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Atomic force microscope-based lithography for site-selective surface grafting of semiconductor nanocrystals… Wang, Tian Si 2006

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A T O M I C F O R C E M I C R O S C O P E - B A S E D L I T H O G R A P H Y F O R S I T E - S E L E C T I V E S U R F A C E G R A F T I N G O F S E M I C O N D U C T O R N A N O C R Y S T A L S O N P A T T E R N E D S I L I C O N by TIAN SI WANG M.Sc, Jilin University, China, 2003 A THESIS SUBMITTED IN PARTIAL. F U L F I L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF SCIENCE T H E FACULTY OF G R A D U A T E STUDIES (Physics) T H E UNIVERSITY OF BRITISH COLUMBIA October 2006 © TIAN SI WANG, 2006 ' 11 Abstract A three dimensional optical microcavity was designed in a textured silicon planar waveguide to have a resonant wavelength near 1.5 pm, and a quality factor of ~4000. The design is based on planar photonic bandgap concepts, and was achieved using a commercial finite-difference-time-domain electro-magnetic simulation tool. This microcavity is intended to be integrated with PbSe semiconductor nanocrystals synthesized by collaborators to exhibit a strong excitonic resonance also near 1.5 pm. To study the coupling of this excitonic resonance, with the optical microcavity mode, a process for locally attaching the PbSe nanocrystals on the silicon microcavity surface in a region of high electric field intensity had to be developed. Accordingly, a lithographic process was developed based on the use a con-ducting atomic force microscope (AFM) tip to oxidize the silicon surface at a precise location with respect to the photonic crystal microcavity. The A F M lithography has to be done after the silicon microcavity is first uniformly coated with an organic monolayer designed to repel the PbSe nanocrystals. Two different organic monolayers, OTS (Octadecyltrichlorosilane), and oc-tadecene, were used in this study. Two different A F M microscopes were adapted for this process development work. By varying the applied bias volt-age and pulse duration on bare silicon, and silicon-on-insulator substrates, and on monolayer-coated versions of the same substrates, the optimum con-ditions for oxide dot formation were determined. While it is relatively easy to form oxide dots with diameters down to ~50 nm on bare silicon and silicon-on-insulator substrates using ~ -5 V, 100 ms pulses, higher voltages -and longer pulse durations were required to form oxide dots on the monolayer coated samples, and the uniformity of the oxide dots formed on the monolayer samples was found to be poorer than on the bare samples. An AFM-oxidized dot with ~ 190 nm diameter was successfully formed within 50 nm of the centre of an octadecene-coated microcavity formed in a silicon-on-insulator substrate. This proves that this process is capable of site-selectively defining a site for nanocrystal attachment on the microcavities, but further work is Abstract iii needed to make the process "routine". I V Contents Q Abstract ii Contents iv List of Tables vi List of Figures vii Acknowledgements xii 1 Introduction 1 2 Background 4 2.1 Optical "Semiconductors": Photonic Crystals 4 2.1.1 One dimensional photonic crystal: Bragg stacks . . . . 4 2.1.2 Photonic crystal slab (PCS) 6 2.2 Defect modes and microcavities 9 2.3 Numerical calculation methods 14 2.3.1 F D T D algorithm 14 2.3.2 Application of FDTD to identify microcavity modes . . 17 3 Design of Photonic Crystal Slab Microcavities 19 3.1 The FDTD Solutions Implementation . 19 3.1.1 Physical Parameters ' 19 3.1.2 Numerical Parameters 20 3.2 2D Photonic Crystal Design 22 3.2.1 "Pure" 2D Band Structure 22 3.2.2 3D F D T D Analysis of a 2D Patterned Slab Waveguide 24 3.3 3D FDTD Analysis of Optical Microcavity 29 3.3.1 Demonstration of microcavity device and resonant scat-tering spectrum 34 Contents v 4 A F M Nanolithography 37 4.1 Introduction 37 4.2 Material Preparation 42 4.2.1 Semiconductor layers 42 4.2.2 Organic monolayer preparation 42 4.3 A F M lithography 46 4.3.1 A F M settings for anodic oxidation 46 4.3.2 Mechanism of A F M Anodic Oxidation 50 4.4 Results and discussion 51 4.4.1 A F M tip-induced anodic oxidation on a bare SOI sub-strate 51 4.4.2 A F M anodic oxidation of OTS-modified Si and SOI substrates 56 4.4.3 A F M anodic oxidation of alkyl-terminated Si/SOI sub-strate 59 4.4.4 MFP-3D A F M anodic oxidation of alkyl-terminated SOI substrate 68 5 Conclusion 69 Bibliography . 7 1 s vi List of Tables 4.1 Nominal specifications of probe tip 46 vii List of Figures 1.1 The basic scheme for realizing a microcavity with a quantum dot grafted selectively in the region of maximum E field of the microcavity mode(s) using A F M lithography 3 2.1 Schematic diagram of a Bragg stack, an example of a ID pho-tonic crystal. The crystal is composed of alternating layers of materials with a reflective index contrast. Light within a cer-tain wavelength range travelling in the direction of periodicity will exponentially decay through the stack 5 2.2 Schematic diagram of the physical structure of (top) and dis-persion diagram (bottom) of a planar waveguide slab in air. 7 2.3 Schematic diagram (top) of the physical structure of a peri-odically textured planar waveguide slab in air and the corre-sponding dispersion diagram (bottom) showing bound mode, leaky mode and radiation mode dispersions 8 2.4 Schematic diagram of a defect in a ID photonic crystal. The thicker layer interrupts the crystal's periodicity and acts as a defect : 9 2.5 (a) The transverse waveguide mode excites the structure from the left, (b) Schematic of a P B G waveguide microcavity with dimensions for operation at A = 1.51^m. The orange box indicates the simulation area during FDTD numerical calcu-lation. The yellow cross identifies the point downstream of the heterostructure texture (air/Si/SiC>2) • • 11 2.6 (a) The transmitted intensity spectrum is monitored at yellow cross (shown in 2.5(a)). (b) The field distribution is shown when the incident frequency excites the resonance at 1.51 \im. 12 2.7 Schematic diagram of a defect in a 2D planar photonic crystal. A microcavity is formed by removing one or more air holes. . 13 List of Figures viii 2.8 In a Yee cell of dimension Ax,Ay,Az, note how the H field is computed at points shifted one-half grid spacing from the E field grid points 15 3.1 Periodic Boundary Conditions (PBC) in FDTD simulation. . . 21 3.2 2D unit cell used for bandstructure calculations 23 3.3 A A;-space diagram demonstrating the crystal symmetry di-rections of a hexagonal array. The solid black dots represent reciprocal lattice vectors. The 1st Brillouin Zone is repre-sented with a dotted line and the high-symmetry points are K and M 24 3.4 T E band structure of a "pure" 2D hexagonal photonic crystal described in the text 25 3.5 T M band structure of a "pure" 2D hexagonal photonic crystal described in the text 26 3.6 Band structure of the TE-like modes of the 2D patterned slab waveguide surrounded by air (a=480 nm and d=0.408a). The solid line represents the light line. Only the part of dispersion diagram from the M point to the K point in reciprocal space is plotted. The material was taken to have a fixed index, nsiab — 3.48. The radius of the holes is defined by the ratio r/a = 0.385a. The resulting TE-like bandgap extends between a normalized frequency, A / = 0.44 — 0.31. The region above the light line corresponds to leaky modes] the parts of the frequency bands that are below the light line are guided modes. 28 3.7 Schematic of a 2D slice through the middle of the patterned high-index slab. The center three air holes are missing, which forms a high-Q microcavity. A dipole E M source with T E polarization was introduced to excite the resonant mode of the microcavity. Three point receptors (yellow crosses) made sure that all the microcavity responses would be recorded. . . 30 3.8 (a)Plot of the Ey component of the field decaying as a function of time on a logarithmic scale, (b) Zooming into the upper part of the field profile for measuring the cavity Q-factor 31 3.9 Plot of resonance frequency of cavity mode as a function of radius of air-hole 32 List of Figures ix 3.10 Plot of cavity mode Q factor as a function of radius of air-hole. Based on these results, a target hole spacing of 180 nm was chosen for the purpose of fabricating real microstructures. It offers a reasonably high Q, and the resonant frequency is easily accessible with the optical parametric oscillator used to characterize the microcavities 32 3.11 2D slice through the middle of the silicon slab described in the text showing the field (E) magnitude profile of x dipole-like mode: /resonance = 191.91 THz or 1.56 jum, which is in the telecommunication frequency range. The units of the x and y coordinates are given in metres. 33 3.12 SEM graph of the central region of a SOI-based microcavity with interspacing of a = 480 nm and air-hole radius of r = 180 nm 34 3.13 Schematic diagram of the microreflectivity set-up. The nano-positioner on which the sample sits, as well as the short fo-cal length of the focusing microscope objective lens-, allow for precise localization of the light from the optical parametric oscillator. Precise positioning is achieved with the help of a CCD camera to image the samples. When the camera is re-moved from the beam path, the beam is focused into an FTIR ..spectrometer with an ellipsoidal mirror 35 3.14 Resonant scattering spectrum obtained using an excitation source polarized to excite a single x dipole-like mode of SOI-based microcavity. The broad background is due to leakage of the exciting laser pulse through the imperfect crossed polariz-ers, and the sharp feature represents the scattering from the microcavity mode excited by this broad laser spectrum. . . . 36 4.1 Experimental procedure for fabricating site-selective PbSe nanopar-ticles assemblies. R is the terminated organic monolayer and Y is the terminal ligand for surface-grafting 40 4.2 Concept of A F M and the optical lever: (a) a cantilever touch-ing a sample; (b) the optical lever. (By courtesy of Dr. David Baselt) 41 4.3 Schematic diagrams of fully processed sample (a), the SOI wafer (b), and the silicon wafer (c) 44 List of Figures x 4.4 Schematic representation of the reaction of OTS with a OH-terminated silicon surface 45 4.5 Schematic representation of the reaction of octadecene with a H-terminated silicon surface. The symbol A means heating for 2 hours 45 4.6 Cantilever:CSCll/Ti-Pt, used for all the experiments. . . . . 46 4.7 Schematic diagrams of baseplate and jumper configuration. . 48 4.8 Schematic view of Extended Electronics Module and illustra-tion table of toggle switch settings 49 4.9 Schematic view of the sample-mount consisting of a iron sam-ple disk, a copper piece (square cap) and a iron screw for good ohmic contact 50 4.10 Contact A F M topographic images of (a) a pre-made square-. pattern array (image shows a region 5 x 5 pm2, with a vertical range scale of lOnm) and (b) oxide dot arrays made by using A F M anodic oxidation to the right of the square array (image shows a region 10 x 10 pm2, with a vertical range scale of lOnm) 53 4.11 The dependence of oxide dot size on (a) the varying pulse voltage, —1 ~ —12 V for a fixed pulse duration of 100 ms, and (b) the varying pulse duration, from 100 ms to 1 s for a fixed pulse voltage of -5V 54 4.12 Relationship between oxide dot diameter and (a) voltage and (b) pulse duration for bare patterned SOI sample, 55 4.13 Comparison of surface profiles (a) before HF etching and (b) after HF etching, of island-like OTS films grown on, silicon. . 