RICE UNIVERSITY. Fourier Transform Infrared Spectroscopy of 6.1-Angstrom Semiconductor Quantum Wells by Jun Tang A THESIS SUBMITTED

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1 RICE UNIVERSITY Fourier Transform Infrared Spectroscopy of 6.1-Angstrom Semiconductor Quantum Wells by Jun Tang A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE Master of Science APPROVED, THESIS COMMITTEE: Junichiro Kono, Chair Assistant Professor of Electrical and Computer Engineering Frank K. Tittel J.S. Abercrombie Professor of Electrical and Computer Engineering William L. Wilson, Jr., Professor of Electrical and Computer Engineering HOUSTON, TEXAS April, 2002

2 ABSTRACT Fourier Transform Infrared Spectroscopy of 6.1-Angstrom Semiconductor Quantum Wells by Jun Tang The 6.1-Angstrom (Å) family of III-V semiconductors InAs, GaSb, and AlSb and their alloys and heterostructures has unique properties that may find application in next generation multi-functional semiconductor devices. In this project, we investigate intersubband transitions in 6.1-Å quantum wells. The short-term objective is to explore high-photon-energy (or short-wavelength) intersubband transitions that are expected to occur in these systems due to their extremely large conduction-band offsets. The ultimate goal of this project is to construct a solid-state terahertz (THz) emitter based on 6.1-Å quantum wells under intersubband pumping. We have established reliable and reproducible sample preparation methods for measuring intersubband transitions using Fourier-transform infrared spectroscopy. In particular, we observed intersubband transitions in 6.1-Å quantum wells in a previously unexplored short-wavelength range. We systematically studied intersubband transition energies, intensities, and linewidths as functions of well width and temperature, and compared the results with calculations based on an 8-band k p theory. Experimental methods, experimental results, and discussion will be presented in detail. Furthermore, transmission electron microscopy (TEM) was used to assess the quality of interfaces in 6.1-Å quantum wells. A description is given for the sample preparation procedure together with some TEM pictures. 2

3 Acknowledgements I am very thankful to my advisor Dr. Junichiro Kono for his enormous technical and moral support. I would like to thank Dr. Frank K. Tittel and Dr. William L. Wilson for serving on my Thesis Committee. I would like to thank Professor Masataka Inoue and Professor Shigehiko Sasa and their group at the Osaka Institute of Technology for providing high quality samples and Dr. Cun-Zheng Ning at NASA Ames Research Center for providing theoretical support. I am also grateful to Dr. Marie P. Johnson for helping me to fix all grammatical errors; otherwise I would not have been able to put my thesis together in time. I owe thanks to my colleagues and fellow graduate students, Jigang Wang, Diane C. Larrabee, Bruce Brinson, Dr. Zhiqiang Chen and Dr. Giti A. Khodaparast for their help and valuable discussions. 3

4 Table of Contents Abstract Acknowledgements Table of Contents List of Figures List of Tables ii iii iv vi x 1. Introduction Angstrom Semiconductors Semiconductor bandgap engineering Properties of 6.1-Å quantum wells 5 3. Intersubband Transitions and Infrared Generation Intersubband transitions in quantum wells Envelope function approximation Theory of intersubband transitions Short-wavelength intersubband transitions Optically-pumped quantum wells for infrared generation The quantum fountain laser Far-infrared difference frequency generation in semiconductor heterostructures Proposed schemes for terahertz wave generation Motivation for terahertz wave generators Laser scheme Difference frequency generation scheme How to implement THz generators Samples Studied and Experimental Methods Samples studied Fourier-transform infrared (FTIR) spectrometer Methods to measure interband transitions 38 4

5 4.4 Methods to measure intersubband transitions Brewster angle incident measurements Multipass geometry measurements Parallelogram geometry Trapezoid geometry Optical modulation for ISBT measurements Experimental Results and Analyses Interband measurements Interband measurements on InGaAs quantum wells Bulk InAs bandgap measurements Multi-reflection interference fringes in InAs/AlSb quantum wells Theoretical derivation for the wavelength independent coating The periodicity of multi-interference fringes Intersubband measurements Intersubband transition energy vs. well width Intersubband transition energy vs. temperature Intersubband transition linewidth vs. well width and temperature ISBT integrated absorption intensity Transmission Electron Microscopy Introduction to transmission electron microscopy TEM specimen preparation TEM photomicrographs for 10 nm InAs well Conclusions and Future Work 73 References 74 5

6 List of Figures 1. An illustration of a semiconductor quantum well and confined states Lattice constants and bandgaps of some semiconductors Schematic band diagram for InAs/Al x Ga 1-x Sb single quantum wells Band diagrams of InAs/AlSb and GaAs/AlAs quantum well Graphical solutions for Equations (9) and (11). Solutions are located at the intersections of the straight line with slope k with curves y = cos kl / 2 (even wave functions) or y = cos kl / 2 (odd wave functions) Conduction band energy vs. in-plane wavevector and joint density of states of intersubband transitions and interband transitions. Adopted from [13] Layer structure of a square QW sample for near-infrared ISBTs [14] and 1-4 absorption spectra for a coupled InGaAs/AlAs QW sample [14] Conduction band profile of the coupled quantum wells in a quantum fountain laser [6]. The wavy lines indicate the pump and emission intersubband transitions Emission spectrum of the quantum fountain laser at 77K, showing stimulated emission. [6] A schematic illustration of difference frequency generation used in [6] The band diagram and subband positions of a single period of the MQW used in [22] Far-IR power as a function of photon energy difference between the pump beams at 7 K. [22] An illustration of the conduction band diagram of a sample in the laser scheme The conduction band diagram and wavefunctions of an AlSb/InAs triplewell structure, calculated by Dr. Cun-Zheng Ning s group at NASA Ames Research Center

7 16. The four lowest energy levels with corresponding wavefunctions for an In 0.53 Ga 0.47 As/AlAs 0.56 Sb 0.44 /InP/AlAs 0.56 Sb 0.44 /InP triple quantum well structure biased with a dc electric field of 25 kv/cm THz gain spectra (without pump-probe coherence) for different pumping intensities. The maximum gain as a function of the pump intensity is shown in the inset THz gain spectra calculated including the Raman enhancement for different pump intensities with pump-probe coherence included An illustration of the conduction band diagram of the sample to be used in our difference frequency generation scheme The conduction band diagram and wavefunctions of an InAs/AlSb double QW structure, calculated by Dr. Cun-Zheng Ning s group at NASA Research Center Calculated wave functions for a THz wave generator based on DFG [11] Second-order susceptibility vs. applied dc voltage [11] A picture of sample cross-section taken by transmission electron microscopy A block diagram of FTIR A typical interferrogram taken with a globar source, a KBr beamsplitter, and a MCT The Fourier transform of the interferrogram in Figure Illustration of setup for the interband measurements Illustrative band diagrams for sample 209 doped and undoped Illustration of Brewster angle incident measurement The ratio of two samples transmission spectra (209 doped/209 undoped) measured in the Brewster-angle geometry Parallelogram geometry for intersubband transition measurements Electric field distribution for coated and uncoated MQWs Absorption spectrum of sample 209 doped taken using the parallelogram geometry shown in Figure Trapezoid geometry for intersubband transition measurements. 45 7

8 35. Absorption spectrum of sample 209 doped taken using the trapezoid geometry shown in Figure Control signal from the Sample Shuttle program Near-infrared transmission spectra for (a) doped and (b) undoped InGaAs quantum wells Measured E1-H1 energy and calculated InGaAs bandgap vs. temperature. E C, E V, E F are the energy levels of conduction band, valence band, and Fermi energy respectively Transmission spectrum for an InAs film grown on GaAs. The spectrum is normalized to that of a GaAs substrate Measured and calculated InAs bandgap Transmission spectra of InAs/AlSb QW before and after anti-interference coating (200Å NiCr) Incident, transmitted and reflected electric and magnetic fields at the interface of two dielectrics with indices of refraction n 1 and n 2 with a surface charge of conductivity σ and thickness d. [30] Illustration of multi-reflection interference Intersubband resonances observed for InAs/AlSb quantum wells with different well widths at various temperatures Theoretical and experimental results for the well width dependence of the E 1 -E 2 separation in InAs/AlSb QWs at 300K (Calculation by Dr. Cun-Zheng Ning from NASA Ames Research Center) The temperature dependence of the observed ISBT energies for four InAs QW samples with different well widths ISBT linewidth vs. temperature and well width Integrated ISBT absorption intensity for InAs/AlSb multiple quantum wells with different well widths at 4.5K and 300K Interband photoluminescence energy and intersubband absorption energy versus well width for InAs/AlSb multiple quantum wells (PL data taken by Prof. M. Inoue s group at Osaka Institute of Technology) An illustration of the acceptance angle of objective lens. 64 8

9 51. A diagram of TEM An illustration of the specimen stack A picture of dimple grinder and post-dimple specimen Specimen under iron guns TEM picture taken at 50k magnification of 10nm InAs/AlSb well TEM picture taken at 200k magnification Two pictures taken at 1M magnification. 72 9

10 List of Tables 1. Structures of Samples 209 doped and undoped Detailed structure of InAs/AlSb QWs The spectral ranges of Jasco-660 FTIR accessories 38 10

