the optical quality fused quartzsubstrate refractive index’s spectral dependence, shown in Figure 3.14, allother optical functions being held at their nominal values, is shown with thesolid line with the solid points, these solid points corresponding to the ex-perimental data points of Palik [112]. This figure was published as Figure 2dof Moghaddam et al. [107]. Copyright permission was granted to the author.The online version of this figure is depicted in color.90Figure 3.14: The 3rd-order polynomial fit model for the optical quality fusedquartz substrate refractive index’s spectral dependence. The experimentaldata points of Palik [112] are indicated with the solid points. The cor-responding 3rd-order polynomial fit is indicated with the solid line. Thenominal optical quality fused quartz substrate refractive index value, i.e.,n2 = nquartz = 1.49, is indicated with the dashed line. This figure was pub-lished as Figure 2e of Moghaddam et al. [107]. Copyright permission wasgranted to the author. The online version of this figure is depicted in color.91tabulation provided by Palik [112]. Through the use of a 3rd-order polyno-mial fit, the optical quality fused quartz substrate refractive index’s spectralvariation may be modeled, the resultant spectral dependence also being de-picted in Figure 3.14; a recent discussion on the use of polynomial fits formodeling the refractive index’s spectral variation is provided by Moghaddamand O’Leary [113, 114, 115]. For the case of an uncoated substrate, withinthe framework of Heavens’ formalism [103], using this 3rd-order polynomialfit, the resultant reflectance spectra are shown in Figures 3.10 and 3.12, thecorresponding transmittance spectra being shown in Figures 3.11 and 3.13.This more accurate model for the substrate’s refractive index spectral de-pendence is found to lead to results that are almost imperceptibly distinctfrom those determined using the more elementary model; it was still assumedthat the medium of incidence and the substrate are non-absorbing, i.e., thatk0 = 0 and k2 = 0. Accordingly, for the purposes of this analysis, this moreelaborate model for the refractive index associated with the substrate is notemployed in our subsequent analysis.The absorption that occurs for photon energies in excess of 5.5 eV is nowexamined. Palik et al. [112] find that the lowest photon energy for whichkquartz is experimental resolvable, 7.8 eV, corresponds to a kquartz value of924.7× 10−6. For the substrate thickness used for these depositions, i.e., about1.60 mm, neglecting the reflections that occur at the surface, for this partic-ular photon energy, about 75 % of the incident flux should reach the backof the substrate. It is thus concluded that for high photon energies, suchas 7.8 eV, that the absorption within the substrate itself is significant. Itis noted, however, that over the photon energy range that is experimentallyprobed here, i.e., between 0.826 and 6.52 eV, that the transmittance spectraonly reduces from its low photon energy value of around 0.94 to about 0.86for the highest photon energy considered by the National Research Council ofCanada experimental collaborators, 6.52 eV, i.e., a reduction in the transmit-tance by about 10 % is observed over this spectral range. It is thus concludedthat while the absorption within the optical quality fused quartz substratedoes indeed influence the results when the photon energy is between 5.5 and6.52 eV, its influence is expected to be relatively minor. Accordingly, absorp-tion within the optical quality fused quartz substrate will not be consideredin the subsequent analysis.One final issue is worthy of mention. As the spectral response of the en-tire thin-film-silicon/substrate system is considered in this analysis, the anti-reflective character of the thin-films of silicon, in of themselves, should not be93a concern, i.e., reflectances below that associated with an uncoated substrateand transmittances above that associated with an uncoated substrate willnot present a problem. In contrast, for the normalization approaches used bysome, whereby the experimentally acquired spectra corresponding to overallthin-film/substrate systems are normalized with the respect to those associ-ated with that corresponding to an uncoated substrate, this would constitutea considerable source of error. In light of how accurately the spirit of theexperimentally determined uncoated substrates have been captured (recallFigures 3.10, 3.11, 3.12, 3.13, and 3.14), the nominal optical function spec-tral dependence assignments for the ambient (medium of incidence) and theoptical quality fused quartz substrate, i.e., n0 = nair = 1, n2 = nquartz = 1.49,and k2 = kquartz = 0, are taken as reasonable selections.3.8 Inversion process for optical functionsFrom the experimental measurements of the reflectance and transmit-tance spectra, Denton’s equations, i.e., Eqs. (3.3) and (3.4), were set-up,where the thickness associated with each individual thin-film of silicon, d, isset as prescribed in Table 3.1. Within the context of Matlab’s ‘solve’ func-94tion, Denton’s equations were used to determine the refractive index and theextinction coefficient corresponding to each photon energy in the spectrumfor which a reflectance and transmittance value was available; Matlab® isa mathematical problem solver that is commonly used in the engineeringand scientific sectors at the time that this thesis was written. Since Den-ton’s equations harbor phase terms, for some of the thin-films of silicon thatwere considered, a multitude of viable solutions were available, some beingphysical, others being unphysical; phase ambiguity is responsible for this.Denton’s equations were resolved iteratively. In order to ensure the timelyacquisition of these optical function, a maximum of 10 iterations per photonenergy value was used for these computations.In order to obtain physically reasonable solutions, initially crude limits onthe range of values that are to be expected were set. For the refractive index,for example, the range of viable values was initially set between 1 and 10; it isnot physically possible for the refractive index of a regular solid to be belowunity, and the highest refractive index values corresponding to thin-films ofsilicon tend to be well below 10, so this range of values is not unreasonable.For the extinction coefficient, only positive values were considered; it is notphysically possible for this extinction coefficient to be negative, as that would95suggest an increase in the beam intensity as it further penetrates into a givenmaterial. With these crude limitations set, all the feasible solutions acrossthe measurement spectra were obtained and stored.Then, for all the thin-films of silicon, the acquired solutions were com-pared with benchmark data, Palik’s [112] reported data for the refractiveindex spectra being used for this purpose. This was done in order to elimi-nate unphysical solutions and to select the closest spectra to the benchmark.To confirm the validity of the results, the calculated optical functions werethen inserted to Heaven’s equations in order to calculate the reflectance andtransmittance spectra. These calculated reflectance and transmittance spec-tra were then compared with the measurements of reflectance and transmit-tance spectra for all the thin-films. Further discussion on this verificationprocedure are presented in Section 3.9.The main drawback of using existing thin-film software packages to ob-tain the optical functions is the result discrepancy which is commonly foundfor the same input reflectance and transmittance data. In other words, differ-ent software package yield different optical functions, including the refractiveindex and the extinction coefficient, for the same reflectance and transmit-tance spectra for a given thin-film. That is why it was decided to develop96a customized Matlab code to extract optical functions from reflectance andtransmittance spectral measurement. Moreover, the use of a customized codeallows one to examine intermediary results, something not typically allowedusing commercially offered thin-film optical software packages. More infor-mation, regarding available commercial thin-film optics software packages, isprovided in Appendix A.The ‘solve’ function in Matlab uses the Newton-Raphson algorithm tosolve non-linear equations. The algorithm itself is based on an initial guessand draws upon the use of subsequent iterations as it resolves a final solution.After each iteration, the obtained solution value will be closer to the actualsolution value. Figure 3.15 shows the solution error, which is the differencebetween each iteration value with the actual solution, of the refractive indexas a function of the iteration number for a representative thin-film (grown at256 ◦C) for the photon energy set to 1 eV, on a logarithmic scale. As seenin Figure 3.15, the solution error of the refractive index decreases exponen-tially with the iteration number, and goes below 10−5 after 20 iterations.97Figure 3.15: The solution error of the refractive index as a function of theiteration number for a representative thin-film (grown at 256 ◦C) for thephoton energy set to 1 eV . The solution error is plotted on a logarithmicscale. The online version of this figure is depicted in color.983.9 Acquisition and confirmation of the opti-cal functionsAs has been mentioned before, the theoretical framework of Heav-ens [103] forms the basis of this optical function analysis. In particular,through the use of Eqs. (3.3) and (3.4) and the experimental evaluationsof the reflectance and transmittance, the spectral dependence of the opticalfunctions of interest are evaluated. Essentially, through the experimentalevaluations for the reflectance spectra, R, and the transmittance spectra, T ,coupled with the inversion of Eqs. (3.3) and (3.4), the silicon thin-film opticalfunctions of interest are acquired; of course, the experimental evaluations ofR and T are first used to evaluate 1+RTand 1−RT, as demanded of the formal-ism of Heavens, i.e., Eqs. (3.3) and (3.4) [103]. A number of solutions areobtained through this inversion process, some of which are physical, whileothers are not; phase ambiguities are responsible for most of the unphysicalsolutions that are acquired. Some representative physical and unphysicalsolutions, corresponding to the refractive index and the extinction coeffi-cient, for a representative UHV prepared thin-film of silicon, i.e., that grownat 256 oC, are depicted in Figures 3.16 and 3.17, respectively, the spectral99Figure 3.16: The spectral dependence of the refractive index correspondingto the silicon thin-film grown at 256 ◦C. The physical solution, and threerepresentative unphysical solutions, are depicted. This figure was publishedas Figure 4a of Moghaddam et al. [107]. Copyright permission was grantedto the author. The online version of this figure is depicted in color.100Figure 3.17: The spectral dependence of the extinction coefficient correspond-ing to the silicon thin-film grown at 256 ◦C. The physical solution, and threerepresentative unphysical solutions, are depicted. This figure was publishedas Figure 4b of Moghaddam et al. [107]. Copyright permission was grantedto the author. The online version of this figure is depicted in color.101results corresponding to the other thin-films of silicon being very similar.10The process through which the unphysical solutions were identified andeliminated is worthy of mention. Prior to any further consideration, solutionsfor the optical functions that exhibited features that are obviously inconsis-tent with the basic physics underlying materials are eliminated. As a result,refractive index and extinction coefficient solutions, that, starting from lowphoton energies, exhibit a monotonic decline accompanying photon energyincreases are eliminated, for example. Moreover, those solutions for the opti-cal functions that did not exhibit a peak, or exhibit other such oddities, areeliminated.10Based on the measurements of reflectance and transmittance spectra, the followingratios were first calculated: 1+RT and1−RT . Based on the values of refractive index for theambient, i.e., n0 = 1, and the substrate, i.e., n2 = 1.49, and the extinction coefficient of 0for the fused quartz, the Heaven’s equations for 1+RT and1−RT have two unknowns. In orderto solve this system of equations, the ‘solve’ function is used in Matlab which acquires thesolutions for each photon energy. The ‘solve’ function uses the Levenberg-Marquardt andtrust-region methods, these being based on a number of non-linear least-squares solvingalgorithms. The trust-region algorithm is a sub-space trust-region method and is based onthe interior-reflective Newton method. Each iteration involves the approximate solution ofa large linear system using the method of preconditioned conjugate gradients. In addition,the Levenberg-Marquardt algorithm uses a search direction that stems from a solution ofthe linear set of equations.102Following this initial pre-screening process, the primary means throughwhich the accuracy of the optical function solutions is confirmed is throughconsistency with the experimentally acquired reflectance and transmittancespectra. The approach that is employed in order to confirm the correctnessof the optical function solutions, i.e., the refractive index and the extinctioncoefficient, involved the substitution of the acquired silicon thin-film opti-cal function solutions into the formalism of Heavens [103]. A comparison ofthe resultant spectra with those determined through experiment is used togauge the accuracy of the acquired optical functions. The reflectance andtransmittance results, corresponding to such an analysis, for the three sili-con thin-films grown at 98 ◦C, are depicted in Figures 3.18, 3.19, and 3.20respectively, the experimental results also being depicted on these figures;transmittance results are shown in Figures 3.19 and 3.20 on two differentscales. It is noted that, for all cases considered, the experimental spectraare virtually indistinguishable from that acquired through the substitutionof the acquired optical functions into the formalism of Heavens [103]. Ananalogous result, for the case of the various growth temperatures consideredin this analysis, is presented in Figures 3.21, 3.22, and 3.23, respectively, oneof the 98 ◦C spectra shown in Figures 3.18, 3.19, and 3.20, i.e., that grown103Figure 3.18: The room-temperature reflectance spectra corresponding tothree silicon thin-films grown at 98 ◦C. The experimental data sets are de-picted with the solid lines. The film thicknesses corresponding to each sampleare also depicted on this figure. The reflectance spectra obtained, througha substitution of the acquired optical functions into the formalism of Heav-ens [103], are shown with the dashed lines. A linear scale is employed. Thisfigure was published as Figure 5a of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.104Figure 3.19: The room-temperature transmittance spectra corresponding tothree silicon thin-films grown at 98 ◦C. The film thicknesses corresponding toeach sample are also depicted on this figure. The experimental data sets aredepicted with the solid lines. The transmittance spectra obtained, througha substitution of the acquired optical functions into the formalism of Heav-ens [103], are shown with the dashed lines. A linear scale is employed. Thisfigure was published as Figure 5c of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.105Figure 