THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF PHYSICS

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1 THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF PHYSICS ELECTRICAL AND THERMAL TRANSPORT IN BISMUTH TELLURIDE/ANTIMONY TELLURIDE SUPERLATTICES GROWN BY MOLECULAR BEAM EPITAXY JACOB J. WISSER SPRING 2016 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Physics with honors in Physics Reviewed and approved* by the following: Nitin Samarth Professor of Physics Thesis Supervisor Richard Robinett Professor of Physics Honors Adviser * Signatures are on file in the Schreyer Honors College.

2 i ABSTRACT Thermoelectric materials have exciting low-temperature applications in waste recovery and refrigeration. One of the most promising thermoelectric materials to date is a superlattice of bismuth telluride (Bi2Te3) and antimony telluride (Sb2Te3). These heterostructures have reportedly exhibited thermoelectric efficiencies at room temperature that are more than twice that of industrial thermoelectrics. The purpose of this thesis is to grow these superlattices by molecular beam epitaxy and independently verify these claims. We begin by developing a growth protocol to grow films on a thickness scale that would allow for the measurement of thermal transport through the film. A comprehensive characterization procedure for each sample was paramount to improving the quality of these films. By characterizing the samples with x-ray diffraction, x-ray reflectivity, and transmission electron microscopy, we demonstrate the growth of superlattices with well-defined interfaces and superlattice period. After growth and characterization, we perform electrical and thermal transport measurements on the samples. We use the standard Hall bar geometry for electrical transport to determine resistivity, carrier concentration, and carrier mobility as a function of temperature. In addition, we also characterize the transport through topological surface states in these films. For thermal measurements, we implemented the 3ω method for measuring the thermal conductivity of electrically conducting films.

3 ii TABLE OF CONTENTS LIST OF FIGURES... iii LIST OF TABLES... vi ACKNOWLEDGEMENTS... vii Chapter 1 Introduction and Theoretical Considerations The Thermoelectric Effect and Figure of Merit, ZT The Power Factor, α 2 σ The Thermal Conductivity, κ The Effect of the Topological Insulator State on ZT Chapter 2 Superlattice Growth and Characterization MBE Growth Reflection High-Energy Electron Diffraction Atomic Force Microscopy X-Ray Diffraction X-Ray Reflectivity Raman Spectroscopy Transmission Electron Microscopy Chapter 3 Electrical and Thermal Transport Electrical Transport Resistivity as a function of temperature Carrier concentration and mobility Weak Anti-localization Thermal Transport The 3ω Method Chapter 4 Future Investigations: Toward a Figure of Merit Appendix A MBE Growth Procedure Appendix B Device Fabrication Processes BIBLIOGRAPHY... 46

4 iii LIST OF FIGURES Figure 1-1. Bi 2Te 3/Sb 2Te 3 layered structures. Figure 1-1 a) is bulk Bi 2Te 3, b) shows a 30Å period superlattice consisting of 20Å Bi 2Te 3/10Å Sb 2Te 3 repetitions, and c) depicts a 60Å period superlattice consisting of 10Å Bi 2Te 3/50Å Sb 2Te 3 repetitions. The goal of this thesis is to study transport properties in the cross-plane direction (perpendicular to the superlattice interfaces), but we also study in-plane transport (parallel to the interfaces). Reproduced from [2] Figure 1-2. Thermoelectric circuits exhibiting the a) Seebeck effect and b) the Peltier effect. The Seebeck effect arises when a heat source causes positive and negative charges to migrate toward the cold side in the p and n-type materials, respectively. This separation of charge causes a voltage to appear. In the Peltier effect, a voltage is applied between the p and n-type materials, drawing charge carriers away from the cold side. The heat is dissipated at the hot side through a heat sink, and the cold side continues to cool. Thermoelectric refrigerators operate based on the Peltier effect. Modified from [3] Figure 1-3. Figure of merit for several materials as a function of temperature. We are primarily concerned with low-temperature refrigeration applications, so we study the Bi 2-xSb xte 3 alloy and the Bi 2Te 3/Sb 2Te 3 superlattice. Reproduced from [1] Figure 1-4. Optimal superlattice period for ZT. Below 60A, electron tunneling becomes a factor and destroys the advantage of electron confinement in 2-D. Above this period, phonon scattering by the boundaries is decreased. The b/a ratio corresponds to the ratio of Bi 2Te 3/Sb 2Te 3 thicknesses. Reproduced from [7] Figure 1-5. Phonon interface scattering in Si/Ge superlattices (modeled in a). As the in-plane phonon momentum (α p) is increased in b), phonon modes are increasingly confined to either the Si or Ge layer and are unable to propagate through the superlattice. Reproduced from [12] Figure 1-6. Band structure for topological insulator displaying the quatnum spin-hall effect. Edge states (represented by the blue and green curves) exist in the gap between the valence and conduction band. These channels are spin-textured, and propagate in the opposite direction around the sample. Reproduced from [14] Figure 2-1. MBE system used to grow the samples in this thesis Figure 2-2. RHEED collected at the end of two different growths. 2-1 a) depicts a "spotty" pattern indicitive of three-dimensional growth, while b) depicts a streaky pattern suggesting epitaxial two-dimensional growth Figure 2-3. AFM section data for two superlattice growths. Both growths were 60Å period (10Å Bi 2Te 3/50Å Sb 2Te 3) superlattices. The plots beneath the images contain height data taken along a straight line across the image such as in b). The surface roughness of the sample in a) is ~50 nm, while that of b) is around 5-10 nm