11 Chapter 1 Introduction Semiconductor heterostructures, which have been under extensive research investigations in recent years, is a very appealing field with many potential applications. Infrared (IR) detectors and lasers can be made using electronic transitions between quantum-confined states in semiconductor heterostructures within the conduction band or the valence band, instead of interband transitions across the bandgap in a traditional device. With the aid of molecular beam epitaxy (MBE), the thickness of each layer in a semiconductor heterostructure can be precisely controlled and continuously tuned. Thus, the separation between the confined states can be almost continuously changed for different wavelength applications [1]. A good example is the wide output wavelength range, from 4 µm to 24 µm [2], of the quantum cascade laser (QCL) [3, 4] whose core is a GaAs/AlGaAs multiple quantum well (MQW). Among all the possible applications of semiconductor heterostructures, terahertz (THz) wave generators have been receiving much attention. Due to their current availability, limitations and further potential applications, they continue to attract much interest in semiconductor industry and research. Several groups have been devoting their work at solving some of the inherent problems in the development of THz QCLs [5]. 1. Internal loss of the radiation due to free carrier absorption. This loss is proportional to λ 2 and becomes quite strong towards long-wavelengths. 2. Strong electron-electron scattering due to the high density of injected electrons which severely reduces the population inversion. 11

12 These problems can be circumvented by using optical rather than electrical pumping, which removes the need for doped layers and contacts. An example of optical pumping is the successful quantum fountain laser using GaAs/AlGaAs asymmetrical double quantum wells, operated in the mid-infrared (MIR) regime [6]. However, a CO 2 laser must be used to provide the 120 mev pump due to the small conduction band offset (~300 mev) at the GaAs/AlGaAs heterojunction; the bulky size of the CO 2 laser makes quantum fountain lasers impractical for everyday applications. In addition, the emission photon energy is restricted to be the difference between the pumping photon energy and the LO phonon energy, i.e., there is no flexibility in wavelength design. 6.1-Å compound semiconductors refer to InAs, AlSb, GaSb and their alloys. Their lattice constants match quite well, making them suitable for semiconductor bandgap engineering. More importantly, the extremely large conduction band offset (~ 2 ev) between InAs and AlSb gives greater design flexibility than GaAs/AlGaAs based heterostructures. Also, the large conduction band offset makes optical pumping by a near-infrared (NIR) laser diode and the integration of the pumping and lasing system possible. More details will be covered in the following chapters. Some unique properties of 6.1-Å materials and their applications are reviewed in Chapter 2. Next, theoretical descriptions of intersubband transitions and previous work done by other groups and possible improvements are presented. Two THz generation schemes and their plausibility are discussed, followed by experimental milestones to implement the schemes. Then the data collection methods and experimental results will be presented in Chapters 4 and 5. In Chapter 6, TEM specimen preparation and pictures are presented. Conclusions and future work are described in Chapter 7. 12

13 Chapter Angstrom Semiconductors 6.1-Å semiconductors refer to InAs, AlSb, GaSb and their alloys. This chapter will first describe the idea of semiconductor bandgap engineering. Then the unique properties of 6.1-Å materials will be presented. 2.1 Semiconductor bandgap engineering A semiconductor quantum well is comprised of a thin layer of a narrow bandgap semiconductor sandwiched by two layers of a wide bandgap semiconductor. The interfaces are called semiconductor heterojunctions. There will be confined quantum states (Figure 1) within the conduction band or the valence band (also called subbands) if the center layer is thin enough. Transitions between subbands are called intersubband transitions (ISBT). Conduction band ISBT E2 Confined states E1 material A material B Valence band H1 H2 Confined states Well width (L) 0 z Figure 1. An illustration of a semiconductor quantum well and confined states. 13

14 From quantum mechanics, we know that the position and number of confined states can be varied by changing the well width and the band offset (well depth). This provides the basic concepts of semiconductor bandgap engineering: changing the energy separation between confined states by changing the quantum-well well width or the alloy composition of the barrier material using molecular beam epitaxy (MBE) or chemical vapor deposition (CVD). Since MBE can deposit material with atomic level precision, the energy separation between the subbands can be tuned almost continuously. However, semiconductor heterojunctions and quantum wells can be formed only between certain semiconductors, those whose lattice constants match well, such as GaAs and AlAs as shown in Figure 2. 3 Band Gap (ev) 2 1 AlP GaP Si AlAs GaAs Ge InP AlSb GaSb InAs InSb Lattice Constant (A) Figure 2. Lattice constants and bandgaps of some semiconductors. 14

15 As we can see in Figure 2, 6.1-Å semiconductors are also quite good for this purpose. Their lattice constants are all around 6.1 Å. 2.2 Properties of 6.1-Å quantum wells In this section, some unique properties of 6.1-Å systems are described. Probably the most interesting and important property is the so-called type-ii band alignment of InAs/Al x Ga 1 x Sb heterostructures, i.e., the band gap of InAs is not contained in the band gap of Al x Ga 1 x Sb, unlike the standard (type-i) case shown in Figure 1. In particular, the bottom of the conduction band of InAs lies below the top of the valence band of GaSb (type-ii broken-gap ). Figure 3 shows an ideal band diagram of Al x Ga 1 x Sb/InAs/Al x Ga 1 x Sb without including any band bending. The effective bandgap can be varied over a wide range (from 0.15 ev to 0.3 ev) by changing the Al content, x. The system can be either semiconducting or semimetallic (Figure 3) [7]. Also the electrons and holes are spatially separated and confined in different layers. Al x Ga 1-x Sb/InAs/Al x Ga 1-x Sb x = 0 x = 0.3 x = 1 CB VB 0.8 ev 0.4 ev 2.3 ev E g = ev E g = - 0 ev E g = 0.3 ev Semimetallic Semiconducting Figure 3. Schematic band diagram for InAs/Al x Ga 1-x Sb single quantum wells. 15

16 The maximum conduction band offset at the InAs/Al x Ga 1 x Sb heterojunction is ~2 ev (when x = 1), a huge value compared to the typical offset at traditional GaAs/Al x Ga 1 x As heterojunctions (< 0.5 ev). The large conduction band offset gives great flexibility in the quantum engineering of energy levels and wavefunctions. In particular, intersubband transitions can be designed to occur in the NIR region. This is impossible to do with GaAs/Al x Ga 1 x As structures. Consequently, this makes 6.1-Å quantum wells ideal for IR detectors and lasers. Conduction band E 2 E 2 E 1 ISBT < 0.5 ev ISBT 2.1 ev 1.5 ev E 1 Valence band 0.4 ev AlSb/InAs/AlSb AlAs/GaAs/AlAs Figure 4. Band diagrams of InAs/AlSb and GaAs/AlAs quantum well. Another interesting aspect is that there is always a high electron concentration on the order of cm -2 found in not-intentionally doped wells. Most of the electrons are believed to come from surface donors and the electron density can be adjusted by changing the top GaSb barrier layer thickness, i.e., the distance from the donors to the InAs well. Furthermore, the electrons in InAs wells have small effective masses (bandedge mass = 0.023m 0 ) compared to the electrons in GaAs wells (band-edge mass = 0.067m 0 ). Correspondingly, the electron mobility of InAs is much higher,

17 cm 2 /Vs at room temperature, than that of GaAs. Also this material system has large nonparabolicity and large g factor. Additionally, these two-dimensional electron gases (2DEG) with high-mobilities have led to many interesting experimental observations: Negative persistent photoconductivity (NPPC) illuminating the sample at lowtemperature reduces the carrier concentration of the 2DEG in the InAs well. In contrast, persistent photoconductivity (PPC) happens in GaAs/Al x Ga 1 x As systems. This can be explained by the relative position of the Fermi level and the deep donor level in the barrier layers. In GaAs/Al x Ga 1-x As systems, the deep donor level is lower and carriers reside at this level at low temperature. When illuminated carriers are photoexcited to the Fermi level and the carrier density increases (PPC). In InAs/Al x Ga 1 x Sb systems, due to the deep potential, the Fermi level lies below the deep donor level of AlGaSb layer (many electrons in the well without intentional doping). Due to illumination, the electrons will be photoexcited and captured by the donors and the carrier concentration will decrease (NPPC) [8]. Zero-field spin splitting (Rashba effect) the splitting of an electron subband without applying any magnetic field. An asymmetric system creates an electrical field perpendicular to the layer, which is converted into an effective magnetic field that interacts with an electron moving along the layer. This equivalent magnetic field leads to a finite spin splitting even without any external magnetic field. This effect can happen in InAs/AlGaSb systems because of the large spinorbit coupling [9]. 17

18 Chapter 3 Intersubband Transitions and Infrared Generation This chapter will first introduce the physics of intersubband transitions in quantum wells and then review two examples of GaAs/AlGaAs-based IR generators the quantum fountain laser and difference frequency generation (DFG) using the secondorder nonlinearity of a GaAs/AlGaAs quantum well. Next how they can be improved by using 6.1-Å materials will be described. Two THz wave generation schemes are introduced here, one is a laser scheme and the other is a DFG scheme. Their feasibilities are discussed by reviewing two theory papers [10, 11]. How the two schemes can be implemented is described in the final section. 3.1 Intersubband transitions in quantum wells This section will introduce the intersubband transition (ISBT) in a single square quantum well, which is formed by a sufficiently thin layer of material A embedded between two thick layers (thickness much greater than the penetration length of the confined wave functions) of materials B, where B has a bandgap larger than A. Figure 1 shows the band diagram of an ideal single square well. It has two assumptions: Ideal interfaces. For z > L/2, the electron experiences a potential the same as in a perfect bulk B material; for z < L/2, the electron experiences a potential the same as in a perfect bulk A material. Perfect lattice matching. The relative lattice mismatch δa/a between A and B is less than 0.1%. The GaAs-GaAlAs system satisfies this condition. For InAs-AlGaSb, the 18

