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Linear transmission and reflection spectroscopic studies of colloidal PbS(x) nanocrystal films : paving… Ning, Hailong 2009

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Linear Transmission And Reflection Spectroscopic Studies Of Colloidal PbS(x) Nanocrystal Films Paving The Way for Nonlinear Optics in Such Films by Hailong Ning B.Sc., Harbin Institute of Technology, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate Studies (Physics)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2009 c Hailong Ning 2009  Abstract This thesis investigates the feasibility of conducting nonlinear degenerate four-wave-mixing experiments on colloidal PbS or PbSe semiconductor nanocrystal films. It concludes that such experiment cannot be effectively carried out in the conventional forward geometry due to large scattering from the emulsive nanocrystal films, while it may be possible in the backward geometry. These conclusions were reached by studying the linear transmission and reflection spectra from a variety of PbS and PbSe NC films on both silicon and glass substrates. These studies suggest that the electronic structure of the PbS and PbSe NCs in close-packed films are well-maintained while the scattering inside these NC films is Rayleighlike and quite strong. Theoretical fitting of these spectra reveals the refractive indices and absorption rates of these films, which match those recently reported in the literature. It also suggests the presence of a distinct interfacial layer with a low concentration of nanocrystals between silicon and the dense NC emulsion, which was also confirmed by optical microscopy. This layer, on the order of 100 nm thick, has important consequences for optical studies of these films.  ii  Table of Contents Abstract  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iii  List of Tables  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vi  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vii  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  1 Introduction & Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  2  1.1  Colloidal PbS And PbSe Nanocrystals . . . . . . . . . . . . . . . . . . . . .  1  1.2  Cavity QED  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4  1.3  Thesis Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8  1.4  Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  9  Experiment Techniques & Sample Preparation 2.1  2.2  2.3  . . . . . . . . . . . . . .  10  Background: Optical Characterization . . . . . . . . . . . . . . . . . . . . .  10  2.1.1  Linear Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . .  11  2.1.2  Nonlinear Degenerate Four-Wave-Mixing Spectroscopy  . . . . . . .  12  Basic Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13  2.2.1  Linear Absorption Experiments  . . . . . . . . . . . . . . . . . . . .  14  2.2.2  Nonlinear DFWM Experiments  . . . . . . . . . . . . . . . . . . . .  16  2.2.3  Photoluminescence Measurements . . . . . . . . . . . . . . . . . . .  21  Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21  iii  Table of Contents 3 Experimental Results  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  23  Attempts To Obtain DFWM Signals . . . . . . . . . . . . . . . . . . . . . .  23  3.1.1  DFWM In Transmission Geometry  . . . . . . . . . . . . . . . . . .  23  3.1.2  DFWM In Reflection Geometry  . . . . . . . . . . . . . . . . . . . .  26  3.2  Sample Morphology Under Optical Microscope . . . . . . . . . . . . . . . .  28  3.3  Transmittance & Reflectance Profiles  . . . . . . . . . . . . . . . . . . . . .  29  3.3.1  Transmission & Reflection Spectra At Different Spots . . . . . . . .  29  3.3.2  Average Reflectivity Of Films On Different Substrates . . . . . . . .  32  Forward Scattering Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . .  32  3.4.1  Rescaling Transmission Spectra  . . . . . . . . . . . . . . . . . . . .  33  3.4.2  Polarization Dependence  . . . . . . . . . . . . . . . . . . . . . . . .  35  3.4.3  Using Apertures Of Different Sizes . . . . . . . . . . . . . . . . . . .  36  4 Quantitative Analysis Of Linear Spectra . . . . . . . . . . . . . . . . . . .  37  3.1  3.4  4.1  Simulation Method  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  37  4.2  Modeling Sample Structure . . . . . . . . . . . . . . . . . . . . . . . . . . .  40  4.3  Simulated Transmission & Reflection Spectra . . . . . . . . . . . . . . . . .  43  5 Conclusion & Recommendations For Future Work . . . . . . . . . . . . .  46  5.1  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  46  5.1.1  Nonlinear DFWM Experiment . . . . . . . . . . . . . . . . . . . . .  46  5.1.2  Linear Reflection & Transmission Spectroscopy  . . . . . . . . . . .  47  Recommendations For Future Work . . . . . . . . . . . . . . . . . . . . . .  48  5.2.1  Lock-in Detection  48  5.2.2  DFWM In Backward Geometry  . . . . . . . . . . . . . . . . . . . .  49  5.2.3  Origin Of The Scattering . . . . . . . . . . . . . . . . . . . . . . . .  50  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  51  5.2  Summery & Conclusions  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Appendices A Aligning Parabolic Mirror PM1 . . . . . . . . . . . . . . . . . . . . . . . . .  57  B Aligning Autocorrelator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  59 iv  Table of Contents C Calculating Effective Refractive Index Of NC Films . . . . . . . . . . . .  61  v  List of Tables 3.1  Average reflectivity at Brewster’s angle from different interfaces . . . . . . .  32  4.1  Simulated parameters based on the three-layer model. . . . . . . . . . . . .  44  vi  List of Figures 1.1  Schematic illustration of a PbSe nanocrystal capped with oleic acid ligands and the absorption and photoluminescence spectrum from a solution of such NC with a diameter of 5nm. . . . . . . . . . . . . . . . . . . . . . . . . . . .  2  1.2  Schematic illustration of the atom-photon interaction in an optical cavity. .  4  2.1  Schematic illustration of degenerate four-wave-mixing process . . . . . . . .  13  2.2  Layout of the general experimental setup and the photon flow(arrows), including three types of light sources, the beam steering area, autocorrelator, and the collection and detection systems. . . . . . . . . . . . . . . . . . . .  2.3  14  Diagram of all the optical components for different types of measurements. White light and semiconductor laser sources are coupled into a cryostat along the dashed lines, and the dashed line after mirror M8 also represents the optical axis of the collection system. As for the OPO laser, the fixed and the delayed arms are labeled as solid and dot-dashed lines, respectively. All the beams are parallel to the optical table and at the same height. . . . . . . .  2.4  15  Experimental configuration of sample mount and detection system for linear transmittance and reflectivity measurements. The light is incident at Brewster’s angle of the substrate so that reflection only comes from substratesample interface. Both reflection (red dashed line) and transmission (grey dashed line) are then collimated and sent into the spectromemter. . . . . .  2.5  16  Schematic illustration of the SHG autocorrelator. Beams from the fixed and delay arms are focused on the nonlinear crystal. The second harmonic signal is then generated along the optical axis when pulses from both arms overlap spatially and temporally. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  18  vii  List of Figures 2.6  Schematic illustration of the beam coupling area for the DFWM experiment. The forward-going optical circuit consists of A3, L1, PM1, A4, M10 and L3 and it serves to couple incident beams on the sample and to collect the DFWM signal. The backward optical circuit consists of L1, M9 and L3, allowing beam spots on the sample to be observed on the CCD (red arrows).  2.7  19  Diagram of experimental setup of lock-in detection system for DFWM experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20  3.1  Schematic illustration of the signals in the oscilloscope.  24  3.2  Cross section profiles of the light measured after the parabolic mirror. The  . . . . . . . . . . .  dashed line indicates the cross section profiles of the two laser beams only through a pure silicon substrate while the red and the blue lines are the profiles of those through a silicon substrate deposited with a PbSe (PbS) QD layer. The two green arrows indicate the two predicted positions of the DFWM signal, which are 5.10mm and 16.35mm, respectively.  . . . . . . .  25  . . . . . . . . . . .  26  3.3  Plot of lock-in amplifier signal versus pulse delay time.  3.4  Cross section profiles of the reflected laser beams. The data plotted in the blue line were taken on a pure silicon substrate and those plotted in red line were taken on a silicon substrate drop-cast with a QD layer on its back surface. The green dashed and solid lines are those from Figure 3.2, and all the data are plotted in the same scale. The grey arrow indicates the predicted position of the DFWM signal in reflection geometry. . . . . . . . . . . . . .  3.5  Pictures of a PbS NC film under optical microscope. The estimated film thickness at different spots: (a) 0µm; (b) 6µm; (c) 13µm; (d) 27µm. . . . .  3.6  27 28  Transmission and reflection spectra measured at different positions of a dropcast PbS NC film on a silicon substrate. Different colors represent the measurements taken at different positions (i.e., the red is labeled as 1 and the blue as 2 for references), and the dashed and the solid lines stand for transmission and reflection, respectively. The absorption spectrum of PbS NC solution is also plotted in green. . . . . . . . . . . . . . . . . . . . . . . . . .  30  viii  List of Figures 3.7  Transmission and reflection spectra measured at different positions of a dropcast PbS NC film on a silicon substrate. Different colors represent the measurements taken at different positions, and the dashed and the solid lines stand for transmission and reflection, respectively. . . . . . . . . . . . . . .  3.8  31  Rescaled transmission spectra whose raw data were presented in Furgures 3.6 and 3.7 in the same colors. The absorption spectrum of PbS NCs in solution is shown in a green dashed line. . . . . . . . . . . . . . . . . . . . . . . . . .  3.9  33  Transmission spectra collected with (red) and without (blue) a polarizer oriented to pass p-polarized light inserted between the sample and the spectrometer. The absorption spectrum of PbS NCs in solution is shown in a green dashed line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  34  3.10 Transmission spectra collected with an aperture of different diameters inserted between the sample and the spectrometer. From the black to the dark green lines, the aperture diameters were 0.3mm, 1mm, 2mm and no aperture, and the corresponding DC signals are 6.6mV, 13mV, 27mV and 68mV. The absorption spectrum of PbS NCs in solution is shown in a green dashed line.  35  4.1  Schematic illustration of optical waves in layered media . . . . . . . . . . .  38  4.2  Schematic illustration of the models used to simulate R & T spectra. (a) two-layer structure: silicon substrate and NC layer (b) three-layer structure: silicon substrate, interfacial oil layer and NC layer. . . . . . . . . . . . . . .  41  4.3  The normalized absorption spectrum of the PbS NC solution. . . . . . . . .  42  4.4  Simulated reflection (blue) and transmission (red) spectra based on the twolayer model. The green lines are experimental data R2 and T2 that are presented in Figure 3.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4.5  43  Simulated reflection (blue) and transmission (red) spectra based on the threelayer model and the corresponding experimental data (green). (a) R1 and  4.6  T1 presented in Figure 3.6; (b) R2 and T2 presented in Figure 3.6. . . . . .  44  Simulated absorption coefficient of an ∼ 8µm thick PbS NC film.  45  . . . . .  ix  List of Figures A.1 Schematic illustration of the way to align PM1. The red solid line is the incident beam and the other lines are reflection from optical components, and they are drawn slightly off each other for the purpose of identification, which should overlap in experiment. . . . . . . . . . . . . . . . . . . . . . .  