57 4.14 A F M height images of an 5 x 5 oxide dot arrays that was written (a) on a high-quality OTS-modified silicon surface and (b) a high-quality OTS-modified SOI surface. Voltage, -12 V; pulse duration, 100 ms, for both (a) and (b) 58 4.15 Roughness analysis images of octadecyl-terminated SOI are shown (a)before and (b)after HF dipping for ~ 15 s. (The vertical scale is 5 nm for both images - 61 List of Figures x i 4.16 Contact A F M height images (range: 5 nm) of the 3 x 4 oxide dot arrays fabricated on an octadecyl-modified silicon surface by the A F M anodic oxidation: pulse voltage, (a)-5 V and (b)-6 V; pulse duration, 100 ms; humidity, ambient air. Oxidation was performed after dipping the as-grown monolayers in HF for ~ 15 s. 62 4.17 Contact A F M height images (range: 5 nm) of the 3 x 4 oxide dot arrays fabricated on an octadecyl-modified silicon surface by the A F M anodic oxidation: pulse voltage, (a) -7 V and (b) -8 V; pulse duration, 100 ms; humidity, ambient air. Oxidation was performed after HF dipping for ~ 15 s 63 4.18 Contact A F M height images (range: 3 nm) of the 3x4 oxide dot arrays fabricated on an octadecyl-modified SOI surface by the A F M anodic oxidation: pulse voltage, (a) -8 V and (b) -9 V; pulse duration, 5 s; humidity, ambient air. The dots were written after HF dipping the monolayer for ~ 15 s 64 4.19 Contact A F M height images (range: (a) 3 nm and (b) 5 nm) of the 3 x 4 oxide dot arrays fabricated on an octadecyl-modified SOI surface by the A F M anodic oxidation: pulse voltage and duration, (a) -10 V and 5 s;'(b) -12 V and 12 s; humidity,.ambi-ent air. The dots were written after HF dipping the monolayer for ~ 15 s 65 4.20 A F M images of oxide dot arrays written by A F M anodic ox-idation on octadecyl-terminated SOI every quarter of 1 hour after the sample was soaked in DI water. The arrays were all written using pulses of-5 s and 100 ms for all arrays, (vertical range is 5 nm in each image) . 66 4.21 Isometric (3D) plots corresponding'to the same images shown in Figure 4.20 67 4.22 A single oxide dot(central white spot on microcavity) over-lapping the high field region of the fundamental cavity mode, 68 X l l Acknowledgements First off, I am truly grateful and indebted to my advisor and supervisor, Dr. Jeff Young, for the honor of being a member of this highly reputable research group. I am genuinely inspired by and will permanently benefit from the rigor of his scholarship in general, but in particular, his sound logical reasoning and. systematical scientific thinking. The routine weekly "Group Meeting" has proven to be especially valuable throughout my entire program of master studies. A variety of activities at these meetings, such as paper reading, note taking, interaction with people, formal organization of thoughts and experiment results, public speech and presentations and even a few rote memories, have eventually given me such profound ideas and strong interest over time that claim the ultimate foundation of this thesis. Thanks to Dr. Andras Pattantyus-Abraham for cleanroom training and sample preparation. Thanks to Murray McCutcheon for patient help with my FDTD simulations and allowing me to share his brain wisdom. Thanks to Mohamad Banaee for his eager communication and talk with me on the Nonlinear Optics and Quantum Optics. Thanks also to Dr. Georg Rieger for his explanation of the optical experiments. I would also like to acknowledge Mike Whitwick for his extensive assis-tance with my A F M experiments and all other students in M B E lab for their easy chatting. Finally, I would like to extend sincere thanks to my family in China for having provided unwavering support and nurturing understanding whatever the situation maybe and whenever it was most needed throughout these years. 1 Chapter 1 Introduction As the exponential shrinkage of integrated electronics predicted by Moore [1] continues, the miniaturization of microelectronic devices is approaching the physical limits of integration on one tiny semiconductor chip. Thus, within the past decade, scientific efforts have turned to quantum computing and all-optical signal processing of information data flow. Instead of employing bits of Is and Os for computation in conventional computers, quantum computing makes use of quantum bits, or more exactly "qubits", the state of which can be any superposition of two basis states. Combinations of qubits can he put into "entangled" quantum states that can be used to perform certain types of calculations exponentially faster than classical computers. A lot of systems have been proposed as practical basis for realization and manipulation of qubits, including ion traps, nuclear magnetic resonance (NMR) of single molecules, and cavity quantum electrodynamics (CQED) [2, 3]. The work in this thesis is most related to the CQED approach, and in particular the possible implementation of CQED on a silicon chip. This is attractive because it makes use of the microelectronic technology well-established already in the semiconductor industry, and because it can be relatively easily integrated with optical communications technology. The basic idea is to replace the macroscopic Fabry-Perot cavities and cold atoms used in conventional CQED experiments with, respectively, "photonic crystal 3D microcavities" formed in silicon waveguides, and "artificial atoms" synthesized from semiconductor nanoparticles. Any of the numerous schemes for CQED-based quantum information processing can in principle be real-ized in an integrated photonic chip if sufficiently high quality cavities and nanocrystals can be fabricated and integrated. In order to perform a quantum calculation using such qubits, it is neces-sary to control the single qubit state by some external means, and it is also desirable to carry out conditional operations involving at least two qubits [4]. To perform conditional control on photons it is necessary to rely on the nonlinear optical response of material in the microcavity. Semiconductor Chapter 1. Introduction 2 nanocrystals, sometimes called artificial atoms, with dimensions on the order of a few nanometers, are known to exhibit exceptionally large nonlinear opti-cal responses associated with excitonic transitions between discrete quantum confined valence and conduction band states. Based on experimental and theoretical studies of these artifical atoms, it should be possible to use a sin-gle quantum dot to conditionally control the state of two coupled photonic qubits [5]. One scheme for manipulating photonic "qubits", based on the high-Q res-onant modes of a silica microsphere has been published [6]. The microsphere was assumed to support two qubits, each consisting of a T E / T M polarized pair of modes with the same angular momentum, which is different for the two qubits. Using the fact that the energy separation between the basis states of the two qubits is large, the state of each one can be independently controlled by applying a (near) resonant magnetic field that coupled the oth-erwise orthogonal T E and T M modes through the magnetic field dependence of silica's refractive index. Coupling of the two "qubits" was implemented via the intrinsic third order optica! susceptibility of the silica (the refractive index of the silica depends weakly on the intensity of the optical frequency electric field). The same basic scheme can be adopted in photonic crystal based micro-cavities where pairs of high-Q localized defect states (labeled not by T E or T M quantum numbers, but rather by the symmetry group to which they belong) can serve as the basis states of the photonic qubits. The small mode volume Vm of the photonic crystal based defect states (as compared to the microsphere states) facilitates the use of artificial quantum dots (ideally a sin-gle quantum dot) as a means of substantially enhancing the effective optical nonlinearity of the cavity [7]. The long term goal of the research group in Dr. Young's laboratory is to create a prototype device for CQED by selectively putting single quantum dots within wavelength-scale optical cavities formed out of photonic crystals in semiconductor waveguides (seen the schematic diagram in Figure 1.1). A waveguide used to couple light into and out of the quantum dot and mi-crocavity system will allow for a single-photon level study of the system's nonlinear optical properties [8]. This is a multi-faceted project that is being worked on by many group members. The author's principal contributions were: (i) designing a high-Q photonic crystal microcavity (Q ~ 4,000) using a finite difference time domain solver. Samples were then fabricated by Dr. Chapter 1. Introduction 3 Andras Pattanryus-Abraham in the cleanroom fabrication facility in the Ad-vanced Materials and Process Engineering Laboratory (AMPEL) . (ii) developing a novel lithography process for accurately defining a 50 nm diameter site, at a well-defined location within any given microcavity, suitable for attaching one or just a few semiconductor nanocrystals. In this thesis, Chapter 2 explains the general concepts of photonic crys-tals, the numerical methods used for the simulation work, and the fabrication methods. Chapter 3 describes the design of a high-Q microcavity based on the results. In Chapter 4, the results of the fabrication efforts we described. Finally, Chapter 5 summarizes the simulation and experimental results and suggests topics for future work on the overall project. Long term goal of overall project F a b r i c a t i o n o f p r o t o t y p e d e v i c e f o r c a v i t y Q E D resist covering patterned wet etching QD graf t ing to h igh f ie ld ( E ) reg ion of m i c r o cav i t y Figure 1.1: The basic scheme for realizing a microcavity with a quantum dot grafted selectively in the region of maximum E field of the microcavity mode(s) using A F M lithography. 4 Chapter 2 Background 2 . 1 O p t i c a l " S e m i c o n d u c t o r s " : P h o t o n i c C r y s t a l s Is it possible to create a structure or material capable of controlling a light beam in the same manner that a semiconductor controls electric current? In 1987, two independent articles were published, one by Eli Yablonovitch, then at Bell Communications Research Labs [9]; the other by Sajeev John, then at Princeton University [10], who suggested that artificially-textured di-electric materials could in principle be used to establish "optical bandgaps" for photons, in analogy with the electronic bandgaps fundamental to semi-conductors. While Yablonovitch's work was motivated by the possibility of inhibiting the spontaneous emission in a laser diode to improve its efficiency, John's work focussed on trying to localize light in analogy with Anderson Localization of electrons. In both cases, the problem came down to pro-hibiting propagation of light waves of a given frequency in a given dielectric structure, regardless of the direction or polarization of the propagating radi-ation. In the same way that the atomic periodicity of semiconductor crystals forbids the propagation of the electrons with an energy located in zones called band gaps, they proposed inhibiting the propagation of the photons in dielectric materials with structures having similar periodicities but with a different length scale. Due to their similarity with semiconductors, these materials were named photonic crystals and the forbidden spectral regions were named photonic band gaps. 2.1.1 One dimensional photonic crystal: Bragg stacks This phenomenon of band gaps can be intuitively understood by looking at the simplest case of a one-dimensional periodic structure. It can be extended to two or three dimensions. A prototypical example of a one-dimensional Chapter 2. Background 5 (ID) photonic crystal is a Bragg stack: a multilayer film composed of al-ternating materials exhibiting a contrast in refractive index. A schematic diagram of a Bragg stack is shown in Figure 2.1. These multilayer films are used as dielectric mirrors: they efficiently reflect light (with wavelengths in a range of approximately twice the stack's optical period) that impinges upon the stack at normal incidence to the direction of periodicity, where the op-tical period is the quotient of the vacuum wavelength of the light and the average index of the structure. Light in this forbidden range of wavelengths is diffracted backwards; the reflection is perfect for a infinitely thick stack without losses. Hence, for normally incident radiation, there is a photonic stopband, the width of which is a function of the contrast in refractive index. For an infinite structure, the extinction of transmitted light is perfect; for a finite structure, however, some tunnelling or non-zero transmission of wave-lengths within the photonic stopband, is expected. This stopband shifts for light incident off normal to the direction of periodicity, particularly for light incident on other faces of the crystal, and hence a ID Bragg stack cannot possess a complete bandgap. A B A B A B A B ?.A te *A te 4 4 4 4 4 4 4 4 Figure 2.1: Schematic diagram of a Bragg stack, an example of a ID photonic crystal. The crystal is composed of alternating layers of materials with a reflective index contrast. Light within a certain wavelength range travelling in the direction of periodicity will exponentially decay through the stack. Although it may seem straightforward to extend the idea of band gaps to 2D and 3D, there are in fact nontrivial effects that occur in these higher dimensional structures. In 3D periodically textured dielectrics it is possible to realize a full photonic band gap (exponentially decaying radiation within a band of frequencies, regardless of the polarization and propagation direction), Chapter 2. Background 6 however, 3D photonic crystals are challenging to fabricate at optical or near infrared wavelengths. The periodicity must be comparable to the wavelength of the bandgap—on the order of hundreds of nanometers—for use in laser and detector technology. Also, only certain lattice types can support a full bandgap and then only if the magnitude of dielectric contrast is sufficiently high. Despite considerable effort, a high-quality bulk 3D photonic crystal useful in the optical or near infrared part of the spectrum is still not available. 