3.20: The room-temperature transmittance spectra corresponding tothree silicon thin-films grown at 98 ◦C. The film thicknesses corresponding toeach sample are also depicted on this figure. The experimental data sets aredepicted with the solid lines. The transmittance spectra obtained, througha substitution of the acquired optical functions into the formalism of Heav-ens [103], are shown with the dashed lines. A logarithmic scale is employed.This figure was published as Figure 5d of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.106Figure 3.21: The room-temperature reflectance spectra corresponding to thesilicon thin-films grown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493, and572 ◦C. These experimental data sets are depicted with the solid lines. Thereflectance spectra obtained, through a substitution of the acquired opticalfunctions into the formalism of Heavens [103], are shown with the dashedlines. A linear scale is employed. This figure was published as Figure 5b ofMoghaddam et al. [107]. Copyright permission was granted to the author.The online version of this figure is depicted in color.107Figure 3.22: The room-temperature transmittance spectra corresponding tothe silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256, 335, 415,493, and 572 ◦C. These experimental data sets are depicted with the solidlines. The transmittance spectra obtained, through a substitution of theacquired optical functions into the formalism of Heavens [103], are shownwith the dashed lines. A linear scale is employed. This figure was publishedas Figure 5e of Moghaddam et al. [107]. Copyright permission was grantedto the author. The online version of this figure is depicted in color.108Figure 3.23: The room-temperature transmittance spectra corresponding tothe silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493,and 572 ◦C. These experimental data sets are depicted with the solid lines.The transmittance spectra obtained, through a substitution of the acquiredoptical functions into the formalism of Heavens [103], are shown with thedashed lines. A logarithmic scale is employed. This figure was published asFigure 5f of Moghaddam et al. [107]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.109to a thickness of 303 nm, also being included [108].11,12The results of a detailed error analysis, obtained by taking the absolutevalue of the difference between the solution acquired results and that ofexperiment, are presented in Figures 3.24, 3.25, 3.26, and 3.27, for the variouscases considered in this analysis. For all cases, the absolute error found is11For a uniform thin-film, of thickness d, Cody et al. [108] assert that the maxima occurwhen4pin (λ) dλ= 2mpi,where n (λ) is the spectral dependence of the refractive index, λ is the wave-length invacuum, and m is an integer that can assume the values 0, 1, 2, .... Cody et al. [108] alsoassert that the minima occur when4pin (λ) dλ= 2(m+12)pi,where, as with the condition for the maxima, m is an integer that can assume the values0, 1, 2, .... The reflectance and transmittance spectral oscillations that are observed inFigures 3.18, 3.19, 3.20, 3.21, 3.22, and 3.23 are mostly consistent with this expectationof Cody et al. [108]. Deviations from the principle of Cody et al. [108] arose from theinhomogeneities that are present within some of these thin-films of silicon.12There is evidence to suggest that there are inhomogeneities that occur in the opticalproperties as one goes deeper into a given thin-film, these inhomogeneities reflecting thestructural inhomogeneities that are present. In effect, a given thin-film may be thought ofas being comprised of a stack of thin-film layers, each layer within such a stack having itsown optical properties.110Figure 3.24: The spectral dependence of the absolute error associated withthe room-temperature reflectance spectra corresponding to three silicon thin-films grown at 98 ◦C, where the absolute error corresponds to the absolutedifference between the experimental results and those obtained through thesubstitution of the acquired optical functions into the formalism of Heav-ens [103]. The film thicknesses corresponding to each sample are also de-picted on this figure. The data sets are depicted with the solid lines. Thisfigure was published as Figure 6a of Moghaddam et al. [107]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.111Figure 3.25: The spectral dependence of the absolute error associated withthe room-temperature reflectance spectra corresponding to the silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493, and 572 ◦C,where the absolute error corresponds to the absolute difference between theexperimental results and those obtained through the substitution of the ac-quired optical functions into the formalism of Heavens [103]. The data setsare depicted with the solid lines. This figure was published as Figure 6b ofMoghaddam et al. [107]. Copyright permission was granted to the author.The online version of this figure is depicted in color.112Figure 3.26: The spectral dependence of the absolute error associated withthe room-temperature transmittance spectra corresponding to three siliconthin-films grown at 98 ◦C, where the absolute error corresponds to the abso-lute difference between the experimental results and those obtained throughthe substitution of the acquired optical functions into the formalism of Heav-ens [103]. The film thicknesses corresponding to each sample are also depictedon this figure. The data sets are depicted with the solid lines. This figurewas published as Figure 6c of Moghaddam et al. [107]. Copyright permissionwas granted to the author. The online version of this figure is depicted incolor.113Figure 3.27: The spectral dependence of the absolute error associated withthe room-temperature transmittance spectra corresponding to the siliconthin-films grown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493, and572 ◦C, where the absolute error corresponds to the absolute difference be-tween the experimental results and those obtained through the substitutionof the acquired optical functions into the formalism of Heavens [103]. Thedata sets are depicted with the solid lines. This figure was published as Fig-ure 6d of Moghaddam et al. [107]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color.114upper bounded by 3×10−3, this being less than the experimental uncertaintyitself for many cases. Clearly, the acquired solutions for the optical functionsare satisfactory in terms of their accuracy.Two other means of eliminating unphysical solutions were employed.First, the Kramers-Kronig relations were applied in order to check that theacquired optical function solutions are Kramers-Kronig consistent. This isdone through repeated applications of the Kramers-Kronig relationship. Inparticular, for each optical function, the Kramers-Kronig relationships areapplied twice and it is ensured that the resultant optical function is the sameas the initial optical function, i.e., before this process was initiated. Thisis found to be the case for all of the acquired optical functions.13 Second,as was mentioned before, the results are benchmarked with representativesilicon thin-film optical function results. It would be expected that simi-larly prepared thin-films should all exhibit similar optical functional spectraldependencies, and that similarly prepared thin-films should exhibit opticalfunctional dependencies that are reasonably close with each other and thatsingularities and discontinuities usually do not occur in nature. This criterion13This Kramers-Kronig means of pruning out the unphysical solutions is still underdevelopment. For the purposes of this particular analysis, it is found that it provided arather effective means of performing this task.115was found to be extremely effective at eliminating the unphysical solutionsthat arise from the inevitable phase ambiguities that can occur.3.10 Optical functions resultsThe results of this analysis are now presented, these results being deter-mined from the experimental reflectance and transmittance spectral depen-dencies depicted in Figures 3.2, 3.3, 3.4, and 3.5. The analysis is started witha consideration of the spectral dependence of the refractive index, n (~ω), forthe samples considered in this analysis. In Figure 3.28, refractive index re-sults, corresponding to the set of silicon thin-films, of various thicknesses,i.e., 135, 303, and 605 nm, that had all been prepared at 98 ◦C are depicted.It is noted that, for all three cases, the refractive index initially increasesmonotonically in response to increases in the photon energy, ~ω, exhibitsa peak, and then starts to decrease in response to further increases in thephoton energy, ~ω; the decrease, however, is found to be relatively modestfor the 605 nm case. It is also noted that the refractive index associated withthe thickest film is always lower than that associated with the other films,there being a general trend towards lower values of the refractive index as116Figure 3.28: The spectral dependence of the refractive index, n (~ω), corre-sponding to three silicon thin-films grown at 98 ◦C. The experimental datasets are depicted with the solid lines. The film thicknesses corresponding toeach sample are also depicted on this figure. This figure was published asFigure 3a of Moghaddam et al. [106]. Copyright permission was granted tothe author. The online version of this figure is in color.117the film thickness is increased, although it is noted that this trend is notabsolute and that some cross-over is observed between the spectral results.While the fundamental cause for this thickness dependence remains unknownat present, similar observations have been made by other researchers in thefield. Consider, for example, the experimental results of Sridhar et al. [116]in which a very similar dependence is found. The results of Mu¨llerova´ etal. [117] also display a similar trend.14 The refractive index range reportedhere is representative of that found elsewhere in the silicon thin-film scientificliterature [6].How the spectral dependence of the refractive index is modified by thegrowth temperature is now examined. In Figure 3.29, the spectral depen-dence of the refractive index, n (~ω), is plotted for the thin-films of silicongrown at 98 (303 nm), 138, 177, 217, 256, 335, 415, 493, and 572 ◦C. It is14As was mentioned in footnote 12, there is evidence to suggest that there are inho-mogeneities that occur in the optical properties as one goes deeper into a given thin-film,these inhomogeneities reflecting the structural inhomogeneities that are present. In effect,a given thin-film may be thought of as being comprised of a stack of thin-film layers, eachlayer within such a stack having its own optical properties. These differences become mag-nified the thicker the thin-film, the thin-films grown at 98 ◦C exhibiting large differencesin their thicknesses when contrasted with those grown at the other growth temperatures;recall Table 3.1118Figure 3.29: The spectral dependence of the refractive index, n (~ω), corre-sponding to the silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256,335, 415, 493, and 572 ◦C. The experimental data sets are depicted with thesolid lines. The film thicknesses corresponding to each sample are also de-picted on this figure. This figure was published as Figure 3b of Moghaddamet al. [106]. Copyright permission was granted to the author. The onlineversion of this figure is depicted in color.119noted that, similar to the 98 ◦C results depicted in Figure 3.28, for all cases,the refractive index initially increases monotonically with the photon energy,~ω, exhibits a peak, and then starts to decrease in response to further in-creases in the photon energy, with the exception of the 493 ◦C case which justexhibits a monotonically increasing dependence on the photon energy, ~ω;it is suspected that the peak occurs at photon energies beyond the spectralrange shown in Figure 3.29 for the 493 ◦C case. It is noted that the refractiveindex generally increases as the growth temperature is increased, althoughit is observed that this trend is not absolute, and note that some cross-overoccurs between the different spectral results.The behavior of the extinction coefficient, k (~ω), for the silicon thin-filmsconsidered in this analysis, is now considered, these spectral dependenciesbeing depicted in Figures 3.30 and 3.31; henceforth, for each optical function,the first figure will focus on the set of three silicon thin-films that havebeen prepared at 98 ◦C, the second figure corresponding to the nine siliconthin-films that have been prepared at different growth temperatures, thesilicon thin-film grown at 98 ◦C being the 303 nm one for the second figure;the first and second figure results are presented separately so that one hasa sense of the impact of the aforementioned inhomogeneity effects (recall120Figure 3.30: The spectral dependence of the extinction coefficient, k (~ω),corresponding to three silicon thin-films grown at 98 ◦C. The experimentaldata sets are depicted with the solid lines. The film thicknesses correspondingto each sample are also depicted on this figure. This figure was published asFigure 4a of Moghaddam et al. [106]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.121Figure 3.31: The spectral dependence of the extinction coefficient k (~ω),corresponding to the silicon thin-films grown at 98 (303 nm), 138, 177, 217,256, 335, 415, 493, and 572 ◦C. The experimental data sets are depictedwith the solid lines. This figure was published as Figure 4b of Moghaddamet al. [106]. Copyright permission was granted to the author. The onlineversion of this figure is depicted in color.122footnotes 12 and 14). In all cases, it is seen that the extinction coefficientincreases monotonically with the photon energy, ~ω, achieves a peak at somepoint, and then decreases in response to further increases in the photonenergy. The peaks in these plots seem to all occur in the vicinity of ~ω beingequal to 3 eV. It is clear that these results vary as a function of the growthtemperature. In particular, it is noted that as the growth temperature isincreased that the extinction coefficient diminishes.In Figures 3.32, 3.33, 3.34, and 3.35, the spectral dependence of the realand imaginary parts of the dielectric function, 1 (~ω) and 2 (~ω), respec-tively, are plotted, these results corresponding to the reflectance and trans-mittance spectral data depicted in Figures 3.2, 3.3, 3.4, and 3.5; the relativedielectric functions are depicted. These optical dispersion relationships aredetermined from n (~ω) and k (~ω), i.e.,1 (~ω) = n2 (~ω)− k2 (~ω) , (3.5)and2 (~ω) = 2 n (~ω) k (~ω) . (3.6)123Figure 3.32: The spectral dependence of the real part of the dielectric func-tion, 1 (~ω), corresponding to three silicon thin-films grown at 98 ◦C. Theexperimental data sets are depicted with the solid lines. The film thicknessescorresponding to each sample are also depicted on this figure. This figurewas published as Figure 5a of Moghaddam et al. [106]. Copyright permissionwas granted to the author. The online version of this figure is depicted incolor.124Figure 3.33: The spectral dependence of the real part of the dielectric func-tion, 1 (~ω), corresponding to silicon thin-films grown at 98 (303 nm), 138,177, 217, 256, 335, 415, 493, and 572 ◦C. This figure was published as Fig-ure 5b of Moghaddam et al. [106]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color.125Figure 3.34: The spectral