57  x  Acknowledgements First of all, I would like to acknowledge my supervisor, Dr. Jeff Young. He not only helped provide the motivation for this work but also provided guidance during the entire course of the experiment and the theoretical analysis of this work. His ways to approach research and to trouble-shoot problems have had a great impact on me. I would also like to acknowledge our collaborator, Dr. Frank van Veggel’s group in the Department of Chemistry, University of Victoria, who synthesized the PbS and PbSe nanocrystals and also provided plenty of useful information on these materials. Dr. Haijun Qiao, who assisted me in preparing the samples and also provided much invaluable advice and discussion in the course of the experiment, deserves special mention. Without his help, I could not have finished this work. Dr. Georg Rieger taught me to use most of the apparatus in our laboratory and also assisted me in setting up the experiment in the early stage - his help was highly appreciated. Thanks are also due to Luke Sandilands, who did a lot of earlier work in designing and setting up the DFWM experiment. Other significant figures who I would like to acknowledge are my dear colleague and friend - Charles Foell, who often provided profound discussions (not only limited in physics) and helped me in the clean room, and Hamed Mirsadeghi, who provided useful theoretical reference for this work. In the end, I would also like to place special mention to my beloved families - my wife and parents who have been so supportive to me.  xi  Chapter 1  Introduction & Motivation 1.1  Colloidal PbS And PbSe Nanocrystals  Semiconductor nanocrystals (NCs) are also called quantum dots(QDs). As manifested in the name, these QDs exhibit three-dimensional quantum confinement when their radii are reduced below the corresponding electron-hole-pair (exciton) Bohr radius in the bulk material, which furnishes them with unique properties. For example, the electronic states are quantized due to ”particle-in-a-box” confinement, and atom-like exitonic transitions are shifted above the bulk bandgap to higher energies with decreasing NC size. Among these quantum materials, II-VI and III-V type QDs cannot be strongly confined, since the Bohr radii of the holes in most of these materials are about 1nm[1]. In contrast, quantum dots formed of IV-VI materials such as PbS and PbSe, are showcase examples for extreme quantum confinement [2], because electrons and holes in lead chalcogenide have similar and relatively large Bohr radii. The Bohr radius of excitons in PbS and PbSe are 20nm and 46nm respectively. Since colloidal chemistry can be used to control the diameters of these PbSe and PbS QDs from 2nm to 18nm [3], large quantization energies are expected, offering the ability to easily tune the optical transitions of these small band gap materials over a wide range of the infrared spectrum. This makes them attractive for both applications as well as fundamental studies. Colloidal NCs are nanometer-sized crystallites synthesized as colloidal particles in a solvated suspension. Since this solution-based technique for synthesizing high-quality colloidal QDs was first reported [4], QD solution samples have been routinely prepared in a number of semiconductor systems with resulting fundamental transitions from 2 microns to 0.4 microns [5] and the size variations of particles in solution can be made less than 5%. Such techniques also allow passivation of the surface of the NCs with organic materials to stabilize their properties. As illustrated in Figure 1.1, a PbSe NC with a 5nm diameter is capped with oleic acid ligands to prevent it from being oxidized, and its absorption spectrum in 1  1.1. Colloidal PbS And PbSe Nanocrystals solution shows well-defined quantized optical transitions.  Figure 1.1: Schematic illustration of a PbSe nanocrystal capped with oleic acid ligands and the absorption and photoluminescence spectrum from a solution of such NC with a diameter of 5nm.  Bearing many novel and potentially useful properties, e.g., fluorescence yields as high as 80% in solution, significant size-tuning of transition energies and great cost effectiveness [3][4], PbSe and PbS QDs hold great promise in areas such as, near-infrared fluorescent biological imaging [6][5], low temperature-dependent lasers [7] and field-effect transistors [8]. Also, these lead chalcogenide NCs are among few materials that can provide quantized electronic transitions at technically important infrared wavelengths, making themselves strong candidates in areas like quantum computing and quantum information processing [9]. In addition, although still in the phase of laboratory-based study, PbSe QDs have shown a  2  1.1. Colloidal PbS And PbSe Nanocrystals great potential for application in the area of photovoltaics (e.g. Sargent et al. [10] recently reported a solution-cast PbS QD photovoltaic device that has a power conversion efficiency of 3.6% in the infrared region). Due to the large quantum-mechanical confinement and cubic band structure, there is also much physics that remains to be understood concerning the detailed electronic and optical properties of PbSe and PbS QDs. Examples of important fundamental properties include long interband carrier relaxation times[11], ultrafast intraband carrier relaxation times[12], carrier multiplication[13][14], optical gain[7], etc. However, unlike the prototypical CdSe NCs, which have a wurtzite or zinc-blende band structure and whose basic optical properties have been explained satisfactorily [15][16], the electronic and optical structures of PbSe and PbS have proved to be significantly more difficult to understand. For example, despite its apparent simplicity, the second excited transition [17] in PbSe NCs (see the arrow in Figure 1.1) has generated a ten-year scientific debate on its origin, whether from 1Se − 1Ph and 1Sh − 1Pe transitions or from 1Ph − 1Pe transition (Here 1Se − 1Ph represents the exitonic recombination between an electron of 1S orbital and a hole of 1P orbital). The strong quantum confinement of both electrons and holes in lead salt NC leads to a simple and sparse energy spectrum, suggesting a relatively slow intraband carrier relaxation due to the so called ”phonon bottleneck” effect in which electron-phonon coupling is very small because of the mismatch between electronic transitions and phonon energies. However, it has been found that the intraband relaxation of these NCs occurs on a sub-picosecond time scale [18], and comprehensive explanations and modelings on this phenomenon are still missing. The lack of understanding of the electron scattering processes in this system must be addressed in order to access their suitability for applications such as quantum information processing, photovoltaics and nonclassical light sources. So far, most of the studies on these PbSe and PbS QDs have been conducted in solutions or dilute glass-forming media, however, very little is known about their properties in the form of solid state films, which could be dramatically different, as suggested by previous studies on other QD materials[19][20]. Particularly, our research group is currently conducting studies of electron-photon coupling in an optical microcavity, which involves placing monolayers or individual PbSe (PbS) quantum dots onto a silicon-on-insulator (SOI) photonic crystal microcavity. Thus, it is their properties in films and on silicon that are of particular note to us.  3  1.2. Cavity QED  1.2  Cavity QED  When an atom is trapped in an optical cavity in such a way that the dimensions of the cavity are comparable to the wavelength of the emitted radiation of the atom and this atomic transition coincides with one of the resonant modes of the cavity, the interaction between the atom and the light field can be strongly affected, because they can exchange energy in a resonant manner. If the dipole coupling of the atom and the cavity mode is sufficiently large, the atom-photon interaction can be faster than the process of losing photons out of the cavity mode, or having the atom spontaneously decay into the vacuum. Under these conditions, the photon is reabsorbed by the atom before it leaks from the cavity. This reversible interaction between the atom and the cavity field is called cavity quantum electrodynamics (cavity QED).  Figure 1.2: Schematic illustration of the atom-photon interaction in an optical cavity.  The first detailed theoretical analysis of cavity QED traces back to the work of Jaynes and Cummings in 1963. In its simplest form[21], the Jaynes-Cummings model consists of a two-level atom interacting with an single quantized mode of a lossless optical cavity. The Hamiltonian of the two-level atom can be written as1 , Hat = h̄ωat σ+ σ− . 1  (1.1)  The atomic Hamiltonian can be also written as Hat = 21 h̄ωat σz , where σz = 2σ+ σ− − 1.  4  1.2. Cavity QED where σ+ and σ− are referred to as pseudo-spin operators and correspond to an upward and a downward electronic transition in the atom, respectively. For the cavity with a single mode frequency ωc , the Hamiltonian takes the form, Hc = h̄ωc a† a.  (1.2)  where a† and a are creation and annihilation operators, respectively. The positive-frequency part of the quantized electric field inside the cavity is (Schrödinger picture), s +  E =i  h̄ωc ε(r)a. 20 V  (1.3)  where 0 , ε(r) and V are the free-space permittivity,the cavity mode function and the mode volume of the cavity. Then the atom-photon coupling (within rotation wave approximation) gives the interaction Hamiltonian inside the cavity, Hint = −d · E + σ+ − d∗ · E − σ− = ih̄(gaσ+ − g ∗ a† σ− ). with the atom-photon coupling strength defined as g =  q  (1.4) (1.5)  ωc 2h̄0 V  ˆ d · ε(R), where d = h1|d|2i  is the dipole matrix element and R the position of the atom. The total Hamiltonian for the Jaynes-Cummings model is therefore, H0 = h̄ωat σ+ σ− + h̄ωc a† a, Hint = ih̄(gaσ+ − g ∗ a† σ− ).  (1.6) (1.7)  When there is no interaction between the atom and the cavity photon, the system can be represented by the product states in the joint Hilbert space, the so called bare states, Ψj,n = |j i|ni.  (1.8)  where |j i (j=1,2) and |ni (n=1 for a single cavity photon) are atom states and cavity photon number states, respectively. When turning on the interaction inside the cavity, the  5  1.2. Cavity QED states of both types are then entangled, the so called dressed states, 1 Ψ± n = √ (|1 ; ni ∓ |2 ; n − 1i). 2  (1.9)  The above derivation is the simplified Jaynes-Cummings model in an ideal situation where the atom is a perfect two-level system and the optical cavity is lossless. However, in addition to this atom-photon coupling dynamics, ”imperfect” dissipative processes must be included, as depicted in Figure 1.2, the leaking of the cavity photon into the reservoir modes, the coupling of the atom to external modes other than the resonant mode and the loss of the coherence of the quantum phase. Three key parameters determine when the system is ”strongly coupled”:[22]: • the photon decay rate of the cavity κ • the dephasing rate of the atom γ • the atom-photon coupling strength g, which can be combined to define the critical atom number N0 and the critical photon number n0 , N0 ≡ n0 ≡  2γ⊥ γk ∝ V, 3g 2 2γ⊥ κ ∝ κV. g2  (1.10) (1.11)  where γk and γ⊥ are the longitudinal atomic population decay rates and the transverse dephasing rates, respectively. To realize a reversible atom-photon interaction in the optical cavity then requires max{N0 , n0 }  1 or max{κ, γ}  g, which is also called the strong coupling limit. When min{N0 , n0 }  1 or min{κ, γ}  g, the atom-photon interaction is irreversible, the so called the weak coupling limit. Weak coupling enables manipulation of the spontaneous emission of the cavity atom through the Purcell effect[23] and has been applied to make cavity-enhanced single-photon sources[24][25]. For both weak and strong coupling, according to (1.10) and (1.11), the atom-photon interaction can be enhanced by suppressing the cavity decay rate and reducing the mode volume. Efforts to increase the coupling have recently led to the development of high Q and small volume resonators[26], where Q is the quality factor of the cavity 6  1.2. Cavity QED Q = ωc /κ. The three most common types of microcavities are Fabry-Perot microposts, whispering gallery microdiscs and photonic crystal microcavities. Among these optical microcavities, the Fabry-Perot type consists of two mirrors with ultrahigh reflectance and it affords relatively simple cavity-coupling to external probes[27][28]. The whispering gallery resonators are typically dielectric spherical or toroidal structures in which light is confined by continuous total internal reflection and can achieve ultrahigh Q with excellent surface