5 iv Figure 2-4. X-ray diffraction spectrum in the Bragg-Brentano scan geometry (10/50 superlattice sample). Peaks matched with known Miller indices for Sb 2Te 3, Bi 2Te 3, and InP are denoted in blue, green, and purple text, respectively. This scan confirms the presence of all expected species. Most peaks not identified can be explained by secondary radiation lines Figure 2-5. Omega "rocking curve" scan of the Sb 2Te 3 (0 0 6) peak. The red curve is the collected data and the black dashed curve shows a Gaussian fit with a FWHM of.227, which is typical for these films. The FWHM of the InP (111) rocking curve is about.020, which places the lower limit on the FWHM that we can obtain for films on these substrates Figure 2-6. Raw scan data (a) and the calculated reciprocal space map (b). The reciprocal space map is plotted in terms of reciprocal lattice units. The second, less-intense peak in the reciprocal space map could possibly be due to the aluminum cradle that holds the sample during these scans Figure 2-7. XRR data for a 10/50 superlattice sample. The blue curve is the measured data and the red curve is the fitted data up to the angle at which the reflection fringes begin to disappear Figure 2-8. Raman-active modes and Raman spectrum. In Figure 2-8 a), bismuth (or antimony) atoms are represented by the larger blue spheres with tellurium being represented by green spheres. The arrows indicate the direction of vibration for each phonon mode (modified from [17]). The Raman spectrum in Figure 2-8 b) displays all of these modes as well as a mode for tellurium [18] Figure 2-9. TEM data for two growths of a 10/50 superlattice. Figure 2-9 a) and c) provide surface and interface data from the same growth, respectively. The same is true for b) and d) for a different growth. Bi 2Te 3 layers appear as a lighter gray than Sb 2Te 3, as the heavier Bi atoms scatter the electrons at a higher angle Figure 3-1. Etched Hall Bar used for electrical transport measurements. In this case, we make electrical contact directly to the material itself, rather than using contact pads Figure 3-2. Resistivity as a function of temperature for: a) two superlattice samples and b) an alloy sample Figure 3-3. Carrier concentrations and mobilities of two superlattice samples and an alloy sample.32 Figure 3-4. Electron scattering in a real material. The length of the red and green paths is the same, and carriers that traverse these paths will have the same phase in the weak localization regime. In the weak anti-localization regime, the time reversed paths cause the carriers to have opposite spins and therefore opposite phases. Reproduced from [20] Figure 3-5. Two-dimensional magnetoresistance data collected from the alloy sample. Figure 3-5 a) is raw R xx data converted to two-dimensional ρ xx by using the sample dimension. 3-5 b) plots Δσ xx for four temperatures displaying WAL over a smaller magnetic field range.. 35 Figure 3-6. Phase coherence length as a function of temperature for the alloy sample. Inset: fitting of the Δσ xx cusp out to 1T to determine the phase coherence length

6 v Figure 3-7. Predicted temperature fluctuations for our reference and superlattice samples. The constant temperature difference between the two samples allows us to calculate the thermal conductivity Figure ω data taken at T = 10K Figure 4-1. Device to measure the thermal conductivity and Seebeck coefficient in the cross-plane direction. Similarly to the 3ω measurement, it is also necessary to fabricate a reference sample without the superlattice present. The Seebeck coefficient is then defined as α = ΔV 2ω / ΔT 2ω. Reproduced from [26] Figure B-1. Hall bar device fabrication process. The end result of this process is a superlattice in the shape of the Hall bar covered in photoresist. We then scratch the resist to expose the film and make electrical contact Figure B-2. Device fabrication for the 3w devices. The end result is a layer of SiO2 and Ti/Au in the shape of a Hall bar. The device pictured is the superlattice sample, for the reference sample we perform the same process on a bar substrate

7 vi LIST OF TABLES Table 1-1. Dispersion relations, Seebeck coefficients, and electrical conductivities for a material in bulk and 2D superlattice configurations. k x, k y, and k z denote the particle wavevector, a is the superlattice quantum well thickness, m x, m y, and m z are the charge carrier effective masses in each direction. F is the Fermi-Dirac integral, and ζ * is the reduced chemical potential. These parameters are calculated assuming a scattering parameter equal to zero [4] [5].... 7