dependence of the imaginary part of the dielectricfunction, 2 (~ω), corresponding to three silicon thin-films grown at 98 ◦C.The experimental data sets are depicted with the solid lines. The film thick-nesses corresponding to each sample are also depicted on this figure. Thisfigure was published as Figure 6a of Moghaddam et al. [106]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.126Figure 3.35: The spectral dependence of the imaginary part of the dielectricfunction, 2 (~ω), corresponding to silicon thin-films grown at 98 (303 nm),138, 177, 217, 256, 335, 415, 493, and 572 ◦C. This figure was published asFigure 6b of Moghaddam et al. [106]. Copyright permission was granted tothe author. The online version of this figure is depicted in color.127As with the case of the refractive index, n (~ω), extrema are observed forphoton energies between 3 and 4 eV. In light of the fact that both n (~ω)and k (~ω) initially increase in response to increases in the photon energy,~ω, these effects are countervailing; recall Eq. (3.5). Hence, the wide rangeof results for the case of 1 (~ω). The highest value of 1 (~ω), about 38for the case of the 493 ◦C deposited sample of silicon thin-film, is noted tobe considerably greater than that associated with c-Si. Clearly, this offersopportunities for device applications requiring a high refractive index. Thespectral dependence of the imaginary part of the dielectric function, 2 (~ω),is shown in Figures 3.34 and 3.35 on a linear scale.In Figures 3.36 and 3.37, the optical absorption spectra, corresponding tothe silicon thin-films considered in this analysis, are depicted. These spectraare determined using the spectral dependence of the extinction coefficient,k (~ω), as it can be demonstrated thatα (~ω) = 2ωck (~ω) , (3.7)where c denotes the speed-of-light in vacuum. With the exception of thesilicon thin-films grown at 493 and 572 ◦C, it is noted that for values of ~ω128Figure 3.36: The spectral dependence of the optical absorption coefficient,α (~ω), corresponding to three silicon thin-films grown at 98 ◦C. The ex-perimental data sets are depicted with the solid lines. The film thicknessescorresponding to each sample are also depicted on this figure. This figurewas published as Figure 7a of Moghaddam et al. [106]. Copyright permissionwas granted to the author. The online version of this figure is depicted incolor.129Figure 3.37: The spectral dependence of the optical absorption coefficient,α (~ω), corresponding to silicon thin-films grown at 98 (303 nm), 138, 177,217, 256, 335, 415, 493, and 572 ◦C. This figure was published as Figure 7bof Moghaddam et al. [106]. Copyright permission was granted to the author.The online version of this figure is depicted in color.130in excess of 3 eV that these optical absorption spectra appear to convergetowards a common trend; that is, they all lie within a common range of opticalabsorption values. Substantive differences between these optical absorptionspectra are really only noticeable in the tail region, where exponential opticalabsorption tails are evident. The optical absorption coefficient associatedwith the silicon thin-film grown at 572 ◦C, however, is seen to be exhibit adistinctive spectral dependence when contrasted with those corresponding tothe other silicon thin-films. As will be commented upon later, it is suspectedthat this may be on account of its high crystalline volume fraction [33].3.11 Technical achievementsIn this chapter, I have detailed the manner in which these UHV preparedthin-films of silicon have been grown and discussed how their near-normalreflectance and normal transmittance spectra have been experimentally ac-quired. I then presented the experimentally measured reflectance and trans-mittance spectra, these providing the experimental basis for the subsequentoptical function analysis. A detailed uncertainty analysis, which I feel couldbe useful for other experimentalists in the broader thin-film community, i.e.,131beyond the confines of just the silicon thin-film community itself, was thenpresented, issues that have yet to be reported upon in the scientific litera-ture being explicitly examined. Following the presentation of the spectraldependence of the uncertainty, I then presented the formalism upon whichmy optical function analysis is rooted. A detailed discussion on the opti-cal function assignments associated with the underlying optical quality fusedquartz substrate and the ambient was then presented. A presentation on themanner in which the optical functions have been acquired, how the unphysi-cal solutions were eliminated, and means of confirming the validity of a givenoptical function’s spectral dependence, were then made, an assessment of theerror that occurs also being provided. Finally, a detailed presentation of thespectral dependence of all of the optical functions of the UHV thin-films ofsilicon was then presented.I identify a number of significant technical achievements that were pre-sented herein. First, the detailed uncertainty analysis that has been pre-sented, while admittedly lengthy, provides a great deal of material that thin-film researchers can draw upon. Such details, while extremely important,are usually not reported upon in scientific papers as they are not consideredas ‘important’ as say the properties of a new material or a previously unre-132ported phenomena. The detailed expose´ into how the optical functions wereacquired from experimental measurements of the near-normal reflectance andnormal transmittance spectra, coupled with the approaches that I took interms of eliminating unphysical solutions, represents another practical con-tribution that could be viewed of as being of use to those within the broaderthin-film community. Once again, explicit discussions on such matters, whilenot common in the scientific literature, are extremely useful, as they provideless experienced researchers with a guide that they can draw upon. So veryuseful but perhaps with less scientific cache´ than traditional scientific fare.Finally, the report on the spectral dependence of the optical functions for thevarious UHV prepared thin-films of silicon provides an experimental basis forunderstanding how the growth temperature influences the optical functionsassociated with this form of silicon thin-film. From a materials perspective,this of course is the most interesting aspect of this analysis.So, within this chapter, I have presented results that are useful from aninstrumentation perspective and from a materials perspective. This experi-mental data provides the experimental basis for the subsequent analysis thatis presented in Chapter 4.133Chapter 4Crystallinity, order, and thesilicon thin-film continuum4.1 OverviewPD-a-Si’s favorable electronic properties have long been recognized asstemming from hydrogen’s affinity for the dangling and weakened bonds thatare present within PD-a-Si, hydrogen atoms passivating these dangling andweakened bonds [5, 20]. Hydrogen atoms, which are light and mobile, are alsogiven credit for alleviating some of the stress that exists within the networkof atoms that constitute PD-a-Si, i.e., the hydrogen atoms are able to contortthemselves into bonding configurations that would not typically occur withonly silicon atoms present. Regrettably, PD-a-Si’s electronic degradation134accompanying its exposure to light, which has been identified as a criticalweakness of PD-a-Si, has also been attributed to the ample population ofhydrogen atoms that are present within it [22, 101, 102]. So, with respectto PD-a-Si, hydrogen atoms play both beneficial and detrimental roles. Thisbegged the question: can silicon thin-film be prepared in another form, onethat retains PD-a-Si’s favorable electronic properties without its troublesomeinstability?The hydrogen concentrations that are present within PD-a-Si have beenshown to vastly exceed that associated with the dangling bonds presentwithin a-Si in its unhydrogenated forms [18, 122, 123]. This has led someto speculate that with greater control over the atomic species present withina deposition process, it might be possible to prepare an alternative typeof silicon thin-film with just the amount of hydrogen atoms needed so asto passivate the dangling bonds but not so much as to make the materialprone to PD-a-Si’s instability. With the observation that an UHV deposi-tion process, which is used in MBE, affords considerable control over theatomic species that are present during a given deposition process, using anUHV MBE system, a series of silicon thin-films and superlattices have beenprepared, the hope being that this type of silicon thin-film will provide the135silicon thin-film community with this long sought after form of this material.The results of these investigations have suggested that this particular formof silicon thin-film offers a constellation of material properties that make ita potentially useful material for electronic and opto-electronic device appli-cations [26, 27, 28, 29, 31, 32, 33].In the previous chapter, the optical properties of a sequence of UHVprepared silicon thin-films, grown using a variety of different temperatures,was reported upon. These results were determined through an analysis ofexperimentally acquired reflectance and transmittance results, the spectraldependence of a number of key silicon thin-film optical functions being de-termined. In order to allow for the acquisition of these optical functions, atransparent substrate, i.e., optical quality fused quartz, was employed for allof the depositions. The optical functions considered in Chapter 3 includedthe refractive index, the extinction coefficient, the real and imaginary partsof the dielectric function, and the optical absorption coefficient, these beingthe optical functions most commonly encountered in optical response char-acterizations. Noting that variations in the growth temperature itself allowsfor a transition between thin-films of silicon that are purely amorphous in na-ture (prepared at the lower growth temperatures) and those that are mostly136crystalline in nature (prepared at the higher growth temperatures), the UHVdeposited thin-films of silicon may be viewed of as being part of a silicon thin-film continuum, growth temperature variations allowing for transitions acrossthis continuum; recall the work of Orapunt et al. [33]. Noting that the partic-ular form of UHV prepared silicon thin-film spans over a considerable rangeof this continuum, the experimental results gleaned from the UHV preparedsamples affords one with a unique opportunity to probe how the placementof a given thin-film of silicon within this aforementioned continuum shapesthe optical properties of the resultant thin-film of silicon, this being an openproblem that has long challenged the silicon thin-film community.Accordingly, in this chapter, drawing upon some previous work of Na-tional Research Council of Canada experimental collaborators [32, 33] thathad explored how the underlying micro-structure of these UHV preparedthin-films of silicon is shaped by the growth temperature, the relationshipbetween the underlying micro-structure and the spectral dependence of theseaforementioned optical functions is explored. Micro-structural informationis gleaned from a conjuncture of GIXRD and Raman spectroscopic experi-mental results that have been reported upon earlier. The optical functionsthemselves were acquired from measurements of the reflectance spectra at137near-normal incidence and the transmittance spectra at normal incidence,these results being reported upon in Chapter 3. The UHV prepared siliconthin-films that are considered here were all grown on optical quality fusedquartz substrates, the growth temperature being varied from 98 to 572 ◦C.In order to limit the scope of the analysis, the optical function that is fo-cused upon for the purposes of this particular analysis is the refractive index,the implications of these results, in terms of the applications of this type ofsilicon thin-film, also being explored.This chapter is organized in the following manner. In Section 4.2, somepreviously reported experimental results, performed on some of the UHVprepared thin-films of silicon, are presented, these results forming the basisfor the subsequent investigation. In Section 4.3, the concept of a silicon thin-film continuum is introduced, the placement of the UHV prepared thin-filmsof silicon into this continuum being performed; GIXRD results, acquired bythe National Research Council of Canada experimental collaborators, aredrawn upon for the purposes of this analysis. Then, in Section 4.4, a collec-tion of Raman spectra, acquired for the UHV prepared thin-films of silicon,are presented, Raman related measures of the disorder being correlated withthe form of the refractive index in Section 4.5; these Raman results were138also acquired by the National Research Council of Canada experimental col-laborators. A critical comparative analysis of some of the acquired opticalfunctions associated with the UHV prepared thin-films of silicon and thatcorresponding to more conventionally prepared forms of silicon thin-film isthen presented in Section 4.6. How the spectral dependence of the opticalabsorption spectrum is related to the band structure of c-Si is then exploredin Section 4.7. The device potential of the UHV prepared form of siliconthin-film is examined in Section 4.8. Finally, a summary of the technicalachievements reported upon in this chapter is provided in Section 4.9.4.2 Background experimental dataIn this chapter, experimental data, harvested from a variety of experi-mental measurements, is employed in order to glean insights into the prop-erties of this particular form of silicon thin-film prepared through UHV de-position. In this section, some of the previously reported experimental data,which forms the backdrop for the current analysis, is described. The experi-ments, from which this experimental data was drawn from, were performedby the National Research Council of Canada experimental collaborators. The139experimental data, upon which the current analysis is based, include thosefocused on GIXRD, Raman, and secondary ion mass spectroscopic measure-ments. While these experiments were not performed by me, they inform myinterpretation of the results, and thus, are an important component of thescientific record.In Figure 4.1, GIXRD spectra, for a selection of UHV prepared siliconthin-film samples deposited on optical quality fused quartz substrates, areshown. It is noted that the samples deposited at the lower growth tempera-tures exhibit a form representative of an underlying a-Si “lattice” structure,the peaks being broad and relatively unstructured. For the higher growthtemperatures, however, distinct peaks become evident, suggesting the pres-ence of silicon crystallites within such samples, as would be expected of µc-Si or nc-Si. An estimate to the mean crystallite size, D, may be acquiredthrough knowledge of the GIXRD peak spectral breadth, β2θ, this connectionoccurring through the use of Scherrer’s equation, which may be expressed asD =0.94λβ2θ cos (θ), (4.1)the X-ray source having the wavelength λ; the GIXRD machine used by140Figure 4.1: GIXRD spectra for a number of silicon thin-films preparedthrough UHV evaporation. A variety of growth temperatures are employed,the GIXRD spectra corresponding to the higher growth temperatures ex-hibiting distinctive peaks representative of the presence of silicon crystalliteswithin the samples. This image is the same as Figure 1 of