2.1.2 Photonic crystal slab (PCS) The fabrication of two-dimensional (2D) photonic crystals, on the other hand, is much easier to execute, as it can be based on existing epitaxial growth and lithographic techniques developed in the microelectronics industry. Pure 2D photonic crystals are periodic in two directions and homogeneous in the third; a photonic bandgap can exist for radiation propagating in the plane of peri-odicity, although such structures also cannot possess a full photonic bandgap. However, by fabricating a 2D photonic crystal in a planar waveguide, many of the useful properties of a photonic bandgap material can be exploited. Both the total internal reflection restricting light to planar propagation within the waveguide, and the in-plane Bragg diffraction property of the photonic crys-tal, allow one to make use of the photonic pseudo-bandgap of such structures [11]. This thesis deals exclusively with 2D photonic crystal structures made in semiconductor slab waveguides. An untextured planar waveguide, a 2D high-index semiconductor slab in air, for instance, will support bound modes that exhibit a dispersion similar to that shown in Figure 2.2. The dispersion of light in air and within the bulk semiconductor are represented by the straight lines—known as light lines—with slopes proportional to the reciprocal of the refractive index of the corresponding material. Above the air light line, there exists a continuum of radiation modes. Below the slab light line, no electromagnetic modes exist. Between the light lines is a region in which bound modes—modes that are confined to the planar waveguide by total internal reflection at the semiconductor-air int er face—exist. When periodic texturing is added, such as. a 2D array of air holes, pho-tonic bands can arise, just as the periodic potentials within a semiconductor give rise to the electronic bands. In accord with Bloch's theorem, the disper-sion diagram can be zone-folded into the first Brillouin zone. Some bound mode bands are zone-folded into the region above the air light line, as de-Chapter 2. Background 7 In-plane wavevector Figure 2.2: Schematic diagram of the physical structure of (top) and disper-sion diagram (bottom) of a planar waveguide slab in air. picted in Figure 2.3; such modes are considered "leaky" as they have Fourier components radiating out of the slab and hence serve well to couple light into and out of the textured waveguide to probe its optical properties. Such structures can be designed such that there is a full bandgap for bound modes; in this situation, it is only the radiation modes that overlap this bound mode that prevent the structure from possessing a true bandgap for light. Chapter 2. Background 8 region Tvmired region Air undercut ar wavegu ide s iah be l i r i I l ou in zono boundary Leaky mode / / Radiation modes I / / / / / / / / i j • ! • 1 • | • Bound \ ^ ^ ^ ^ / ' j modes > I n p l a n e w a v e v e c t o r Figure 2.3: Schematic diagram (top) of the physical structure of a periodi-cally textured planar waveguide slab in air and the corresponding dispersion diagram (bottom) showing bound mode, leaky mode and radiation mode dispersions. Chapter 2. Background 9 2.2 D e f e c t m o d e s a n d m i c r o c a v i t i e s Defects in semiconductors, such as impurities in the crystal structure, can give rise to states within the electronic bandgap. By analogy, defects in photonic crystals can yield modes within the photonic bandgap that are localized in the vicinity of the defect. A defect in a photonic crystal is an interruption in its periodicity. Consider for instance a ID periodic stack in which one of the layers is wider than the others, as schematically illustrated in Figure 2.4. This layer serves as a defect as it breaks the crystal's periodicity. Depending on the thickness of the defect layer, light within the stopband of the ID crystal can be trapped between two perfect reflectors. If the width of the defect is on the order of a single wavelength, there may be only one frequency at which such a mode can resonate. Figure 2.4: Schematic diagram of a defect in a ID photonic crystal. The thicker layer interrupts the crystal's periodicity and acts as a defect. Taking these considerations into account, the author designed a P B G microcavity for operation near the telecommunications c-band to illustrate the concepts related to introducing a defect in a P B G waveguide. For the device shown in Figure 2.5(b), the waveguide consists of a 1.5 fim thick silicon slab on a silicon dioxide substrate, where. tetch is the depth of silicon waveguide. The dielectric contrast is realized by introducing one dimensional air slots in the silicon waveguide layer. The air slots are etched through the waveguide, on a pitch, a, of 500 nm and a width of 100 nm. A defect is engineered by incorporating a break in the periodicity of the P B G device, where is the defect width of 810 nm. The spectrum shown in Figure 2.6(b) was obtained by exciting the structure from the left, using the fundamental mode of the untextured waveguide (shown in Figure 2.5(a)), and monitoring Chapter 2. Background 10 the field strength at the point downstream of the textures, at the yellow cross marked in Figure 2.5(b), as a function of the frequency of the launched mode. Al l calculations were done using the finite difference time domain technique (FDTD) described below in section 2.3. The calculations show that this structure has a wide stop-band of 54.2 THz and a resonance with a predicted wavelength of 1.51/im. The defect mode isstrongly confined within the P B G microcavity, as shown in Figure 2.6(b). Chapter 2. Background 11 0.9 0.8 0.7 >> in 0.6 nten 0.5 L U 0.4 0,3 0.2 01 -1.0 -0.5 0.0 0.5 1.0 y (microns) (b) Figure 2.5: (a) The transverse waveguide mode excites the structure from the left, (b) Schematic of a P B G waveguide microcavity with dimensions for operation at A = l.bl/im. The orange box indicates the simulation area during FDTD numerical calculation. The yellow cross identifies the point downstream of the heterostructure texture (air jSi/'SzC^)-Chapter 2. Background 12 Figure 2.6: (a) The transmitted intensity spectrum is monitored at yellow cross (shown in 2.5(a)). (b) The field distribution is shown when the incident frequency excites the resonance at 1.51 pm. Chapter 2. Background 13 For a planar waveguide textured with a two dimensional array of air holes, one method of introducing a defect is to shrink, enlarge or omit one or more of the holes. This results in a microcavity in which a mode can be confined in two directions by the periodic texturing and in the third direction by total internal reflection. States within the bandgap are localized in the vicinity of the lattice defect and thus the localized photonic defect states are essentially 3D optical microcavity modes, see Figure 2.7. wafer 1S4 nm Buried mM« tJtpm ti*n#* wait* mm Figure 2.7: Schematic diagram of a defect in a 2D planar photonic crystal. A microcavity is formed by removing one or more air holes. Salient properties of a resonant cavity mode for the purposes of CQED are its lifetime, given in units of the optical period by its Q value, and mode volume, Vcav.- For instance, the Purcell enhancement factor of the cavity structure, defined as the ratio of spontaneous emission rate of an embedded dipole state within the cavity to that in free space, is proportional Chapter 2. Background 14 to Q and inversely proportional to Vcav [12]. Applications in optoelectronics and quantum computing mostly demand a sustained high electric field per photon, achieved with a high Q value and a low cavity volume. In recent experimental studies of high-Q defect photonic nanocavities in 2D PC slabs [13], Q values in excess of ~1,000,000 and mode volumes of approximately 0.07 / im 3 have been attained. In the 2D photonic crystal waveguide geometry, the Q is ultimately limited by radiation into the upper and lower half-spaces. 2 . 3 N u m e r i c a l c a l c u l a t i o n m e t h o d s Various methods of simulating the electromagnetic properties of photonic crystals have been either adopted from electronic band calculations, taking into account the vector aspect of the light, or specifically developed for pho-tonic crystals. These simulations concern either 2D or 3D structures. For more complicated structures, particularly those containing complex "defect" structures, the finite difference time domain (FDTD) method, has become the technique of choice. This technique was originally developed for calculations concerning microwave devices, by Yee [14] The F D T D method has the advantage of being more general than many other methods. The technique is based on finite differences that come from a .spatial and temporal discretization of the Maxwell equations. In particular, no approximation of the "slowly-varying envelope approximation" type is made in either the spatial or temporal domains. With sufficiently dense discretization , accurate results for sub-wavelength scale structures, and a few optical cycle pulses can be obtained, limited by the available computational resources. Imagine a region of space which contains no flowing currents or isolated charges. Maxwell's curl equations can be written in Cartesian coordinates as six simple scalar equations. Two examples are: 2.3.1 F D T D algorithm dH, x -l,dE, y dEz (2.1) dt ti dz dy Chapter 2. Background 15 dEv l,dHx dHz, \ n n s "« = 7 ( & - *T> ( 2 2 ) T h e o t h e r f o u r a re s y m m e t r i c e q u i v a l e n t s o f t h e a b o v e a n d a re o b t a i n e d b y c y c l i c a l l y e x c h a n g i n g t h e x , y a n d z s u b s c r i p t s a n d d e r i v a t i v e s . M a x w e l l ' s e q u a t i o n s d e s c r i b e a s i t u a t i o n i n w h i c h t h e t e m p o r a l c h a n g e i n t h e E field is d e p e n d e n t u p o n t h e s p a t i a l v a r i a t i o n o f t h e H f i e l d , a n d v i c e v e r s a . T h e F D T D m e t h o d so l ves M a x w e l l ' s e q u a t i o n s b y f i r s t d i s c r e t i z i n g t h e e q u a t i o n s v i a c e n t r a l d i f f e r ences i n t i m e a n d s p a c e a n d t h e n n u m e r i c a l l y s o l v i n g these e q u a t i o n s i n s o f t w a r e . F i g u r e 2.8: I n a Y e e ce l l o f d i m e n s i o n Ax,Ay,Az, n o t e h o w t h e H field is c o m p u t e d a t p o i n t s s h i f t e d one-ha l f g r i d s p a c i n g f r o m t h e E f i e l d g r i d p o i n t s . T h e m o s t c o m m o n m e t h o d t o so l ve these e q u a t i o n s is b a s e d o n Y e e ' s m e s h [14] a n d c o m p u t e s t h e E a n d H f i e l d c o m p o n e n t s a t p o i n t s o n a g r i d Chapter 2. Background 16 with grid points spaced Ax,Ay and Az apart. The E and H field compo-nents are then interlaced in all three spatial dimensions as shown in Figure 2.8. Furthermore, time is broken up into discrete steps of At. The E field components are then computed at times t = nAt and the H field at times t = (n + l/2)At, where n is an integer representing the compute step. For example, the E field at a time t = nAt is equal to the E at t = (n — I)At plus an additional term computed from the spatial variation, or curl, of the H field at time t. This method results in six equations that can be used to compute the field at a given mesh point, denoted by the integers i,j, k. For example, two of the six are: H . ^ , ^ = H „ t &y(i,j,k) _ % ( i j , f c - l ) , _ A t ^z(i,j,k) _ ^ ( i j - l . f c ) , x(ij,fc) x(tj,fe) Az{ p{iJ:k) p.