finish[29], however, the probing of whispering gallery modes must be phase-matched. Mimicking the arrangement of the atom lattice in a crystal, photonic crystals are materials with a spatial periodicity in their dielectric constant. Hence, just as electrons experience energy band gaps in real crystals, light with certain frequencies can be prohibited to propagate along certain directions in photonic crystals, thus establishing so called photonic band gaps. Microcavities based on introducing engineered ’defects’ in photonic crystals can have extremely small mode volumes and also enable light emitters (e.g. quantum dots) to easily graft onto these devices[9]. Cavity-QED-based quantum information processing schemes [30] require suitable photon emitters. In principle, neutral atoms or ions would be ideal candidates since they define the limit of miniature light sources. However, optically active atoms and ions are also extremely chemical active, which in practice makes it very difficult to isolate them from their surroundings, although such experiments have been demonstrated with cold cesium atoms[31]. Alternatively, semiconductor quantum dots (QDs), also called ”artificial atoms” have attracted much attention in cavity QED research. Two distinct types of QDs can be adopted in this regime: one is the epitaxially grown self-assembled QDs on III-V semiconductor substrates, e.g. InGaAs on InP and InGaAs on AlGaAs; the other is the colloidal semiconductor QDs, e.g. CdSe QDs and PbSe QDs. Epitaxial QDs have already showed their utilities in a variety of quantum technologies such as single-photon emission[32], quantum gate operation[33] and vacuum Rabi splitting[34]. Their main drawback is their relatively high cost and the lack of compatibility with silicon chip technology. In contrast, colloidal semiconductor QDs synthesized by the solution technique can in principle be attached to any substrate and in particular, can be grafted onto silicon via certain surface techniques [9]. Colloidal QDs are also less expensive and more easily size-tunable at technologically important infrared wavelengths. Although colloidal semiconductors bear the above merits and have showed their great promise towards Cavity QED[35][36][37][38], there are still many technical difficulties that remain to be addressed, for example, to pre7  1.3. Thesis Goals cisely position a single colloidal quantum dot at the antinode of the cavity electric field while maintaining its original electronic and optical properties. In our research group, Purcell enhancement has been demonstrated in the silicon-based photonic crystal cavities coupled to a small number of PbSe QDs [9], and efforts continue to try and achieve the strong coupling regime with this material system.  1.3  Thesis Goals  As discussed above, the photon decay rate of the cavity, the dephasing rate of the atom and the strength of the atom-photon coupling are the most important parameters associated with cavity QED. Thus, knowing all of these parameters is a prerequisite for comprehensively estimating the capability of engineering exciton-photon strong coupling in photonic crystal cavities containing grafted PbSe (PbS) NCs. While the other two parameters can be easily predicted by theories or measured in experiments, the dephasing rate of the excitonic states of PbSe and PbS NCs are often more difficult to precisely probe due to the random orientations of these NCs and the large size distribution in their solutions or films. However, it has been demonstrated that nonlinear coherent spectroscopy can overcome the above obstacles [39], e.g., different forms of four-wave-mixing. The Original Goal: The original goal of this thesis research was to carry out degenerate four wave mixing on thin emulsive films of PbSe and PbS nanocrystals, since it is their properties in films that are relevant to most of their applications. The Emergent Goal:  Despite trying various techniques, it proved too difficult to observe  any nonlinear signal in the presence of the large linear scattered background signal generated from these samples. In addition, according to the previous studies on other NCs, their properties in closed-packed films could be dramatically different from those in solution. Therefore, a thorough characterization of the linear optical properties of these PbSe and PbS NC films become the emergent goal of the thesis.  8  1.4. Outline  1.4  Outline  The next chapter starts with outlining the theoretical basis for linear spectroscopic and nonlinear degenerate four-wave-mixing (DFWM) experiments. The corresponding experimental setup and techniques are then described. The experimental results are discussed qualitatively in Chapter 3. Firstly, the feasibility of conducting DFWM on PbSe and PbS emulsive NC films is investigated in forward and backward scattering geometries, respectively. The results of linear transmission and reflection measurements on silicon and glass substrates deposited with PbS (PbSe) NC films or polymer films are then presented. A quantitative analysis of the linear reflection and transmission spectra follows in Chapter 4. The transmission and reflection spectra which were measured on silicon substrates are fit with numerical simulations. This fitting procedure provides a measure of the refractive indices and absorption rates of the NC films, and also suggests the existence of an oil layer between the PbS (PbSe) film and silicon substrate, which is consistent with morphologic measurements.  9  Chapter 2  Experiment Techniques & Sample Preparation This chapter starts with a review of basic concepts behind different types of optical measurements in Section 2.1. Section 2.2 provides a detailed description of the corresponding experimental techniques and setups. Finally, a discussion of the sample preparation techniques is presented in Section 2.3.  2.1  Background: Optical Characterization  Linear and nonlinear spectroscopies are powerful experimental tools for studying properties of semiconductors. The original goal of this thesis research was to carry out nonlinear spectroscopy, degenerate four wave mixing (DFWM), on thin solid emulsion films of nanometer scale PbSe and PbS nanocrystals. While DFWM experiments of nanocrystals in dilute liquid and frozen solutions [40] have been reported, we are unaware of any such experiments done in dense emulsions. Some linear spectroscopic measurements reported for emulsive films suggest that the optical properties of the nanocrystals may be substantially different than in solution. Despite trying various techniques, it proved too difficult to observe any nonlinear signal in the presence of the large linear scattered background signal generated from these samples. The main part of the thesis research then became a systematic characterization of the linear absorption and scattering properties of PbSe and PbS emulsive films, both on silicon and glass substrates. The following sections describe the principles involved in the various spectrosopic techniques used in this research.  10  2.1. Background: Optical Characterization  2.1.1  Linear Spectroscopy  Linear spectroscopy is a straightforward experimental tool to study the optical and electronic properties of semiconductor nanocrystals, yet it yields a lot of information. The most widely used techniques of linear spectroscopy are transmission (absorption), reflection, luminescence and luminescence-excitation spectroscopy [41]. Among these techniques, the transmission (absorption) measurement can be used to estimate the binding energy of the excitons and also places an upper limit on the their intrinsic dephasing rates which partially contributes to the broadening of the electric transitions [42]. Transmission and reflection spectroscopy are also very useful for determining the thickness and optical constants of films, the general requirement being that the films have a smooth surface and lie on a smooth substrate whose optical properties are known [43]. For nonscattering films with low absorption, Fabry-Perot fringes appear in both transmission and reflection spectra due to the multiple-beam reflections at the front and rear film surfaces. The thickness and optical constants can be obtained by fitting the spectra (i.e. reflectance, transmittance and Fabry-Perot modes), albeit with considerable labor. However, since the locations of these interferometric fringes in the spectrum simply obey the following rule, [44], 1 1 1 = − 2nd λp λp+1  (2.1)  where n is the refractive index of the film, d is the film thickness, and λp , λp+1 the wavelengths of two adjacent maxima in the spectrum, the thickness and refractive index of the film can be mutually determined, if either of them is provided. When absorption of films is so strong that Fabry-Perot modes disappear in the spectra and the reflection signal is mostly attributed to the reflected beam from a single interface, the film thickness and optical constants can be determined by measuring the reflectance at each side of the film on a transparent substrate as well as the transmittance. In particular, the reflectance from the substrate-film and air-film interfaces can yield the optical constants via Fresnel’s law and the film thickness can be calculated from the transmitted signal according to Beer-Lambert law [45]. The above discussion only applies when the media are nonscattering. However, the scat-  11  2.1. Background: Optical Characterization tering on nanocrystal films cannot generally be ignored due to their inhomogeneous nature, and the diffuse scattering usually presents a very complex problem in linear spectroscopic analysis because of its wavelength dependence. Unfortunately, a quantitative theoretical evaluation on light scattering from NCs is still missing [46], although some experimental results have been qualitatively explained [47].  2.1.2  Nonlinear Degenerate Four-Wave-Mixing Spectroscopy  Linear spectroscopy can not be used to measure intrinsic dephasing rates in samples like NCs, where there is large inhomogeneous broadening comparable to or greater than the intrinsic homogeneous broadening. Nonlinear, degenerate four-wave-mixing can directly measure the dephasing rate and is largely immune to inhomogeneous effects. The principle of this pump-probe type of measurement is illustrated in Figure 2.1. A strong pump laser pulse with wavevector ~k2 generates a coherent polarization in the sample and the probe laser pulse, ~k1 , whose intensity is much weaker, arrives at the sample with a delay τ . If τ is smaller than the dephasing time of the polarization excited by the first pulse, an interference grating is created from which k1 is self-diffracted along the phase matching direction 2~k1 − ~k2 , the so called DFWM signal. The word ”degenerate” here means that two pulses are generated by a common laser source. In time-resolved four-wave-mixing (TR-FWM) experiments, the diffracted light is recorded as a function of real time t, and in time-integrated four-wavemixing experiments, the diffracted light is measured as a function of the delay τ between the two pulses. The dephasing rate then can be extracted from the decay constants of these curves. Further quantitative detail about four-wave-mixing technique is discussed in the previous work that was done in our lab [39] and also in textbooks [42][48]. The DFWM technique described above together with combinations of incident pulse polarizations can be applied to a variety of material systems and provides a wealth of information about the nature of elementary excitations. For example, if two pulses are co-linear polarized, they can produce a density grating while cross-linearly polarized pulses can create an orientational grating. Likewise, combinations of circular polarized beams can be employed to study two photon coherence. Although work has been done using a cross-polarized four-wave-mixing technique to experimentally investigate the dephasing mechanism of excitonic structures inside PbSe and PbS NCs that were dispersed in solvent or glass-forming media [40], little is known  12  2.2. Basic Experimental Setup  Figure 2.1: Schematic illustration of degenerate four-wave-mixing process  about their properties in films, which is more relevant to our research group.  