Orapunt et al. [33].Copyright permission was granted to the author. The online version of thisfigure is depicted in color.141the National Research Council of Canada experimental collaborators useda CuKα1,2 X-ray source. The sharp spectral peaks, when they are present,suggest that the crystallites are about 10 nm in dimension, indicating thatthe higher growth temperature silicon thin-film samples, prepared throughUHV deposition, are nc-Si in nature.Identifying how the properties of silicon thin-film vary as the materialtransitions from amorphous to crystalline remains an open problem in thesilicon thin-film field. The distinctive transition in the nature of the siliconthin-film form, from a-Si to nc-Si, in response to increases in the growthtemperature, suggests that this particular silicon thin-film form provides onewith an opportunity to try to address fundamental matters concerning thecharacter of silicon thin-film all within the context of a single material system.In fact, as will be expounded upon later, the entire silicon thin-film genomemay be considered as being part of a continuum, which ranges from a purelyamorphous material to a purely crystalline material. Identifying where theUHV prepared thin-films of silicon exist within this continuum will help usaddress fundamental issues related to silicon thin-film’s genome.In addition to the amount of crystallinity that is present, thin-films ofsilicon possess disorder. The nature of the disorder that is present within a142given sample of silicon thin-film, will also play a role in shaping its materialproperties. The Raman spectrum provides a means of probing the natureof the disorder within a given material. The Raman spectrum has beenacquired corresponding to each and every UHV prepared silicon thin-filmthat had been deposited on optical quality fused quartz substrates. TheseRaman spectra form the basis of the analysis that is presented in Section 4.4.In order to assess the growth temperature’s influence on the form of theRaman spectrum, it is instructive to examine the changes that occur in theRaman spectrum in response to growth temperature variations. Accordingly,in Figures 4.2, 4.3, and 4.4, the Raman spectra associated with the UHV de-posited silicon thin-films, grown at 415, 493, and 572 ◦C, are depicted, thiscorresponding to the growth temperatures range over which a phase transi-tion, from a primarily amorphous form into a crystalline form, is observed.A pronounced transverse optical (TO) phonon-related peak is noted for allcases, a corresponding transverse acoustic (TA) phonon-related feature alsobeing observed. A longitudinal acoustic (LA) phonon-related feature, of lesssignificance than the two previously mentioned features, is also observed. Ad-ditional sharp peaks, centred around 507 and 518 cm−1, are observed. The518 cm−1 sharp peak and the weaker peak centred about 507 cm−1 are be-143Figure 4.2: The 415 ◦C UHV prepared silicon thin-film sample Raman spec-trum. The solid black line represents the spectrum itself, the decompositionof this spectrum into its underlying spectral peaks being represented withthe dashed lines. A green line is used to show the estimated instrumentalbackground, i.e., the baseline. This image is the same as Figure 2 of Ora-punt et al. [33]. Copyright permission was granted to the author. The onlineversion of this figure is depicted in color.144Figure 4.3: The 493 ◦C UHV prepared silicon thin-film sample Raman spec-trum. The solid black line represents the spectrum itself, the decompositionof this spectrum into its underlying spectral peaks peaks being representedwith the dashed lines. A green line is used to show the estimated instru-mental background, i.e., the baseline. This image is the same as Figure 3 ofOrapunt et al. [33]. Copyright permission was granted to the author. Theonline version of this figure is depicted in color.145Figure 4.4: The 572 ◦C UHV prepared silicon thin-film sample Raman spec-trum. The solid black line represents the spectrum itself, the decompositionof this spectrum into its underlying spectral peaks peaks being representedwith the dashed lines. A green line is used to show the estimated instru-mental background, i.e., the baseline. This image is the same as Figure 4 ofOrapunt et al. [33]. Copyright permission was granted to the author. Theonline version of this figure is depicted in color.146lieved to be related to the increasing crystallinity that accompanies increasesin the growth temperature.Following the usual procedure adopted in the field, an assessment of thecrystalline volume fraction may be pursued through a peak decompositionprocess. A representative peak decomposition process is that discussed byOrapunt et al. [33]. With certain peaks ascribed to the crystalline phase andother peaks being related to the amorphous phase, one can determine thecrystalline volume fraction by determining the integrated areas under thevarious Raman spectral peaks, greater integrated areas under the crystallinephase related peaks suggesting a higher crystalline volume fraction. Furtherdiscussions on this approach are provided by Tay et al. [31] and Orapunt etal. [33].For the UHV prepared thin-films of silicon deposited on optical qualityfused quartz substrates, it was found that there was very little crystallinity forgrowth temperatures less than 400 ◦C. Above this temperature, however, thecrystalline volume fraction was found to dramatically increase. In particular,crystalline volume fractions of 0.84, 57, and 83 % were found for the thin-films of silicon grown at 415, 493, and 572 ◦C, respectively. Clearly, a phasetransition is occurring over this relatively narrow range of growth tempera-147tures. A plot of the crystalline volume fractions’ dependence on the growthtemperature, for thin-films of silicon grown on a multitude of substrates, in-cluding optical quality fused quartz substrate, is depicted in Figure 4.5. Itis interesting to note that thin-films of silicon grown on c-Si and SiO2/c-Sisubstrates also exhibit similar phase transitions, albeit at lower growth tem-peratures. While these results make intuitive sense, an exact explanation hasyet to be obtained.From Figure 4.5, it is clear that two quantitative metrics, associated withthe transition from amorphous-to-crystalline, may be defined. In particular,there is:1. Tonset, the crystallinity onset temperature, a temperature at whichpoint the thin-film of silicon is amorphous in character but is just aboutto start its crystallization process.2. Tsaturation, the crystallinity saturation temperature, a temperature atwhich point the crystallization process has more or less been completed.In Orapunt et al. [80], Tonset was evaluated through an assessment as to whenthe crystalline volume fraction starts to increase, Tsaturation being estimatedthrough a process of linear extrapolation. In light of the gradual manner in148Figure 4.5: The relationship between the crystalline volume fraction and thegrowth temperature for silicon thin-film samples deposited on c-Si, SiO2/c-Si, and optical quality fused quartz substrates. This image is the same asFigure 5a of Orapunt et al. [80]. Copyright permission was granted to theauthor. The online version of this figure is depicted in color.149which saturation is achieved, i.e., complete crystallization, it was determinedthat this process of linear extrapolation was the best approach one couldadapt. However, as can be seen from Figure 4.5 directly, deviations fromthis extrapolation are obviously in evidence; note for example, the 572 ◦Cdata point for the specific case of the thin-film of silicon deposited on opticalquality fused quartz.4.3 Silicon thin-film continuumAs has been mentioned earlier, silicon thin-film, in its various forms, maybe considered as being part of a continuum. At one end of this continuumis a-Si, a silicon thin-film type that is bereft of any crystallinity. At theother end of this continuum, however, is c-Si itself, c-Si wafers now beingproduced with diameters of 45 cm. Fundamentally, the properties of anyparticular sample of silicon in its thin-film form is a strong function of itscorresponding grain size, a-Si having an effective ‘grain’ size that is ideallyof the order of the dimensions of the silicon atom itself, the aforementioned45 cm c-Si wafers being thought of as having grain sizes of the order of thedimensions of the wafer. All other types of silicon thin-film possess grain sizes150that are in between these limiting cases. A stylized schematic representationof this silicon thin-film continuum is featured in Figure 4.6, with some of thekey properties, i.e., the electron and hole mobilities and the correspondingcrystallite grain sizes, associated with representative forms of silicon thin-film, also being shown.For each of the UHV prepared thin-films, a GIXRD analysis was pursued.While the films prepared at the lower growth temperatures, i.e., below 335 ◦C,exhibit GIXRD spectra that are representative of that found for the casea-Si itself, evidence of c-Si-based diffraction becomes clear for the highergrowth temperatures. Indeed, for the 493 and 572 ◦C growth temperatures,a conjuncture of a-Si and c-Si diffraction peaks becomes apparent, suggestingthe presence of a mixture of these two phases of silicon for these two particularsamples. In addition, some residue of crystallinity remains in the GIXRDspectra associated with the UHV prepared silicon thin-films prepared at 335and 415 ◦C.Further analysis demonstrates that for the UHV prepared thin-films ofsilicon grown at 335 and 415 ◦C, there are actually small crystallites em-bedded into an a-Si background, the mean crystallite sizes being between 2and 3 nm for both of these thin-films of silicon, in spite of the fact that the151Figure 4.6: A stylized representation of silicon thin-film’s structural continuum.The various types of silicon thin-film, i.e., a-Si, nc-Si, µc-Si, and poly-crystallineSi (poly-Si), are depicted in the top-most row. The grain sizes are depicted in thenext row down. The corresponding electron and hole mobilities are then depictedin the next two rows. In the final row, the growth temperatures needed in order toachieve the various types of silicon thin-film, corresponding to the UHV preparedthin-film form of silicon, are depicted, as will be seen from the sequence of exper-imental results that are subsequently presented. The last rows (in red text andblack arrows) correspond to the interpretation of the GIXRD results as to wherethe UHV prepared silicon thin-films are situated on this continuum based on theGIXRD results. This figure was published as Figure 1 of Moghaddam et al. [125].Copyright permission was granted to the author. The online version of this figureis depicted in color.152corresponding crystalline volume fractions are very small for both cases.15This suggests that this form of silicon thin-film spans over a broad rangeof the silicon thin-film continuum, this not typically occurring for the caseof more conventionally prepared forms of silicon thin-film. Indeed, for moreconventionally prepared forms of silicon thin-film, one typically encounters amore narrow range of mean crystallite sizes for any particular given meansof silicon thin-film preparation [89].16 These results allow one to place theUHV prepared films into the framework of the silicon thin-film continuum,as is shown in Figure 4.6. The details of the GIXRD analysis are furtherdiscussed by Orapunt et al. [33].15Transmission electron microscopy (TEM), performed on the aforementioned UHVprepared thin-films of silicon deposited onto c-Si and oxidized c-Si substrates that havebeen prepared using very similar growth conditions, has shown the presence of smallcrystallites within an a-Si matrix for the case of the thin-films of silicon grown at 335and 415 ◦C. Presumably, the same structure is present for the UHV prepared thin-filmsof silicon grown on the optical quality fused quartz substrates at 335 and 415 ◦C. TEMcould not be performed on the samples grown on optical quality fused quartz substratesthemselves owing to their special nature.16The results of Mukhopadhyay et al. [89] are representative of that typically found forconventional forms of silicon thin-film, the mean crystallite sizes and crystalline volumefractions results reported by them being representative of the field.1534.4 A Raman spectroscopic analysisFor the suite of UHV prepared silicon thin-films, the Raman spectraare now considered, these experimental measurements being performed bythe National Research Council of Canada experimental collaborators. InFigure 4.7, the Raman spectra associated with the silicon thin-films preparedat the lower growth temperatures, i.e., lower than or equal to 415 ◦C, aredepicted, a representative PD-a-Si Raman spectrum also being displayed,this spectrum being from Sokolov et al. [124]. Several phonon bands areclearly in evidence from these spectral results. In particular, large peaks areobserved in and around 465 cm−1, this peak being representative of the a-SiTO phonon band [5]. Another peak, of lower magnitude and greater spectralbreadth, is observed for all of the spectra between 100 and 200 cm−1, thisspectral feature being related to the a-Si TA phonon band [5]. Broad spectralsignatures, in the vicinity of 340 cm−1, are also noted, this characteristicbeing related to the a-Si LA phonon band [5]. Other secondary spectralfeatures are also observed in these Raman spectra, these being beyond thescope of the current analysis.In Figure 4.8, the Raman spectra corresponding to those films prepared atthe higher growth temperatures, i.e., equal to and above 415 ◦C, are depicted,154Figure 4.7: The Raman spectra associated with the UHV prepared siliconthin-films for the lower growth temperatures. In this plot, the Raman spectracorresponding to the silicon thin-films grown at 98, 138, 335, and 415 ◦C areshown. A benchmark PD-a-Si Raman spectrum is also depicted, this partic-ular Raman spectrum being acquired from Figure 2 of Sokolov et al. [124]; itcorresponds to curve B of this plot. In order to ease with the visualization,these Raman spectra have all been offset from each other. The nominal loca-tions of the TA, LA, and TO phonon bands are clearly shown. Parts of thisfigure are in common with Figure 1a of Tay et al. [32]. Copyright permissionwas granted to the author. The online version of this figure is depicted incolor.155Figure 4.8: The Raman spectra associated with the UHV prepared siliconthin-films for the higher growth temperatures. In this plot, the Raman spec-tra corresponding to the silicon thin-films grown at 415, 493, and 572 ◦C areshown. A benchmark c-Si Raman spectrum is also depicted, this particularRaman spectrum being acquired from an online source. In order to ease withthe visualization, these Raman spectra have all been offset from each other.The nominal locations of the TA, LA, and TO phonon bands are clearlyshown. This figure was published as Figure 2b of Moghaddam et al. [125].Copyright permission was granted to the author. The online version of thisfigure is depicted in color.156a representative c-Si Raman spectrum also being displayed. It is noted that adramatic shift in the Raman spectral form occurs corresponding to increasesin the growth temperature. In particular, the TO-peak is observed to becomevery pronounced for growth temperature beyond 415 ◦C, so much so thatthe spectral features associated with the 415 ◦C Raman spectrum becomevirtually indistinct by comparison. In addition to becoming very pronounced,the TO-peak