(ij,k-i) Ay A*(ij-i,fc) • (2.3) u-n+l/2 rrn+1/2 rjn+1/2 rr«+l/2 £ n + i = _g,„ + A f / f l v ( i j + i , t ) _ y(»j,fcK _ A i A ( i , i , W ) _ ^MiJ.fcK x(ij,fc) x(ij,fc) / i ( i j . + l i f c ) Ay //(ij,fc+i) M ( i i J i f c ) (2-4) The other four are symmetric equivalents of the above and are obtained by cyclically exchanging the x,y and z subscripts and derivatives. These equations are iteratively solved in a "leapfrog" manner, alternating between computing the E and H fields at subsequent At/2 intervals, which resembles Euler's method for numerical integration. However, due to the relatively well-behaved time evolution of electromagnetic fields, the numerical integration is extremely stable as long as the simple condition (Equation 2.5) is maintained. This condition is equivalent to maintaining a condition of causality. That is, the time step must be small enough that a signal travelling at the speed of light will not travel further than the distance from one grid point to the next within a single time step. A K { J - ^ + - ^ + -^}- 1 (2.5) ~ 1 V Aa;2 Ay 2 Az2i v ; The appeal of the FDTD method stems from its computational simplicity, which also lends it to high speed calculations. At any moment in compu-tational time, the electric and magnetic fields are stored on a uniform grid Chapter 2. Background 17 which represents the computational space. The fields are stored in a "dual grid" (Figure 2.8) which holds the electric and magnetic fields at slightly off-set spatial positions to facilitate the evaluation of the curls which are present in the Maxwell equations. The dielectric properties describing the materials structure are stored on a similar grid. The numerical evaluation of the time evolution of the field is especially fast and simple because the changes in the fields depend only on the field immediately surrounding it and just at the last moment in time. This allows the calculation to be done with only a single copy of the fields in memory and with entirely local operations. Thus the calculation time and memory scale linearly with the number of grid points. 2.3.2 Application of F D T D to identify microcavity modes The FDTD method is very useful for finding the time evolution of an elec-tromagnetic field. However, it is often the time-independent or steady state (single frequency) solution that is desired. In this thesis, we use a short pulse oscillating dipole to explore the properties of photonic crystal microcavities. ' Typically, the first step in isolating individual modes of an optical mi-crocavity is to map out the frequency spectrum of all the modes excited by a short-pulsed (broad band) oscillating excitation dipple in proximity to the cavity. The fields within the microcavity are evolved over time, and the variation in any components of any of the resultant fields is recorded for the excited modes of interest. Experimentally, this procedure is like exciting the structure with a short pulse and examining the local field with a spectrum analyzer. Care must be taken to ensure that all microcavity modes are revealed. Problems can arise if the sources or monitors are located at nodes of the modes, or if they are orthogonally polarized to the total field orientation of the mode. This issue can be addressed by using a few sources and detectors, with the orientation of the dipoles randomly oriented. Sometimes the dipole orientation can he carefully chosen to isolate modes of a specific polarization. Thus is particularly helpful in identifying degenerate modes. With the frequencies of the eigenmodes of a microcavity determined, the final step is to extract the spatial field pattern of the desired cavity modes of interest. This can be accomplished by filtering the field with a digital filter Chapter 2. Background 18 with a bandpass frequency centered on the desired cavity mode, to minimize the contribution of the initial field excitation. This is typically accomplished by apodizing the excitation field in the time domain. 19 Chapter 3 Design of Photonic Crystal Slab Microcavities 3.1 The F D T D S o l u t i o n s Implementation T h e F D T D software used to s imulate P C S m i c r o c a v i t y structures for this the-sis, F D T D Solutions™, was developed by Lumerical Solutions Inc. T h i s section provides technical i n f o r m a t i o n a n d references on the s i m u l a t i o n m e t h -ods used w i t h i n FDTD Solutions a n d i t introduces terminology a n d n o t a t i o n that is i m p o r t a n t for unders tanding other parts of this thesis. T h e objective of FDTD Solutions is to provide a general s i m u l a t i o n pack-age for c o m p u t i n g the propagat ion of l ight waves i n a r b i t r a r y (two or three dimensional) waveguide geometries. T h e s i m u l a t i o n is based on the wel l-k n o w n finite-difference t i m e - d o m a i n ( F D T D ) technique described i n the pre-vious chapter. T h i s section describes the physica l a n d m o d e l l i n g parameters required by the code. 3.1.1 Physical Parameters T w o phys ica l parameters are required i n order to perform a n F D T D s imula-t i o n • T h e refractive index d i s t r i b u t i o n n(f) as an funct ion of space. • T h e electromagnetic field exc i ta t ion source. F r o m these parameters, the physics dictates the electromagnetic field as a funct ion of (r,t), or space a n d t ime. Chapter 3. Design of Photonic Crystal Slab Microcavities 20 Refractive Index Distribution FDTD Solutions utilizes the following formula to specify the material proper-ties of a material structure at each point in the simulated volume. D(r) = e0er(r,cu)E(r) ' (3.1) Here D and E are the displacement and electric fields, respectively, while e0 is the permittivity of the free space and er is the relative permittivity in the dielectric regions. The relative permittivity is allowed to be a function of wavelength. This information is specified through the use of the computer aided de-sign (CAD) interface, which allows users to define and visualize the physical structures to be simulated, including structure size in terms of \im and the refractive index distribution. Electromagnetic field excitation In order to perform a simulation, an "external" excitation source must be specified. This is introduced in the form ^L(r,t) = f(f) x g(t) (3.2) where f(f) is the spatial excitation at the launch position (two or three dimensions) and g(t) defines the temporal variation of the excitation. The user can introduce E M sources such as dipoles, plane waves and Gaussian beams, and at the same time specify the field amplitude, centre frequency and spectral bandwidth and polarization of each source. For this thesis work, the author always used a dipole excitation source with T E polarization. An example is shown in Figure 3.7. 3.1.2 Numerical Parameters Boundary Conditions FDTD Solutions uses perfectly matched layer (PML) boundary conditions by default. However, Periodic, Symmetric and Anti-Symmetric boundary conditions (PBC, SBC and ABC) are also available. These boundary condi-tions can be applied to each of the three coordinates separately, and in some cases, to each of the six boundaries independently. Chapter 3. Design of Photonic Crystal Slab Microcavities 21 P M L By default, many simulations employ an absorbing boundary condition that eliminates any outward propagating energy that impinges on the domain boundaries. One of the most effective is the perfectly matched layer (PML), in which both electric and magnetic conductivities are introduced in such a way that the wave impedance remains constant, absorbing the energy without inducing reflections. P B C Periodic boundary conditions (PBC) are also important because of their ap-plicability for P B G structures. There are a number of variations on the PBC, but they all share the same common thread: the boundary condition is cho-sen such that the simulation is equivalent to an infinite structure composed of the basic computational domain repeated endlessly in all dimensions. PBCs are most often employed when analyzing periodic structures. A PBC stipulates that any field which leaves the boundary on one side of the domain should reenter the domain on the opposite side with possibly a phase shift. This can be expressed mathematically as E(Xl + a) = E(Xi)elk'a (3.3) Figure 3.1: Periodic Boundary Conditions (PBC) in F D T D simulation. Chapter 3. Design of Photonic Crystal Slab Microcavities 22 where the structrue is assumed to be periodic along the coordinate Xi with period a and a phase difference k\a. The Spatial and Temporal Grid In order to produce an accurate simulation, the spatial grid must be small enough to resolve the smallest feature of the simulation area, which usually is dictated by the wavelength in the material(s) to be simulated. Typically, the grid spacing must be less than A/10, where A is not the wavelength in vacuum, but rather in the material(s). Since the FDTD algorithm is performed in the time domain, a stable simulation must adhere to the requirement of "the causality condition", that is the "Courant Condition" which relates the spatial and temporal step size as described above. 3.2 2D Photonic Crystal Design In this section we analyze the photonic bandstructure associated with a defect-free 2D hexagonal pattern of air holes in a semiconductor host. We begin the analysis with a "pure" 2D-band structure calculation in which the dielectric slab is infinitely thick. For this purpose, "BandSolve" was used, which is a fully integrated C A D tool for generating and analyzing photonic band structures. The simulation engine is a product of RSoft Design Group Inc., and is based on the plane-wave expansion technique. We then perform a 3D FDTD calculation to investigate more accurately the 2D band structure for a slab of finite thickness. 3.2.1 "Pure" 2D Band Structure An illustration of the top view of the 2D photonic lattice used for this cal-culation is shown in Figure 3.2. The 2D photonic crystal is composed of a dielectric material with a hexagonal array of air holes. In this subsection we treat the structure as infinite in the third direction. The modes of the struc-ture that propagate perpendicular to the cylinders can be classified as T E (electric field polarization normal to the axis of the infinitely long air holes) and T M (electric field polarized parallel to air holes axis). The properties of 2D photonic crystal are determined by the interhole spacing a, the ratio r/a, and the refractive index of the material nsiab- The ratio r/a affects the size Chapter 3. Design of Photonic Crystal Slab Microcavities 23 of T E and T M bandgaps. Also, as the r/a ratio is increased, the frequencies of the photonic crystal modes tend to rise, owing to the larger air fraction and resulting lower average index [15]. In the 2D calculations we take r/a equal to 0.385. The refractive index of silicon was fixed at 3.48. Figure 3.2: 2D unit cell used for bandstructure calculations. Dispersion diagrams showing normalized frequency versus in-plane (per-pendicular to the hole axis) wave vector for T E and T M modes of the 2D photonic crystal are given in Figures 3.4 and 3.5, respectively. The frequen-cies are always expressed as a/A, where A is the free space wavelength. In addition we use the term dielectric band when referring to the lower-frequency band that defines the bandgap, and air band to describe the band on the high energy side of the gap. The band diagrams show a bandgap for TE-polarized modes but no gap for TM-polarized modes with this refractive-index contrast and relative small r /a ratio. This makes it difficult to design localized defect states that have T M components and limits the number of possible localized defect modes, because T M modes will in general not be well contained by the photonic crystal. In the TE-band diagram of Figure 3.4 the fundamen-tal bandgap lies between normalized frequencies, 0.44~0.31 and is formed between the air band at the M point and the dielectric band at the K point. Chapter 3. Design of Photonic Crystal Slab Microcavities 24 Figure 3.3: A fc-space diagram demonstrating the crystal symmetry direc-tions of a hexagonal array. The solid black dots represent reciprocal lattice vectors. The 1st Brillouin Zone is represented with a dotted line and the high-symmetry points are K and M . 