2.2  Basic Experimental Setup  In this thesis, several different types of experiments were done, including linear absorption, PL and nonlinear DFWM. The optical setup of these experiments are arranged in a compatible way, allowing to switch between them simply and reproducibly. An overall view of this optical setup is shown in Figure 2.2. It consists of five basic parts: light sources, a beam steering area, an autocorrelator, and collection and detection systems. A more detailed diagram of optical path is illustrated in Figure 2.3. When aligning these optics, all the beams should first be made perfectly parallel to the optical table and at the same height2 , which can be done by checking their parallelism and height after letting them bounce across the room several times. This is of great importance for the DFWM experiment in particular and will benefit other measurements as well. Some alignment procedures are described in Appendix A and B, and the detailed function of each component is discussed in the following sections. 2  The height of the beam over the entire optical setup is set the same as the center of RR2. This is because the hight of RR2 is fixed while those of other optical components can be adjusted.  13  2.2. Basic Experimental Setup  Figure 2.2: Layout of the general experimental setup and the photon flow(arrows), including three types of light sources, the beam steering area, autocorrelator, and the collection and detection systems.  2.2.1  Linear Absorption Experiments  To provide a continuous broadband spectrum, a fiber optical illuminator with a halogen lamp is used to conduct linear absorption measurements. Light is collimated by lens L1 after coming out of the fiber, and it is then directed into the cryostat system by mirror M5, M7 and M8. Note that mirrors like M5, M7 and M8 in Figure 2.3 rest on kinematic mounts so that they can be inserted and removed from the system without realigning other components. The sample storage and detection systems for this measurement are illustrated in Figure 2.4. The incident beam is p-polarized relative to the sample surface by P2 and focused by a 180mm focal length lens (L1) onto the sample surface which is mounted in the cryostat, resulting a 240µm-diameter spot on the sample. The cryostat used in this thesis is a Janis Research Supertran System model ST-4. With continuous cryogen (liquid helium or nitrogen) flow and built-in silicon diode temperature sensor, as well as a Lakeshore model 330 autotuning temperature controller, the temperature in the sample chamber can be held from 1.5 to 325K stably. 14  2.2. Basic Experimental Setup The sample in the cryostat is oriented in such way that p-polarized light is incident at Brewster’s angle of the substrate and hits the substrate and QD layer in sequence. This particular sample arrangement can remove Fabry-Perot interference effects caused by the substrate slab, for there is no reflection at the air-substrate interface, and thus it provides a background-free measurement of the reflectance of the substrate-sample interface. The reflection from the sample is collimated and sent into a BOMEM DA8 Fourier transform spectrometer, while the collimated transmission passes through a p-polarizer (P3) and an aperture (A5) before it goes into the BOMEM.  Figure 2.3: Diagram of all the optical components for different types of measurements. White light and semiconductor laser sources are coupled into a cryostat along the dashed lines, and the dashed line after mirror M8 also represents the optical axis of the collection system. As for the OPO laser, the fixed and the delayed arms are labeled as solid and dot-dashed lines, respectively. All the beams are parallel to the optical table and at the same height.  15  2.2. Basic Experimental Setup  2.2.2  Nonlinear DFWM Experiments  For the DFWM experiment, the two laser pulses are derived from a common source. The laser used here is a Spectra-Physics Opal optical parametric oscillator (OPO) pumped by a Tsunami model 3960-S1S Ti: Sapphire laser which is in turn pumped by a 9W SpectraPhysics Millennia laser (532 nm). The OPO produces tunable wavelength pulses, from 1400nm to 1580nm, with full-width at half-maximum (FWHM) about 130fs at a repetition rate of 82MHz. The average output power of the OPO is about 100mW but it can reach up to 150mW at 1500nm. When conducting the DFWM experiment, the laser is tuned to the absorption peak of the QD layer.  Figure 2.4: Experimental configuration of sample mount and detection system for linear transmittance and reflectivity measurements. The light is incident at Brewster’s angle of the substrate so that reflection only comes from substrate-sample interface. Both reflection (red dashed line) and transmission (grey dashed line) are then collimated and sent into the spectromemter.  Beam Steering and Pulse Delay System  The beam steering system is also depicted  in Figure 2.3. The wave plate W1 and polarizer P1 placed after the output of the OPO are to adjust the intensity of laser while keeping it s-polarized. The initial OPO beam is directed to beam splitter BS1 which has a splitting ratio close to 50:50 for s-polarized light 16  2.2. Basic Experimental Setup at 45◦ incidence, from 1400nm to 1600nm. The reflection from BS1 goes into the delay arm (dashed line) and is reflected in the opposite direction and shifted laterally 1cm by retroreflector RR1. This gold-coated retro-reflector is sitting on a three-dimensional translation stage, two of which (along y and z) are used to align the reflected beam. The third one, along the x axis offers manual control of the time delay, τ . Moving along x by a distance d shifts τ by 2d/c, where c is the speed of light, and thus: for d = 1mm, ∆τ = 6.67 ps. The transmission at BS1 goes into the fixed arm. It is then reflected and shifted by another retro-reflector RR2, which is attached to a Mini-Shaker (Brüel & Kjaer, model 4810). The Mini-Shaker is an extremely stable, single axis vibrator with a maximum displacement of 6mm. It is mounted horizontally so that its central axis is 165.1mm off the optical table. The shaker is driven by a current source, which is in turn driven with a sine wave from a function generator (usually at 19Hz). A more detailed description of the Mini-Shaker can be found in Dr. Alexander Bush’s thesis [39]. Two optical choppers (Model SR540, Stanford Research System) C1 and C2 are used to square-wave modulate the laser intensity, with a frequency ranging from 4Hz to 3.7KHz. This lock-in technique, elaborated below, is used to look for small signals in the presence of a large noisy background. The beam splitter cube BSC1 splits beams from both fixed and delay arms into two sets. One set of beams that goes along z is sent to the cryostat and detection system, while the other set is directed to the autocorrelator, discussed next. Autocorrelator  The autocorrelator is used for two purposes: it defines the ”zero delay”  position for DFWM experiments, and it can also be used to measure the FWHM (duration) of the OPO pulses. The setup of the autocorrelator is shown in Figure 2.5. Laser pulses from the two arms are focused by a 200mm focal length lens (L2) onto a BBO nonlinear crystal which has a strong second-order nonlinearity. When the two pulses overlap spatially and temporally inside the nonlinear crystal, a signal with double the frequency of the input pulses is generated along direction ~k1 + ~k2 , via second harmonic generation(SHG), where ~k1 and ~k2 are wavevectors of pulses from the fixed and delay arms, respectively. Unwanted infrared beams are blocked by a NIR bandpass filter F1 (Thorlabs FB750-40, FWHM 40nm, peak transmission > 75% ). An aperture A6 is added between filter F1 and a Si-PIN detector D1 (455-UV, UDT Sensors, Inc.), to block upconverted stray light along ~k1 and ~k2 direction. The stray light is mostly due to second harmonic of the individual pulses, even though they are far from being optimally phase matched. 17  2.2. Basic Experimental Setup  Figure 2.5: Schematic illustration of the SHG autocorrelator. Beams from the fixed and delay arms are focused on the nonlinear crystal. The second harmonic signal is then generated along the optical axis when pulses from both arms overlap spatially and temporally.  The SHG signal is then optimized by making the two pulses overlap completely in space, and its intensity reaches maximum as the two pulses arrive at the crystal simultaneously, which corresponds to τ = 0. The FWHM of pulses can also be obtained by fitting the intensity of the SHG signal versus delay τ . A detailed description for aligning the autocorrelator can be found in Appendix B. Beam Coupling System Beams coming from the fixed and delay arms are directed into the coupling system by mirrors M3 and M4, respectively. Except for being parallel to the optical table and at the same height, they should be parallel to each other as well. Each of the two beams are then individually truncated by aperture A3 to a beam spot of 2mm diameter and then focused by L1 onto the sample. In this experiment, the sequence of layers on the sample is not important, for only transmitted light is concerned. Since two incident beams before L1 have a separation of 12mm, a 10mm wide silicon-based mirror M9 (deposited with aluminium thin film) is inserted in between to direct the scattered light from the sample surface into a CCD camera so that spots on the sample can be observed (Here a strip of white paint or thin tape can be put on the edge of the sample to provide a better vision of the laser spot). This is used to make sure that they are optimally overlapped on the sample. If not, adjustments on lens L1 should be made first, and further careful adjustment can also be made with M3 and M4, if necessary. In principle, there are four beams emerging from the cryostat, i.e., two DFWM beams as indicated in the Figure 2.6 (red dashed lines), and two partially absorbed laser beams. These are all collected and collimated by mirror PM1, which is a gold-coated parabolic  18  2.2. Basic Experimental Setup mirror with a 28.75mm focal length, 25.4mm diameter and 90◦ off-axis (57.5mm from the center of the mirror to the focal point). A good alignment of PM1 is rather crucial for detecting DFWM signals, which can then couple all the light into detector D2. One proper way to align it is illustrated in Appendix A. The purpose of adding an aperture A4 between PM1 and M10 is twofold: moving the aperture along the z direction provides a measurement of the cross section profiles of all the beams and any linearly scattered light in the forward direction; it can also block unwanted light when looking for the DFWM signal. Another 200mm focal length lens L3 is used to focus the transmitted beam onto an InGaAs detector D2 (IGA-030-E-LN6N, Electro-Optical System Inc.). The detector has two settings of output responsivity, with one a hundred times more sensitive than the other. In this experiment, the more sensitive setting is used to look for small DFWM signals but at the cost of low bandwith (<500Hz).  Figure 2.6: Schematic illustration of the beam coupling area for the DFWM experiment. The forward-going optical circuit consists of A3, L1, PM1, A4, M10 and L3 and it serves to couple incident beams on the sample and to collect the DFWM signal. The backward optical circuit consists of L1, M9 and L3, allowing beam spots on the sample to be observed on the CCD (red arrows).  19  2.2. Basic Experimental Setup Detection System Due to the inhomogeneous nature of the QD layer, laser beams are highly scattered by the sample. As will be mentioned in the next chapter, the result of measurements of the cross section beam profiles after PM1 showed that the scattered laser light is diffused into all directions, obscuring the weak DFWM signal in a large noisy background. Thus, a lock-in detection system was used to help extract the small signal. This  Figure 2.7: Diagram of experimental setup of lock-in detection system for DFWM experiment.  technique requires that the sample excitation source be modulated at a fixed (low) frequency in a relatively quiet part of the system noise spectrum; this modulation frequency should be far from the power line frequency and its harmonics, and as high as possible to avoid inverse frequency (1/f ) noise. The lock-in then detects the response from the experiment in a very narrow bandwidth at the excitation frequency. To further improve signal to noise ratio, two choppers are used, chopping beams from the delayed and the fixed arms at f1 and f2 , respectively. Suppose the two beam are modulated as I1 = I10 sin(2πf1 t)  (2.2)  I2 = I20 sin(2πf2 t)  (2.3)  so the DFWM signal in the 2~k1 − ~k2 direction can be written as, IDF W M  ∝ I12 I2  (2.4)  2 ∝ I10 I20 {1/2 sin(2πf2 t) − 1/4 sin[2π(2f1 + f2 )t] − 1/4 sin[2π(2f1 − f2 )t]} (2.5)  20  2.3. Sample Preparation Since the detection frequency is limited by the bandwidth of the detector D2, if f1 = 275Hz and f2 = 200Hz, then the 2f1 − f2 component provides a convenient monitoring frequency for the lock-in. As illustrated in Figure 2.7, reference signals from choppers C1 and C2 are sent into a nonlinear circuit, which is realized using a DAQ card (Model 6210, National Instruments) based on Labview 8, to generate a signal with frequency 2f1 − f2 . By setting the input sampling rate for each channel at 125kS/s and the output clock rate at 500kS/s, the signal delay caused by AD-DA transitions can be reduced to less than 1ms. The lock-in amplifier then takes the generated signal as a reference and filters signals at this frequency from all of those coming out of the detector.  