position shifts to higher wave-numbers in response to growthtemperature increases, from a nominal a-Si value of 465 cm−1, observed forthe case of the silicon thin-film prepared at 415 ◦C, to 514 cm−1 for the 493 ◦Ccase, and ultimately to 515 cm−1 for the 572 ◦C case. Noting that the Ramanspectra associated with c-Si itself is centered about 521 cm−1, one can ascribethese changes in the character of the TO-peak as being related to the onsetof crystallinity in the thin-films of silicon; the dependence of the crystallinevolume fraction on the growth temperature is presented in Figure 4.5. Theobservations found in these Raman spectra agree with those found in theGIXRD spectra depicted in Figure 4.1.It is now recognized that insights into the amount of network structuralorder that is present within a given sample of a-Si may be gleaned through ananalysis of the corresponding Raman spectrum [126, 127]. The short-range157order that exists, for example, may be quantified through an evaluation ofthe TO-peak breadth, ΓTO, smaller ΓTO values corresponding to greateramounts of short-range order. For the UHV prepared thin-films of silicon,ΓTO’s growth temperature dependence is depicted in Figure 4.9 . For bench-marking purposes, a PD-a-Si ΓTO evaluation is also depicted, the Sokolov etal. [124] PD-a-Si Raman spectrum shown in Figure 4.8 being employed forthis particular aspect of the analysis.It should be noted that the baseline from each Raman spectrum wasremoved prior to the ΓTO evaluation, details of this baseline removal processbeing presented in Orapunt et al. [33]; for this analysis, the full-width athalf-maximum is used for the evaluations of ΓTO. It is noted that, for thelower growth temperatures, i.e., growth temperatures lower than 450 ◦C, thebreadth of the TO-peak is, within the range of experimental error, constant,although a significant dispersion in the ΓTO values, from sample-to-sample,is observed. It is found that the low-temperature grown silicon thin-filmΓTO values are lower bounded by that corresponding to PD-a-Si. Withan increase in the growth temperature beyond 450 ◦C, however, and theTO-peak breadth is found to dramatically diminish, suggesting an enhancedshort-range order for these particular thin-films of silicon.158Figure 4.9: The breadth of the TO-peak, ΓTO, plotted as a function of thegrowth temperature for the UHV prepared silicon thin-films. Benchmarktemperature dependencies, corresponding to sets of silicon thin-films pre-pared by Fortner and Lannin [128] and Gupta et al. [127], are also depicted.The samples of Fortner and Lannin [128] were prepared through the use ofion implantation of c-Si samples followed by annealing, the temperature inthis case being the annealing temperature. The samples of Gupta et al. [127],however, were prepared through the use of hot-wire deposition, the temper-ature in this case being the hot-wire deposition temperature. The rms bondangle deviation, ∆θ, based on a literal extension of the relationship of Bee-man et al. [129], i.e., ΓTO = 15+6∆θ, is shown on the right-axis of this plot.This figure was published as Figure 3 of Moghaddam et al. [125]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.159Through an ion implantation of c-Si wafers, followed by a process ofannealing, Fortner and Lannin [128] produced forms of a-Si with variousamounts of disorder.17 Through the course of their study, the Raman spec-trum for each of the samples of a-Si was determined. Accordingly, in Fig-ure 4.9, in addition to the aforementioned results corresponding to the UHVprepared thin-film of silicon, the dependence of the breadth of the TO-peaksthat were found by Fortner and Lannin [128], ΓTO, on the annealing temper-ature, is plotted. It is noted that, for the most part at least, the short-rangeorder exhibited by the a-Si samples of Fortner and Lannin [128] is less thanthat associated with the low-temperature prepared samples of UHV grownthin-films of silicon. It is also noted that no sudden short-range orderingis observed as the annealing temperature is increased beyond 450 ◦C, sug-gesting that the UHV prepared thin-films of silicon are quite distinct in thisregard.1817As the starting material considered by Fortner and Lannin [128] is a bulk c-Si wafer,the samples of a-Si considered by Fortner and Lannin [128] are not prepared in siliconthin-film form.18It should be noted, however, that the exact equivalence of the growth temperatureand the annealing temperature, in terms of the a-Si preparatory environment, could bequestioned. While this analogy is probably not exact, the absence of a dramatic shift tosmaller ΓTO values for the case of the a-Si samples of Fortner and Lannin [128] suggests160Another collection of silicon thin-film data that could be considered isthat of Gupta et al. [127], who prepared a series of silicon thin-films throughhot-wire deposition, variations in the deposition temperature being consid-ered for this set of thin-films. Once again, in Figure 4.9, ΓTO’s dependenceon the hot-wire deposition temperature, found from the experimental resultsof Gupta et al., is plotted [127]. It is observed that the short-range order ex-hibited by the samples of Gupta et al. [127] is comparable with that exhibitedby the low-temperature grown UHV silicon prepared thin-films considered inthis analysis. As with the results of Fortner and Lannin [128], no suddenincrease in the amount of short-range ordering is experienced as the hot-wiredeposition temperature is increased beyond 450 ◦C, suggesting that the UHVprepared thin-films of silicon are quite distinct when contrasted with otherforms of silicon thin-film [38].19,20a fundamental difference in the nature of these forms of a-Si.19As with the a-Si samples of Fortner and Lannin [128], while the exact equivalence ofthese temperatures could be questioned, the absence of a dramatic shift to smaller ΓTOvalues for Gupta et al. [127]’s thin-films suggests a fundamental difference in the natureof these forms of a-Si.20The analysis of Song et al. [38] demonstrated that the conversion of PD-a-Si into acrystalline version of silicon thin-film can be achieved through annealing. The minimumannealing temperature required in order to realize this phase transformation was foundto be 700 ◦C by Song et al. [38], suggesting that for many applications it may not be161The short-range order within a-Si may be characterized through the spec-ification of the bond angle distribution’s root mean square (rms) value, ∆θ,about its c-Si value, i.e., cos−1( − 13) ' 109.5◦. In principle, GIXRD ex-perimental results should provide one with an opportunity to evaluate thisparameter. Unfortunately, it has proven difficult to directly extract ∆θ val-ues from such results, and thus, alternate means of determining the rmsbond angle distribution are often sought. Building upon a body of evidencethat had percolated within the silicon thin-film community for quite sometime, Beeman et al. [129] argue that the breadth of the TO-peak itself, i.e.,ΓTO, is intimately connected to ∆θ for the case of a-Si. For an assumedstructural model for a-Si, a potential profile that allows for the description ofthe harmonic interactions within this material, and a Raman-specific inter-action scattering potential, they computed the Raman spectrum associatedwith a-Si for various ∆θ selections. Based on their model calculations, theyconclude thatΓTO = 15 + 6∆θ, (4.2)practical or, at the very least, place limitations on the substrate that can be used.162ΓTO and ∆θ being in units of cm−1 and degrees, respectively; of course, thevalidity of this relationship may become questionable if there is a substantialdeviation from the assumed a-Si structure. Applying this relationship to theexperimental data that is available in Figure 4.9 allows one to study how therms bond angle distribution, ∆θ, varies with the growth temperature. Notethat the UHV prepared thin-films of silicon grown at 493 and 572 ◦C exhibitvery small ΓTO values, and thus, through the literal application of Eq. (4.2),are found to exhibit virtually no rms bond angle distribution, i.e., ∆θ ∼ 0◦,this being the rms bond angle distribution corresponding to the case of idealc-Si itself. While there is undoubtedly some short-range disorder in thesesamples, and the literal application of Eq. (4.2) to these samples probablystretches credulity, the observation that the short-range order found withinthe UHV prepared thin-films of silicon grown at 493 and 572 ◦C is muchgreater than that associated with the other thin-films of silicon, remainsvalid. This suggests that the UHV prepared thin-films of silicon have brokenthrough some sort of silicon thin-film order ‘barrier’ that these other formsof a-Si have not been able to breach.21 It is speculated that this may be21It is curious to note that Beeman et al. [129] themselves found that a fully bondeda-Si network can not be devised for ∆θ ≤ 6.6◦. It would be interesting to study howthis ‘order’ barrier could be interpreted in terms of the fundamental network limitations163related to the broad span of the silicon thin-film continuum over which theUHV prepared form of silicon thin-film exists.Another short-range order Raman related metric is the TO-peak position,ωTO. This peak parameter is typically resolved through a peak decomposi-tion procedure, greater peak positions corresponding to greater amounts ofshort-range order. In Figure 4.10, how the location of the TO-peak, ωTO,varies in response to changes in the growth temperature, is depicted for thesamples of UHV prepared silicon thin-films. For the high-temperature grownsamples, i.e., those prepared at 493 and 572 ◦C, the focus is on the location ofthe peaks associated with the a-Si phase; as was mentioned earlier, the sam-ples grown at 493 and 572 ◦C are fundamentally mixtures of an amorphousphase and a crystalline phase, the resultant Raman spectrum correspondingto responses from each of these distinct phases. The results presented inFigure 4.10 indicate that the short-range order increases as the growth tem-perature is increased. It should be noted, however, that these mixed phasesamples, i.e., those films grown at 493 and 572 ◦C, in light of the dominanceof the c-Si Raman TO-peak (recall Figure 4.8), the peak decompositions areprone to a considerable amount of uncertainty. Benchmark results corre-identified by Beeman et al. [129].164Figure 4.10: The location of the TO-peak, ωTO, plotted as a function ofthe growth temperature for the UHV prepared silicon thin-films. A bench-mark temperature dependency, corresponding to the sets of silicon thin-filmsprepared by Gupta et al. [127], is also depicted; regrettably, Fortner andLannin [128] did not evaluate ωTO for their silicon thin-films, and thus, acomparison, of the form shown in Figure 4.9, was not possible. For thepurposes of the evaluations performed here, ωTO is set to the TO-peak po-sition associated with the amorphous phase of the UHV prepared siliconthin-films. This position is ascertained through the peak decomposition pro-cedure outlined in Orapunt et al. [33]. This figure was published as Figure 4of Moghaddam et al. [125]. Copyright permission was granted to the author.The online version of this figure is depicted in color.165sponding to Gupta et al. [127] are also depicted in Figure 4.10, ωTO notbeing evaluated for the case of Fortner and Lannin [128]. As with the caseof ΓTO, the results for ωTO suggests that the thin-films of UHV preparedsilicon have broken through some sort of silicon thin-film order ‘barrier’ thatthe forms of a-Si prepared by Gupta et al. [127] have not been able to breach.Once again, one could speculate that this may be related to the broad span ofthe silicon thin-film continuum over which the UHV prepared form of siliconthin-film exists.Gupta et al. [127] assert that insights into the amount of intermediate-range order, i.e., beyond the nearest-neighbor bonding, that exists within a-Si, may be gleaned through an examination of the ITA/ITO ratio, where ITAand ITO represent the integrated TA- and TO-peak intensities. In order toperform such an evaluation, a peak decomposition must be performed withrespect to the various peaks that are present and the various phases thatare present. As with the evaluation of the breadth of the TO-peak, ΓTO,and with the determination of the location of the TO-peak, ωTO, baselineremoval and peak decomposition must be performed prior to the ITA/ITOratio evaluation. In Figure 4.11, the ITA/ITO ratio is plotted as a functionof the growth temperature for the UHV prepared thin-films of silicon. It is166Figure 4.11: The ITA/ITO ratio plotted as a function of the growth temper-ature for the UHV prepared silicon thin-films. Benchmark ITA/ITO tem-perature dependencies, corresponding to sets of silicon thin-films preparedby Fortner and Lannin [128] and Gupta et al. [127], are also depicted. Thesamples of Fortner and Lannin [128] were prepared through the use of ionimplantation of c-Si samples followed by annealing, the temperature in thiscase being the annealing temperature. The samples of Gupta et al. [127],however, were prepared through the use of hot-wire deposition, the temper-ature in this case being the hot-wire deposition temperature. The intensityratios determined here are computed through the use of a peak decomposi-tion process, the details which are provided by Tay et al. [32]. This figurewas published as Figure 5 of Moghaddam et al. [125]. Copyright permissionwas granted to the author. The online version of this figure is depicted incolor.167noted that for the growth temperatures less than 500 ◦C, that the ITA/ITOratio remains constant, within the range of experimental error.For the UHV prepared silicon thin-films prepared at the higher growthtemperature, i.e., 572 ◦C, however, the ITA/ITO ratio exhibits a dramaticdecline, suggesting a dramatic increase in the amount of intermediate-rangeorder. In order to provide a benchmark, results corresponding to Fortnerand Lannin [128] and Gupta et al. [127] are also depicted. As with the short-range order analyzes, the results for ITA/ITO suggest that the thin-filmsof UHV prepared silicon have broken through some sort of silicon thin-filmorder ‘barrier’ that these other forms of a-Si have not been able to breach.Once again, one could speculate that this may be related to the broad span ofthe silicon thin-film continuum over which the UHV prepared form of siliconthin-film exists.4.5 Analysis of refractive index dependenceUsing the refractive index results, corresponding to the UHV preparedsilicon thin-films grown at the different tempretaures, shown in Figures 3.28and 3.29, it can be seen that, for all cases, starting from the photon energy168being set to nil, initially the refractive index increases monotonically in re-sponse to increases in the photon energy. Eventually, however, a peak isachieved, further increases in the photon energy resulting in a decrease inthe refractive index value. The refractive index spectral results, with themaxima associated with each spectra indicated, are plotted in Figure 4.12.With the maximum of the refractive index resolved for the UHV preparedsilicon thin-films, one can now examine how the variations in the refractive in-dex are influenced by the growth temperature. In Figure 4.13, the maximumof the refractive index is plotted as a function of the growth temperaturefor the eleven UHV prepared silicon thin-films considered in this analysis.The spectral range considered in this analysis, i.e., photon energies between0.826 and 6.52 