3.2.2 3D F D T D Analysis of a 2D Patterned Slab Waveguide In subsection 3.2.1 the 2D photonic crystal was formed from an infinitely thick dielectric slab. Here we shrink the dielectric slab to a thickness of the order of the wavelength of light and surround it with air, thus providing a high degree of localization in the third direction, through total internal reflection. The properties of the 2D photonic crystal are still determined by a, r /a, and nsia0, but now the thickness of the slab is also important. The 2D bandstructure for these slab-based photonic crystals describes zone-folded T E and T M slab modes that are mixed together (renormalized) by scattering from the dielectric texture etched into the slab. If the zone folding results in a mode that lies above the light line of the cladding (usually air for our structures) then those modes are leaky in that they radiate into the Chapter 3. Design of Photonic Crystal Slab Microcavities 25 TE Band Structure 0.9 0.8 f07 «! 0.5 s S* 0-4 -i c B- 0.3 0.2 0.1 0:0 • * 1 - * - * • * : • . \ . ':--+;-•.. . . . • r ••v*v.= : * . • ".' ' . * • * > •ifr?-'"'1:.' ^ ^ ^ ^ ^ - * * • • • * -* ; "-»;... Figure 3.4: T E band structure of a "pure" 2D hexagonal photonic crystal described in the text. cladding as they propagate in the plane. Modes below the cladding light line are true, infinitely long lived modes localized to the slab. The resonant modes of a 2D patterned dielectric slab surrounded by air, however, are not purely T E or T M but rather what we designate TE-like and TM-like. The TE-like and TM-like modes are classified by how they transform under reflection through a plane in the slab, at its midpoint. TE-like modes are even under reflection, and TM-like modes are odd. TE-like modes are composed of even T E slab modes and odd T M slab modes, whereas TM-like modes are formed from even T M slab modes and odd T E slab modes [16]. Given the relative difficulty involved in establishing bandgaps for T M versus T E modes even in pure 2D crystals (see Figs. 3.2 and 3.3), we focus on designing defect cavities that support TE-like localized modes. Also, depending on the thickness of the dielectric slab, there can be higher-order guided modes supported by the patterned slab. Here we consider dielectric slabs approximately a half-wavelength thick in which there is a bandgap between the fundamental (0th order) air and dielectric band TE-like modes. Chapter 3. Design of Photonic Crystal Slab Microcavities 26 TM.Band Structure 0.8 - * • 0.7 - * - A • • • * ... * • ST 0.6 - • • * * la • .... • * II. o 0.5 * .: *...••• a/2 * 0.4 -? c 0) 0.3 -• 3- * o~ Q) Fr 0.2 -0.1 -0.0 * : :"*V. r M K r Figure 3.5: T M band structure of a "pure" 2D hexagonal photonic crystal described in the text. A 3D FDTD simulation is used to model the fundamental TE-like band structure of the optically thin patterned waveguide. By applying appropriate Bloch boundary conditions over a 2D unit cell of the photonic crystal, one can obtain the spectral response for a given in-plane wave vector. The peaks in the frequency spectrum give the eigenmodes of the photonic crystal at the in-plane k vector determined by the boundary conditions. The interested reader is referred to Ref. [9] for further details. In our case the unit cell consists of an in-plane geometry given by the 2D unit cell of the hexagonal lattice. In the z direction we do not have periodicity, so a full description of the slab and surrounding air must be given, The Bloch boundary condition is applied to all four sides normal to plane of the slab, and the P M L boundary condition [14] is applied to the top boundary. At the bottom boundary we apply an even mirror reflection positioned at the middle of the slab to select out only the TE-like modes of the structure. A uniform spatial resolution of 16 points per interhole spacing is used to discretize the unit cell, and the initial field is evolved for 1000 femto-seconds. This gives a normalized frequency Chapter 3. Design of Photonic Crystal Slab Microcavities, 27 resolution of 0.01 and a spatial resolution of approximately 10 points per wavelength in the high-index slab for frequencies within the bandgap. In these 3D calculations a slab refractive index of 3.48 is used. The TE-like band structure (from point of M to K in partial k space) for a 2D patterned slab waveguide with thickness d = 0.408a is plotted in Figure 3.6, because that is the most relevant region for defining the bandgap between the air band band at the M point and the dielectric band at the K point, as can be seen from the "pure" 2D TE-band diagram above. Comparing the band structures for the "pure" 2D PC (seen Figure in 3.4) and the 2D PC slab (see Figure in 3.6), the pure 2D results are in quite good agreement with the real 3D results for the two lowest even guided modes (TE-like modes). For a heterostructure-slab-waveguide-based 2D photonic crystal (seen Figure 2.7), T E and T M modes are no longer separable due to the lack of translational symmetry in the z plane. However, the modes in photonic crystal slabs have a strong similarity to the modes in unperturbed slab waveguides, as shown by many authors (e.g., [17]). The slab structure used to obtain the bandstructure shown in Figure 3.6 (a=480 nm, d=196 nm and r=184.8 nm) results in a TE-like bandgap centered at 1.5 /im, very close to the desired operating wavelength where the PbSe nanocrystals are resonant. The mode energies of the final structures are verified using FDTD calculations which also serve to extract the expected Q value of the defect modes. Chapter 3. Design of Photonic Crystal Slab Microcavities 28 0.7 0.6 h 0.5 CD •3 : CT CO •o a> N 0.4 A f = 0.44—0.31 0.3 >• e • • • • • • •• t " 0:2 0.1 0:0 1 ' < 1 l ; -•• • . - J 0.58 0.59 0.60: 0 61 0.62 0.63 0:64 0.65 0.66 N o r m a l i z e d w a v e v e c t o r (k.a/2r.) Figure 3.6: Band structure of the TE-like modes of the 2D patterned slab waveguide surrounded by air (a=480 nm and d=0.408a). The solid line represents the light line. Only the part of dispersion diagram from the M point to the K point in reciprocal space is plotted. The material was taken to have a fixed index, nsiab = 3.48. The radius of the holes is defined by the ratio r/a = 0.385a. The resulting TE-like bandgap extends between a normalized frequency, A / = 0.44 — 0.31. The region above the light line corresponds to leaky modes; the parts of the frequency bands that are below the light line are guided modes. Chapter 3. Design of Photonic Crystal Slab Microcavities 29 3 . 3 3 D F D T D A n a l y s i s o f O p t i c a l M i c r o c a v i t y We now introduce a defect into the uniform photonic crystal by removing three air holes and analyze the properties of the localized modes that de-velop. By analyzing the defect modes in three dimensions, we are able to evaluate the effectiveness of the vertical confinement of the defect modes for a finite-thickness dielectric slab. The FDTD calculations in this section are performed for different air hole radii between 125 ~ 200 nm. The interhole spacing, a, is held constant at 480 nm and the slab thickness is fixed at 196 nm. From other literature this type of defect geometry is known to support at least one "x dipole-like" localized mode, so mirror boundary conditions were applied in the x, y and z directions to achieve an eightfold reduction in the computational volume and to eliminate TM-like modes. Symmetric boundary conditions were used at the x boundary in the x direction and anti-symmetric boundary conditions were used at the y boundary in the y direction, as shown in Figure 3.7. The computational mesh has a resolution of 15 points per interhole spacing, or approximately 15 points per wavelength for frequencies within the photonic crystal bandgap. The number of rings of air holes that surround the defect is five, as shown in Figure 3.7. A TE-polarized point dipole electric field is used to excite the TE-like modes of the defect structure. A fast Fourier transform (FFT) is applied to the resulting time series of the field at a point of low symmetry in the cavity, to pick out the resonance peaks of the defect modes. Determining the cavity Q-factor The most accurate way to measure the Q-factor for a cavity is to use time-domain field data, and note how fast the envelope of the field decays as a function of time when plotted on a logarithmic scale, as in Figure 3.8(a). Note that the peak field decays very slowly, so it. is necessary to zoom into the upper part of the field profile. Zoom in until you can observe the slope of the signal in the time-domain field data, as shown in Figure 3.8(b). Given the slope, the Q-factor can be calculated from the following formula, such that Chapter 3. Design of Photonic Crystal Slab Microcavities 30 Figure 3.7: Schematic of a 2D slice through the middle of the patterned high-index slab. The center three air holes are missing, which forms a high-Q microcavity. A dipole E M source with T E polarization was introduced to excite the resonant mode of the microcavity. Three point receptors (yellow crosses) made sure that all the microcavity responses would be recorded. - 2 x TT x logw(e) x fR ^ 2 x m m = (logw(fieldstart) ~ logw{fieldend))/(timestart - timeend) where fn is the resonant frequency of the mode, and m is the slope of the field decay in SI units. Plots of the defect mode frequency and Q value as a function of the air-hole radius are shown in Figures 3.9 and 3.10 Field distribution of the cavity mode of interest Figure 3.11 shows the field distribution for the cavity mode with resonance frequency of 191.91 THz, corresponding to an air hole radius of 180 nm. This plot clearly shows that the mode is quite localized in the vicinity of the three missing holes, and therefore this structure is a useful one for developing the nanocrystal grafting process. Chapter 3. Design of Photonic Crystal Slab Microcavities 31 Figure 3.8: (a)Plot of the Ey component of the field decaying as a function of time on a logarithmic scale, (b) Zooming into the upper part of the field profile for measuring the cavity Q-factor. Chapter 3. Design of Photonic Crystal Slab Microcavities 32 194 174 I 1 • ' • 1 • 1 • 1 • 1 130 140 150 160 170 180 r a d i u s o f a i r - h o l e (nm) Figure 3.9: Plot of resonance frequency of cavity mode as a function of radius of air-hole. 120 130 140 150 150 170 180 r a d i u s o f a i r - h o l e (nm) Figure 3.10: Plot of cavity mode Q factor as a function of radius of air-hole. Based on these results, a target hole spacing of 180 nm was chosen for the purpose of fabricating real microstructures. It offers a reasonably high Q, and the resonant frequency is easily accessible with the optical parametric oscillator used to characterize the microcavities. Chapter 3. Design of Photonic Crystal Slab Microcavities 33 Figure 3 .11: 2D slice through the middle of the silicon slab described in the text showing the field (E) magnitude profile of x dipole-like mode: /resonance = 1 9 1 . 9 1 THz or 1.56 pm, which is in the telecommunication fre-quency range. The units of the x and y coordinates are given in metres. Chapter 3. Design of Photonic Crystal Slab Microcavities 34 3.3.1 Demonstration of microcavity device and resonant scattering spectrum Samples with dimensions tuned around those corresponding to the field dis-tributions plotted in Fig. 3.8 were fabricated in silicon using electron-beam lithography and reactive plasma etching techniques by Andras Pattantyus-Abraham, another member of our group. A scanning electron microscope image of one such sample is shown in Figure 3.12. In order to verify that the samples support high-Q localized modes, a micro-reflectivity apparatus was developed in our research lab to study the resonant modes of the microcavity structures, schematically shown in Figure 3.13. A train of short pulses (~ 130/s) from a tunable optical parametric oscillator was focussed with a 100 X objective lens directly on the microcavity, from the top half space. This excitation beam is polarized, and a crossed-polarizer is located in the retro-reflected beam path to cancel most of the un-scattered beam, and reveal resonant scattering features when the cavity supports localized, high Q modes. A typical resonant scattering spectrum that shows a single high-Q cavity mode is shown in Figure 3.14. o o o o o o o o c DOOOOOOOOC O O O O O O O O C DOOOOOQjj)Q( •OOOOO a_ CD uu I I O O O O O O O O O Q O O O DOOOOOOOOOOOOC o o o o o o o o o p o o o )OOOOOOOOOOOOC S4700 20.0kV 6.0mm x20.0k SE(U) 10/28/05 i i t i i i I I i r i 2.00um Figure 3.12: SEM graph of the central region of a SOI-based microcavity with interspacing of a = 480 nm and air-hole radius of r = 180 nm. Chapter 3. Design of Photonic Crystal Slab Microcavities 35 TO I"! IK ( w i t h I r i C a A s d e t e c t o r ; CCD c a m e r a Polarizing beamsplitter Neutral density filter^ Benin, s top El L i p s o ' i (iai mirrcav Mi<. I V S I . . i p i - o b j e c t i v e l e n s vNanopoM;t'ipjie,i" T r a n s l a t i o n s t a g e . Simple Figure 3.13: Schematic diagram of the microreflectivity set-up. The nano-positioner on which the sample sits, as well as the short focal length of the focusing microscope objective lens, allow for precise localization of the light from the optical parametric oscillator. Precise positioning is achieved with the help of a CCD camera to image the samples. When the camera is removed from the beam path, the beam is focused into an FTIR spectrometer with an ellipsoidal mirror. Chapter 3. Design of Photonic Crystal Slab Microcavities 36 •t—' " l O c B A / 4f% / \ / 6250 6300 6350 6400 Wavenumber (cm"1) Figure 3.14: Resonant scattering spectrum obtained using an excitation source polarized to excite a single x dipole-like mode of SOI-based micro-cavity. The broad background is due to leakage of the exciting laser pulse through the imperfect crossed polarizers, and the sharp feature represents the scattering from the microcavity mode excited by this broad laser spectrum. 