2.2.3  Photoluminescence Measurements  A semiconduction laser diode with a 635nm central wavelength, 10nm linewidth and 4mW output power is used to inject electrons and holes into high energy states of the PbSe (PbS) nanocrystals, from which they relax to form excitons, some of which recombine by emitting a photon at the ground state exciton energy, which is detected as photoluminescence. This photodiode also assists in aligning other experiments; the setup of this PL measurement is quite similar to that used for the transmission measurement. The laser is sent and focused into the cryostat by mirror M8 and lens L1, respectively. The generated PL is then collimated by L5 and directed into the spectrometer by M11. Note that, if QDs are deposited on silicon substrate, the QD layer should be in front, for silicon is opaque to visible light, while the orientation of sample if deposited on a glass substrate is not important.  2.3  Sample Preparation  This section describes the samples and the details of their preparation. The PbS and PbSe QDs used in this thesis were prepared by our collaborator, Dr. Frank van Veggel’s group at University of Victoria. They synthesized the colloidal PbS NCs by following the modified organometiallic synthetic route using trioctylphosphine (TOP) [49]. PbS NCs prepared using this method have increased PL emission and slightly narrower FWHM compared with results reported using more conventional synthesis [50]. High-quality colloidal PbSe NCs were synthesized in a similar manner which is described in the literature [51]. The colloidal PbSe and PbS NCs arrive dispersed in trichloroethylene (TCE) solvent,  21  2.3. Sample Preparation with solution concentration around 5mg/mL. Since the DFWM experiment requires relatively thick solid state films (in order to maximize the nonlinear interaction), the solution was concentrated to more than 100mg/mL by dry nitrogen gas, and drop-cast on RCA1-cleaned substrates 3 , such as silicon (double-side-polished intrinsic silicon wafer, 350µm thick) and glass (micro-objective slide). The NCs can also be dispersed in hexane solvent and drop-cast into a film, but the author found that it is hard to control the concentration of droplets in this manner due to the high volatility of hexane. Spin-coating rather than drop-casing can also be used to prepare solid state films, however, the uniformity and morphology of these films is not much better than the drop-cast ones, because low rotation speeds (500 rpm) have to be chosen during the spincoating process to get films thicker than 200nm. PbSe and PbS QDs are very sensitive to oxygen and their electronic structures will change, if exposed in air for more than a few minutes. Thus, the exposure of samples to air should be minimized when preparing them. The whole process of sample preparation includes concentrating the original NC solution by nitrogen gas (30mins for 3mL 5mg/mL solution), drop-casting the concentrated NC solution onto a substrate (1min) and attaching the sample to the sample holder of the cryostat (2min), and the last two steps should be done in a dry nitrogen environment. The sample should be kept in vacuum once made.  3 The RCA-1 clean, also called ”standard clean-1”, is a procedure for removing organic residue and films from silicon wafers.  22  Chapter 3  Experimental Results This chapter presents the data obtained using the techniques discussed above. Emphasis here is placed on its presentation and qualitative interpretation; the modeling and quantitative analysis follows in Chapter 4.  3.1 3.1.1  Attempts To Obtain DFWM Signals DFWM In Transmission Geometry  As discussed in section 2.2.2 and shown in Figure 2.6, scanning aperture A4 along the z axis allows one to measure the positions of the incident laser beams, which were Xf ixed = 8.85mm and Xdelay = 12.60mm for beams from the fixed and the delay arms, respectively. According to the phase matching condition, the generated DFWM signal by a positive pulse delay is expected to show up at 2Xdelay − Xf ixed = 16.35mm and at 2Xf ixed − Xdelay = 5.10mm for a negative pulse delay. The initial attempt to search for DFWM signals involved placing aperture A4 at 16.35mm with the Mini-Shaker on and then monitoring the signals of the autocorrelator and detector D2 on different channels of an oscilloscope. As shown in Figure 3.1, while the autocorrelator showed a clean Gaussian-like curve on one channel of the scope, an interferogram instead of the typical pump-probe exponential decay curve was observed at the other channel. The power of the two incident beams measured in front of the cryostat were 1.2mW for the fixed and 0.4mW for the delay. With such input laser powers, the background DC signal4 was 1.2V while the peak-to-peak value of the interferogram measured on the scope was 0.3V. When placing the aperture at 5.10mm, a similar interferogram was observed with a 1.5V DC background and an 0.5V AC peak-topeak value. Such strong background signals will obscure any nonlinear DFWM signals, which are expected to be at most on the order of a few millivolts. 4  ”DC” here means the signal from the detector was measured by a Voltmeter on the DC setting.  23  3.1. Attempts To Obtain DFWM Signals  Figure 3.1: Schematic illustration of the signals in the oscilloscope.  Cross Section Profile Technique In order to better understand the origin of the large background signal observed at the DFWM detection positions, the cross section profile of the transmitted light was measured by scanning aperture A4 with the Shaker off. The measurement was done at one of the smoothest parts of the sample (i.e. where the DC signal at the DFWM position was a minimum) and when measuring either of the beams, the other was blocked in front of the cryostat. Figure 3.2 shows the scattered light distribution in the transmitted direction with the exciting lasers passing only through the silicon substrate and through a drop-cast PbSe (PbS) QD layer on a silicon substrate. In the former case (dashed line) the two input laser beams are clearly evident with peaks located at 8.85mm and 12.60mm respectively, while in the presence of the QDs (solid lines) the laser beams were partially absorbed and also scattered over the entire scan range. The DC signals at these two predicted DFWM positions in the dashed line plot are both about 50mV with the same input laser power as above, however, they are above 500mV in both red and blue solid line plots and were found linearly proportional to the input laser power, which suggests a strong linear scattering from the QD sample. Such a strong scattering background explains  24  3.1. Attempts To Obtain DFWM Signals  Figure 3.2: Cross section profiles of the light measured after the parabolic mirror. The dashed line indicates the cross section profiles of the two laser beams only through a pure silicon substrate while the red and the blue lines are the profiles of those through a silicon substrate deposited with a PbSe (PbS) QD layer. The two green arrows indicate the two predicted positions of the DFWM signal, which are 5.10mm and 16.35mm, respectively.  the origin of the large background signal at the DFWM position. Lock-in Technique  In an attempt to discriminate against the linear scattering back-  ground, the lock-in technique discussed in Section 2.2.2 was also employed. The scan aperture was placed at the predicted DFWM positions and the lock-in amplifier was set to extract signals with a frequency of 2f1 − f2 . The lock-in signal versus the laser pulse delay is plotted in Figure 3.3. An interferogram similar to that recorded on the oscilloscope (see section 3.1.1 above), consistently showed up in the repeated measurements, which must be due to linear interference of the scattered beams from the fixed and delay arms. So, while  25  3.1. Attempts To Obtain DFWM Signals  Figure 3.3: Plot of lock-in amplifier signal versus pulse delay time.  the lock-in approach substantially reduced the DC background level, it failed to reduce the size of the interferometric ”background” to the same degree, and this residual interferometric signal is still too strong and complex in nature to allow easy detection of weak DFWM signals. A detailed mathematical discussion on this point will be discussed in the final chapter.  3.1.2  DFWM In Reflection Geometry  As concluded in the last section, it is too difficult to conduct the forward DFWM experiment in the presence of a large scattering background signal. After carrying out a number of linear spectroscopic studies of the films as described below, it became apparent that the amount of light diffusely scattered in the backward direction can be substantially less than in the forward direction. In order to investigate the feasibility of this geometry, the scattered  26  3.1. Attempts To Obtain DFWM Signals beam profiles were measured by scanning an aperture through the beams reflected from the sample, rather than in transmission. The measurement was done first on a pure silicon slab and then on a silicon slab drop-cast with a QD layer on the back surface. Figure 3.4 shows the results from these measurements (blue and red lines), and the previous measurements of the transmitted beams (green lines) are also included and plotted in the same scale.  Figure 3.4: Cross section profiles of the reflected laser beams. The data plotted in the blue line were taken on a pure silicon substrate and those plotted in red line were taken on a silicon substrate drop-cast with a QD layer on its back surface. The green dashed and solid lines are those from Figure 3.2, and all the data are plotted in the same scale. The grey arrow indicates the predicted position of the DFWM signal in reflection geometry.  Since a 35mm focal length lens was used to collimate the reflected beam in this experiment, with an f-number similar to that of the parabolic mirror used in the transmission measurement, the DFWM signal generated in this geometry, in principle, should appear 27  3.2. Sample Morphology Under Optical Microscope at the same absolute scan position as in the transmission geometry discussed above, i.e, 16.35mm. The DC voltage at this position was 70mV on the silicon slab and slightly lower on that with the PbSe (PbS) NC layer, which is mostly due to absorption by the NC layer. Because the background DC voltage levels in both measurements are sufficiently low, the reflection geometry holds some promise to conduct DFWM experiment; this will be discussed further in the final chapter.  Figure 3.5: Pictures of a PbS NC film under optical microscope. The estimated film thickness at different spots: (a) 0µm; (b) 6µm; (c) 13µm; (d) 27µm.  3.2  Sample Morphology Under Optical Microscope  The experimental data together with the theoretical simulation that will be discussed in the next chapter have independently led to many suggestions about the properties of the 28  3.3. Transmittance & Reflectance Profiles drop-cast PbSe and PbS NC films, e.g., the roughness of the NC-air interface, the thickness and structure of the NC layer. Thus, in order to verify these speculations, a NIKON OPTIPHOT-2 Microscope with a 50× magnification was used to investigate the morphology of the NC film. The film thickness can also be estimated, with an uncertainty of 3µm, by measuring the movement of the objective lens along the optical axis of the microscope between focusing on the sample and on the substrate. Figure 3.5 shows the pictures that were taken at different spots of a sample and the corresponding film thickness. Several conclusions can be instantly drawn from them: the film thickness varies at different locations on the sample; small features that are out of focus in each picture suggest a rough surface; in 3.5(a), a transparent thin oil layer on the edge strongly supports the three-layer model and the simulation results in Chapter 4.  