8 vii ACKNOWLEDGEMENTS I would first like to thank Professor Nitin Samarth for his guidance through this research project. As I prepare to enter graduate school, I know that his mentoring has set me up for success as a graduate researcher. I would also like to thank my academic advisor Richard Robinett, who has always taken the extra step to help me organize my class schedule and make the most of my collegiate academics. I am also greatly indebted to Professor Srinivas Tadigadapa, who helped me set up and collect thermal transport measurements in his lab. Through my research experiences, I have had more than a little help along the way from my group members. I would like to thank Anthony Richardella for sharing his expertise in MBE growth and x-ray diffraction with me, as well as always being around to answer my many questions. I would also like to thank Abhinav Kandala, Thomas Flanagan, James Kally, Di Xiao, Eugene Freeman, and everyone that has fielded my questions along the way. Finally I want to extend my deepest thanks to Shaun Mills in Professor Ying Liu s lab for teaching me many of the experimental techniques as a freshman that I would later utilize to write this thesis. I also thank my family, whose love and support has gotten me through some of the more difficult times I ve had. I want to thank my mom for showing me the wonders of science as a child, my dad for teaching me the drive and discipline to accomplish my dreams, and my brother for always being around when I needed a break from science. I also want to thank my best friend, Amy Ketcham, who has always been by my side and tried her best to act interested in my work. I love all of you guys and know that I would not be where I am without you. I would finally like to acknowledge the support of the Goldwater scholarship, the Teas scholarship, and the Bert Elsbach scholarship in physics.

9 1 Chapter 1 Introduction and Theoretical Considerations Today s most efficient energy conversion processes are only able to convert about onehalf of stored energy into useful work. The rest of the energy is lost to heat. Thermoelectric materials have the unique property of being able to convert a temperature gradient into electricity, and vice versa. This characteristic of thermoelectric materials makes them particularly useful in waste recovery (converting a temperature gradient into electricity) and refrigeration applications (converting electricity into a temperature gradient). Although waste recovery in many high-temperature industrial processes is dominated by steam cycle recovery, low-temperature waste recovery and refrigeration techniques have not advanced as far. An efficient thermoelectric material would revolutionize low-temperature refrigeration, but due to their current inefficiency, today s thermoelectric refrigerators are only used in niche applications where traditional refrigeration methods would be cumbersome. The thermoelectric effect is one of the most well-understood and established fields of physics, and yet it is extremely difficult to find a material efficient enough at converting heat to electricity (or vice-versa) to replace current industrial methods. The purpose of this thesis is to further investigate claims made by Venkatasubramanian et. al. [1] that Bi2Te3/Sb2Te3 superlattices exhibit extraordinary thermoelectric properties that led to a more than two-fold increase in thermoelectric efficiency. While quite exciting, these claims have yet to be independently verified and to the best of our knowledge no group has reported an efficiency of this magnitude since.

10 2 This thesis will mainly focus on superlattices of Bi2Te3/Sb2Te3, but we also investigate an alloy of BixSb2- xte3. Figure 1-1 provides an illustrated example of our superlattice samples. The BixSb2-xTe3 alloy is currently used in niche refrigeration techniques such as cooling CCD arrays or photomultiplier tubes. The goal of this Figure 1-1. Bi2Te3/Sb2Te3 layered structures. Figure 1-1 a) is bulk Bi2Te3, b) shows a 30Å period superlattice consisting of 20Å Bi2Te3/10Å Sb2Te3 repetitions, and c) depicts a 60Å period superlattice consisting of 10Å Bi2Te3/50Å Sb2Te3 repetitions. The goal of this thesis is to study transport properties in the cross-plane direction (perpendicular to the superlattice interfaces), but we also study in-plane transport (parallel to the interfaces). Reproduced from [2]. thesis is to begin the process of measuring thermoelectric properties of these samples to investigate the validity of Venkatasubramanian et. al. s claims. These samples were grown by molecular beam epitaxy (MBE), which allowed for the precise control of the superlattice period and alloy proportions. To characterize these samples, we use a combination of atomic force microscopy (AFM), x-ray diffraction (XRD), x- ray reflectivity (XRR), Raman spectroscopy, and transmission electron microscopy (TEM). After complete characterization, we present complete in-plane electrical transport characterization and begin the process of measuring the cross-plane thermal conductivity using the 3ω method.