37 C h a p t e r 4 A F M N a n o l i t h o g r a p h y 4.1 I n t r o d u c t i o n A t o m i c Force Microscopes ( A F M ) have been c o m m e r c i a l l y available for more t h a n a decade now. A l t h o u g h they are most often used to reveal atomic-level topographica l i n f o r m a t i o n from sol id surfaces w i t h nanometre scale la tera l resolut ion, they have also been used to "wri te" features on surfaces for l i tho-graphy purposes. Surface features have been w r i t t e n us ing the A F M probe t i p to scratch, oxidize, or reduce the surface of interest. In this thesis, the m e t h o d of loca l surface o x i d a t i o n of s i l icon surfaces is achieved by a p p l y i n g a negative voltage to a m e t a l coated A F M t ip i n contact w i t h the s i l icon sur-face. It is quite wel l established that the oxygen involved i n the react ion is suppl ied from a water miniscus that n a t u r a l l y forms t h r o u g h c a p i l l a r y forces between the t i p a n d the sample surface, under ambient condit ions. B y scan-n i n g the t i p whi le a bias voltage is appl ied , an ox id ized track, or p a t t e r n can be i m p r i n t e d on the s i l icon surface [18]. T h e p r i m a r y part of the author 's thesis work was devoted to developing a procedure for using a c o n d u c t i n g t i p A F M microscope to loca l ly oxidize the s i l icon microcavi t ies i n as s m a l l an area a n d as close to the peak field d i s t r i b u t i o n of the m i c r o c a v i t y as possible. A s ment ioned i n C h a p t e r 1, the q u a n t u m dot (of P b S e i n this case) graft ing to the high-field region of the m i c r o c a v i t y i n the photonic crysta l plays an i m p o r t a n t role i n real iz ing a basic prototype device for C Q E D . T h i s can be accompl ished by a l ter ing the local surface chemistry t h r o u g h scanning probe microscopy techniques, using the scheme described i n F i g u r e 4.1. First, the m i c r o c a v i t y is modi f ied w i t h a densely packed organic monolayer. T h e purpose of this monolayer is to prevent b o n d i n g of the P b S e nanopart ic les to the m i c r o c a v i t y surface except where i t has been loca l ly destroyed by the A F M o x i d a t i o n process. Second, the covering monolayer is loca l ly degraded a n d replaced w i t h a SiC>2 i s land by a p p l y i n g a p r o g r a m m e d voltage pulse between the conduct ive A F M t i p a n d the substrate under ambient condit ions. Third, the resul t ing oxide i s l a n d is Chapter 4. AFM Nanolithography G> 38 removed by aqueous HF etching, which yields a small Si-H terminated area on the silicon surface, that is otherwise protected by an organic monolayer. Because the organic monolayer must be present when the anodized oxide dot is etched away using HF acid, the monolayer must be robust to this HF exposure. Finally, the UV-mediated nanoparticle grafting reaction is then carried out to yield nanoparticles attached to a well-defined area, and ideally, nowhere else. Control of the anodized spot size and grafting conditions should ultimately allow a single nanoparticle to be grafted in the desired region. Lithography is not explicitly supported by the NanoScope III system. Instead, the Nano Script™ language is employed to manipulate the tip rel-ative to the sample surface. The NanoScript library commands enable one to perform lithography. The AFM-based lithography process developed in this work includes the following steps: • Write a lithography program that manipulates the vertical position and voltage applied to the tip once it is positioned over the sample. • Engage the surface; obtain an image. Determine the site where the oxide dot is to be formed. • Adjust the sample using X and Y offsets to position the lithography site at the center of the screen. • Run the lithography program. • Reimage the site to evaluate the results. The NanoScript language includes commands to translate (move) the tip over the sample while controlling microscope parameters such as bias voltage and setpoint. Lithography programs may be run in contact mode A F M and tapping mode A F M ; each mode produces its own unique results. The A F M (Figure 4.2) operates by measuring attractive or repulsive forces between a tip and the sample. In its repulsive "contact" mode, the instrument lightly touches a tip at the end of a leaf "cantilever" to the sample. As a raster-scan drags the tip over the sample, some sort of detection apparatus measures the vertical deflection of the cantilever, which indicates the local sample height. Thus, in contact mode the A F M measures hard-sphere repulsion forces be-tween the tip and sample. In tapping mode, the AFM'derives topographic Chapter 4. AFM Nanolithography 39 images from measurements of attractive forces; the tip does not touch the sample [19]. Tips may be translated with feedback on or off, regardless of operating mode. If feedback is on and gains are properly set, the tip will be moved with constant contact force (contact AFM). Chapter 4. AFM Nanolithography 40 M o n o l a y e SI r formation I 1 ) f R R R R R R R R R R I I I I I I i Si A F M anod i za t i on R R HF e t ch ing R R H ! 1 n Gra f t ing of Q D s R R (2) 1 R 1 (3) Si | 4 ) R I Si H Figure 4.1: Experimental procedure for fabricating site-selective PbSe nanoparticles assemblies. R is the terminated organic monolayer and Y is the terminal ligand for surface-grafting. Chapter 4. AFM Nanolithography 41 Figure 4.2: Concept of A F M and the optical lever: (a) a cantilever touching a sample; (b) the optical lever. (By courtesy of Dr. David Baselt) Chapter 4. AFM Nanolithography 42 4.2 Material Preparation 4.2.1 Semiconductor layers Two principal types of substrate wafer were used in this thesis: moderately doped (1 — lOQcm) p-type Si(100) and an SOI (Silicon On Insulator) wafer. The SOI wafer consists of a 194 nm thick undoped Si(100) device layer, above a buried oxide layer of thickness 1.2 pm, all on top of a 750 micrometer thick n-type Si(100) handle layer. The layer structure is depicted schematically in Figures 4.3(b) and 4.3(c). 4.2.2 Organic monolayer preparation Two different types of organic monolayers were studied: octadecyltrichlorosi-lane (Cl z Si (CH 2 ) l 7 CH z , OTS, 95%), and octadecene (H2C = CH(CH2)15(CHZ), alkene). Al l chemicals were purchased from Aldrich (USA). The other reagents were of analytical grade, and used as received. DI water was used throughout the experiments. Al l the organic monolayer chemistry was de-veloped by Dr. Andras Pattantyus-Abraham. Preparation of OTS layers The reaction of OTS with OH-terminated Si surfaces (see Figure 4.6) was performed as follows (by courtesy of Dr. Andras Pattantyus-Abraham). • sonicate new vials in soap and water for 15 min. • Rinse in H20, IPA, H20 and dry in heat gun. • clean sajnples in RCA (DI : NH4OH : H202 = 4 : 1 : 1 ) solution for 15 min, then rinse in DI H20. • strip native oxide by ~ 60s dip in HF(49%) : H20 = 1 : 20 • re-oxidize samples m'H2SOA : H202 = 2 : 1 at 100 °C for 40 min. Wash three times in DI water, dry with heat gun. • place samples into cleaned vials (two samples per vial) and pump down for 1 min, then place under N2. add 1 ml hexadecane or 1 ml 4 : 1 = hexadecane : chloroform, then add 3 pi OTS. r Chapter 4. AFM Nanolithography 43 • flush vial with N2 and seal with plastic cap for 2 hour. Preparation of Alkyl layers The hydrosilylation reaction of octadecene with hydrogen-terminated (H-terminated) Si surfaces (seen in Figure 4.5) was performed as follows (by courtesy of Dr. Andras Pattantyus-Abraham). • filter octadecene through a ~8 cm activated alumina column into a clean schlenk flask. • degas further by 3 x freeze-pump-thaw cycles (thaw by placing in stirred water) • clean p-type Si(100) pieces by RCA clean (DI : NH4OH : H202 = 4 : 1 : l,v/v/v) for 15 min. • remove oxide by ~10 s dip in aqueous HF solution (H20 : HF = 20 : l,v/v). • rinse, then dry in N2 stream • place Si sample into flask under N2 stream. • Transfer octadecene into flask using a long syringe. • degas and then heat to ~ 200°C under slow stream for 2 hours. • Cool to room temperature, and then rinsed with hexane; sonicate and dry with N2-Chapter 4. AFM Nanolithography 44 (a) SOI-based photonic crystals. UndopedSi(IOO) Figure 4.3: Schematic diagrams of fully processed sample (a), the SOI wafer (b), and the silicon wafer (c). Chapter 4. AFM Nanolithography 45 C 1 B H 3 7 C 1 8 H 3 7 I I H H H M H; OHOHOHOHOH O O SI0 2 HF I I Piranha I I I I I OTS/hexadecane si si 9 0 ° c SI 1 5 m i n Si Figure 4.4: Schematic representation of the reaction of OTS with a OH-terminated silicon surface. sto2 SI H H H H H R R R H i C ^ R V * Si SI Figure 4.5: Schematic representation of the reaction of octadecene with a H-terminated silicon surface. The symbol A means heating for 2 hours. Chapter 4. AFM Nanolithography 46 4.3 A F M lithography 4.3.1 A F M settings for anodic oxidation All work reported here was done using a Multimode Nanoscope III SPM (Digital Instruments, USA) or an MFP-3D A F M (Asylum Research, USA), in contact mode with a conductive silicon tip coated with Ti-Pt metals (UL-TRASHARP, USA). The bare or monolayer-modified silicon substrate was subject to a programmed voltage pulse via the internal (Analog 2) signal line from the Nanoscope controller. Figure 4.6: Cantilever:CSC 11/Ti-Pt, used for all the experiments. radius of curvature less than 40 nm tip height 15..20 micron full tip cone angle less than 30° thickness of Ti lst-layer 20 nm thickness of Pt 2nd-layer 10 nm Table 4.1: Nominal specifications of probe tip. Chapter 4. AFM Nanolithography 47 Tip holders To use a conductive tip with the Nanoscope instrument, the standard tip holder had to be electrically insulated from the rest of the instrument. This was achieved by completely covering the tip holder with a piece of latex rubber cut from a Kimberly Clark glove type. Biasing the tip When it is necessary to apply voltage to the tip or sample, minor changes must be made to the jumpers in the Nanoscope III microscope's baseplate and the toggle switches on the Extender Electronics Module. The location and orientation of the jumpers in the baseplate of the MultiMode A F M and the toggles on the backside of the Extender Electronics box are shown in Figures 4.7(b) and Figure 4.8(b). The jumpers can easily be changed through the rectangular opening in the bottom of the baseplate using a pair of non-conducting tweezers. The setting switches on the back of the Extender Electronics Module can easily be toggled by pressing the buttons. The jumper cofiguration in Figure 4.7(b) connects the Analog 2 sig-nal from the Nanoscope III controller to the tip. The "Analog 2" volt-age line is normally used by the NanoScope to control the attenuation of the main feedback signal. The input attenuation must be disabled for the duration of the A F M lithography work. To do this, click on the Micro-scope/Calibrate/Detector option to display the Detector Parameters window. Switch the Allow in attenuation field to Disallow. Return to the main Feedback Controls panel; the Analog 2 field should now be enabled. This signifies that voltage is now being supplied via the "Analog 2" pin located on the MultiMode baseplate header. Remember to restore (Allow in attenuation) upon completion' of A F M pulsing. Chapter 4. AFM Nanolithogfaphy 48 (b) Jumper configuration for application of voltage to tip. Figure 4.7: Schematic diagrams of baseplate and jumper configuration. Chapter. 