19 lattice mismatch is larger than this criterion (over 0.6%), so that strain effects have to be taken into account in calculations [12]. An electron in an ideal square quantum well formed in the conduction band can be simplified as a particle of mass m* subjected to a potential energy V b (z) V b 0 ( z) = V 0 z > L / 2 z < L / 2 (1) where L is the thickness of the quantum well (Figure 1) Envelope function approximation The confined electron states can be calculated using the envelope function approximation, which has two basic assumptions [12]: 1. The interface potential is well localized at the A B interface so that inside each layer the wavefunction can be expanded by the cell-periodic parts of the Bloch wave functions. 2. The cell-periodic parts of the Bloch functions are assumed to be the same throughout the entire heterostructure. So, the heterostructure wavefunction can be written as ψ ( r) z (2) ik = r e uck ( r) χ n ( ) where z is the growth direction, k is the bi-dimensional wavevector which is parallel to the heterostructure interface, u ck (r) is the cell-periodic part of the Bloch wavefunction in A or B material (the same), and χ (z) is the envelope wavefunction, determined by the Schrödinger equation, n 2 2 h 2 2m *( z) z [ 2 + V ( z)] χ ( z) = ε χ ( z) b n n n (3) 19

20 where m*(z) is the effective electron mass, ε n is the confined energy levels which exist for energies ε such that V ε 0 and χ n (z) is the confined wave functions. 0 < χ n (z) must satisfy the following boundary conditions: χ n (z) and m 1 * ( z) z be continuous at the interfaces and lim χ ( z) z = 0 for bounded states. For simplicity, let us assume the carrier mass m* to be both position and energy independent. Then the solution wave functions are Acos kz χ n ( z) = B exp[ κ ( z L / 2)] B exp[ κ ( z + L / 2)] z < L / 2 z > L / 2 z < L / 2 for even states, (4) or Asin kz χ n ( z) = B exp[ κ ( z L / 2)] B exp[ κ ( z + L / 2)] z < L / 2 z > L / 2 z < L / 2 for odd states, (5) where 2m * k = ( ε + h 2 V 0 ) 2m * ε and κ =, (6) 2 h Thus, 2 2 k ε n = h V0. (7) 2m * For even states, the boundary conditions at z = L/2 yield Acos( kl / 2) = B. (8) kasin( kl / 2) = κb Therefore, cos( kl / 2) = k / k, (9) 0 20

21 where k = 2m * V = k + κ. (10) 2 For odd states a similar procedure generates 0 h sin( kl / 2) = k / k. (11) y Slope k n = 4 n = 3 n = 2 n = 1 Figure 5. Graphical solutions for Equations (9) and (11). Solutions are 1 located at the intersections of the straight line with slope k 0 with curves y = cos kl / 2 (even wave functions) or y = cos kl / 2 (odd wave functions). The equations can be solved graphically (Figure 5). There is always one bound state. The number of bound states is π/2 π 3π/2 2π kl/2 2 2m * V0L 2 1+ Int[( ) 1/ ] (12) 2 2 π h where Int[x] indicates the integer part of x. As V 0 increases, the number of bound states increases. For an infinite quantum well (V 0 ), there are an infinite number of bound states and their corresponding energies are given by 21

22 E n π h n =, n = 0, 1, 2, (13) 2 2m * L Theory of intersubband transitions Electrons in a quantum well can make transitions between subbands through the absorption or emission of photons. There is an additional term in the Hamiltonian of the electrons related to the electric field intensity of the radiation, due to the interaction between the electrons and the radiation field, leading to electronic dipole oscillation. Using first-order perturbation theory (the additional interaction as a perturbation), the intersubband transition probability from the initial state (i) to the final state (j) is proportional to the square of the momentum matrix element (p if ) [12] p if = ih ψ ψ (14) fk ' ik where ψ ik and ψ fk represent the wave functions for the initial and the final states, respectively. Based on the envelope function approximation, these can be written as ψ ψ ik fk ' = u ck = u ( r) χ ( r) ck ' i ( r) χ ( r) f (15) χ i (r) and χ f (r) denote the envelope functions given by Equation (3). So we obtain p if = χ ( r) p χ ( r) ( m0 / m*) (16) f i For a well grown in the z direction, the electrons are confined only in the z direction, so only the z component of the matrix element is nonzero. This is the first selection rule of intersubband transitions: the radiation must propagate parallel to the interfaces of the quantum well so that the electric field has a component in the growth direction. In the case of single square quantum wells, χ i (r) and χ f (r) are required to have opposite parity to a non-zero value for the matrix element. This is the second selection 22

23 rule of intersubband transitions. The oscillator strength, which gives the strength of the equivalent oscillating dipole, is defined as f 2 2 = χ f ( z) p χ i ( z) (17) m * ωh It is a good measure of the strength of a transition. Right now, we just treat the electrons as independent particles. It ignores many-body effects, such as the depolarization shift, which is due to the dynamic screening of the applied field by resonantly induced dipoles. The transition energy should be the energy difference of the electron at the initial state and final state. The electron s energy relative to the conduction band edge can be written as 2 h E( k) = ( k x + k y + k z ) 2m *, n = 1, 2, 3, (18) k L = nπ z where L is the well width. Figure 6 shows a plot of the electron energy vs. magnitude of its in-plane wavevector. Because of the conservation of momentum, the intersubband transition is vertical in Figure 6 (the momentum of photons is negligible). This energy is independent of the in-plane momentum. So the intersubband transition will correspond to a sharp peak. Normally this peak is broadened by scattering and non-parabolicity of the energy band. This is in contrast to an interband transition, which is a continuum absorption above the band gap. Figure 6 also shows the density of states for both intersubband transitions and interband transitions. 23

24 E n = 3 n = 2 n = 1 k - Density of States 1->2 Intersubband transition 2->3 Interband transition hν Figure 6. Conduction band energy vs. in-plane wavevector and joint density of states of intersubband transitions and interband transitions. Adopted from [13] Short-wavelength intersubband transitions Intersubband transitions in the conduction band of a QW have been widely implemented for applications as photodetectors, optical modulators, nonlinear optics and MIR lasers. However, they are restricted to long wavelengths due to the small GaAs/AlGaAs conduction band offsets (< 0.5 ev). There are numerous efforts to increase the ISBT energy to the optical communication regime (the NIR range) due to its potential applications in the development of ultrafast switches or modulators, wide wavelength range detectors, and NIR lasers. One approach is ISBTs in high indium content InGaAs/AlAs QWs (whose conduction band offset is adjustable by the content of indium). However, the lattice mismatch between InGaAs and AlAs limits the indium content and number of QWs that can be grown. This can be solved with an InGaAs buffer layer with linearly graded indium composition prior to the growth of multiple QWs (Figure 7) [14]. Using the same method, J. H. Smet et al. were able to achieve an 24

25 ISBT at 0.8 ev (1.55 µm) [15] in a 3 monolayer (ML) sample. Several other materials systems have been used for achieving NIR ISBTs: T. Mozume et al. achieved 1.45 µm (0.85 ev) in InGaAs/AlAsSb quantum wells [16]; R. Akimoto et al. observed 1.6 µm intersubband transitions in ZnSe/BeTe type-ii superlattices [17];and C. Gmachi et al. achived 1.55 µm in GaN/AlGaN multiple quantum wells [18]. Figure 7. Layer structure of a square QW sample for near-infrared ISBTs [14] Coupled double QW samples have been also used [14] for short-wavelength ISBTs. The sample used in [14] had 100 periods and each period consisted of 10 ML and 7 ML In 0.5 Ga 0.5 As separated by a 3 ML AlAs barrier (see inset of Figure 8). They observed 3 absorption peaks: 1-2, 1-3 and 1-4 (only 1-3 and 1-4 peaks shown in Figure 8). The 1-3 and 1-4 transition energies were 0.53 ev (2.34 µm) and 0.78 ev (1.59 µm), respectively. A coupled QW can be designed to have 1-3 and 1-4 transition strengths comparable to the 1-2 transition by adjusting the envelope function overlap (electric dipole matrix elements). This is impossible in single QWs because the 1-3 transition is forbidden (non-overlapping envelope functions) and the 1-4 transition is much weaker than the 1-2 transition. More recently, ISBTs at 1.3 µm and 1.55 µm in a coupled InGaAs-AlAsSb DQW were reported by A. Neogi et al. [19]. 25

26 Figure and 1-4 absorption spectra for a coupled InGaAs/AlAs QW sample [14]. 3.2 Optically-pumped quantum wells for infrared generation In this section, experimental work [6, 22] by two groups will be reviewed: quantum fountain laser and far-infrared generation using difference generation The quantum fountain laser First, I would like to briefly introduce how a laser works. The active material of a laser is a three level system and a population inversion is formed between two of them so that it can be used as a light amplifier by stimulated emission. Then the active material is placed in a resonant cavity. The spontaneous emission is bounced back and forth and narrowed within the cavity and is amplified until the threshold value is reached before it is produced as the output of the laser [20]. The quantum fountain laser [6, 21] reported by O. Gauthier-Lafaye et al. in 1997 clearly shows how semiconductor heterostructures can be designed to work as an optically-pumped MIR laser. The core region of the quantum fountain laser is a simple three-level system formed in a GaAs/AlGaAs asymmetrically coupled double quantum 26

27 well. The conduction band diagram and confined subband wavefunctions are depicted in Figure 9. Only three levels are related to the laser action. The E 1 -E 3 and E 2 -E 3 intersubband transitions were found to occur at energies of 119 and 80 mev, respectively, with a 10 mev linewidth at 300 K. In equilibrium, most electrons reside in the ground state. A CO 2 laser was used as the optical pump to pump the electrons from the ground state to the E 3 level. The E 1 -E 2 energy difference is 39 mev (close to the optical phonon energy: 36 mev in GaAs), which is designed to take advantage of the optical phonon resonance, quickly depopulating the electrons in the E 2 level. This way they were able to create an electron population inversion between the E 3 and E 2 states. 119meV 80meV 39meV Figure 9. Conduction band profile of the coupled quantum wells in a quantum fountain laser [6]. The wavy lines indicate the pump and emission intersubband transitions. Figure 10 shows the stimulated emission from state E 3 to E 2 at 77 K [6]. The emission peaked at 80 mev (approximately 15.5 µm wavelength) with a width of less than 1 mev. This was much smaller than the linewidth of the spontaneous emission at 77 K, which was around 10 mev. Therefore, this was a clear indication of laser action. The output power of the stimulated emission changed little at temperatures below 80 K, but dropped sharply above 80 K and laser emission vanished at 110 K. This is due to thermal 27