eV, corresponds to the spectral range over which the experi-mental reflectance and transmittance spectra were acquired. It is noted thatwhile for low temperatures the refractive index value is independent of thegrowth temperature, beyond a 300 ◦C growth temperature a considerable in-crease in the refractive index maxima values are found. Benchmarks results,corresponding to PD-a-Si and c-Si, are also depicted, the PD-a-Si result,corresponding to the refractive index spectral results of Klazes et al. [119],the c-Si results being from Palik [112] and a variety of online sources. The169Figure 4.12: The spectral dependence of the refractive index, n (~ω), corre-sponding to the silicon thin-films grown at 98 (303 nm), 138, 177, 217, 256,335, 415, 493, and 572 ◦C. The experimental data sets are depicted withthe solid lines. The refractive index maxima, associated with each spectrum,is clearly indicated. This figure was published as Figure 6 of Moghaddamet al. [125]. Copyright permission was granted to the author. The onlineversion of this figure is depicted in color.170Figure 4.13: The maximum value of the refractive index as a function of thegrowth temperature for the eleven UHV prepared silicon thin-films. Repre-sentative PD-a-Si and c-Si refractive index maxima values are also depicted.This figure was published as Figure 7 of Moghaddam et al. [125]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.171dramatic increase in the maximum refractive index values that are found forgrowth temperatures above 300 ◦C are most probably related to the onsetof crystallinity found in the UHV prepared silicon thin-film samples for thehigher growth temperatures; the dependence of the crystalline volume frac-tion on the growth temperature is depicted in Figure 4.5. It is noted thatthe maximum refractive index values exceed those typically encountered forsilicon thin-film; see, for example, [130], the maximum refractive index valuefound for these more conventional forms of silicon thin-film typically beingaround 5 [130], the results of Abdulraheem et al. [130] being representativeof that found elsewhere in the field. The reasons for this difference are notclear at the present moment.In an effort to connect the micro-structural results, i.e., the Raman resultsreported in the previous section, with the refractive index results, the maxi-mum refractive index values are related to the measures associated with theamount of order that is present. In Figure 4.14, for example, the maximumof the refractive index is plotted as a function of the TO-peak breadth, ΓTO,ΓTO being considered a measure of the amount of short-range order, as wasdiscussed earlier [127]. It is noted that generally the maximum refractiveindex decreases in response to increases in ΓTO, as would be expected as172Figure 4.14: The maximum refractive index value plotted as a function of theRaman TO-peak breadth, ΓTO, for the eleven UHV prepared silicon thin-films. This figure was published as Figure 8a of Moghaddam et al. [125].Copyright permission was granted to the author. The online version of thisfigure is depicted in color.173one transitions from a crystalline form of silicon thin-film to one that is moreamorphous in nature; results corresponding to other forms of silicon thin-filmcould not be presented on this plot, the range of ΓTO values being relativelytight for PD-a-Si and the other forms of silicon thin-film; one could speculatethat this is also related to the broad span of the silicon thin-film continuumover which this particular form of silicon thin-film exists when contrastedwith more conventional forms of silicon thin-film. It is also observed thatthere are a wide range of maximum refractive index values correspondingto a relatively narrow band of ΓTO evaluations. That is, the transition inthe dependence of the maximum refractive index on the growth temperatureappears to be that of a step-function, one obtaining either a-Si type behaviorwith large ΓTO values and low refractive index maxima or c-Si type behaviorwith small ΓTO values and high refractive index maxima. This result seemsconsistent with the presence of some sort of silicon thin-film order ‘barrier’that the UHV prepared silicon thin-films have seemingly been able to breach,this ‘barrier’ cleaving the silicon thin-film continuum into two distinct types:(1) an amorphous type of silicon thin-film, and (2) a crystalline type of sil-icon thin-film, the transitions between these silicon thin-film types beingquite abrupt. Indeed, the dependence of the crystalline volume fraction on174the growth temperature, depicted in Figure 4.5, is found to be quite abrupt,the UHV prepared silicon thin-film grown at 415 ◦C being almost completelyamorphous while that prepared at 493 ◦C having a crystalline volume frac-tion that exceeds 50 %; the thin-film of silicon prepared at 572 ◦C is mostlycrystalline.Further insight into the dependence of the optical properties on theamount of short-range order may be gleaned through an examination ofωTO’s role in shaping these optical properties. Accordingly, in Figure 4.15,the dependence of the maximum refractive index value is plotted on the Ra-man TO-peak location, ωTO, where ωTO is also believed to be related tothe amount of short-range order [127]. It is noted that generally the max-imum refractive index increases in response to increases ωTO, as would beexpected as one transitions from an amorphous form of silicon thin-film toone that is more crystalline in nature. For this case, however, following thecluster of results corresponding to the low-temperature grown purely amor-phous samples, i.e., those prepared for growth temperatures lower than andequal to 217 ◦C, it is noted that further increases in ωTO correspond tofurther increases in the refractive index. The absence of a cleavage in theresults, i.e., the fact that for growth temperatures above 217 ◦C, it is noted175Figure 4.15: The maximum refractive index value plotted as a function of theRaman TO-peak position, ωTO, for the eleven UHV prepared silicon thin-films. This figure was published as Figure 8b of Moghaddam et al. [125].Copyright permission was granted to the author. The online version of thisfigure is depicted in color.176that further increases in ωTO result in a monotonic increase in the refractiveindex maxima, suggests that the interplay between short-range order and thespectral dependence of the refractive index is more complicated than whatcould have been concluded from Figure 4.14 in of itself. One could speculatethat the short-range order probed by ΓTO is distinct from that interrogatedby ωTO, i.e., the two short-range order metrics probe different short-rangelength scales. Clearly, further work will be required in order to properlyaccount for these differences.The analysis can be continued by examining the role that intermediate-range order plays in shaping the optical properties. Accordingly, in Fig-ure 4.16, the dependence of the maximum refractive index value on theITA/ITO ratio is plotted, ITA/ITO being considered to be related to theamount of intermediate-range order [127]. It is noted that generally themaximum refractive index decreases in response to increases in the ITA/ITOratio, as would be expected as one transitions from a crystalline form of sil-icon thin-film to one that is more amorphous in nature. For this case, it isnoted that, as with the results presented in Figure 4.14, there are a widerange of maximum refractive index values corresponding to a narrow bandof ITA/ITO evaluations. That is, the transition in the dependence of the177Figure 4.16: The maximum refractive index value plotted as a function of theITA/ITO ratio for the eleven UHV prepared silicon thin-films. This figurewas published as Figure 8c of Moghaddam et al. [125]. Copyright permissionwas granted to the author. The online version of this figure is depicted incolor.178maximum refractive index on the growth temperature appears to be thatof a step-function, one obtaining either on amorphous type behavior withlarge ITA/ITO and low refractive index maxima or a crystalline-type behav-ior with small ITA/ITO values and high refractive index maxima. As withFigure 4.14, this result seems consistent with the presence of some sort of sil-icon thin-film order ‘barrier’ that the UHV prepared silicon thin-films havebeen able to breach, this ‘barrier’ cleaving the silicon thin-film continuuminto the two aforementioned distinct types. Clearly, further work is going tobe required in order to account for these results.4.6 A critical comparative analysisIt is instructive to contrast the current results with those associatedwith more traditional forms of silicon thin-film and c-Si. The examinationstarts with the spectral dependence of the refractive index, n (~ω). In Fig-ure 4.17 , a sequence of refractive index results are depicted, correspondingto the thin-films of silicon grown at 138, 335, 415, 493, and 572 ◦C. Thesespectral dependencies are contrasted with that associated with a sample ofconventionally prepared PD-a-Si as well as that associated with c-Si, these179Figure 4.17: The spectral dependence of the refractive index corresponding to thesilicon thin-films grown at 138, 335, 415, 493, and 572 ◦C. The experimental datais depicted with the solid lines. Representative PD-a-Si and c-Si spectral resultsare also depicted, these spectra being depicted with dashed lines. The PD-a-Sispectral dependence is determined through a fit of the theoretical expression ofForouhi and Bloomer [118] with a representative PD-a-Si experimental data set;the PD-a-Si data set of Klazes et al. [119] is employed, the sample preparationconditions being consistent with that typically employed for the preparation ofconventional PD-a-Si. The c-Si spectral dependence, however, is obtained from avariety of online sources and Palik [112]. This figure was published as Figure 8aof Moghaddam et al. [106]. Copyright permission was granted to the author. Theonline version of this figure is depicted in color.180results also being depicted in Figure 4.17. The PD-a-Si spectral depen-dence is determined through a fit of the theoretical expression of Forouhiand Bloomer [118] with a representative PD-a-Si experimental data set; thePD-a-Si data set of Klazes et al. [119] is employed, the sample preparationconditions being consistent with that typically employed for the preparationof conventional forms of PD-a-Si. The c-Si spectral dependence, however, isobtained from a variety of online sources and Palik [112].It is interesting to note the contrast in the spectral dependence of n (~ω)for these different cases. While the PD-a-Si spectral dependence exhibits asoft and rounded peak for ~ω in the vicinity of 2.7 eV, the peak associatedwith c-Si is seen to be much sharper in nature, and instead is located in thevicinity of 3.35 eV, this being in the neighborhood of the lowest direct en-ergy gap of c-Si, as defined by Adachi [120]. One could conceivably view thePD-a-Si result as being a “smeared-out” version of the c-Si result, the disor-der present within PD-a-Si leading to this smearing, the optical resonancesclearly present within c-Si being much less intense for the case of PD-a-Si.The thin-films of silicon that were grown by the National Research Coun-cil of Canada experimental collaborators for the purposes of this study areseen to exhibit spectral dependencies that are somewhat similar in form to181the PD-a-Si result, although it is noted that higher growth temperatures arecorrelated with higher refractive index values. Quantitatively, the maximumrefractive index over the spectral range that is considered here, i.e., photonenergies between 0.826 and 6.52 eV, is found to increase from around 4 forthe case of the silicon thin-films grown at 98 ◦C to above 6 for that grown at572 ◦C, the maximum refractive index values corresponding to these siliconthin-films being roughly between that associated with PD-a-Si and c-Si. Thiscould potentially be related to the greater amounts of crystallinity that arepresent within the higher growth temperature prepared thin-films of silicon;recall the analysis of Orapunt et al. [33] and Figure 4.5.In Figure 4.18, the spectral dependence of the optical absorption coeffi-cient on the photon energy, α (~ω), corresponding to the silicon thin-filmsgrown at 138, 335, 415, 493, and 572 ◦C, are depicted. Results correspondingto a sputtered form of this material (SD-a-Si), these results coming from theexperimental results of Freeman and Paul [6], are also depicted on this plot,as are representative results corresponding to PD-a-Si, these results beingfrom Cody et al. [35]. Optical absorption data corresponding to c-Si, theseresults being obtained from various online sources and Palik [112], is alsodepicted in Figure 4.18. Note that over the range of incident photon energies182Figure 4.18: The optical absorption spectrum corresponding to the siliconthin-films grown at 138, 335, 415, 493, and 572 ◦C. The experimental datais depicted with the solid lines. Representative PD-a-Si, SD-a-Si, and c-Sispectral results are also depicted, these spectra being depicted with dashedlines. The PD-a-Si spectral dependence is from Cody et al. [35] while thatcorresponding to SD-a-Si is from Freeman and Paul [6]. The optical absorp-tion data corresponding to c-Si is from various online sources and Palik [112].This figure was published as Figure 8b of Moghaddam et al. [106]. Copyrightpermission was granted to the author. The online version of this figure isdepicted in color.183considered, the SD-a-Si optical absorption spectrum provides an upper boundto the other optical absorption spectra plotted in Figure 4.18. It is also seenthat the PD-a-Si optical absorption spectrum provides a lower bound to theother optical absorption spectra plotted in Figure 4.18, with the exception ofthe silicon thin-film grown at 572 ◦C, which seems to exhibit its own distinctform. The optical absorption tail breadths appear to be bounded betweenthat associated with the SD-a-Si spectrum (the upper bound) and the PD-a-Si spectrum (the lower bound), suggesting that the order within the UHVprepared silicon thin-films lies between that of PD-a-Si and SD-a-Si. Finally,it is noted that the optical absorption spectrum associated with the siliconthin-film grown at 572 ◦C exhibits a form which appears closer to that ofc-Si than that of either PD-a-Si or SD-a-Si. Given that the silicon thin-filmgrown at 572 ◦C is characterized by c-Si grains embedded within an a-Sinetwork, as was shown by Tay et al. [32] for the case of a silicon thin-filmgrown on a SiO2/c-Si substrate and by Orapunt et al. [33] for the case ofsilicon thin-films grown on optical quality fused quartz substrates, this resultdoes not come completely unexpected [121].2222In contrast, for the case of PD-a-Si, O’Leary [121] demonstrated that there is afundamental discontinuity in the optical absorption spectrum as the disorderless limit isapproached.1844.7 Relationship between the optical absorp-tion spectra and the band structureKey features in the spectral dependence of the optical absorption coef-ficient may be directly related to the form of c-Si’s band structure, whichis depicted in Figure 4.19. In particular, in Figure 4.20, the 572 ◦C thin-film optical absorption spectrum is presented. It is noted that the abrupttransition in form of the optical absorption spectrum, from a monotonicallyincreasing functional form to a more or less level function, occurs at photonenergies in the neighbourhood 3.4 eV, which exactly corresponds with thelowest direct energy gap associated with c-Si, i.e., the separation in energybetween the minimum of the conduction band and the maximum of the va-lence band at the center of the Brillouin zone. The distinctiveness of the572 ◦C result remains until the photon energy becomes lower than 2 eV,at which point localized effects, related to the presence of disorder, start toinfluence the results, the 572 ◦C spectrum having less disorder than thosecorresponding to the other prepared thin-films of silicon. As a result of thisdisorder, deviations from the band structure defined form of the optical ab-sorption spectrum are expected. For the other samples being considered in185Figure 4.19: The c-Si band structure associated with the conduction andvalence bands at 300 K, along with different band gap values shown in eV.Copyright permission was granted to the author.186Figure 4.20: The 572 ◦C thin-film optical absorption spectrum plotted ona logarithmic scale. The online version of this figure is depicted in color.