4. AFM Nanolithography 49 c  : ^ T i p or Sample (a) Toggles switches on back of Extended Electronics Module. Mode Tip or Sample Voltage Stir face 'Potential GN'D/Sitrface Potential Analog 2 TtippingMode Contact A F M MFM Surface PoicnU.il • V Apply *x>ltagc let Mp or sampled.5** for.electnc ricld gradient imaging: tunneling AFM) (b) Exteded Electronics Module toggle switch settings Figure 4.8: Schematic view of Extended Electronics Module and illustration table of toggle switch settings. Chapter 4. AFM Nanolithography 50 4.3.2 Mechanism of A F M Anodic Oxidation. The key for the site-selective nanoparticle assembly is to fabricate the guiding template. By applying a programmed voltage pulse between the A F M tip and the monolayer-coated silicon, the monolayer is degraded and the underlying silicon is oxidized to form silicon dioxide via an electrochemical mechanism. The A F M tip, the silicon substrate, and the condensed water layer create a nanometer-sized electrochemical cell. Given enough potential between the tip and the substrate, an electrochemical reaction takes place and H+ and OH" ions are generated by electrolysis of H2O. As a result, a hydroxyl group terminated region is formed on the silicon surface after removing the degraded organic molecules by ultrasonication in ethanol, and DI water. Because current must flow between the tip and the substrate in order to anodize the sample surface successfully, a good electrical contact to the sample must be achieved. A special sample-mount setup, seen in Figure 4.9 was designed and made to aid in getting good contact. The sample mount, designed to securely hold the wafer and a dummy sample of the same thickness as the wafer, were made from a copper block by the machine shop at Physics and Astronomy Department. copper piec Iron screw iron sample d Figure 4.9: Schematic view of the sample-mount consisting of a iron sample disk, a copper piece (square cap) and a iron screw for good ohmic contact. Chapter 4. AFM Nanolithography 51 4 . 4 Results and discussion A F M conductive anodization employing the set-ups discussed in subsection 4.3.1 was performed on both bare silicon, and silicon coated with different organic monolayer masks, described in sections 4.2. These results and some of their implications are as discussed in this section. In order to re-image nano-scale features written at particular locations on a sample with the Digital Instruments (DI) Nanoscope, it is best to locate them with respect to a characteristic feature in a much larger pattern that is easily visualized with a simple optical imaging system that was added to the DI system. In this work, large, 90 micron square photonic crystal arrays were etched into the substrate to act as these easily-identified reference points. The alignment procedure then consists of three steps. F i r s t , "eye-step"— With the sample in the A F M , illuminate it with white light from a fibre illu-minator and locate the large photonic crystal patterns by eye. By hand, move the visible patterns around below the A F M tip; S e c o n d , "magnifier-step"— By adjusting the x-y translation stage (10 x 10 u-m2), bring the observable features into the field view of the 45 x objective imaging lens; T h i r d , "AFM-step"—engage the A F M tip and record a topographical A F M image (89 x 89 p,m2). If no features associated with the visible-to-the-eye patterns are found, move (with x-y translation stage) the sample and take another A F M image. Repeat this procedure until the photonic crystal pattern is found, by re-peatedly scanning again and again. By repeatedly shifting and imaging, the pattern should be found within at most one hour. Once an A F M image of the photonic crystal pattern is obtained, fine tune the position until a corner of the pattern is near the centre of the A F M field of view. Use this corner as a reference for all writing and reimaging of the oxide dot patterns. 4.4.1 A F M tip-induced anodic oxidation on a bare SOI substrate Figure 4.10 shows A F M images of the photonic crystal reference feature alone, 4.10(a), and after a series of a silicon dioxide dot arrays were created on a bare SOI wafer using this procedure. Figure 4.11(a) shows that the dependence of oxide dot size on the varying voltage in a range of between IV and 12V at a fixed pulse duration of 100 ms, by negatively biasing a conductive A F M tip with respect to the sample substrate. Similarly, Figure 4.11(b) shows that the dependence of oxide dot Chapter 4. AFM Nanolithography 52 diameter on the pulse duration between 100 ms and Is for a fixed negatively bias voltage of 5 V. Figure 4.12 summarizes the results. The dependence of the size of oxide dot on pulse voltage and pulse duration are seen in Figure 4.12 (a) and (b) respectively for a hydrogen-passivated undoped silicon surface of the SOI sample. For a constant pulse duration of 100 ms, the threshold pulse voltage negatively applied to the A F M tip with respect to the underlying sample substrate is -5 V. The size of the oxide dot increases monotonically with applied bias and pulse duration over the range of parameters used in this study. The humidity (not controlled in this work) is known (ref [20]) to also effect the dot diameter, which can vary by ~ 30% for relative humidity ranging from 20% to 55%. This possibly explains why the dot diameters nominally at -5 V and 100ms in the two graphs of 4.12 are not identical. From several trials under various ambient conditions, we conclude that -5 V and 100 ms voltage pulses can reliably result in oxide dots with ~ 50 nm diameter if the A F M system is "quiet" and. well tuned. Chapter 4. AFM Nanolithography 53 0 2.5 5.0 7.5 10.0 (b) Figure 4.10: Contact A F M topographic images of (a) a pre-made square-pattern array (image shows a region 5 x 5 pm2, with a vertical range scale of lOnm) and (b) oxide dot arrays made by using A F M anodic oxidation to the right of the square array (image shows a region 10 x 10 pm2, with a vertical range scale of lOnm). Chapter 4. AFM Nanolithography 54 Height flnsle Surface Nornal Clear C a l c u l a t o r 08 -09 -10 •07 -12 -11 111004H.004 Height NanoScope Contact AFM Scan s i z e 3.000 MM S e t ^ o i n t 0 U Scan r a t e 5.036 Hz Number of samples 512 (a) Height Angle Surface Horwal C l e a r C a l c u l a t o r i Height (b) Figure 4.11: The dependence of oxide dot size on (a) the varying pulse volt-age, — 1 ~ —12 V for a fixed pulse duration of 100 ms, and (b) the varying pulse duration, from 100 ms to 1 s for a fixed pulse voltage of -5V. Chapter 4. AFM Nanolithography 55 240 r 220 200 • | 180 2 160 • O "O 140 • 4> "O 120 X O 100 0) 01 E ns 5 Humidity: ambient air Pu lse duration = 100ms Pulse voltage/V ( a ) 120 110 100 90 80 70 60 50 40 30 Humidity: ambient air B ias voltage - -5V 0.4 0.5 0.6 0.7 Pulse duration/s (b) Figure 4.12: Relationship between oxide dot diameter and (a) voltage and (b) pulse duration for bare patterned SOI sample. Chapter 4. AFM Nanolithography 56 4.4.2 A F M anodic oxidation of OTS-modified Si and SOI substrates. Dr. Andras Pattantyus-Abraham and Ms. Amy Liu spent several months refining the procedure for growing OTS monolayers on Si and SOI substrates. The literature documents two growth modes [22]: one involves an "island ag-gregation" mechanism which starts with the building of islands in solution that adhere to the substrate and grow together into a complete monolayer; and the other is a "continuous" mechanism which initiates with incomplete monolayers of OTS molecules that are distributed over the substrate in a disordered manner, but which fill out to form a highly ordered, uniform film structure. Figure 4.13(a) shows an example of the "island" type growth mode. Dip-ping this film in HF acid reduced the island size, but the surface remains rough, as seen in Figure 4.13(b), Hoffmann and Friedbacher [21] found that with increasing water content or increasing soaking time in the absorbate solution, island type growth is strongly favored. This is consistent with the experience of Pattantyus-Abraham and Liu, who, by controlling the surface pretreatment, the water content in the growth solution, and the soaking time, were successful in growing smooth OTS monolayers in a normal clean lab environment with a RMS roughness ~ 0.259 nm Figure 4.14(a) shows the A F M image of the 5 x 5 oxide dot array written on such a high quality OTS-modified silicon surface. In contrast, such an assembly of oxide dot arrays could not be formed on OTS-modified SOI sur-faces, an example of which is shown in Figure 4.14(b). A possible explanation for this poor result on OTS-coated SOI will be discussed after the results on the octadecyl-coated samples are described below. Further efforts to improve the quality of the A F M oxidiation dots on SOI were abandoned when the OTS layer resistance to HF etching was tested. Using 20 : 1 = H20 : HF, the "contact angle" of the OTS monolayers decreased from ~ 105° to ~ 98° in 10s. ("Contact angle" refers to the angle a water drop makes with a surface it is placed on. "Good" organic monolayers typically have contact angles between 105° and 110°.) Because a similar solution takes at least 10 s to completely remove the oxidation dots formed using the conducting A F M tip, this rendered OTS useless as an appropriate "resist" layer to protect the silicon surface from nanodot adhesion. Chapter 4. AFM Nanolithography 57 (a) top view of island-like (white spots) OTS grown on a silicon substrate before H F etching(500nm x 500nm) (b) top view of the film shown in (a), after H F etching (lum x lum) Figure 4.13: Comparison of surface profiles (a) before HF etching and (b) after HF etching, of island-like OTS films grown on silicon. Chapter 4. AFM Nanolithography 58 Height Bnsle Surface Nornal Clear C a l c u l a t o r HanoScope Scan s i z e Setpoint Scan r a t e NuM)»er of sawples Contact AFH 2.000 MM 0 U 2.035 Hz (a) Height ftnale Surface Norxal Clear C a l c u l a t o r NanoScope Contact AFH Scan s i z e 2.000 un Setpoint 0 U Scan r a t e 2.035 Hz NuMher of sauples 512 (b) Figure 4.14: A F M height images of an 5 x 5 oxide dot arrays that was written (a) on a high-quality OTS-modified silicon surface and (b) a high-quality OTS-modified SOI surface. Voltage, -12 V; pulse duration, 100 ms, for both (a) and (b). Chapter 4. AFM Nanolithography 59 4.4.3 A F M anodic oxidation of alkyl-terminated Si/SOI substrate The OTS film degradation in HF was almost certainly related to the pres-ence of oxygen in the bonding region (seen in Figures 4.13(a) and 4.13(b)). Monolayers on silicon traditionally rely on siloxane chemistry on oxidized surfaces. Silane-based monolayers show good stability, but the associated silicon-oxygen(5i — O) bonds are susceptible to hydrolysis and are thermally labile. Furthermore, the reproducibility of the synthesis of the monolayers is . sometimes problematic. An alternative approach to the formation of organic monolayers involves a direct thermal reaction between an alkene, such as octadecene, and an H-terminated silicon surface to form stable organic alkyl films (octadecene in this case) via a silicon-carbon (Si — C) linkage. These monolayers involving Si — C bonds (see Figure 4.5) have several advantages over the silane-based layers: (1) The coating does not require the formation of an intervening oxide layer. (2) The film formation procedure is simpler. (3) The coated surface has fewer particulates than an OTS-covered surface. When dipped in HF, the as-grown alkyl monolayers smooth, but remain intact, as determined by contact-angle measurements. Figures 4.15(a) and 4.15(b) show A F M images of an octadecene layer on silicon, as-grown and after dipping in HF. Figures 4.16 and 4.17 show a typical oxide dot array fabricated by A F M anodic oxidation on an octadecyl-terminated Si substrate after HF dipping for ~ 15 s, with an interspacing of 300 nm. Figure 4.16(a) and 4.16(b), respectively