28 population of the subband E 2 which destroyed the population inversion. This work clearly demonstrated that optical pumping can also create electron population inversion just like electrical pumping used in a quantum cascade laser (QCL). Also optical pumping significantly simplifies the design complexity by removing the doped layers and contact layers. However, a bulky CO 2 laser has to be used to provide the 119 mev pumping energy. This can be improved by incorporating InAs/AlSb MQWs instead of GaAs/AlGaAs MQWs as the active material, in which E 1 and E 3 levels can be positioned at larger separations so that a compact laser diode can be used to provide the pump energy. Figure 10. Emission spectrum of the quantum fountain laser at 77 K, showing stimulated emission. [6] Far-infrared difference frequency generation in semiconductor heterostructures Semiconductor heterostructures, such as quantum wells, can be used for tunable wave generation by DFG. New nonlinear crystals with an extremely large second order nonlinear susceptibility, χ (2) (ω 3 = ω 1 ω 2 ), in the IR region can be created by MBE and band-gap and wave function engineering. Here ω 1 and ω 2 are the angular frequencies of 28

29 the pump beams. These beams, through nonlinear interaction with the material, set up electron oscillations, which act as the source for the desired wave at frequency ω 3 = ω 1 ω 2 [23]. Of course, the polarization of the pumping beams must be parallel to the quantum well growth direction, as determined by the ISBT selection rule. The electron oscillations are optically excited via intersubband transitions in the coupled quantum wells, and the second-order nonlinear susceptibility χ (2) is described by χ (2) 3 e N ( ω3 = ω1 ω2 ) = ε ( E 0 23 z13z23z12 hω + iγ )( E hω + iγ 1 13, (19) ) where ε 0 is the permittivity of vacuum, N the electron density in the wells, e the electronic charge, z 13, z 23, z 12 the relevant matrix elements, E ij the energy of the i j transition, and Γ ij the corresponding transition linewidths (HWHM). E 3 E 2 ω 3 ω 1 ω 2 E 1 Figure 11. A schematic illustration of difference frequency generation used in [6]. From equation (19), it can be seen that the following procedures can enhance the nonlinear susceptibility χ (2) : 1. taking advantage of doubly resonant effects (ħω 3 = E 3 E 2; ħω 1 = E 3 E 1 ). 2. modifying the wave functions to maximize the product of z 13, z 23, z

30 3. minimizing the linewidths of the relevant transitions by modulation doping. Electrons are introduced in the well by doping only the barrier regions, which can strongly reduce scattering and thus the linewidths of the intersubband transitions. The first direct observation of far-ir generation by DFG in association with the DFG within semiconductor heterostructure was done at the AT&T Bell Laboratory by C. Sirtori et al. in 1994 [22]. The heterostructure they used was grown by MBE on a semiinsulating GaAs substrate. It was comprised of fifty modulation doped coupled double quantum wells. Each period (Figure 12) consisted of two wells, 61 and 70 Ǻ thick, respectively, separated by a 20 Ǻ Al 0.33 Ga 0.67 As barrier. The periods were separated by 950 Ǻ Al 0.33 Ga 0.67 As barrier layers. Electrons were modulation doped in the barrier layers and the resulting electron sheet density in the wells was 4.1 x cm meV 122meV 14meV AlGaAs/GaAs/AlGaAs/GaAs/AlGaAs Figure 12. The band diagram and subband positions of a single period of the MQW used in [22]. By applying two CO 2 laser beams as pumps (resonant with E 1 -E 3 and E 2 -E 3 transitions, respectively), the output wave at a third frequency ω 3 (20.5 mev) was observed. It was slightly larger than the E 1 -E 2 peak position (19.3 mev) obtained by 30

31 absorption measurements. They also observed that the power of the output beam was proportional to the product of the power of the two pump beams and the relation of the output beam s relation to the pump beams polarization angles, which confirmed that the ω 3 wave is the DFG output. The maximum second-order nonlinear susceptibility χ (2) (Figure 13 inset) of their sample was ~ 1.0 x 10-6 m/v, many orders larger than in bulk semiconductors and other media at similar wavelengths. Again they used CO 2 lasers as pumps and the power of each pump beam was 100 mw. Figure 13. Far-IR power as a function of photon energy difference between the pump beams at 7 K. [22] 3.3 Proposed schemes for terahertz wave generation Motivation for terahertz wave generators Coherent and intense terahertz (THz) waves (within the frequency range from 100 GHz to 10 THz) have a wide range of applications, including chemical, biological, and 31

32 astrobiological detection; environmental sensing, and pollution monitoring; materials and security inspection; collision avoidance for aircrafts and ground vehicles. In addition, they can act as light sources for linear and nonlinear THz spectroscopy in fundamental condensed matter research. Also potential uses of THz communication and network systems have been suggested due to the high resolution and wide bandwidth offered by THz systems [24]. However, there are no coherent, compact, and economic light sources now. Currently existing coherent THz sources include CO 2 -laser pumped molecular gas lasers, free-electron lasers, and p-type Ge lasers, but none of them can be used widely in practice. CO 2 -laser pumped molecular gas lasers and free-electron lasers are impractical due to their bulky size. Furthermore, the huge amount of power that free-electron lasers consume makes them impractical. P-type Ge lasers have to be operated in high magnetic fields and at low temperatures. High quality bulk Ge crystals, which are required by p- type Ge lasers, are hard to process. For another type of electromagnetic wave generators, electronic devices, there are some whose frequencies are approaching the THz regime, such as resonant tunneling diodes (RTD), field effect transistors (FET), bipolar transistors, and Gunn diodes. But the highest operating frequency is only 712 GHz (by RTD) and their outputs are very weak and incoherent. Due to the current lack of compact coherent THz wave generators there is a technology gap in the electromagnetic spectrum between electronic and photonic devices. Above the gap, there are quantum cascade lasers (QCL), quantum fountain lasers working in the mid-infrared (MIR) regime and laser diodes working in the near-infrared (NIR). Below the gap, commercial electronics can work at frequencies up to 10s GHz. 32

33 Much effort has been aimed at closing the gap from both ends. They can be categorized as: 1. developing new devices that can generate power at THz frequencies directly 2. mixing down from a higher frequency (difference frequency generation) 3. multiplying up from a lower frequency We use the first two methods to develop a new coherent photonic device and to utilize DFG to mix down from a higher frequency. Both are all-intraband-transition schemes (all transitions happen in the conduction band between subbands): the first one is a laser scheme in a triple-well structure with Raman enhancement; the second one is based on DFG in a double-well structure Laser scheme In this scheme, we use a coupled triple-well pumped by a NIR laser for THz generation. The active material, which is a triple-well structure, is shown in Figure 14. This is a four-level system. The subband energies are so designed that we can utilize i) a NIR pump, which pumps electrons from state 1 to state 4, and ii) longitudinal-optical (LO) phonon scattering between state 3 and 2, an ultrafast process which depopulates the electrons from state 3, to create carrier population inversion between the two lasing states (E 3 and E 4 ). So this kind of structure can be used as the active region in a laser and put in a resonant cavity. Lasing can happen as long as the optical gain can compensate the loss. 33

34 E 4 E 3 E 422 THz LO Phonon E 1 AlSb/InAs/AlSb/GaSb/AlSb/GaSb/AlSb Figure 14. An illustration of the conduction band diagram of a sample in the laser scheme. Figure 15 depicts the conduction band diagram and confined wavefunctions of our first design, an InAs/AlSb triple well for the laser scheme. AlSb/InAs/AlSb/InAs/AlSb/InAs/AlSb Figure 15. The conduction band diagram and wavefunctions of an AlSb/InAs triple-well structure, calculated by Dr. Cun-Zheng Ning s group at NASA Ames Research Center. The plausibility of our laser scheme will be demonstrated by a detailed review of a theoretical paper that discusses the optical gain in a similar structure. The active material structure with calculated energy levels and wave functions is depicted in Figure 34

35 16. The material is biased under a dc electric field with 25 kv/cm strength, which can be used to adjust the positions of subbands. The sheet carrier density is cm -2. The calculated energy level differences are E 43 = 21.2 mev, E 32 = 42.1 mev, E 41 = 810 mev. Figure 16. The four lowest energy levels with corresponding wavefunctions for an In 0.53 Ga 0.47 As/AlAs 0.56 Sb 0.44 /InP/AlAs 0.56 Sb 0.44 /InP triple quantum well structure biased with a dc electric field of 25 kv/cm. [25] The simulation was done by applying a pump and probe fields to the sample. The pump is resonant with the energy difference between E 4 and E 1. The probe photon energy is the energy difference between levels E 4 and E 3 (the lasing levels). The polarizations of both the pump and probe fields are along the well growth direction, governed by the selection rules of the intersubband transition. Level E 2 is incorporated to depopulate the electrons from level E 3 through emission of longitudinal-optical (LO) phonons, and therefore helps to create population inversion between level E 3 and level E 4. Figure 17 illustrates numerical studies of the THz gain spectra for the above structure, without the pump-probe interaction (Raman enhancement). So the gain resulted only from the pump-induced population inversion. The pump energy is E 41 = 35