3.3  Transmittance & Reflectance Profiles  This section presents the results of transmission and reflection spectroscopic measurements on different substrates deposited with PbS NC films or a reference layer of photoresist. While a variety of measurements were done on both PbS and PbSe NC samples, only those of PbS NCs are reported here, since samples made of these two types of nanocrystals exhibit qualitatively identical properties. In these measurements, light (p-polarized) was always incident at Brewster’s angle of the substrate, while the transmitted and reflected light from the sample were collected and directed into the spectrometer respectively, as shown in Figure 2.4 and described in Section 2.2.1. An aperture with variable size and polarizers were inserted between the collection lens for the transmitted beam and the spectrometer, in order to study the effects of diffuse scattering on the transmission spectra.  3.3.1  Transmission & Reflection Spectra At Different Spots  The transmission and reflection spectra were both measured through different positions of a drop-cast sample where the morphology of the air-NC interface and the film thickness varied as suggested by the above microscopic measurement. One particular area on one sample had an optically smooth surface over an ∼ 2mm range, larger than the beam size on the sample (∼ 240µm diameter). Transmission and reflection spectra from two spots on this smooth  29  3.3. Transmittance & Reflectance Profiles  Figure 3.6: Transmission and reflection spectra measured at different positions of a dropcast PbS NC film on a silicon substrate. Different colors represent the measurements taken at different positions (i.e., the red is labeled as 1 and the blue as 2 for references), and the dashed and the solid lines stand for transmission and reflection, respectively. The absorption spectrum of PbS NC solution is also plotted in green.  area exhibited clear Fabry Perot fringes, as shown in Figure 3.6. Pairs of spectra taken from other, rougher and thick regions of the sample are shown in Figure 3.7. In all of these plots the raw reflection and transmission spectra were normalized by the spectrum of the incident white light, and reflection and transmission data plotted in the same color were obtained from the same spot on the sample. Two obvious and common features can be observed from these spectra: 1) the dip in the transmission spectra, which coincides with the absorption peak of the NCs in solution, is not evident in reflection; 2) while the reflectance shows a relatively weak wavelength dependence (save for the Fabry-Perot fringes in Figure 3.6), the transmittance renders a strongly varying background over the entire spectrum. Comparing the spectra measured at different spots, it can been seen that the transmittance rather than 30  3.3. Transmittance & Reflectance Profiles reflectance strongly depends on the lateral position. Moveover, the spectra of relatively high transmittance (plotted in Figures 3.6 in red and blue) implies thin NC layers, which is also consistent with the fact that there are weak Fabry-Perot (FP) fringes observed above the noise level in the corresponding reflection spectra. The visibility of these fringes varies not much in the reflection spectra except at the dip of the transmission, while the relatively weak FP fringes observed in the corresponding transmission spectra are only observed at the longest wavelengths. The next chapter shows how the presence of clear FP fringes is essential for extracting accurate optical parameters from quantitative fits of these spectra. FP fringes comparable to or below the noise level are also observed in the reflection spectra (in Figure 3.7) from thicker regions, however, since they lack distinct visibility, no reliable quantitative fitting could be done with these spectra.  Figure 3.7: Transmission and reflection spectra measured at different positions of a drop-cast PbS NC film on a silicon substrate. Different colors represent the measurements taken at different positions, and the dashed and the solid lines stand for transmission and reflection, respectively.  31  3.4. Forward Scattering Profiles  3.3.2  Average Reflectivity Of Films On Different Substrates  Table 3.1 enumerates the reflectivity measurements over wavelengths from 1100nm to 1700nm on different substrates deposited with different types of thin films. Since the wavelength dependence is very small in the reflectivity spectrum, only the averaged reflectance is presented here. As shown in the table, the reflectance of a Si-PbS interface is much different from that of a Glass-PbS interface, while it is quite similar with that measured at the boundary between silicon and e-beam resist whose refractive index is 1.63. These results, taken by themselves, would suggest that the average refractive index of the PbS NC films is 1.68 and that the absorption coefficient in these films is 0.08. This would be very unusual, since a simple estimate of the average effective refractive index of a close-packed PbS 3D crystal, using the Maxwell-Garnett theory, gives 3.12 − 0.11i.5 This paradox was resolved after considering both the transmission and reflectivity data together, as explained in the next chapter. A detailed account of the calculation of the effective refractive index of the NC film can be found in Appendix C. Sample layer PbS NCs PbS NCs Zep520A  Substrate Si Glass Si  nsub 3.5 1.5 3.5  nsample 1.68 − 0.08i 1.68 − 0.08i 1.63  θin 74◦ 56◦ 74◦  Reflectivity 17.6% 0.125% 18.3%  Table 3.1: Average reflectivity at Brewster’s angle from different interfaces  3.4  Forward Scattering Profiles  The reflectivity spectra are remarkably similar and reproducible from all areas of the sample. In contrast, the transmission spectra varied a great deal from spot to spot. This is partly expected since different spots have different thickness, and hence the overall absorption will vary from spot to spot. What is less obvious is the extent to which the slowly varying background signal observed in transmission was sensitive to alignment and the collection f-number. To more fully characterize the transmission spectra [52], a variable aperture and a polarizer were placed between the sample and the collection lens for transmission, and the dependence of the transmission spectra on these elements was determined. 5 The complex refractive index in this thesis is written as ñ = n − iκ, which n and κ denote the refractive index and absorption coefficient respectively.  32  3.4. Forward Scattering Profiles  3.4.1  Rescaling Transmission Spectra  In order to better understand the transmission spectroscopic data, it is useful to rescale them in a semi-log manner, namely, − log(T /Tsilicon )  (3.1)  where T is the transmission through the sample (the silicon slab and QD layer) and Tsilicon is the transmission only through the silicon slab. The spectra rescaled in this way make comparison between them more straightforward, e.g. if two sets of data are proportional to each other by a factor C, they will have the same shape but only differ from each other in the rescaled plot by a constant − log(C). In addition, the semi-log scaled transmission is pro-  Figure 3.8: Rescaled transmission spectra whose raw data were presented in Furgures 3.6 and 3.7 in the same colors. The absorption spectrum of PbS NCs in solution is shown in a green dashed line.  33  3.4. Forward Scattering Profiles portional to the absorption coefficient of a homogeneous, nonscattering medium, according to Beer-Lambert’s law. Figure 3.8 shows the rescaled transmission spectra that were presented in Section 3.3.1. While there is a distinct exciton absorption peak in all of the spectra, suggesting that the close packed nature of the emulsion does not qualitatively alter the electron-hole absorption resonance, all transmission spectra through the films show a slowly varying background with a shape and overall strength that both vary with sample thickness.  Figure 3.9: Transmission spectra collected with (red) and without (blue) a polarizer oriented to pass p-polarized light inserted between the sample and the spectrometer. The absorption spectrum of PbS NCs in solution is shown in a green dashed line.  34  3.4. Forward Scattering Profiles  3.4.2  Polarization Dependence  Figure 3.9 shows the results of the measurements of the polarization dependence of the transmitted beams through the sample, whose raw data are normalized and rescaled in the above manner. The red (blue) curves are measurements taken with (without) a p-polarizer which is colinearly polarized with respect to the incident light. As shown in the graph, the two curves have exactly the same shape and only differ from each other by an offset that is due to the (white) absorption of the polarizer. An s-polarizer (cross polarized with respect  Figure 3.10: Transmission spectra collected with an aperture of different diameters inserted between the sample and the spectrometer. From the black to the dark green lines, the aperture diameters were 0.3mm, 1mm, 2mm and no aperture, and the corresponding DC signals are 6.6mV, 13mV, 27mV and 68mV. The absorption spectrum of PbS NCs in solution is shown in a green dashed line.  to the incident light) was also used but no significant signal was detected. Therefore, the 35  3.4. Forward Scattering Profiles above measurements suggest that there is very little polarization mixing in the transmitted light.  3.4.3  Using Apertures Of Different Sizes  Figure 3.10 shows the results of varying the size of an aperture located on the optical axis, in transmission through a fixed position on a silicon slab deposited with a PbS QD layer. The minimum DC signal (average transmitted intensity) was only 10% of the signal measured with no aperture. The continuous increase of transmitted light as the aperture increases is consistent with the highly diffuse forward scattering beam profiles shown at the beginning of this chapter. It appears that the pure specular component of the transmitted signal most closely resembles the absorption spectrum in solution, with an increasing background contribution (both in spectral variation and overall strength) appearing as more diffusely scattered light is detected.  36  Chapter 4  Quantitative Analysis Of Linear Spectra The sample consisting of a silicon substrate and a PbS NC layer can be considered to have a multilayer structure. In this chapter, the reflection and transmission from such stratified structures are simulated and the key physical parameters extracted from the fits are discussed.  4.1  Simulation Method  In this work, the reflection and transmission coefficients of the incident light in the stratified media are calculated by the matrix method[53], in which two ideal situations are assumed: each layer is isotropic and homogeneous and the interfaces between layers are parallel-planelike. These approximations allow the electromagnetic field in each layer to be described by 2 × 2 matrices due to the fact that equations of propagation of the electric field are linear and that the tangential component of the electric field is conserved at planar interfaces between materials with different optical constants. In particular, with reference to Figure 4.1, each of the layers (l = 1, 2, 3, ..., m) is described by its thickness dl and complex refractive index ñl = nl − iκl , where nl and κl denote the refractive index and absorption coefficient of the lth layer respectively and are wavelength dependent, and n0 and nm+1 are the refractive indices of the media where the light enters and leaves the sample respectively. The incident and transmitted media are always air in our case, so no,m+1 = 1. A plane wave incident towards the above multilayer structure in the x − z plane can be written as, (Ae−ikz z + Beikz z )ei(wt−kx x) .  (4.1)  37  4.1. Simulation Method  Figure 4.1: Schematic illustration of optical waves in layered media  where A and B denote the electric fields for the forward and backward propagating light respectively; kz and kx are the z and x components of the wavevector respectively. Since the multilayer structure are parallel to the x − y plane, kx is conserved in all the layers and kz in the lth layer is thus given by,  kl,z =  q  (2πñl /λ)2 − kx2  (4.2)  where λ is the wavelength of the incident light. Consider the boundary conditions of an electromagnetic field for homogeneous and isotropic materials − the tangential components of the electric and magnetic fields vary continuously when crossing an interface. Therefore,  38  4.1. Simulation Method the amplitudes of the electric fields in lth layer, Al and Bl , can be calculated recursively, A0  !  