11 1.1 The Thermoelectric Effect and Figure of Merit, ZT 3 The thermoelectric effect consists of three related phenomena: the Seebeck, Peltier, and Thompson effects. Figure 1-2 depicts simple thermoelectric circuits that exhibit the Seebeck and Peltier effects. The Seebeck effect is observed when a temperature gradient is applied across a junction between two conductors that have opposite-sign charge carriers. The temperature gradient causes the charge carriers in both materials to flow away from the heat source and toward the cold side. The p-type material will develop a build up of positive charges at the cool side, and the n-type material will experience a build up of negative charges at the cool side. Such a separation of charges causes an electric potential to develop across the junction between the materials, and the magnitude of this electric potential is characterized by the Seebeck coefficient, α: α = dv dt J=0, (1.1) where the derivative of voltage with respect to temperature is evaluated at zero current density. The Seebeck coefficient is an intrinsic property of the material, and is often a function of temperature. Thermocouples operate on the basis of the Seebeck effect. If the Seebeck coefficient of a material is known at a certain temperature, one can measure the voltage that develops across the conductor junction and calculate the temperature difference. The Peltier effect is in some ways the inverse of the Seebeck effect. If an electrical current is run across the junction between two conductors (one p-type and one n-type), the charge carriers will flow to one side of the device. Since these charge carriers also carry thermal energy, this will result in a temperature gradient across the device (much like the one that we imposed to measure the Seebeck effect). If the hot side is connected to a heat sink, heat will

12 4 continue to flow from the cold side to the heat sink as long as the current is flowing. This socalled Peltier cooling is extremely useful in refrigeration applications and is characterized by the Peltier coefficient, π: dq dt = πi, (1.2) where Q is the heat flux and I is the electrical current provided to the device. While refrigerators operating on the Peltier effect are not widespread, they do have some niche applications. For example, photomultiplier tubes need to be cooled to detect photons with little thermal interference, but traditional refrigeration methods are often too cumbersome. By running a current through a thermoelectric device, one can develop a temperature difference across the photomultiplier tube, and by running water over the device as a heat sink it is possible to cool down the tube such that thermal excitations will not interfere with the detection of photons. As one might expect, the Seebeck and Peltier effects are very closely related, and these coefficients obey the so-called Thompson relation: π = Tα, (1.3) where T is the absolute temperature. a) Heat source b) p n p n Heat sink V Figure 1-2. Thermoelectric circuits exhibiting the a) Seebeck effect and b) the Peltier effect. The Seebeck effect arises when a heat source causes positive and negative charges to migrate toward the cold side in the p and n-type materials, respectively. This separation of charge causes a voltage to appear. In the Peltier effect, a voltage is applied between the p and n-type materials, drawing charge carriers away from the cold side. The heat is dissipated at the hot side through a heat sink, and the cold side continues to cool. Thermoelectric refrigerators operate based on the Peltier effect. Modified from [3].

13 5 The Thompson effect appears when the Seebeck coefficient is dependent on the absolute temperature. The temperature gradient that appears when current is run through the device will cause the Seebeck coefficient to vary along the device, and so there will be a slight correction to the Peltier equation. We now have: dq dt = τ(j T), (1.4) where τ is the Thompson coefficient, q is the heat per unit volume, and J is the current per unit area (current density). The Thompson coefficient is very closely related to the Seebeck coefficient, or more specifically the Seebeck coefficient s dependence on temperature: τ = T dα dt. (1.5) The Seebeck, Peltier, and Thompson effects combined fully characterize the thermoelectric effect. In order for these materials to be viable industrial options, they must be very efficient at converting electrical energy into a temperature gradient (or vice-versa). To quantify this efficiency, we calculate the coefficient of performance in much the same way we would for any refrigerator (η = W/Qh), where Qh is the input energy and W is the power delivered to the circuit from the thermoelectric device). Upon maximizing the coefficient of performance, we can define a new parameter Z such that the maximum efficiency only depends on Z and the temperature difference: Z = α2 σ κ, (1.6) where α is the Seebeck coefficient as mentioned above, σ is the electrical conductivity, and κ is the thermal conductivity (α 2 σ is often called the power factor). Z is often multiplied by the absolute temperature T to be made dimensionless. ZT is often called the thermoelectric figure of merit, and is central to thermoelectric research. The goal of modern thermoelectric research is to

14 discover materials that have a high value of ZT. As a reference, Figure 1-3 provides the ZT of 6 many modern thermoelectric materials. To be competitive with modern industrial refrigeration techniques, the ZT would need to be raised to about 3. The Bi2Te3/Sb2Te3 superlattices in Figure 1-3 have the highest recorded room temperature figure of merit to date, and are the subject of this work. From examining ZT, we can determine the properties of an efficient thermoelectric material. It is clear that an ideal thermoelectric material would have a high Seebeck coefficient and electrical conductivity, and a low thermal conductivity. The high Seebeck coefficient produces a large electrical potential for a given Figure 1-3. Figure of merit for several materials as a function of temperature. We are primarily concerned with low-temperature refrigeration applications, so we study the Bi2-xSbxTe3 alloy and the Bi2Te3/Sb2Te3 superlattice. Reproduced from [1]. temperature gradient, the high electrical conductivity allows for charge carriers to flow freely and produce a large current, and the low thermal conductivity prevents heat from flowing through the material and maintains the temperature gradient. While sounding somewhat simple, these conditions are quite experimentally challenging to realize. In particular, the ratio σ/κ is limited by the Wiedemann-Franz law: σ = 1, (1.7) κ LT where L = WΩ/K 2 is the Lorenz number, and T is the absolute temperature. The Wiedemann-Franz law states that at a given temperature the thermal and electrical conductivities are proportional to one another. Intuitively, this makes sense because electrons (or holes in p-