36 0.81 ev. In Figure 17 it can be seen that the peak gain appears at around 20 mev (the energy difference between E 4 and E 3 ) and the THz gain increases as the pump intensity increases. However, the rate of increase of the maximum gain becomes smaller with increasing pump intensity (saturated). This gain saturation behavior is due to population inversion saturation at high pump intensities. Figure 17. THz gain spectra (without pump-probe coherence) for different pumping intensities. The maximum gain as a function of the pump intensity is shown in the inset. [25] In Figure 18 the THz gain spectra for different pump intensities calculated with the pump-probe coherence included are shown. By comparing Figures 17 and 18, it can be seen that for small pump intensities, the coherent pump probe interaction contributes positively to the THz gain in addition to the pump-induced population inversion. For high pump intensities, however, the Raman scattering contributes negatively to the THz gain due to the light-induced population redistribution at large pump intensities. Also, there is a blue shift in the peak position. 36

37 Figure 18. THz gain spectra calculated including the Raman enhancement for different pump intensities with pump-probe coherence included. [25] From above, we can conclude that a pump with an intensity of 0.5 mw/cm 2 will be strong enough, because the THz gain will not increase significantly after the intensity is larger than 0.5 mw/cm 2 either with or without Raman enhancement Difference frequency generation scheme As we saw in the DFG experiment described earlier [22], a semiconductor heterostructure with a large second-order nonlinear susceptibility can be fabricated using MBE. Our second scheme is THz generation by doubly resonant difference frequency generation (DFG) in a coupled double quantum well (Figure 19). It utilizes the large second-order nonlinear susceptibility of the structure to achieve the difference frequency between two NIR pump beams. 37

38 E 3 E 2 THz ω 3 ω 1 NIR Pumps ω 2 E 1 AlSb/InAs/AlSb/GaSb/AlSb Figure 19. An illustration of the conduction band diagram of the sample to be used in our difference frequency generation scheme. Now let us look at a theoretical paper [11], which calculates the second-order nonlinear susceptibility in a similar structure -- AlAsSb/InGaAs/InP/AlAsSb quantum well. This will give us a sense of the order of magnitude of the second-order nonlinear susceptibility that can be achieved in specific InAs/AlSb asymmetric double quantum wells (Figure 20). AlSb/InAs/AlSb/InAs/AlSb Figure 20. The conduction band diagram and wavefunctions of an InAs/AlSb double QW structure, calculated by Dr. Cun-Zheng Ning s group at NASA Ames Research Center. 38

39 The sample structure is shown in Figure 21. The sample is biased under a dc electric field with 140 kv/cm strength, which can be used to adjust the positions of subbands. The sheet carrier density is 3 x cm -2. The second-order nonlinear susceptibility for the difference frequency generation in the THz range is calculated. Figure 21. Calculated wave functions for a THz wave generator based on DFG [11]. The large optical nonlinearity (Figure 22) of this structure ( m/v) makes it a possible THz source when pumped by two NIR laser diodes. 39

40 Figure 22. Second-order susceptibility vs. applied dc voltage [11] How to implement THz generators In order to implement the THz generation schemes, several crucial steps must be completed. 1. Find a sound and easy way to measure interband transitions and intersubband transitions in simple InAs/AlSb quantum wells so that we can accurately characterize the quantum well s band diagram bandgap, subband positions and transition linewidths. Also, it helps us understand intersubband transition energy as a function of well width so that we can design and grow quantum wells with desired energies. 2. Observe double absorption peaks in a double InAs/AlSb quantum well a three-level system with only the ground level populated and triple absorption peaks in a triple InAs/AlSb quantum well a four-level system with desired peak spacings. 40

41 3. Measure THz photoluminescence and adjust the sample structure to make all transitions occur at desired wavelengths. 4. Perform NIR pump THz probe spectroscopy to observe pump-induced THz gain and stimulated emission. 5. Fabricate a THz waveguide and cavity to observe lasing in the THz range. 41

42 Chapter 4 Samples Studied and Experimental Methods In this chapter, the samples studied and the equipment and techniques that were employed in these experiments are presented. Section 4.1 lists the detailed structures of the samples studied. In Section 4.2, the structure and principle of a Fourier-transform infrared spectrometer are described. The experimental methods designed to measure the interband and intersubband transitions are described in the following sections. 4.1 Samples studied There are two types of quantum wells used in our experiments: InGaAs/AlGaAs quantum wells and InAs/AlSb quantum wells. Samples 209 doped and 209 undoped are InGaAs/AlGaAs quantum wells, used mainly for characterizing our spectroscopy system. Their detailed structures are shown in Table 1. 42

43 Table 1. Structures of Samples 209 doped and undoped Sample (209 undoped) Sample (209 doped) Layer description Material Thickness (Å) Material Thickness (Å) Substrate GaAs (S-I) GaAs (S-I) Buffer GaAs 500 GaAs 500 Superlattice Al 0.41 Ga 0.59 As 20 Al 0.41 Ga 0.59 As 20 (30 periods) GaAs 20 GaAs 20 Al 0.41 Ga 0.59 As 300 Al 0.41 Ga 0.59 As 300 digital alloy 10 x (12 + 8) = digital alloy 10 x (12 + 8) = GaAs/InAs 200 GaAs/InAs 200 Al 0.41 Ga 0.59 As 100 Al 0.41 Ga 0.59 As 300 Si (10 12 cm -2 ) delta-doping Al 0.41 Ga 0.59 As 200 MQW region 20 periods In 0.19 As 0.81 As 70.3 In 0.19 As 0.81 As 70.3 Al 0.41 Ga 0.59 As 200 Al 0.41 Ga 0.59 As 300 Si (10 12 cm -2 ) delta-doping Al 0.41 Ga 0.59 As 100 Si (10 12 cm -2 ) delta-doping Al 0.41 Ga 0.59 As 500 Al 0.41 Ga 0.59 As 500 Cap GaAs 100 GaAs 100 The structure and growth conditions of InAs/AlSb quantum wells are listed in Table 2. Here, x is the thickness of the InAs wells. The sample is grown on GaAs 43

44 substrates. The buffer layer, which is grown to compensate the large lattice mismatch 7% between the epilayers and the substrate. The 10 nm GaSb cap layer is used to prevent the oxidation of AlSb upon exposure to atmosphere. Table 2. Detailed structure of InAs/AlSb QWs Growth temperature (K) Layer Thickness (nm) 420 GaSb 10 Cap layer 420 InAs x 420 AlSb 10 Multiple quantum wells (20 periods) 500 AlGaSb GaSb/AlSb 6/6 x AlSb GaSb 30 Buffer layers 535 AlSb AlAs GaAs GaAs substrate Substrate Figure 23 shows a cross-section of our sample taken by a JEOL 2010 TEM at 50,000 magnification. 44

45 Figure 23. A picture of sample cross-section taken by transmission electron microscopy. 4.2 Fourier-transform infrared (FTIR) spectrometer FTIR is a tool used to measure infrared spectra, which is a plot of measured infrared radiation intensity versus frequency. A typical FTIR [26] is comprised of an infrared light source, a beam splitter, a fixed mirror, a moving mirror, a detector, a He-Ne laser, and a sample compartment (Figure 24). A He-Ne laser is collinear with the IR beam, which is invisible to human eyes. The core of an FTIR is a Michelson interferometer. It is comprised of a beam splitter, a fixed mirror, and a moving mirror. The incident beam is split into two beams by the beam splitter. These two beams travel different distances and interfere with each other when they meet again at the beam splitter and the interference signal is detected by a detector. The detected signal is called an interferrogram, which is a plot of the interference signal intensity versus the position of the moving mirror. The interferrogram 45

46 of a single wavelength light source is a sinusoidal signal with a periodicity determined by the light source wavelength. An interferrogram of a continuous wavelength light source is the summation of the interferrograms of all wavelengths. Figure 25 shows an interferrogram taken with a globar light source, a KBr beamsplitter, and a Mercury Cadmium Telluride (MCT) detector. To generate a complete interferrogram, the moving mirror is translated back and forth once, which is known as a scan. By increasing scan times, a better signal-to-noise ratio can be achieved, 1/ 2 SNR (N) (20) Light source He-Ne laser Additional detector Fixed mirror Sample Beam splitter Moving mirror polarizer Detector Interferometer Sample chamber Figure 24. A block diagram of FTIR. 46

47 By applying Fourier transformation to the interferrogram, we can obtain the spectrum of the light source, which is the light intensity versus frequency. Figure 26 shows a spectrum taken with a globar source, a KBr beam splitter, and a MCT detector. Intensity (arbitary units) Position (arbitary unit) Figure 25. A typical interferrogram taken with a globar source, a KBr beamsplitter, and a MCT. 100 Fourier Transform Intensity (arbitary units) Frequency (cm -1 ) Figure 26. The Fourier transform of the interferrogram in Figure

48 FTIR can measure the entire spectrum in each scan. It sends the whole source beam at all wavelengths to the detector. This is quite different from a monochrometer, which will select only one wavelength at a time and thus take many more scans and time to take a complete spectrum. Also, since the FTIR can take multiple scans and average them to cancel some of the randomly generated noise, it can obtain much better SNR than with a monochrometer. Our FTIR system (JASCO 660plus) can cover the whole IR range from to 100 cm -1, by using different accessories (listed in Table 3). It has an external light source port and external detector port, which enable us to use our own light sources and detectors, respectively. It is also equipped with an integrated microscope that can be used to do IR micro-spectroscopy of small objects (minimum measurable size 3 µm x 3 µm). Table 3. The spectral ranges of Jasco-660 FTIR accessories Wavenumber (cm -1 ) Light source Beam splitter Window Detector Halogen CaF 2 CaF 2 Si Halogen CaF 2 CaF 2 Ge Globar KBr KRS5 TGS Globar Mylar 5µ PE PE-TGS Globar Mylar 12µ PE PE-TGS Globar KBr KRS5 MCT 4.3 Methods to measure interband transitions Figure 27 illustrates the setup within the sample compartment of the FTIR. Three samples can be placed on the sample holder at a time. For interband experiments, the 48