© Saeed Moghaddam, 2022.187this analysis, the amount of disorder is greater, and thus, the band struc-tural features seen in Figure 4.19 are “washed-out”. Further discussion onthis matter is presented in O’Leary [99].4.8 Device implicationsIt is instructive to consider the device implications of the results pre-sented within the scope of this thesis. Focusing on the use thin-film siliconfor photovoltaic device applications, recalling the exponential attenuation ofthe intensity of monochromatic light propagating through a material, i.e.,Eq. (2.1), it is seen that the fraction of light absorbed by an absorbing layerη = 1− exp (−αL) ,where α is the optical absorption coefficient and L is the thickness of theabsorbing layer; this admittedly crude analysis neglects the reflections thatoccur at the surface of the absorbing layer and many of the non-idealitiesthat must be taken into account for a more realistic treatment of a pho-tovoltaic device. A plot of the fraction of light absorbed as a function ofthe absorbance, i.e., αL, is depicted in Figure 4.21, it being noted that this188Figure 4.21: The fraction of light absorbed as a function of the absorbance,i.e., αL. The online version of this figure is depicted in color. © SaeedMoghaddam, 2022.189fraction becomes1 – exp (−1) ' 63.2%,whenL =1α.In actuality, the light received from the Sun is not monochromatic butrather is spread over a wide range of the electromagnetic spectrum. The air-mass (AM) 1.5G solar spectrum, depicted in Figure 4.22, is a representativesolar spectrum that is commonly used to benchmark the performance ofphotovoltaic devices. In order to rigorously determine the fraction of incidentlight that is absorbed when an absorbing layer is exposed to AM 1.5G light,one would need to perform a wave-length by wave-length analysis and thenintegrate over the entire solar spectrum, i.e., determine the fraction of lightabsorbed at each wave-length of the AM 1.5G solar spectrum, and thenweight this result by the fraction of the solar spectrum corresponding to thewave-length under consideration. This could potentially be quite an involvedprocess, and is beyond the scope of consideration for this thesis.A crude measure of performance may be obtained by focusing on thephoton energy for which the solar spectrum achieves its maximum, this oc-190Figure 4.22: The air-mass (AM) 1.5G solar spectrum. Copyright permissionwas granted to the author. The online version of this figure is depicted incolor.191curring at photon energies in the neighborhood of 1.5 eV for the specific caseof the AM1.5 G solar spectrum. From the optical absorption spectra depictedin Figure 3.37, the absorber thicknesses, required to ensure that 63.2% of thelight is absorbed, can be plotted. It is noted that at the higher growthtemperatures, much thicker films are required, as would be expected consid-ering the reduction in the optical absorption coefficient associated with thesehigher temperature deposited thin-films of silicon. This would suggest thatthicker absorber layers are required in order to ensure that the same fractionof incident light is absorbed for materials deposited at higher growth temper-atures. This suggests higher costs. The corresponding required thicknessesare tabulated in Table 4.1.Related to this theme, it would be instructive to consider how much ofthe incident light would be absorbed if the prepared thin-films of silicon hadbeen used as absorber layers themselves. In Figure 4.23, the fraction of inci-dent light absorbed is plotted as a function of the growth temperature, thethickness of each of the thin-films being as specified in Table 4.1; recall thatthere are three different thin-films of silicon that had been prepared at 98 ◦C.It is observed that the fraction of light absorbed by the higher growth tem-perature prepared thin-films is much lower than that corresponding to lower192Growth temperature (◦C) α (cm−1) Absorber layer thickness (µm)98 (303 nm) 1.62× 104 0.62138 1.34× 104 0.75177 1.01× 104 0.99217 1.42× 104 0.70256 9.35× 103 1.07335 9.18× 103 1.09415 5.94× 103 1.68493 1.96× 103 5.10572 5.07× 102 19.72Table 4.1: The corresponding required thicknesses based on the optical ab-sorption coefficient (α) value at 1.5 eV for the various silicon thin-films con-sidered in this analysis. © Saeed Moghaddam, 2022.193Figure 4.23: The fraction of incident light absorbed plotted as a functionof the growth temperature. The online version of this figure is depicted incolor. © Saeed Moghaddam, 2022.194growth temperatures. Accordingly, thicker films are required if one intendsto employ these high growth temperature prepared thin-films of silicon, thisincurring greater costs. The fraction of incident light absorbed correspondingto all of these thin-films of silicon is also tabulated in Table 4.2.The results presented in Figures 4.13, 4.14, 4.15, and 4.16, also point tothe potential for applications of the UHV prepared silicon thin-film. The in-crease in the refractive index corresponding to increased growth temperaturessuggests that this material could find applications in solar cells as the ab-sorbing media. Through a statistical ray optical analysis, Yablonovitch [131]has demonstrated that the absorption of a randomly textured material maybe enhanced by a factor as large as 4n2, where n denotes the refractive index;achievement of this classical limit was demonstrated by Ingenito et al. [132].For the UHV deposited silicon thin-films, this enhancement can be as greatas around 150 (based on our 572 ◦C UHV prepared thin-film of silicon, forthe maximum of the refractive index, for photon energies between 0.826 and6.52 eV), which is significant when contrasted with the case of conventionalPD-a-Si (around 80).2323In order to simplify matters, this component of the analysis only considers the up-per bound on this enhancement. A more realistic analysis would require an integrativeapproach. This is beyond the scope of this analysis.195Growth temperature (◦C) Fraction of incident light absorbed %98 (303 nm) 38.8138 16.2177 11.9217 25.5256 9.4335 15.2415 10.7493 3.3572 0.9Table 4.2: The fraction of incident light absorbed corresponding to thin-filmsof silicon considered in this analysis. © Saeed Moghaddam, 2022.1964.9 Technical achievementsIn this chapter, drawing upon the silicon thin-film optical results de-termined in Chapter 3, through a collection of GIXRD and Raman spec-troscopic results, acquired from the National Research Council of Canadaexperimental collaborators, I have related these results with the underlyingmicro-structure. I first started with a characterization of silicon thin-film asbeing part of a silicon thin-film continuum and, drawing upon some GIXRDresults, presented where these UHV prepared thin-films of silicon lie on thiscontinuum. Arguing that these UHV prepared thin-films of silicon span overa broader range of the continuum than more conventional forms of siliconthin-film, I noted that a detailed analysis of these UHV prepared forms ofsilicon thin-film provides one with a unique opportunity to probe how disor-der and the placement of a given film within the silicon thin-film continuuminfluences the results. Drawing upon a collection of Raman spectra, de-termined from measurements performed by the National Research Councilof Canada experimental collaborators on these UHV prepared thin-films ofsilicon, I then identified how the growth temperature influences a numberof short-range and intermediate-range measures of disorder associated withthese UHV prepared forms of silicon thin-film. I then connected the refrac-197tive index spectral results, determined in Chapter 3, with these short-rangeand intermediate-range measures of disorder. A critical comparative analy-sis, of two optical functions associated with these UHV prepared thin-filmsof silicon and those prepared through more conventional means, was thenpresented. Finally, the device potential of this UHV prepared form of siliconthin-film was assessed.I identify a number of significant technical achievements presented herein.First, the characterization of this form of UHV prepared silicon thin-filmusing the concept of the silicon thin-film continuum, while in the siliconthin-film community’s vernacular, has never been explicitly probed as it hashere. The Raman spectral results, while being commented upon in earlierpublications, have never been discussed in as great detail as presented here.Moreover, a measure of disorder that has never been probed before, i.e.,the position of the ωTO peak, is presented here. This provides the siliconthin-film community with something new that they can refer to in termsof transitions between the amorphous and crystalline phases of silicon thin-film. The relationship between the spectral dependence of the refractiveindex and these micro-structural Raman observed features is another tech-nical achievement of this body of work. Finally, the projections for potential198device applications represents another interesting technical contribution ofthis work.I would like to note, that while the previous chapter was focused primarilyon instrumentation matters, in this chapter, materials characterization andcorrelations are the primary focus of attention. Presumably, as the long-termcollaboration with Dr. O’Leary’s group with the National Research Councilof Canada experimental collaborators continues to proceed and mature, newopportunities for material science discovery will arise.199Chapter 5ConclusionsThe optical properties associated with a unique form of silicon thin-film that had been deposited onto optical quality fused quartz substratesthrough UHV evaporation have been examined. For the purposes of thisparticular analysis, the role that the growth temperature plays in influencingthe spectral dependence of the optical functions associated with these siliconthin-films was focused upon, for growth temperatures between 98 and 572 ◦C.Through measurements of the specular reflectance spectrum at near-normalincidence and the regular transmittance spectrum at normal incidence, thespectral dependence of the refractive index, the extinction coefficient, thereal and imaginary parts of the dielectric function, and the optical absorp-tion coefficient were resolved for the eleven UHV prepared silicon thin-filmsconsidered in this analysis. It was found that generally the refractive index200increases in response to increases in the growth temperature. Quantitatively,the maximum refractive index over the spectral range that was considered,i.e., photon energies between 0.826 and 6.52 eV, was found to increase fromaround 4 for the case of the silicon thin-films grown at 98 ◦C to above 6 forthat grown at 572 ◦C, the maximum refractive index values correspondingto the silicon thin-films being roughly between that associated with PD-a-Siand c-Si. The optical absorption spectral dependence was also observed toexhibit a fundamental transition in its functional behavior accompanying in-creases in the growth temperature. Both of these observations were noted tobe correlated with the changes that occur in the crystalline volume fractionaccompanying increases in the growth temperature.The problem of solving for the spectral dependence of the optical func-tions from measurements of the reflectance and transmittance spectra is oneof general interest to those within the broader thin-film community. Accord-ingly, as an adjunct to this UHV prepared silicon thin-film optical functionanalysis, details, related to optical function acquisition from experimentalmeasurements of the reflectance and transmittance spectra, were presented.In essence, these details were worked out using the optical function anal-ysis that was performed on the UHV prepared silicon thin-films deposited201onto optical quality fused quartz substrates as a case study. In particular,details related to the optical response measurements, the uncertainty in thereflectance and transmittance results, the analytical framework upon whichthe optical functions were acquired, how the ambient and the optical-quality-fused quartz substrate optical functions were modeled, and means throughwhich unphysical solutions were identified and eliminated, were offered. It isbelieved that that this collection of results will be of general interest to thosewithin the broader thin-film community.Finally, drawing upon some previously reported GIXRD results, a place-ment of the UHV prepared thin-films of silicon into the overall silicon thin-film continuum was performed, noting that the GIXRD evidence suggeststhat this particular form of silicon thin-film seems to span over a broaderrange of the silicon thin-film continuum than conventionally prepared formsof this material. Then, the Raman spectra associated the thin-films of siliconwere analyzed. In particular, two Raman related measures associated withthe amount of short-range order, namely the breadth and position of the Ra-man spectrum’s TO-peak, ΓTO and ωTO, respectively, and a Raman relatedmeasure associated with the amount of intermediate-range order, namelythe ITA/ITO ratio, were plotted as functions of the growth temperature. All202measures of order suggested that the order increases in response to increasesin the growth temperature. These changes found in the nature of the or-der within the thin-films of silicon were then correlated with the changesobserved in the spectral dependence of the refractive index, focusing on themaximum of the refractive index over the spectral range under considerationin this analysis, i.e., photon energies ranging between 0.826 and 6.52 eV. Itwas found that the maximum of the refractive index increases in response toincreased ordering, i.e., as was mentioned before, from about 4 for the siliconthin-films grown at the lower temperatures to above 6 for those grown at thehigher temperatures, this latter value being larger than that found in moreconventional forms of silicon thin-film. Finally, the potential device implica-tions of these results were explored. As a consequence, this particular form ofUHV prepared silicon thin-film was identified as being a promising materialfor use as the absorbing media within solar cells, offering an enhancement inthe absorption which is greater than that offered by conventional PD-a-Si,i.e., as great as 150 for the case of this material versus 80 for the case ofconventional PD-a-Si.Within the scope of this thesis, a number of important opportunitiesfor the acquisition of new knowledge were pursued. Some of these were203purely focused upon the