15 7 type materials) carry both charge and thermal energy. If charge carriers can move freely through a material (high electrical conductivity), then heat can flow freely as well (high thermal conductivity). While this is undesirable for thermoelectric materials, there is a caveat to the Wiedemann-Franz law. The law is only true for the charge carrier contribution to the thermal conductivity. There are other contributions to the thermal conductivity that can be suppressed, which will be discussed later, but the Wiedemann-Franz law presents a fundamental challenge to increasing the electrical conductivity while decreasing the thermal conductivity. 1.2 The Power Factor, α 2 σ To search for effective thermoelectric materials, we first calculate the power factor, or α 2 σ. For simplicity, all thermoelectric coefficients can be calculated under the relaxation-time approximation. We now examine the origin of the high theoretical power factor in superlattices. As a proof of concept, the superlattice dispersion relation can be modeled as free-electron transport in two dimensions, and electron confinement in one dimension. The results are summarized in Table 1-1: Table 1-1. Dispersion relations, Seebeck coefficients, and electrical conductivities for a material in bulk and 2D superlattice configurations. kx, ky, and kz denote the particle wavevector, a is the superlattice quantum well thickness, mx, my, and mz are the

16 8 charge carrier effective masses in each direction. F is the Fermi-Dirac integral, and ζ * is the reduced chemical potential. These parameters are calculated assuming a scattering parameter equal to zero [4] [5]. Bulk E(k) ħ 2 2 k x + ħ2 2 k y + ħ2 2 k z 2m x 2m y 2m z Superlattice ħ 2 2 k x + ħ2 k y + ħ2 π 2 2m x 2m y 2m z a 2 2 α k B e (5F 3 2 ζ ) k B e (2F 1 ζ ) F 0 3F 1 2 σ 3 1 2π 2 (2k BT ħ 2 ) 2 (mx m y m z )1 2 F 1 2 eμ x 1 1 2π 2 (2k BT ħ 2 ) (m xm y ) 2 F 0 eμ x The data in Table 1-1 suggest that 2D superlattices are electrically favorable over their 3D bulk counterparts. In this simplistic model, the quantum wells are treated as infinite square wells. Electron confinement in two dimensions leads to a sharp peak in the density of states around the Fermi energy, which allows for more charge carriers to be available for conduction. Hicks and Dresselhaus [5] predicted this effect to be so drastic that it could lead to an increase in ZT by a factor of 13 for the narrowest of quantum wells. Even when one corrects for the more complex superlattice dispersion relation, we still expect to see an increased ZT over the bulk material [6] [7]. However, there will be an optimal quantum well width below which electron tunneling will negate the two-dimensional confinement effects and lead to a ZT comparable to or less than the bulk, as seen in Figure 1-4.

17 While electron confinement could 9 potentially increase thermoelectric efficiency, there are many other properties that an optimal thermoelectric material should possess. From Table 1-1 the Seebeck coefficient is dependent on the modified chemical potential (ζ * = ζ/kt), which in turn is affected by carrier Figure 1-4. Optimal superlattice period for ZT. Below 60A, electron tunneling becomes a factor and destroys the advantage of electron confinement in 2-D. Above this period, phonon scattering by the boundaries is decreased. The b/a ratio corresponds to the ratio of Bi2Te3/Sb2Te3 thicknesses. Reproduced from [7]. concentration. There exists an optimal carrier concentration above which ionic impurity scattering will begin to take effect and decrease the Seebeck coefficient. BixSb2-xTe3 alloys are of particular interest in this regard, because as antimony is added to bismuth telluride the mobility at the optimal Seebeck coefficient is greatly increased, leading to a larger σ at the optimal α [8]. Additionally, an ideal thermoelectric material will not involve bipolar conduction. When both electrons and holes are present and they move in the same direction, there will heat flowing without any electrical current. The presence of two charge carriers raises the thermal conductivity of the material, which will effectively decrease the figure of merit [9]. Not only is bipolar conduction counterproductive to the thermoelectric effect, but the existence of two charge carriers drastically decreases the Seebeck coefficient. For a material with both electrons and holes present, the total Seebeck coefficient is given by [8]: α t = σ eα e +σ h α h σ e +σ h, (1.8)