49 sample and GaAs (the substrate on which our sample was grown) were mounted on the holder. Then the sample holder was placed in a Janis cryostat, which can be cooled down to 4 K by liquid helium. We took the transmission spectra of the sample and the GaAs substrate separately and calculated their ratio to get the spectrum of the sample heterostructure. Janis cryostat empty IR Detector GaAs substrate Sample holder sample Sample compartment Figure 27. Illustration of the setup for interband measurements. 4.4 Methods to measure intersubband transitions The samples we used to test the methods for intersubband transition measurements were Sample 209 doped and 209 undoped. These samples are InGaAs/AlGaAs multiple quantum wells. Their detailed structures are shown in Table 1. Figure 28 illustrates their band diagrams. 49

50 populated with electrons no electrons E 2 Fermi energy E 1 E 2 E 1 Fermi energy H 1 H 2 Sample 209 doped H 1 H 2 Sample 209 undoped Figure 28. Illustrative band diagrams for sample 209 doped and undoped. One of the two samples is modulation doped, which means by delta-doping in the AlGaAs barrier, electrons are introduced into the quantum wells. That is, the Fermi energy is higher than the bottom of the lowest electron level E 1. Therefore, E 1 is populated with electrons. The other sample is undoped, so its E 1 state is not populated. Hence, an intersubband transition can take place only in the doped sample. Interband transitions (H 1 E 1 ) can take place in both samples. However, resonant excitonic absorption at the band-edge (i.e., E 1 -H 1 excitons) occurs only in the undoped sample since its E 1 state is empty and so excitonic attraction is not screened Brewster angle incident measurements Intersubband transitions can take place only when the electric field of the IR beam has a component parallel to the QW growth direction (see Section 3.1.2). The simplest way to satisfy the rule is to tilt the sample and shine the sample at Brewster s angle (74º for GaAs with a refractive index of 3.3). The Brewster angle is chosen to minimize the reflection at the air-gaas interface. 50

51 74º 17º Figure 29. Illustration of Brewster angle incident measurement. We measured the spectra of Samples 209 doped and 209 undoped and divided the spectrum of the undoped sample by that of the doped sample. The KBr beam splitter and MCT detector were used in this MIR range. Because an intersubband transition can only take place in the doped sample, there is an absorption peak around 1420 cm -1 (7 µm), and the absorption linewidth (FWHM) is about 95 cm -1 (Figure 30) T doped /T undoped E 1 ->E Frequency (cm -1 ) Figure 30. The ratio of two samples transmission spectra (209 doped/209 undoped) measured in the Brewster-angle geometry. 51

52 However, due to the high refractive index of GaAs, the angle of incidence within the sample is still small (17º for GaAs), leading to a small intersubband-active electric field component (along the QW growth direction). Therefore, several other waveguide geometries for the measurement of intersubband absorption have been designed. In the following section, the multipass method which was also used in our experiments will be introduced Multipass geometry measurements There are two multipass geometries: trapezoid and parallelogram [27]. Both experimental geometries were utilized and the results compared Parallelogram geometry The setup for parallelogram geometry is depicted in Figure 31. A BaF 2 polarizer is used to linearly polarize the incoming IR beam. The incident light will bounce between the two surfaces and pass through the quantum wells several times before it gets out (Figure 31). One side of the sample is coated with 1000Å of gold to form a crest instead of a node in the standing-wave pattern at the MQW surface (Figure 32). There is a displacement between the incident beam and the transmitted beam, which makes microscope measurements using this geometry impossible. 52

53 Gold coating (1000Å) Detector InAs/AlSb MQWs Incoming FTIR beam linearly polarized: GaAs substrate s OR p Figure 31. Parallelogram geometry for intersubband transition measurements. Figure 32. Electric field distribution for coated and uncoated MQWs [27]. By measuring the difference between the intersubband-active and nonactive transmission spectra (different polarization directions), we can measure the intersubband transition. Figure 33 shows the results of the remeasurement of Sample 209 doped using the parallelogram multipass geometry. The absorption (over 40%) is much stronger than 53

54 using the single pass (Brewster angle incident) method (Figure 30). The peak position is ~ 1440 cm -1, which is 20 cm -1 away from the peak of the uncoated measurement (~ 1420 cm -1 ). This difference was unnoticed until we observed that the peak position for a double side coated sample moved to ~ 1400 cm -1, also 20cm -1 away from the peak of the uncoated measurement but in the other direction. [T sample (horiz/vert) / T empty (horiz/vert)] Water E 1 ->E Frequency (cm -1 ) Figure 33. Absorption spectrum of sample 209 doped taken using the parallelogram geometry shown in Figure Trapezoid geometry The setup for a trapezoid geometry is depicted in Figure 34. However, when we coated the sample (209 doped), it was impossible to determine visually which side was the quantum well side of the sample, so we coated both sides. There is no displacement between the incident beam and the transmitted beam from the MQW as in the parallelogram geometry. Figure 35 shows the absorption taken using the microscope in 54

55 the open air. The absorption is over 60%. The peak position is ~ 1400 cm 1 and the linewidth is ~ 100 cm -1. The shift of peak position (~20 cm -1 ) due to the coating was reproduced in our later experiments. The absorption intensity is larger in this trapezoid geometry (over 60%) than in the parallelogram sample (over 40%). Because the size of the trapezoid sample was larger than the parallelogram sample, so light passed through the MQWs in the trapezoid sample more times than in the parallelogram sample. The renormalized absorption strengths for both geometries are nearly the same. The feature ~ 1720 cm -1 is due to H 2 O residue (Figures 33 and 35). Incoming FTIR beam linearly polarized: GaAs substrate Detector s OR p InAs/AlSb MQWs Gold coating (1000Å) 38º Figure 34. Trapezoid geometry for intersubband transition measurements. 55

56 [T sample (horiz/vert) / T empty (horiz/vert)] Water E 1 ->E Frequency (cm -1 ) Figure 35. Absorption spectrum of sample 209 doped taken using the trapezoid geometry shown in Figure Optical modulation for ISBT measurements Since the signal was quite weak in multipass geometry measurements, we took 4000 scans (~ 30 mins) for each spectrum to enhance the signal-to-noise ratio (SNR). However, the long term drift of the source intensity, in combination with the CO 2 and H 2 O residues, prevented us from obtaining a better SNR for more than 4000 scans. This problem should be avoidable by using modulation techniques. We can take one scan for one polarization direction, rotate the polarizer by 90º, take another scan, rotate the polarizer by another 90º and continue more scans in this way. A stepper motor can be used to drive the polarizer in synchronization with the FTIR scans in the following way: 1. When one scan is completed, we need a signal (a 100-pulse train) to tell a stepper motor (400 steps per revolution) to rotate 90º. 56

57 2. That the stepper motor should stop (the polarizer is in position) before the next scan begins. This can be done by delaying the scans for enough time to allow the polarizer to be in position. Our FTIR-660Plus is equipped with a Sample Shuttle program, which can provide a control signal (Figure 36) for synchronization. The finite pulse train needed to drive the stepper motor can be generated by a National Instrument PCI-6601 counter board. The control signal acts as the gate of the counters, triggering the finite pulse train generation when the gate value changes. Wait time (5 second) Scan time (15 second) A 100-pulse pulse train Figure 36. Control signal from the Sample Shuttle program. 57

58 Chapter 5 Experimental Results and Analyses In this chapter experimental results and analyses are presented. First interband measurement results will be described. Then the temperature dependence of the ISBT measurements on various InAs/AlSb quantum wells will be presented. By doing these experiments, we can investigate the electronic energy levels in our samples. Also, we can develop a theoretical model that explains our experimental data. 5.1 Interband measurements Interband measurements on InGaAs quantum wells In this experiment, we obtained the relationship between the InGaAs/AlGaAs quantum well bandgap and temperature. The structures of the 209 samples are listed in Chapter 4 in detail. Both samples and a semi-insulating (S-I) GaAs substrate were mounted, put in the cryostat, cooled down to 77 K (liquid nitrogen temperature), and then warmed up gradually. Data were taken during the warming up process. The temperature was controlled using an auto-tuning temperature controller. No spectral features were observed in the MIR region. The FTIR accessories were changed (source: globar -> halogen lamp; beam splitter: KBr -> CaF 2 ; window: KrS 5 -> CaF 2 ; detector: MCT -> Si) so we could measure signals in the NIR range ( cm -1 ). 58

59 Transmission K 109K 124K 155K 182K 210K 250K 280K (a) 0 15,000 12,000 9,000 Frequency (cm -1 ) Transmission K 100K 130K 160K 190K 220K 250K 280K E1->H1 (b) 0 15,000 12,000 9,000 Frequency (cm -1 ) Figure 37. Near-infrared transmission spectra for (a) doped and (b) undoped InGaAs quantum wells. Figure 37 shows NIR transmission spectra for (a) modulation-doped and (b) undoped InGaAs quantum wells. We can see that an absorption peak is present only in the undoped sample. This is due to the E1 - H1 excitonic excitation. The transition 59