material properties of the UHV prepared forms ofsilicon thin-film, while others were focused on improvements to experimentalapproaches, i.e., instrumentation improvements, arrived at as a corollary tothe aforementioned investigations into the properties of the UHV preparedthin-films of silicon, that could potentially have an impact upon the broaderthin-film community.A number of material focused achievements were accomplished duringthe course of this thesis. First and foremost, an evaluation of the spectraldependence of the optical functions associated with these UHV preparedthin-films of silicon, with a view to assessing the suitability of this particularform of silicon thin-film for device applications, was pursued. Second, thechanges in the spectral dependence of these optical functions were related tochanges in the amount of order that is present, these order measures beingevaluated through the use of the Raman spectra corresponding to these UHVprepared thin-films of silicon, these measurements of the Raman spectrabeing pursued by the National Research Council of Canada experimentalcollaborators. Finally, as this particular form of silicon thin-film traversesthe silicon thin-film continuum in a unique manner when it is comparedwith more conventional forms of silicon thin-film, insights may be gleaned204concerning how disorder shapes the optical response of silicon thin-film thatare not available to these more conventional forms of silicon thin-film.From an instrumentation perspective, significant achievements were ac-complished. These were primarily centered on how one can acquire the op-tical functions from measurements of the near-normal reflectance and thenormal transmittance spectra, this being the experimental data that wasavailable from the National Research Council of Canada experimental col-laborators. It is noted that this is a problem of general interest to thosewithin the broader thin-film community, relevant far beyond the confines ofthe silicon thin-film community itself. The improvements that were offeredwithin the scope of this thesis, i.e., means of eliminating unphysical solu-tions and means of confirming and verifying the veracity of proposed opticalfunction solutions, have the potential to benefit this broader thin-film com-munity. It is therefore hoped that the work presented in this thesis will havean impact far beyond just the silicon thin-film community.There is still a lot of work that could be performed based on the large col-lection of results that has been acquired from investigations into these UHVprepared thin-films of silicon. It is believed that opportunities for work existon both the fundamental level and in terms of the potential device applica-205tions of this particular form of silicon thin-film. Some particular problems ofinterest, to those within the silicon thin-film community, that build directlyupon the results presented within this thesis, are offered below.A fundamental open problem in the field of disordered semiconductors isthe role that disorder plays in shaping the optical functions. The disorderassociated with a disordered semiconductor, such as silicon thin-film, is oftencharacterized in terms of the breadth of the optical absorption tail, this tailcharacterizing the abruptness of the termination of the optical absorptionspectrum at the energy gap. With the data that is available, i.e., the spectraldependence of the optical absorption coefficient, the tail breadth associatedwith each spectrum may be easily determined. How these tails breadths arerelated to the Raman measures of disorder and other such features couldprovide a great opportunity for basic work aimed at resolving silicon thin-film’s fundamental character.From an applications perspective, how the electronic response of the UHVprepared thin-films of silicon contrast with those of conventional forms ofsilicon thin-film, remains an important area of investigation. Measurementsof the photoconductivity as a function of time could be pursued in order toresolve the stability of this material and its resistance to the instability that206bedevils conventional PD-a-Si. The ability of the UHV prepared materialto be doped and work as a device is yet another area of research that couldbe pursued. 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Hegmann “Ultrafast carrier dynamics and therole of grain boundaries in polycrystalline silicon thin films grown bymolecular beam epitaxy”, Semiconductor Science and Technology, vol.31, pp. 105017-105025 (2016).[139] https://thinfilmview.com/en/[140] https://www.shuvendujena.tk/prisa/[141] http://www.sspectra.com/[142] https://wp.optics.arizona.edu/milster/[143] https://www.optilayer.com/235Appendix A: commercialthin-film optics softwareanalysisA number of commercial software packages are available for purchasethat allow for the acquisition of the optical functions from measurementsof the reflectance and transmittance spectra. Unfortunately, many of thesedifferent software packages have limitations associated with them. As hasbeen mentioned previously in Section 3.8, different software packages havebeen known to produce different optical function results corresponding to thesame reflectance and transmittance data, this being clearly a distressing anddiscomforting observation. Each software package offers its own advantagesand disadvantages. Table A.1 provides a summary of some of the advantagesand disadvantages offered by each software vendor, as reported by the re-236Software Pros ConsTFV® (Tokyo,Japan) [139] Real time calculations Able to calculate opticalfunctions of substrate withno thin-film The spectrophotometermeasured data files can beread on the chart Sellmeier’s equation is limited for modelingthe optical functions of silicon thin-films inthis experiment Substrate refractive index data must be ac-curate If the film thickness is too thin or too thick,it will not be analyzed correctly If the wavelength range is too wide, it is notpossible to analyze the optical functionsPrisa® (Ma-harashtra,India) [140] Better application for thin-films whose thicknesses areless than 1 µm Calculates the bandgap ofthe thin-films Swanepoel’s equation is limited for model-ing the optical functions of silicon thin-filmsin this experiment Does not use reflectance of the thin-films Substrate’s refractive index is a fixed value,and must be set by the userTFCalc® (Port-land, OR,USA) [141] Able to calculate opticalfunctions for multi-layersystems Works for different light po-larization Sellmeier’s equation is limited for modelingthe optical functions of silicon thin-films inthis experiment Only returns Sellmeier’s coefficients withoutoptical function spectrumThin-filmCalculator(Tucson, AZ,USA) [142] Open-source software allowsuser to modify the softwarecode in Matlab Works for different light po-larization The results can be post-analyzed in Matlab Analyzes reflectance and transmittance as afunction of incident angle, not wavelength Only works at a certain wavelength, doesnot generate optical function spectrum Refraction index of the thin-film and thesubstrate must be inserted by the user,which limits the practicality due to experi-mental variationsOptilayer®(Mu¨nchen,Germany) [143] Data can be analyzed ina variety of units (nm, A˚,cm−1...) Compatible with multiplespectrometers Only analyzes reflectance and transmit-tance, not the optical function Not able to provide optical function spectraof the thin-filmTable A.1: Analysis of available commercial thin-film optics software.237spective vendors. As might have been expected, a lack of transparency andcandor, in terms of the limitations of each software package, was very com-mon; some of the technical manuals seemed to suggest that their softwarepackage is the “best” without providing any evidence to justify their claims.In addition, each software vendor has selected which advantages and disad-vantages to emphasize, thereby making a comparative analysis difficult. It isfor this reason, and the inability to see intermediary results, that I decidedto employ my own Matlab code in order to acquire the optical functions fromthe experimentally acquired reflectance and transmittance spectra.238Appendix B: potential futureexperimental workAs was mentioned previously in the thesis, researchers with the NationalResearch Council of Canada have used UHV evaporation to prepare thin-films of silicon on a variety of substrates at a number of different growthtemperatures. A molecular beam epitaxy deposition system was used forthis purpose, although the thin-films produced are technically not epitaxialas the crystal structure of the underlying substrate, if it exists at all, doesnot project into the thin-films themselves. The substrates considered forthese depositions were c-Si, SiO2/c-Si, and optical quality fused quartz. Thegrowth temperatures considered ranged from 98 to 572 ◦C, this being ofa wide enough range so as to ensure that the transition between purelyamorphous thin-films of silicon at the lower growth temperatures to highlycrystalline forms of this material for the higher growth temperatures; while239the crystalline volume fraction is high, these thin-films are in actual fact nano-crystalline in nature, i.e., they possess a large number of crystallites that areabout 10 nm in dimension. A number of experimental investigations intothe properties of these materials were pursued by these National ResearchCouncil of Canada experimental collaborators. The constellation of workthat was performed is highlighted in Figure B.1 .Initial work performed on this material system focused on light emissionfrom SiO2/Si superlattices fabricated through the use of the UHV evapora-tion growth [133, 134], this being the same approach as that used for thepreparation of the thin-films of silicon considered in this thesis. The resul-tant superlattices were imaged using transmission electron microscopy, theoptical response being interrogated through the use of photoluminescence. Aclear shift in the energy gap was observed in response to reductions in thesilicon layer thicknesses within these superlattices. It was suggested that thisobservation was related to quantum confinement effects within these SiO2/Sisuperlattice structures. It was suggested that these quantum confinementeffects could render these superlattices compatible with today’s c-Si basedtechnologies.Later, once the thin-films of silicon had been deposited, i.e., those de-240Figure B.1: The constellation of experimental work performed by the Na-tional Research Council of Canada experimental collaborators [31, 33, 90,106, 133, 134, 135, 136, 137, 138]. The online version of this figure is de-picted in color. © Saeed Moghaddam, 2022.241posited on the optical quality used quartz substrates and those deposited onthe c-Si and SiO2/c-Si substrates, a wider range of experimental analyzes wasemployed. This included the use of X-ray diffraction, Raman spectroscopy,photoluminescence, reflectance and transmittance measurements (performedon the optical quality fused quartz substrates only owing to the opacity ofc-Si), secondary ion mass spectroscopy (only the thin-films deposited on thec-Si and SiO2/c-Si substrates), Fourier transform infra-red spectroscopy, andscanning and transmission electron microscopy. A tabulation of all of thethin-films of silicon prepared for the purposes of this study is presented inTable B.1. A tabulation of all of the experimental techniques used for thisstudy are shown in Figure B.1, the results corresponding to each experimen-tal technique being published in which papers that were authored by thecollaborators at the National Research Council of Canada.In terms of what new, as yet to be performed, experiments should beperformed, a detailed examination of the impurity profiles within the thin-films of silicon prepared on optical quality fused quartz substrates wouldcertainly be one experimental measurement that would be worthy of pursuitas that would furnish us with insight concerning the similarity between thethin-films fabricated on the optical quality fused quartz substrates and those242Growth temperature(◦C) Substrate Film thickness(nm)98 SiO2 13598 SiO2 30398 SiO2 605138 SiO2 132177 SiO2 125217 SiO2 207256 SiO2 106335 SiO2 180415 SiO2 190493 SiO2 170572 SiO2 180177 c-Si 800216 c-Si 710256 c-Si 445295 c-Si 390335 c-Si 316374 c-Si 367414 c-Si 45498 SiO2/c-Si 365177 SiO2/c-Si 326256 SiO2/c-Si 500295 SiO2/c-Si 300335 SiO2/c-Si 370414 SiO2/c-Si 260493 SiO2/c-Si 400572 SiO2/c-Si 410Table B.1: The list of silicon thin-films prepared by the National ResearchCouncil of Canada experimental collaborators. For each silicon thin-film,the growth temperature, the substrate employed, and the film thicknessesare indicated.243grown on the c-Si and SiO2/c-Si substrates. Following the approach of Tayet al. [31], using available National Research Council of Canada experimen-tal equipment, this impurity profile could be determined using their PhilipsEM430T secondary ion mass spectroscopy profiler, the profiles of the thin-films of silicon that had been deposited on c-Si and SiO2/c-Si substrates beingperformed using this profiler operated at 250 kV, a representative result be-ing shown in Figure 2.7. Whether the operational voltage of this profiler willhave to be altered for the thin-films deposited on optical quality fused quartzsubstrates will have to be assessed. Previously, the thin-films of silicon de-posited on the optical quality fused quartz substrates had not been profiledowing to their delicacy, a secondary ion mass spectroscopic measurement onsuch thin-films of silicon likely to lead to the destruction of the thin-films. Itmight be recommend that a sacrificial thin-film of silicon be prepared, just sothat one can probe the similarity in the impurity profiles. Alternatively, onemight want to consider alternate approaches to impurity profiling than sec-ondary ion mass spectroscopy, such as energy dispersive X-ray spectroscopy;while energy dispersive X-ray spectroscopy is not as sensitive to impuritiesas secondary ion mass spectroscopy, it is non-destruction, and therefore, forthis purpose, offers an advantage.244In light of the importance of the photovoltaic application for silicon thin-film, a light-soaking experiment, in which the conductivity of a sample ofthin-film silicon that has been exposed to light as a function of time, isworthy of examination, a comparison with results corresponding to PD-a-Sidemonstrating the utility of this material compared with the more conven-tional form of thin-film silicon. Following the procedure outlined by Stablerand Wronski [22], which has become a standard for the field, electrical mea-surements could be made using a four-point contact approach; for this tooccur, of course, contacts need to be made with the samples. A varietyof voltages could be applied to the two outer contacts with the samples.Currents and voltages will be measured as a function of time. Exposure tosimulated sunlight will be generated using commonly available light sources,most probably a tungsten source with some kind of filtering. By contrast-ing the dependence of the conductivity over time, the stability of the UHVprepared thin-films of silicon may be contrasted with that of conventionalPD-a-Si. Hopefully, this will demonstrate increased stability for the case ofthe UHV prepared thin-films of silicon.245
Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
O'Leary, Stephen Karrer
The optical response of silicon thin-films grown by ultra-high-vacuum evaporation
Text