18 where σe and αe denote the conductivity and Seebeck coefficient for electrons and σh and αh 10 denote the conductivity and Seebeck coefficient for holes. With little calculation one can see that the total Seebeck coefficient is reduced from the Seebeck coefficient for either carrier, as the Seebeck coefficients of electrons and holes will have opposite signs. To avoid bipolar conduction it is necessary that the chemical potential lies in the valence band and that the material has a large band gap [10]. Both Bi2Te3 and Sb2Te3 are narrow-band semiconductors, but it is possible to increase the band gap by adding a small amount of selenium to the alloy (though not so much that the alloy becomes n-type) [8]. Bipolar conduction is only appreciable at high temperatures for these materials, however, so we do not consider this effect for refrigeration applications. 1.3 The Thermal Conductivity, κ We have seen that both alloys of BixSb2-xTe3 and Bi2Te3/Sb2Te3 superlattices have favorable electrical properties for thermoelectric applications. However, the main advantage of the superlattice comes from reduced thermal conductivity. At low temperatures useful in refrigeration applications, the optimal Seebeck coefficient and electrical conductivity are essentially independent of temperature. Therefore any variation of ZT comes from variation in the thermal conductivity [8]. The total thermal conductivity contains contributions from the charge carriers and the lattice vibrations (phonons). There is also a contribution from any bipolar conduction that takes place, but we will not consider it as ideal thermoelectric materials have only one type of charge carrier. As previously mentioned, the charge carrier contribution to the thermal conductivity is proportional to the electrical conductivity at a given temperature. Without sacrificing electrical conductivity, it is difficult to reduce the charge carrier contribution

19 to the thermal conductivity. Fortunately there are several ways to reduce the lattice (phonon) 11 contribution, which is given by: κ l = 1 C 3 vv ph l mfp, (1.9) where Cv, vph, and lmfp denote the heat capacity, mean phonon velocity, and phonon mean free path, respectively. To reduce the lattice thermal conductivity it is necessary to increase the scattering of phonons, thus reducing the phonon mean free path. Alloys are useful in this respect as the disruption of the long-range order will not a) greatly diminish the charge carrier mobility, but alloy scattering of phonons on a smaller scale will lead to a reduced lattice thermal conductivity [8]. b) While the electronic advantages of the superlattice can certainly lead to a small increase in thermoelectric efficiency, their main attraction is the reduced phonon mean free path. Bi2Te3 and Sb2Te3 already have relatively low phonon mean free paths, but if the quantum well thickness in the superlattice is sufficiently small (without inducing electron tunneling) phonons will begin to scatter off of the superlattice boundaries in addition to other phonons [11]. This effect is exaggerated for phonons with Figure 1-5. Phonon interface scattering in Si/Ge superlattices (modeled in a). As the in-plane phonon momentum (αp) is increased in b), phonon modes are increasingly confined to either the Si or Ge layer and are unable to propagate through the superlattice. Reproduced from [12]. lower frequency, as the relaxation time for phonon-phonon scattering is proportional to the inverse square of the frequency. Boundary scattering of phonons is somewhat analogous to the phenomena of total internal reflection for light waves. The different speeds of sound in the two

20 12 materials plays the role of the index of refraction, and rather than considering a critical angle, we consider a critical in-plane phonon momentum. By solving for the detailed phonon dispersion relation in Si/Ge superlattices using the Boltzmann transport equation, Hyldgaard and Mahan [12] showed that there exists a critical in-plane phonon momentum for which no phonons will be able to propagate through the superlattice. These phonon modes will be strictly confined to either the Si or Ge layers, as seen in Figure 1-5. The critical in-plane momentum corresponds to a critical temperature, which for Si/Ge superlattices corresponds to about one-half of the Debye temperature. While a similar study has not been conducted on Bi2Te3/Sb2Te3 superlattices, this result is still valuable. The Debye temperature of Bi2Te3 is 165K, so even partial phonon mode confinement below this temperature is valuable for thermoelectric refrigeration applications. In fact, significantly decreased lattice thermal conductivity has been observed in Bi2Te3/Sb2Te3 superlattices [13].