60 energy of this feature blue shifts as the temperature goes down. It changes from ev (11146 cm -1 ) at 79 K to ev (10590 cm -1 ) at 280 K. The energy of the E1 - H1 transition is equal to the bandgap of In 0.19 Ga 0.81 As plus the confinement energy minus the exciton binding energy. The energy gap can be calculated by using E g 2 αt ( T ) = Eg (0), (21) T + β where E g (0) = ev, α = mev/k, and β = 204 K for GaAs and E g (0) = ev, α = mev/k, and β = 93 K for InAs. Figure 38 is a plot of the measured E1 - H1 energy and the energy calculated using the In 0.19 Ga 0.81 As bandgap versus temperature. The measured energy is about 100 mev larger than the calculated bandgap. This is primarily due to the confinement energy (the exciton binding energy is only ~ 5 mev). E E Calculated In 0.19 Ga 0.81 As bandgap Measured E1-H1 energy E g E E1-H1 E C E F E V E H1 Bandgap (ev) Temperature (K) Figure 38. Measured E1-H1 energy and calculated InGaAs bandgap vs. temperature. E C, E V, and E F are the energy levels of conduction band, valence band, and Fermi energy, respectively. 60

61 A transmission cut-off (above which the transmission is nearly zero) is present in both the doped and undoped samples. This cut-off position appears at almost the same position and shifts in the same direction in both samples from ev (12016 cm -1 ) at 79 K to ev (11347 cm -1 ) at 280 K. Therefore, it is due to the GaAs substrate Bulk InAs interband absorption measurements In this experiment, absorption was measured in an InAs film sample (grown on a GaAs substrate). The transmission spectra of the sample and GaAs were measured and divided to get the spectrum of InAs. The cut-off edges here correspond to the bandgap energy of InAs. T InAs / T GaAs Frequency (cm -1 ) 4.5K 20K 40K 60K 75K 95K 115K 150K 180K 210K 240K 270K Figure 39. Transmission spectrum for an InAs film grown on GaAs. The spectrum is normalized to that of a GaAs substrate. Figure 39 shows that the absorption edge of the InAs film moves from 424 mev (3417 cm -1 ) at 75 K to 368 mev (2966 cm -1 ) at 300 K, and below 75 K it changes little. The InAs bandgap information is very important to our quantum well design. Figure 40 shows the measured bandgap and the calculated InAs bandgap plotted vs. temperature. 61

62 The measured energy is about 10 mev larger than the calculated bandgap. We attribute this to the Burstein Moss effect [28, 29]. Namely, at a high doping level, the Fermi energy lies within the conduction band; the electron states below the Fermi level are all occupied; due to the Pauli principle, the minimum possible transition energy is the bandgap plus the E F E C. E F Calculated InAs bandgap Measured Bandgap energy E g E exp E C E V Bandgap (ev) Temperature (K) Figure 40. Measured and calculated InAs bandgap Multi-reflection interference fringes in InAs/AlSb quantum wells Our InAs/AlSb quantum wells are grown on GaAs substrates and thick buffer layers are grown to compensate the 7% lattice constant difference between GaAs (5.65 Å) and InAs (6.1 Å). Usually, the transmission spectrum of the sample is taken and then divided by that of GaAs to obtain the spectrum of the quantum wells. However, all we see are interference fringes that are due to the interference between multiple reflections between the surfaces of a thin film. The interference can be reduced by increasing 62

63 surface roughness, making the sample surfaces non-parallel, or with an anti-interference coating [30]. Here we used an anti-interference coating with 200 Å Nichrome (Ni 40 Cr 60 ) to eliminate the back surface reflectivity by impedance matching, which is wavelength independent, to reduce the interference fringes (Figure 41). In the following, I will present a brief derivation of the impedance matching condition. Transmission spectrum after 200 Å NiCr coating interference fringes Frequency (cm -1 ) Figure 41. Transmission spectra of InAs/AlSb QW before and after antiinterference coating (200 Å NiCr) Theoretical derivation for the wavelength independent coating We apply Maxwell s equation and corresponding boundary conditions to the interface between two media of refractive index n 1 and n 2 as indicated in Figure 42. The interface is a metallic film with a thickness of d and conductivity of σ. The thickness is presumed to be much less than the wavelength (λ) or the skin depth (δ) so that the fields have no spatial dispersion over the film thickness [30]. 63

64 Incident beam (σd) n 1 n 2 Reflection Transmission Figure 42. Incident, transmitted and reflected electric and magnetic fields at the interface of two dielectrics with indices of refraction n 1 and n 2 with a surface charge of conductivity σ and thickness d. [30] The boundary conditions are: E + E i H i r H r = E t = H t 4π + σd c (22) where E, and H are the electric and magnetic fields. Indexes i, r, and t are for the incident, reflected and transmitted waves. The effective conductivity of the film is given by σ * = σ iωε/4π (23) where ε is the dielectric constant of the interface. For a propagating electromagnetic wave in a non-magnetic material H = ne, where n is the complex index of refraction, so the second equation of (22) becomes: 4π * n 1( Ei Er ) = ( n2 + σ d) Et (24) c By solving the above equations we find that the power transmission and reflection coefficients are given by 64

65 R 12 4π n2 n1 + σ * d Er 2 = ( ) = c (25) E 4π i n2 + n1 + σ * d c Equation (25) shows that if 4π n 1 n2 = σ * d c, the interface is impedance matched and the power of the reflection is zero. In our case: n 2 = 1 (air), n 1 = 3.3 (GaAs), and σ* = 2.86 x 10 7 Ω -1 m -1 (NiCr); so the coating is ~ 200 Å (clearly wavelength independent) The periodicity of multi-interference fringes Figure 43 illustrates multi-reflection interference on a thin film. The beams reflected by the top and bottom surfaces of the thin film interfere with each other. For normal incidence, their phase difference is 2nd (n is the refractive index and d is the thickness of the film). Equation (26) gives the relation for two adjacent peaks, 2nd 2nd = λ ( m + 1/ 2) = λ m ( + 1 m+ 1 m + 1/ 2) (26) Therefore, the periodicity of the interference fringes is ~ ~ 1 1 υ m+ 1 υ m = = 1/ 2nd. (27) λ λ m+ 1 m d Figure 43. Illustration of multi-reflection interference. 65

66 From the periodicity (900 cm -1 ) of the interference fringes, we can calculate the thickness of the thin film (~ 1.5 µm) that causes the multi-reflection interference. We initially thought that the buffer layer was the cause of the interference fringes. Thus we took the spectrum of the buffer layer and divide the spectrum of the sample by that of the buffer layer. But the interference fringes remained. This suggests that the origin of the interference fringes is the multi-reflection on the surfaces of the InAs/AlSb MQWs itself. Notice that in the spectrum of bulk InAs (Figure 39), there are also wavy interference fringes with a 150 cm -1 periodicity. So it has a thickness around 9 µm. 5.2 Intersubband measurements In this section, the temperature dependence of ISBTs measured for InAs/AlSb quantum wells with various well widths from 4 nm to 10 nm will be presented. ISBT was observed in quantum wells with well widths above 6 nm Intersubband transition energy vs. well width Figure 44 shows MIR transmission spectra for the 7 nm, 8 nm, 9 nm and 10 nm wide InAs quantum wells at different temperatures taken in the parallelogram multi-pass geometry. One can clearly see resonances due to ISBTs. The resonance energy increases with decreasing well width at any temperature, just as expected. In addition, one can clearly see that both the resonance linewidth and position depend on the temperature. 66

67 (T MQW horiz/t empty horiz)/(t MQW vert/t empty vert) nm 8 nm 9 nm 10 nm 300K 4.5K K 4.5K 300K 4.5K 300K Absorption energy (cm -1 ) 4.5K Figure 44. Intersubband resonances observed for InAs/AlSb quantum wells with different well widths at various temperatures. In InAs/AlSb QWs, strain due to the lattice mismatch (over 0.6%) between InAs and AlSb cannot be neglected. An eight-band model that takes account of conduction bands (C1, C2), heavy hole bands (HH1, HH2), light hole bands (LH1, LH2), and spinorbit interaction split-off bands (SO1, SO2) [31] was used with strain and other effects (many-body) as small perturbations. The Hamiltonian can be written as Hχ = E χ H n = n n i H 2 i ( H z z 2 [ H H 2 + )] z (28) 2 2 k where H 0 is the unperturbed Hamiltonian [ H 0 = h + Vb ( z) from Equation (3)], χ n is 2m * the envelope wavefunction of the n-th confined states, and H 1, H 2 are related to the first and second order k p coefficients. The boundary conditions are the continuity of the envelope function and its flux across the interfaces. These conditions are automatically 67

68 taken into account by the Hamiltonian (the current or flux is continuous if is continuous). i H H 2 z E 2 -E 1 (ev) K Calculated by 8 band model IR absoprtion measurements Well width (nm) Figure 45. Theoretical and experimental results for the well width dependence of the E 1 -E 2 separation in InAs/AlSb QWs at 300 K (Calculation by Dr. Cun-Zheng Ning from NASA Ames Research Center). Figure 45 shows the calculated E 1 -E 2 separation at 300 K using the 8 band k p theory together with the experimental data. The experimental results (blue triangles) match quite well with the theoretical results (red squares). A. Neogi et al. [16] also observed an increase of the ISBT energy with decreasing well width in InGaAs/AlAsSb quantum wells. However, they found that the intersubband transition energy tends to saturate at around 2 µm (5000 cm -1 ) for a well width narrower than 2 nm. In our case, the ISBT suddenly disappeared for well widths narrower than 7 nm. As stated in Chapter 3, one of our goals is to implement NIR pumping, utilizing the NIR ISBT that is supposed 68