B0 Al  A1  =  D0−1 D1  =  Pl Dl−1 Dl+1  !  !  Bl  (4.3)  B1 Al+1 Bl+1  !  , l = 1, 2, ..., m.  (4.4)  The matrix Dl results from Fresnel’s law and is written as, Dl =  Dl =  1  !  1  for s-polarized waves, and  kl,z /(2π/λ) −kl,z /(2π/λ) kl,z /(2πñl /λ) kl,z /(2πñl /λ)  !  for p-polarized waves.  −ñl  ñl  The matrices Pl are the so-called propagation matrices that account for propagation through the bulk of the layer, Pl =  eiφl  0  0  e−iφl  !  (4.5)  φl = kl,z dl  (4.6)  The relationship between (A0 , B0 ) and (Am+1 , Bm+1 ) is then, A0 B0  !  M11 M12  =  M21 M22  !  Am+1  !  Bm+1  (4.7)  with the matrix given by, M11 M12 M21 M22  !  = D0−1 [  m Y  Dl Pl Dl−1 ]Dm+1  (4.8)  i=1  Hence, the reflectance and transmittance of the incident electric field from the sample can be obtained by, r = (B0 /A0 ) |Bm+1 =0 = M21 /M11 ,  (4.9)  t = (Am+1 /A0 ) |Bm+1 =0 = 1/M11 .  (4.10) 39  4.2. Modeling Sample Structure Correspondingly, the reflection and transmission coefficients of the incident light are R = |r|2 , km+1,z 2 T = |t| . k0,z  (4.11) (4.12)  Note that in (4.13) T is a real number, because k0 and km+1 are wavevectors of the light propagating in air. The above derivation of the transmittance and reflectance of light incident into a multilayer only applies if there is no scattering from the media. If there is scattering, it can be approximated by adding a term to the P matrix as discussed next, leaving the D matrices unchanged.  4.2  Modeling Sample Structure  In the section, the reflection and transmission are simulated using the above approach. Since the experimental sample consists of a double-side-polished silicon substrate and a drop-cast PbS NC layer, the simplest model for this purpose is to employ a two-layer structure as shown in Figure 4.2(a): a silicon layer with a literature-reported dispersion [54] and a NC layer with a uniform complex refractive index ñnc (λ) = nnc (λ) − ia · Anc (λ). Here, Anc (λ), plotted in Figure 4.3, is the normalized absorption coefficient of the PbS NC solution and a is a variable weighting factor for the associated absorption strength in the film. Considering the highly scattering nature of the NC layer, a Raleigh-like scattering term is also adopted in the simulation by incorporating a power law κsc into the propagation matrix of the NC layer in the following manner, Pnc =  e2πκsc dnc /λ eiφnc  0  0  e−2πκsc dnc /λ e−iφnc  κsc (λ) = b · λ−p  !  (4.13) (4.14)  The hypothesis underlying this model is that the electronic absorption due to the NCs is not significantly altered from that measured in solution, while there is substantial Raleighlike scattering that causes extinction without absorption. This model is parameterized by the refractive index Nnc (λ), the absorption strength a, the thickness dnc , the scattering 40  4.2. Modeling Sample Structure  Figure 4.2: Schematic illustration of the models used to simulate R & T spectra. (a) twolayer structure: silicon substrate and NC layer (b) three-layer structure: silicon substrate, interfacial oil layer and NC layer.  strength b and the power law exponent p. After several attempts, it was found that this large number of parameters can not be uniquely determined by fitting to reflection and transmission spectra from thick regions of the sample where there are no Fabry-Perot fringes evident. However robust fits could be obtained from the spectra shown in Figure 3.6, which do contain clear FP fringes. Fig 4.4 shows the simulated reflection and transmission spectra obtained using the twolayer model, along with the corresponding experimental curves. Although the simulated spectra have similar shapes, the average of the simulated reflectivity6 and the amplitude of the fringes don’t match with the experimental values. In fact, the simulation suggests that the the mean value of reflectivity is sensitive to the refractive index of the NC layer, that the period of the fringes is controlled by the thickness of the layer once the refractive index is 6  The ”average” here means the mean of the reflectivity over the entire spectrum.  41  4.2. Modeling Sample Structure  Figure 4.3: The normalized absorption spectrum of the PbS NC solution.  fixed and that the amplitude of the fringes depends on the scattering strength. However, in the simulation no solution of these parameters can be found to give an averaged reflectivity larger than 12%. An estimate for the refractive index of the NC layer can also be made from the data presented in Table 3.1, which showed that the average reflectivities of the NC layer deposited on silicon and glass are 17.6% and 0.125%, respectively. Applying a single interface Fresnel reflection calculation for the two cases (glass-NC and silicon-NC), it is impossible to find a single refractive index for the NC layer that yields the measured reflectivities. Thus both the fits to the spectra and the comparison of silicon and glass substrate reflectivities suggest that the NC film is not homogeneous. An alternative model is to adopt a three-layer structure, in which an thin layer with low refractive index is inserted between the silicon and NC layers, as illustrated in Figure 4.2(b). Such an interfacial layer could result from the oleate ligands that are used to cap 42  4.3. Simulated Transmission & Reflection Spectra  Figure 4.4: Simulated reflection (blue) and transmission (red) spectra based on the twolayer model. The green lines are experimental data R2 and T2 that are presented in Figure 3.6.  NCs. The simulation results based on this model are presented and discussed in the next section.  4.3  Simulated Transmission & Reflection Spectra  A three-layer model was therefore adopted that had additional parameters to take into account, the refractive index of the interfacial oil layer, no , and its thickness, do . The experimental and modeled reflection and transmission curves using the three-layer structure are shown in Figure 4.5 for two different positions on the sample. The level of agreement between experiment and model suggests that the this new model successfully accounts for the structure of the sample, independently proving the existence of the interfacial oil layer. 43  4.3. Simulated Transmission & Reflection Spectra  Figure 4.5: Simulated reflection (blue) and transmission (red) spectra based on the threelayer model and the corresponding experimental data (green). (a) R1 and T1 presented in Figure 3.6; (b) R2 and T2 presented in Figure 3.6.  Position 1 2  p 1.90 1.65  Nnc 3.18 3.20  dnc (µm) 7.90 7.85  a 0.0191 0.0191  no 1.87 1.87  do (µm) 0.191 0.190  Table 4.1: Simulated parameters based on the three-layer model. The fitting parameters, which are robust with this three-layer model, are presented in Table 4.1. This suggests that the refractive index of the PbS NC film is about 3.2, slightly smaller than the corresponding bulk material value 4.4 (near the absorption edge at 3µm at 300K) [55], while the absorption coefficient of the NC film, given by a · Anc (λ), is shown in Figure 4.6. These values are very close to those recently reported by Nozik et al. [56], which 44  4.3. Simulated Transmission & Reflection Spectra were measured by ellipsometry on thinner films (∼ 100nm) fabricated using a layer-by-layer dip-coating process. They found that the refractive indices of their PbSe NC films were ∼ 3 and that the absorption coefficients were too small to be precisely measured (∼ 0.1 at wavelengths from 1200nm to 1600nm). The simulation also indicates that the refractive index of the oil layer is 1.87, a little higher than that of pure oleic acid 1.46. This suggests that a low concentration of NCs is likely embedded in this layer. While the other simulated parameters are very similar for both sets of data, the power law does depend on sample position, and also the numerical aperture of the optics that collects the transmission (as shown in Section 3.4.3). The exact reason for the sensitivity of this power-law-like scattering to the transmission spectra is not presently understood.  Figure 4.6: Simulated absorption coefficient of an ∼ 8µm thick PbS NC film.  45  Chapter 5  Conclusion & Recommendations For Future Work The thesis described a number of linear spectroscopic studies carried out on colloidal PbSe and PbS nanocrystal films. These were motivated after initial attempts to measure nonlinear, degenerate four-wave-mixing signals from these emulsive films were thwarted by high levels of scattered light in transmission. This Chapter summarizes and draws conclusions from the spectroscopic studies, and makes recommendations for future work.  5.1 5.1.1  Summery & Conclusions Nonlinear DFWM Experiment  In the early stage of this thesis work, the feasibility of conducting degenerate four-wavemixing experiment on colloidal PbSe and PbS nanocrystal films in the transmission geometry was investigated. Two techniques were used to search for DFWM signals. The first involved periodically and continuously varying the time delay between pump and probe pulses, and averaging over many periods the signal measured in the direction where the DFWM signals were expected. The second involved fixing the time delay between pump and probe beams, and using a double modulation and lock-in detection scheme to analyze the signal measured in the expected DFWM directions. In both cases there were large (hundreds to thousands of millivolt) linear scattering signals at the detector that had both DC and interferometric components. Although the lock-in approach reduced these backgrounds, the interferogram due to the superposition of linearly scattered pump and probe beams in the DFWM direction was still tens of millivolts in magnitude. Thus, the forward DFWM geometry is unlikely to yield nonlinear signals that can be reliably extracted from these large linear scattered backgrounds. The possibility of carrying out DFWM experiment 46  5.1. Summery & Conclusions in the backward geometry was then investigated by measuring the scattered beam profile of the light reflected from the NC emulsions. It was found that the DC voltage (at the predicted DFWM position) of the reflected signals on a pure silicon slab and a NC sample were both a few millivolts, significantly less than those measured in the transmission geometry. Therefore, the backward geometry holds some promise for DFWM experiments.  5.1.2  Linear Reflection & Transmission Spectroscopy  The rest of the thesis focused on the linear spectroscopic studies of the PbSe and PbS NC emulsive films. In particular, transmission and reflection spectroscopies were used to characterize drop-cast emulsive films which were deposited on silicon or glass substrates. These were carried out using p-polarized white light incident on the bare substrate at Brewster’s angle, in order to selectively sense the reflection at the substrate/NC film interface, and to avoid substrate-based Fabry-Perot fringes in the transmission spectra. First, the scattering effect in the linear spectra was studied using apertures and polarizers. While the reflection spectra were insensitive to the collection aperture, the transmission spectra were very sensitive to the collection aperture sizes. Both reflection and transmission spectra were essentially p-polarized, indicating little polarization mixing in the scattering process. Second, the structures and optical properties of the PbSe and PbS NC films were studied from a variety of transmission and reflection spectra obtained at different spots of the same sample. It is found that the transmission spectra were very sensitive to the position on the sample, while the reflectivity spectra were relatively insensitive. The average reflectivity varied little over the spectral range of 6000 − 9000 cm−1 from all spots, and the only variation was in the amplitude of Fabry Perot fringes that appeared when probing flat, thin regions of the film. Good fits to the experimental data can only be obtained by assuming there exists a thin interfacial layer with a low refractive index between the silicon substrate and the NC layer. This layer, on the order of 100nm thick, has important consequences for the reflectivity from the sample. The fitting also generates the complex refractive index of the PbS and PbSe NC film and suggests that the scattering from the sample is Rayleighlike and position dependent. A sharp excitonic transition always appears prominent in the transmission spectra measured at different locations of a sample with varying film thickness (a few to tens of microns), or via different collection aperture sizes (1mm to wide open).  