21 1.4 The Effect of the Topological Insulator State on ZT 13 While it was not known that both bismuth and antimony telluride were topological insulators at the time of Venkatasubramanian et. al s discovery, there have been many theoretical studies treating the effect of the topological insulator state on the thermoelectric figure of merit. Topological insulators exhibit insulating bulk behavior, but allow for robust, time-reversal symmetry protected conducting surface states (see Figure 1-6) [14]. These materials are quite valuable for quantum computing applications, but Figure 1-6. Band structure for topological insulator displaying the quatnum spin-hall effect. Edge states (represented by the blue and green curves) exist in the gap between the valence and conduction band. These channels are spin-textured, and propagate in the opposite direction around the sample. Reproduced from [14]. coincidentally also make good thermoelectric materials. The link between the two is the inverted band gap [15]. The inverted band gap leads to Eg 10kBT in Bi2Te3, which is when the figure of merit begins to saturate with respect to the band gap [10]. The inverted band gap in Bi2Te3 and Sb2Te3 is mediated by the strong spin-orbit coupling in Bi and Sb. Conveniently for thermoelectric applications spin-orbit coupling occurs in heavy elements, which also lead to a reduced melting point and therefore a lower thermal conductivity [8] [16]. The contribution to the electrical conductivity and the Seebeck coefficient from these surface states behaves very similarly to the addition of second charge carrier as described above: σtot = σbulk + σss and αtot = (αbulkσbulk + αssσss) / σtot [15]. In bulk semiconductors, the thermopower exhibits a maximum as a function of temperature, which is dependent on the size of the band gap. A larger band gap prevents bipolar conduction, leading to an increased thermopower. However, since the surface

22 14 states are metallic (as confirmed by transport studies), their overall effect is to decrease the total Seebeck coefficient. This effect is evident in both Bi2Te3 and Sb2Te3 films, with up to an 80% decrease in total thermopower from the bulk value for Sb2Te3 films [15]. These calculations and observations stand in opposition to the calculations of Hicks and Dresselhaus [5], which neglected to take into account the as-yet undiscovered topological characteristics of these materials. While topological insulators are still the most efficient thermoelectric materials to-date due to the ideal band gap and low thermal conductivity, calculations accounting for the metallic surface state contributions to the thermopower partially explain why the large predicted ZT value was never observed. Gapping these surface states at low temperatures (usually accomplished by breaking time-reversal symmetry with magnetic doping) seems like a reasonable recourse to fully take advantage of the thermoelectrical benefits of topological insulators.

23 15 Chapter 2 Superlattice Growth and Characterization The growth of superlattices requires very precise control of growth rates and parameters to produce samples with consistent superlattice periods and constituent thicknesses. To maximize ZT we must also optimize the carrier concentration, and therefore also demand precise manipulation of dopant concentrations in the sample. To suit these needs, we grow our twodimensional quantum well superlattices using molecular beam epitaxy (MBE) to deposit each atomic layer one at a time. MBE growth begins with solid sources of the growth materials (bismuth, antimony, and tellurium in our case). After being evaporated, each element forms a molecular beam that will be incident on the sample. Due to each beam s long mean free path there will be little to no interaction between the beams themselves or between the beams and any outside elements before they reach the substrate. Upon reaching the substrate the elements condense and form a single atomic layer (such as Bi2Te3). After sample growth we collect comprehensive characterization data including atomic force microscopy (AFM), x-ray diffraction (XRD), x-ray reflectivity (XRR), Raman spectroscopy, and transmission electron microscopy (TEM) to fully understand the structure of our sample. These data proved invaluable in tweaking MBE growth parameters to yield smoother, cleaner samples with the expected superlattice periods.

24 2.1 MBE Growth 16 Our group uses two systems connected by a UHV buffer chamber (see Figure 2-1). The commercially available EPI 620 and EPI 930 systems are used for II-VI and III-V growths, respectively. The two-system setup is convenient for growths that require elements from both chambers. The MBE process begins with the effusion cells that house the solid source elements. These so-called Knudsen cells permit very precise control of the flux of atoms incident on the sample, and therefore are instrumental in controlling growth rates (and in our case, the superlattice period). In order to increase the atomic mean free path, MBE growth is performed under an ultra-high-vacuum (UHV) as low as Torr. Two vacuum pumps accomplish this goal separately for each chamber: a cryopump (on the II-VI chamber) and an ion pump (on the III-V chamber). The cryopump traps excess gases through condensation on a cooled surface. The ion pump uses a combination of a magnetic field and an electric potential to trap gases in an anode. First, electrons are trapped in the magnetic field at the anode side and used to ionize any gases present in the pump. These ionized gases are then accelerated toward the cathode and trapped. To further increase the vacuum and decrease scattering events in the chamber, we cool the growth chamber with liquid nitrogen during growths. Cooling the chambers with liquid nitrogen also prevents the substrate from overheating from the effusion cells, which allows for slower growth rates and two-dimensional (rather than three-dimensional) growth. To obtain uniform growth across the sample, the substrate is mounted on a rotating stage that operates throughout the growth. We begin our superlattice growth by mounting our (111) indium phosphide (InP) substrates onto molybdenum blocks using melted indium. We then load the bare substrate into the III-V chamber where we begin desorption. Prior to growing our superlattice films, we desorb

25 the InP under arsenic to remove any oxide layer that had accumulated on the substrate. After 17 desorption we are left with a clean, smooth substrate surface for superlattice growth. We confirm the smoothness of our substrate by using reflection high-energy electron diffraction (RHEED), which is described in the next section. After desorption, we transfer the InP to the II-VI chamber via the UHV buffer chamber. Once the sample loaded into the II-VI, we can begin the superlattice growth. To confirm that the film is growing two-dimensionally we collect RHEED data after each superlattice period. We also monitor the sample surface temperature using a pyrometer and adjust the substrate temperature as needed. A comprehensive description of our growth process can be found in Appendix A. RHEED Screen Knudsen Cells II-VI Chamber III-V Chamber Buffer Chamber Transfer Fork Figure 2-1. MBE system used to grow the samples in this thesis.