69 to happen in narrow InAs wells. Therefore, finding out the reason for the disappearance of ISBTs in wells narrower than 7 nm is extremely important Intersubband transition energy vs. temperature Figure 46 shows the temperature dependence of the ISBT energy for the four samples studied. The absorption energy increases with decreasing temperature in all four samples and the temperature dependence is most significant in the narrowest well (7 nm well). This also can be explained by an 8 band k p theory with the temperature dependence of the lattice constant and bandgap where, E g ( T ) = E a( T ) = a(0) + a g 2 αt (0) T + β T ( T 300) (29) where E g (0) is the bandgap at 0 K, a(0) is the lattice constant at 0 K, α T is the expansion coefficient. Thermal shrinkage can lead to a narrower InAs quantum well as temperature decreases. Equation (13) (for an infinitely deep QW) suggests that the energy separation between subbands will increase as the well width decreases, and this is also true for finite QWs. The strain and bandgap change due to the temperature changes, as well as the temperature dependence of the various many-body effects, may also contribute to the temperature dependence of the E 1 -E 2 energy. 69

70 Absorption Frequency (cm -1 ) nm InAs well 8nm 9nm 10nm Temperature (K) 300 Figure 46. The temperature dependence of the observed ISBT energies for four InAs QW samples with different well widths Intersubband transition linewidth vs. well width and temperature In Neogi et al. s experiments on narrow InGaAs/AlAsSb QWs, the ISBT linewidth increased as the well width decreased [16]. Heterostructure interface roughness is a major contributor to the ISBT linewidth, and broadening due to interface roughness is more profound in narrower wells. They did succeed in reducing the ISBT linewidth by improving the interface quality. This is related to our observations for our samples. The linewidth does increase as the well width decreases from 10 nm to 8 nm, but that is not the case for the 7 nm well (Figure 47). The interface defects can also be the reason why ISBT cannot be seen in a well narrower than 7 nm. So we need to take a closer look at the interfaces. Figure 47 shows that the ISBT linewidth decreases as temperature decreases. One of the reasons for this is that at low temperatures, scattering due to LO phonons and longitudinal acoustic (LA) phonons is reduced and thus the linewidth. [32] 70

71 Absorption Frequency (cm -1 ) nm InAs well 8nm 9nm 10nm Temperature (K) Figure 47. ISBT linewidth vs. temperature and well width ISBT integrated absorption intensity The disappearance of ISBTs in wells narrower than 7 nm prompts us to think about the absorption strength. Integrated intensity, the integration of absorption for one pass through the sample at all wavelengths, is used to describe the strength of ISBT absorption. Improving the absorption intensity and reducing the linewidth can be solutions to observing ISBTs in narrow wells. We need to find out how absorption intensity is related to different parameters, especially temperature and well width. Figure 48 shows the integrated intensity for all four quantum wells. The absorption intensity increases from 10 nm to 8 nm and then suddenly drops. However, the integrated intensity is not much smaller in the 7 nm well than in other samples. This indicates that the disappearance of absorption peak in the 6 nm well may not be due to insufficient integrated intensity. 71

72 Integrated Absorbance Absorbance Well width (nm) 4.5K 300K Figure 48. Integrated ISBT absorption intensity for InAs/AlSb multiple quantum wells with different well widths at 4.5 K and 300 K. Figure 48 also shows that the integrated intensity does not change significantly with temperature. The height of the peak may be smaller at high temperature but the peak is wider, leading to almost the same integrated intensity. As we know, a larger electron density in the well can lead to stronger absorption and the electron density increases slightly with temperature. However, our data in Figure 48 does not reflect this trend. Some other factor, which affects the ISBT oscillator strength, must be changing with temperature, canceling out the temperature dependence of the density. Photo-luminescence (PL) experiments were performed on the InAs/AlSb QWs and PL was observed in all QWs narrower than 7 nm (where ISBTs could not be observed). However, PL could not be observed in 7 10 nm QWs where ISBTs were observed). In narrow InAs/AlSb QWs, type-ii superlattice structures are formed so that interband absorptions are possible. 72

73 Figure 49. Interband photoluminescence energy and intersubband absorption energy versus well width for InAs/AlSb multiple quantum wells (PL data taken by Prof. M. Inoue s group at Osaka Institute of Technology). One interesting possibility of the absence of ISBTs in narrower QWs is the coexistence of ISBT and interband absorption in narrow wells. And the interband absorption energy (from the PL experimental) is almost the same as the ISB absorption energy for 6 nm well (Figure 49). Since interband transition happened in both polarizations and the ISBT absorption was taken by the ratio of the spectra of two polarizations, the ISBT features may be canceled to some extent. We need to under stand this. 73

74 Chapter 6 Transmission Electron Microscopy In this chapter, an introduction to transmission electron microscopy (TEM) is presented first. TEM specimen preparation methods are described next. Our electron photomicrographs taken at the sample cross-section are presented at the end. 6.1 Introduction to Transmission Electron Microscopy In a normal microscope, the minimum distance (resolution) that can be resolved is 0.61λ resolution = N. A. N. A. = nsinθ (30) where n is the refractive index of air, λ is the wavelength of the light source, and θ is half of the acceptance angle of the objective lens. The resolution is proportional to the wavelength of the light source. Thus, a source with shorter wavelength should be used to see finer details. θ Figure 50. An illustration of the acceptance angle of objective lens. Ultraviolet and X-ray microscope have been tried as the light source, but they all have their own problems. Ultraviolet can be absorbed by glass lenses and X-ray cannot 74

75 be easily refracted to form images. It turns out that an electron wave is the best alternative. The electron is a charged particle that can be refracted using magnetic lenses (magnetic field) and accelerated by an electric potential. The stronger the potential the faster the electron will move. Therefore, based on the de Broglie relationship (31) the shorter the wavelength, the better the resolution. λ = h / mv (31) Figure 50 shows a diagram of a typical TEM. Electrons are generated and accelerated by the illumination device, passing through the specimen, refracted by the magnetic field and projected to the viewing plane. Magnetic lenses cannot be as easily manipulated as optical lenses and as a result the electron microscope must use very small apertures (smaller acceptance angle) which attenuates the resolution. The resolution an electron microscope can offer is about a thousand fold increase over an optical microscope. 75

76 Sour ce of el ect r ons Condensor l ens Obj ect i ve l ens Speci men Pr oj ect i on l ens Fl uor escent scr een Camer a Figure 51. A diagram of TEM. However, there are several disadvantages of electron microscopes. The electrons are high energy particles that can react with the specimen and result in the emission of x- rays, secondary electrons, ultraviolet radiation, etc. Also, electrons cannot penetrate a specimen very deeply (~ 10 nm). 76

77 6.2 TEM specimen preparation As mentioned in the last section, the electrons cannot penetrate over ~ 10 nm in a specimen. Thus, the specimen has to be processed to precisely the correct thickness. The first step is to build a stack. Two InAs/AlSb MQW samples (well width = 10 nm) are glued face to face to increase the viewable quantum well area and two silicon dummy pieces are attached to make the stack harder to break. A special kind of glue -- M-bond 600/610 has to be used. Then the stack was put into the oven at 170ºC for an hour to let the glue to take effect. After cooling to room temperature, the stack thickness is reduced to 100 µm by using a hand polisher. An optical microscope is used to check the stack thickness by focusing on the stack s top and bottom surfaces. The difference of the height readings is the thickness of the stack. Sometimes the specimen stack will fall apart if the glue is not well spread all over the interfaces between different pieces when the area between different pieces becomes too small. QW epilayers 10 nm QW sample Dummy silicon pieces 100 µm Figure 52. An illustration of the specimen stack. 77

78 The second step is to reduce the specimen thickness further down to around 10 µm using a Gatan dimple grinder which has two major parts a diamond dimple wheel and a thickness measuring system. The measuring system consists of an electrical micrometer and an analog dimple depth indicator that gives a continuous display of dimple depth. Before each dimple, the grinding wheel is lowered until it just touches the specimen mount and then the digital micrometer is reset to zero. Then the specimen is loaded onto the mount and the wheel is gently lowered onto the specimen. After the desired dimple depth is set, the grinding wheel will start rotating until the desired dimple depth is reached. In this way we are able to produce a thin central region on the specimen while leaving a thick, supporting rim which protects the specimen from damage (a picture of post-dimple specimen in the upper-right corner of Figure 52). Pre-dimple can help to make the thin region at the center of the specimen. post-dimple specimen grinding wheel electrical micrometer 100 µm Figure 53. A picture of dimple grinder and post-dimple specimen. 78

79 The last step of specimen preparation is ion-milling: further reducing specimen thickness using ion guns. The specimen was glued on a copper grid, mounted and put in an ion mill. The ion guns are tilted at 15º to reduce sputter damage (Figure 53). The thickness reducing speed of ion-milling is much slower than mechanical processes. This process is continued until a hole appears at the QW edges and the region around the hole has a thickness of approximately 10 nm which is good for TEM analysis. Argon ion beams 15º 100 µm 10 µm Figure 54. Specimen under ion guns. 6.3 TEM photomicrographs for 10 nm InAs wells Figure 54 was taken at 50,000 magnification (the electron acceleration potential was 200 kv). Clearly we can see the 20-period (10 nm InAs + 10 nm AlSb each period) multi-quantum well. Also we can tell that the buffer layer consists of a 200 nm AlGaSb (the left part of the buffer) and a 15-period (6 nm GaSb +6 nm AlSb each period) superlattice. 79

80 20 periods of QW buffer Figure 55. TEM picture taken at 50,000 magnification of 10nm InAs/AlSb well. magnification. Figure 55 was taken at 200,000 magnification. Figure 56 was taken at 1,000,000 80

81 Figure 56. TEM picture taken at 200,000 magnification. 81

82 Figure 57. Two micrographs taken at 1,000,000 magnification. 82