47  5.2. Recommendations For Future Work The fact that the height of the excitonic peak in the logarithmic transmission spectra is essentially constant with respect to the power-law background, and the fact that high quality fits to the thin layer reflectivity and transmission spectra could be achieved assuming the absorption spectrum is the same as that measured in solution, provides strong evidence that the fundamental absorption processes at work in these films are not significantly different than in solution. This result is in contrast with previous reports that indicated either that the excitonic peak is washed out in solid films [19][20], or enhanced [56].  5.2  Recommendations For Future Work  This section contains some suggestions for work that could be tried to facilitate further linear and nonlinear spectroscopic studies of the PbSe and PbS NC films.  5.2.1  Lock-in Detection  Section 3.1.1 showed that the lock-in detection technique, as applied there, was incapable of detecting DFWM signals generated from NC films. Here we show that this is largely a pathological consequence of using a square wave modulation of the two beams. In particular, let E1 and E2 denote the electric field amplitudes of the two beams respectively. The DFWM signal is proportional to E14 E22 . If E1 and E2 are square-wave modulated, it then gives at any instant of time, IDF W M ∝ E14 E22 ∝ E1 E2  (5.1)  On the other hand, the interference of the two beams can be written as, Iinter = E12 + E22 + E1 E2 cos(ωτ )  (5.2)  where ω is the angular frequency of the light and τ the delay between the two pulses. Hence, It can be seen that the DFWM signal is proportional to one of the terms in the linear interference, which means no frequency filter would work in this case. Besides, owing to the finite beam size, the modulated signal was not perfectly a square wave, and so it also has even harmonic frequency components. Thus, the obtained interferogram has contributions from the interference of 2f1 component of the delay beam and f2 component 48  5.2. Recommendations For Future Work of the fixed beam. Nevertheless, having shown in Section 2.2.2, a sinusoidal wave modulation of the incident light intensity still holds promise. To be specific, on one hand the DFWM signal under such modulation takes the following form, IDF W M  ∝ I12 I2  (5.3)  ∝ sin(Ω1 t)2 sin(Ω2 t)  (5.4)  = 1/2 sin(Ω2 t) − 1/4 sin[(2Ω1 + Ω2 )t] − 1/4 sin[(2Ω1 − Ω2 )t]  (5.5)  On the other hand, the linear interference term that can obscure the desired signal is, Iinter = E1 E2 cos(ωτ ) ∝  q  q  sin(Ω1 t) sin(Ω2 t)  (5.6)  At this point, it is not clear of the frequency dependency of the interference. Thus, future work should include Fourier analysis of this term and the corresponding values at frequency 2Ω1 +Ω2 and 2Ω1 −Ω2 should be compared with the estimated strength of the DFWM signal at these frequencies. The DFWM can only be effectively measured under the sinusoidal modulation when the contribution from the interference is negligible.  5.2.2  DFWM In Backward Geometry  The DFWM experiment up to now have been attempted in transmission which suffers from the poor optical quality of the sample. However, cross section measurement of the reflected beam and the linear reflection spectroscopy from such sample showed little sign of the above problem. Thus, it is worth trying the DFWM experiment in the backward geometry (reflection) , which in principle can be described as: two pulses arrive and generate a transient polarization grating inside the sample; and this nonlinear polarization in turns emits an electric field En coherently along the new direction ~kn with a phase mismatch of ∆~kn = ~kn − 2~k1 + ~k2 ; two quantities are conserved during the process, namely, • photon energy: |~kn | = 2|~k1 | − |~k2 | • parallel component of wave vector: knk = 2k1k − k2k Consequentially, there are two possible emission directions: forward and backward. A comprehensive computational and experimental analysis of DFWM in reflection can be 49  5.2. Recommendations For Future Work found at [57].  5.2.3  Origin Of The Scattering  It showed that the scattering not only obscures the transmitted DFWM signal but also manifests itself in the transmission spectra. As mentioned before, the scattering could originate from a rough surface or internal inhomogeneity of the NC sample but no significant evidence has been found to prove which-is-which. However, it is certainly a prerequisite to have more knowledge of the scattering, in order to conduct further spectroscopic study on these NC films. To study the scattering, efforts could be spent in two directions: • preparing NC films with an optical surface: methods have been demonstrated in some experiments to achieve an NC film with optical surface finish [7][56]. Although the electronic and optical properties of the NCs may be altered during these processes, e.g. electronic delocalization, making the linear spectroscopic study less effective, cross section profile measurement can still be done to investigate the scattering from such samples. • preparing NC films with different thickness: in this case, a series of NC films with varied thickness should be made by spin coating or drop casting, and linear spectroscopic measurement should be performed at spots of these films where FabryPerot modes take place in the spectra. Since the surface scattering is less sensitive to the film thickness than the internal single or multiple scattering, it may be able to identify them by analyzing the film thickness dependency of the scattering spectra.  50  Bibliography [1] A. L. Efros, Al. L.; Efros. Interband absorption of light in a semiconductor sphere. Sov. Phys. Semicond., 16:772774, 1982. [2] Frank W. Wise. 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Determining the internal quantum efficiency of pbse nanocrystal solar cells with the aid of an optical model. Nano Letters, 8(11):3904–3910, 2008. [57] A. Honold, L. Schultheis, J. Kuhl, and C. W. Tu. Reflected degenerate four-wave mixing on gaas single quantum wells. Applied Physics Letters, 52(25):2105–2107, 1988. [58] Miao Chen and Roger G. Horn. Refractive index of sparse layers of adsorbed gold nanoparticles. Journal of Colloid and Interface Science, 315(2):814 – 817, 2007.  56  Appendix A  Aligning Parabolic Mirror PM1  Figure A.1: Schematic illustration of the way to align PM1. The red solid line is the incident beam and the other lines are reflection from optical components, and they are drawn slightly off each other for the purpose of identification, which should overlap in experiment.  57  Appendix A. Aligning Parabolic Mirror PM1 This section outlines an effective method to align the parabolic mirror PM1 which is one of the key optical components in the DFWM experiment. The desired way to have it is that its optical axis exactly overlaps with that of the whole system. In the experimental setup, the parabolic mirror is usually mounted on a lens/mirror holder and the holder is fixed onto a 3D translation stage. Accordingly, there are 6 degrees of freedom for PM1, among which the three rotation ones are difficult to deal with, and thus a small beam splitter cube (BSC2) and a plane mirror (M13) are introduced to facilitate the alignment. The semiconductor laser beam (red line) is incident onto BSC2 along the optical axis of the system, and an aperture is placed in the path of the laser beam with the size equal to it waist. The mirror M13 is glued to the back of PM1 by a piece of flat double-side tape. After having all the above components ready, the alignment is carried out as follows: 1. Adjust BSC2 and make the reflection from its front surface (red dashed line) hit the center of A6. 2. Move PM1 until the reflection from BSC2 (red solid line) can reach mirror M13, and then adjust the holder of PM1 until the reflection from M13 (blue dashed line) bounces backward and hits the center of A6. So far, two rotation degrees of freedom of PM1 have been set properly, and the third one which allows PM1 to spin can be set by making the two pinholes on its back in the same height. 3. The Mirror M10 can be inserted right now and it should be set up according to the reflection from M13 (blue solid line). 4. After M10 is set up properly, BSC2 can be removed from the setup. 5. The 3D translation stage where PM1 sits should be adjusted until the beam after M10 is parallel to the incident beam e.g. red dashed line. 6. At the last step, the semiconductor laser can be switched off and the two OPO beams should be introduced, which helps align PM1 along its optical axis (z direction). The stage that only controls the movement along z direction should be adjusted until the two OPO beams after PM1 are parallel to each other over a long distance.  58  Appendix B  Aligning Autocorrelator The following tips are mainly contributed by Luke Sandilands who did a lot of earlier work in designing and setting up the DFWM experiment. First, you should make sure the optical paths of the fixed and delay arms are as close as you can get them by eye. You can measure the paths with a ruler and/or some string. The other important thing is to ensure the beams overlap. You need to make sure the two beams are as parallel to optical axis of the correlator lens as possible as well as symmetric about it. You can check that they overlap using a pinhole. The pinhole mount and the crystal mount aren’t quite the same however (the pinhole isn’t on the axis of the post), so if you find the overlap you need to move the crystal along the optical axis a small amount. I think you could measure it. Only one side of BBO will produce SHG. This is due to the way the crystal is cut. A good thing to do which I found quite helpful was to use a lens to image the two beams after the crystal onto a CCD. You can then observe SHG from each beam individually in this manner. You also need a bandpass filter at the SH frequency to block out the IR beams. Each beam will produce a maximum SHG at different angle so you can measure this and then set the crystal to the midpoint of these two angles when you go to search for the autocorrelation function. You should also of course be able to determine which way you need to rotate the crystal using this method. You should also find the crystal position along the optical axis that maximizes the SHG. As for wavelength, I would use about 1500 nm or so. I think you get higher power at this value which makes finding the signal easier. Also if you use a bandpass a bandpass filter you should make sure that it passes the SH of whatever frequency you use. So to recap you should align the beams as parallel as possible, align the autocorrelator lens as well as possible, ensure the paths are as close to equal as possible, check the overlap with a pinhole (it should be really well overlapped if you aligned the beams/lens properly), then put in the crystal and use the CCD to find a good position and angle for the crystal. 59  Appendix B. Aligning Autocorrelator Then put in your detector in between the two beams. You can then start looking for the signal. To look for signal, I would turn the shaker on with a fairly large amplitude and then vary the path difference slowly while observing the detector output with the scope. You can also try averaging (e.g. 4 samples) if you trigger off the shaker I think. Hopefully you see little autocorrelation spikes. You can then optimize the detector, crystal and autocorrelator lens to maximize this signal.  60  Appendix C  Calculating Effective Refractive Index Of NC Films The effective refractive index of PbS (PbSe) NC film is estimated by the Maxwell-Garnett Theory [58]. In particular, it calculates the effective dielectric function ef f = (nef f −iκef f )2 for spherical particles having dielectric constant s embedded in a medium 0 ,  ef f = 0  s (1 + 2f ) + 20 (1 − f ) s (1 − f ) + 20 (2 + f )  (C.1)  where f is the volume filling factor. In the calculation, the dielectric constants for PbS crystal and oleic acid are s = 25 − 4.5i and 0 = 2.25, respectively. Assume the all the NCs in the emulsive film are close-packed and form a face-centered cubic structure which has the biggest volume filling factor 0.68. Plugging these numbers into (C.1) yields the dielectric constant of the PbS NC film is 9.76 − 0.70i and thus its effective refractive index is 3.12 − 0.11i.  61  

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