show results for voltage pulses of -5 V and -6 V applied to the A F M tip, but keeping the pulse duration of 100 ms all the same. Further increase of the pulse voltage from -7 V and -8 V as seen in Figure 4.17, produced less uniform arrays. Figures 4.18 and 4.19 show the typical oxide dot arrays fabricated by A F M anodic oxidation on octadecyl-terminated SOI substrate after HF dipping for ~ 15 s, with an interspacing of 300 nm. The main thing to note is that it was impossible to observe any oxide dot formation on these SOI-based monolayers using the ~ — 5 V/100 ms pulses that were used on bare silicon and monolayer-coated silicon substrates. Oxide dots could be formed on the SOI monolayers, but only by using higher voltage, and longer duration pulses. In summary, A F M oxidation of bare silicon and SOI is relatively routine Chapter 4. AFM Nanolithography 60 with voltage pulses of order -5 V to -7 V, and pulse durations of ~100 ms to 500 ms. Similar pulses also produce oxide dots on octadecyl-coated (and HF etched) silicon layers, albeit with less uniformity than on the bare surfaces. This might be expected due to the added inhomogeneity of the octadecyl-versus the bare silicon surfaces. These "nominal" pulse parameters have not resulted in oxide formation on alkly-coated (and HF etched) SOI surfaces. By increasing the voltage and pulse duration, relatively non-uniform oxide dots can still be formed on the monolayer-coated SOI samples. An explanation of, and solution for this problem is the subject of on-going investigation by other group members. As noted above, one parameter known to be important for A F M oxidation, that was not monitored or controlled in any of these experiments, is the relative humidity. Variations in the relative humidity likely explain the day-to-day variations in results obtained on bare wafers and the octadecyl-coated silicon substrates. Although it is not obvious why the octadecyl-coated SOI might react differently to the humidity, there is some evidence that better quality oxide dots can be formed on the octadecyl-coated SOI samples when the humidity is higher-than-ambient. Figures 4.20 and 4.21 show topographic and isometric A F M images of four arrays of dots written on an octadecyl-coated monolayer on SOI (at least one month after the monolayer was grown) that was dipped in DI water just before being loaded in the A F M . Each array was written and imaged a quarter of an hour after the preceding one. The quality of the dots written at later times clearly deteriorates as, presumably, the local humidity decreases. Chapter 4. AFM Nanolithography 61 (a) rtut saffase area sunwlt aero crass! w 3ti».h^ .'>j. e**ej»te crew I R o LI ghnea s A na ty si B I [ „„, | a^r| i D C5.S0 1 O C I . S O P K Am off Suwit off iti-ro Crosr off (b) Figure 4.15: Roughness analysis images of octadecyl-terminated SOI are shown (a)before and (b)after HF dipping for ~ 15 s. (The vertical scale is 5 nm for both images. Chapter 4. AFM Nanolithography 62 1.50 5.0 r,M 2.S n M 1.00 — 0.0 n M 0.50 NanoScope Contact AFM Scan size 1.500 UM Setpoint 0 U Scan rate 1.001 Hz Hunber of s a M p i e s 512 0 o "oTso~ 1.00 1.50 U H Si:«HF:~5[UJ,100r»s] 031205k.010 (a) Height (b) Figure 4.16: Contact A F M height images (range: 5 nm) of the 3 x 4 oxide dot arrays fabricated on an octadecyl-modified silicon surface by the A F M anodic oxidation: pulse voltage, (a)-5 V and (b)-6 V; pulse duration, 100 ms; humidity, ambient air. Oxidation was performed after dipping the as-grown monolayers in HF for ~ 15 s. Chapter 4. AFM Nanolithography 63 NartoScope Scan s i z e Setpoint Scan r a t e Himber of s a u r i e s Contact AFM i.S00 un 0 U I.001 H i Si:«HF:-7CUl,100C»s] oaiznsh.ooB (a) # & NanoScope Scan s i z e Setpoint Scan r a t e Number of s a u r i e s Contact AFM 1 . 5 0 0 sin 0 U 1.001 Hz Si:tHF:-8rui , iooti.sl 08120Sh.007 (b) Figure 4.17: Contact A F M height images (range: 5 nm) of the 3 x 4 oxide dot arrays fabricated on an octadecyl-modified silicon surface by the A F M anodic oxidation: pulse voltage, (a) -7 V and (b) -8 V; pulse duration, 100 ms; humidity, ambient air. Oxidation was performed after HF dipping for ~ 15 s. Chapter 4. AFM Nanolithography 64 (a) Height angle Surface Morwul Clear Calcu 1 at or (b) Figure 4.18: Contact A F M height images (range: 3 nm) of the 3x4 oxide dot arrays fabricated on an octadecyl-modified SOI surface by the A F M anodic oxidation: pulse voltage, (a) -8 V and (b) -9 V; pulse duration, 5 s; humidity, ambient air. The dots were written after HF dipping the monolayer for ~ 15 s. Chapter 4. AFM Nanolithography G5 H*i«ti« ftrwrl* S u r f a c e normal C l e a r C a l c u l a t o r NanoScope Contact AFM Scan size 1,500 un S e t p o i n t 0 U Scan r a t e 1.001 Hz Number o f samples 512 SOI:»HF : -10CO],SCs] 0ail05h.010 (a) Height Angle Sur f»ce Normal C l e a r C a l c u l a t o r ftk ttk mm %0 1 ^ ^ 1 , 1 . ... 0 S U 0 5 h . Q 0 2 NanoScope Contact AFM Scan s i z e 1.500 MM S e t p o i n t 0 U Scan r a t e 1.001 Hz Nu»J>er o f samples 512 (b) Figure 4.19: Contact A F M height images (range: (a) 3 nm and (b) 5 nm) of the 3 x 4 oxide dot arrays fabricated on an octadecyl-modified SOI surface by the A F M anodic oxidation: pulse voltage and duration, (a) -10 V and 5 s; (b) -12 V and 12 s; humidity, ambient air. The dots were written after HF dipping the monolayer for ~ 15 s. Chapter 4. AFM Nanolithography 66 (c) top view after 3rd quarter hour (d) top view after 4th quarter hour Figure 4.20: A F M images of oxide dot arrays written by A F M anodic oxida-tion on octadecyl-terminated SOI every quarter of 1 hour after the sample was soaked in DI water. The arrays were all written using pulses of -5 s and 100 ms for all arrays.(vertical range is 5 nm in each image). Chapter 4. AFM Nanolithography 67 (a) after 1st quarter hour (b) after 2nd quarter hour / 1.00 -«f0 (c) after 3rd quarter hour (d) after 4th quarter hour Figure 4.21: Isometric (3D) plots corresponding to the same images shown in Figure 4.20. Chapter 4. AFM Nanolithography 68 4.4.4 MFP-3D A F M anodic oxidation of alkyl-terminated SOI substrate A new AFM—MFP-3D A F M , integrated with a conductive tip-holder specific to A F M lithography was made available towards the end of the project. It's superior optical imaging capability made it much easier to register the A F M -induced oxide dot with respect to the microcavity samples. Finally, a single oxide dot was put into the desired region of an octadecyl-covered microcavity based on SOI. The oxide dot has a height of 11 nm and a width of 190 nm, as shown in Figure 4.22. Figure 4.22: A single oxide dot(central white spot on microcavity) overlap-ping the high field region of the fundamental cavity mode. E 69 Chapter 5 Conclusion An A F M anodic oxidation technique was capable of producing silicon dioxide islands on bare silicon, and bare silicon-on-insulator substrates p-type (100) using applied negative bias voltages of ~ -5 V, and pulse durations from 100 ms to > 1 s, under ambient environmental conditions. Day to day variations in the results obtained for fixed conditions are likely due to the fact that the humidity was not controlled in these experiments, and it is known that hu-midity does influence the size of oxide dots formed under similar conditions. Under similar ambient conditions, it was possible to realize oxide dot forma-tion on both OTS- and octadecene-coated silicon wafers, but the uniformity of the dots was much poorer than on bare samples, and often higher voltages and/or longer pulse durations were required to obtain any oxidation. Much higher voltages (~ —10 V) and longer pulse durations (up to seconds) were required to observe any oxide dot formation on monolayer-coated SOI wafers under ambient conditions, and the results were quite irregular. When octadecene-coated SOI wafers were dipped in deionized water just prior to being placed in the A F M apparatus, good- quality oxide dots were formed using -5 V, 100 ms pulses, immediately following the dip, but the quality of oxide dots degraded significantly when written after 1 hour in the system. From the work reported in this thesis we conclude that octadecene-coated monolayers are robust to HF etching, and with some additional work, good quality silicon dioxide islands should be able to be formed through these monolayers, on the top silicon layer of patterned SOI wafers. Registration of the oxide dot with respect to the prepatterned microcavity surface is rel-atively easy at the ~ 50 nm level, comparable to the smallest oxide dot diameter achieved. Future efforts to improve the A F M oxidation process should focus on controlling the relative humidity in the A F M , and being more systematic about identifying the optimum tip-sample separation for oxide formation on different surfaces. In this study, the setpoint was set to -1.0 V all the time, Chapter 5. Conclusion 70 which is a typical value for A F M imaging using silicon cantilevers. Recent work done by Dr. H. Qiao in Dr. Young's laboratory has determined that the oxide formation is quite sensitive to the tip-sample separation, and with the addition of one extra step (finding the optimum tip-sample separation), the AFM-oxidation process developed in this thesis is capable of routinely forming high-quality, ~ 50 nm oxide dots on octadecene-coated SOI micro-cavities. 71 Bibliography [1] Moore's original statement can be found in his publication: Cramming more components onto integrated circuits. Electronics Magazine., 19 April 1965. [2] S.J. van Enk, J.I. and Cirac, and P. Zoller. Photonic channels for quan-tum communication. Science, 279:205-208, 1998. [3] H.J. Briegel, J.I. Cirac, W. Dur, S.J. van Enk and H.J. Kimble, Mabuchi and H. Zoller. Physical implementations for quantum communication in quantum networks. Quantum Computing and Quantum Communica-tions, 1509:373382, 1999. [4] M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Infor-mation. Cambridge University Press, 2000. [5] I. Wison-Rae, A. Imamoglu Phys. Rev. B, 2002 65,235311. [6] A.Yu. Smirnov , S.N. Rashkeev, A . M : Zagoskin. App. Phys. Lett., 2002, 80, 3503. [7] J. Vuckovic and Y. Yamamoto. App. Phys. Lett., 2003, 82, 2374. [8] A.R. Cowan and Jeff F. Young. Optical bistability involving photonic crystal microcavities and Fano line shapes. Phys. Rev. E, 68, 046606, 2003. [9] John D. Joannopoulos, Robert D. Meade and Joshua N. Winn. Photonic Crystals: Molding the flow of light. Princeton University Press, 1995. [10] S.John. Strong localization of photons in certain dielectric superlattices. Phys. Rev. Lett, 58, 2486 (1987). Bibliography 72 [11] S.G. Johnson, S. Fan, P.R. Villeneuve, J.D. Joannopoulos and L.A. Kolodziejaki. Guided modes in photonic crystal slabs. Phys. Rev. B, 69, 5751-5758, 1999. [12] H. Yokoyama. Physics and device application of optical microcavities. Science, 256, 66-70, 1992. [13] Kartik Srinivasan, Paul E. Barclay, Oskar Painter, Jianxin Chen, Alfred Y . Cho, Clarie Gmachl. Experimental demonstration of a high quality factor photonic crystal microcavity. App. Phys. Lett., 83, 1915-1917, 2003. [14] K. Yee. Numerical solution of initial boundary value problems involving maxwell's equation in isotropic media. IEEE Trans. Antennas Propag., 14:302-307, 1966. [15] Oskar Painter, Kartik Srinivasan and O'Brien, John D. and Scherer, Axel and Dapkus, P. Daniel. Tailoring of the resonant mode proper-ties of optical nanocavities in two-dimensional photonic crystal slab waveguides. Journal of Optics A: Pure and Applied Optics, 3, S161-S170, 2001. [16] K. Srinivasan and O. Painter. Momentum space design of high-Q pho-tonic crystal optical caivities. Opt.Express, 10:670-684, 2002. [17] S.G. Johnson, S. Fan, P.R. Villeneuve, J.D. Joannopoulos and L .A. Kolodziejski. Phys. Rev. B, 60:5751 (1999). [18] research website: A F M lithography. http://chem.skku.ac.kr/ skkim/research/e-litho.htm [19] The tip-sample interaction in atomic force microscopy and its implica-tions for biological applications. Ph.D. thesis by David Baselt, California Institute of Technology. [20] Qiguang Li , Jiwen Zheng and Zhongfan Liu. Site-Selective Assemblies of Gold Nanoparticles on an A F M Tip-Defined Silicon Template. Lang-muir, 19:166-171, 2003. [21] T. Valiant, H. Brummer, U. Mayer, H. Hoffmann, T. Leitner, R. Resch, G.J. Friedbacher. Phys. Chem: B, 102:7190, 1998. Bibliography 73 [22] Yuliang Wang and Marya Liebereman. 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