26 2.2 Reflection High-Energy Electron Diffraction 18 Both the III-V and II-VI chambers are equipped with an in-situ surface-monitoring RHEED apparatus. The apparatus consists of a filament that emits electrons with an energy of 12 kev, a fluorescent screen, and a CCD camera that displays the resulting diffraction pattern. The electrons are collimated and incident on the sample at a glancing angle of a few degrees. Due to this low incidence angle, the electron penetration depth into the sample is also low, and therefore the resulting diffraction pattern will mostly provide information about the sample surface. Electron diffraction in this configuration is very similar to x-ray diffraction. In three-dimensional reciprocal space, the intersection of an Ewald sphere with reciprocal lattice determines which a) b) Figure 2-2. RHEED collected at the end of two different growths. 2-1 a) depicts a "spotty" pattern indicitive of threedimensional growth, while b) depicts a streaky pattern suggesting epitaxial two-dimensional growth. crystal planes will be involved in diffraction. Therefore, for single-crystal growth in three dimensions, we expect to see a well-ordered array of points. In two-dimensions, the reciprocal space now consists of rods instead of points. For a perfect crystal in two-dimensions, the intersection of the Ewald sphere with these rods produces an array of sharp lines. For our purposes, a streaky RHEED pattern indicates that the film is growing two-dimensionally with some disorder, while a randomly spotty RHEED pattern indicates unwanted three-dimensional growth (see Figure 2-2). RHEED is also used to calculate growth rates. As a film is growing nucleation sites develop and more electrons are scattered, rather than reflected. This results in a lower intensity until the surface is 50% covered by the film. After this critical point, the continued nucleation

27 19 begins to result in a smoother surface, which leads to a higher RHEED intensity. The result is an oscillation of the RHEED intensity as a function of time as the film continues to grow. One cycle of these RHEED oscillations corresponds to one layer of atomic growth. Collecting RHEED data before, throughout, and after our growths was instrumental to ensuring high-quality sample growth. We collect a RHEED measurement in real-time after desorbing the sample in the III-V chamber, after each superlattice period is deposited, and before unloading the sample. RHEED is our first method of sample characterization, and provides invaluable surface information before we even unload the sample from the MBE system. 2.3 Atomic Force Microscopy Our next step in characterization is to use atomic force microscopy (AFM) to provide more detailed information on the surfaces of our samples. AFM relies on the slight deflections of a vibrating cantilever scanning over the sample surface. The setup consists of a cantilever (typically a few hundred microns long and a few tens of microns wide) with a laser beam focused onto the tip and reflected to a position-sensitive detector. The tip is then lowered to a few microns above the sample surface (never coming into contact with the surface in tapping mode). As the tip scans across the sample surface, small deflections in the tip from the uneven surface cause a deflection in the laser on the position-sensitive photodetector. These laser deflections coupled with a feedback loop from the piezo-electric scanner produce an image on a computer screen of the sample surface. These images are particularly useful when handling exfoliated samples, as they can determine the thickness of individual flakes, but we use our AFM scans as a second gauge of surface uniformity.

28 As an example of the usefulness of AFM, we present data from our first two growths in Figure 2-3. The growth in Figure 2-3 a) was our first attempt at a) 200 nm b) 20 nm 5 μm 1 μm 20 growing Bi2Te3/Sb2Te3 superlattices, and after the tenth and final period the RHEED came out spotty after nine streaky measurements. As mentioned Figure 2-3. AFM section data for two superlattice growths. Both growths were 60Å period (10Å Bi2Te3/50Å Sb2Te3) superlattices. The plots beneath the images contain height data taken along a straight line across the image such as in b). The surface roughness of the sample in a) is ~50 nm, while that of b) is around 5-10 nm. above, this typically denotes threedimensional growth and the AFM image confirms this suspicion. The large sample roughness from this first growth was not ideal to conduct other characterization measurements that require a smooth surface (such as XRR), and was simply a poor-quality sample. This AFM data combined with transmission electron microscopy data (discussed later) led us to believe that tellurium was being deposited on the surface of the sample. Since we are attempting to grow a material with a low cross-plane thermal conductivity, it is entirely possible that the thermal conductivity was low enough that the temperature of the surface was significantly lower than that of the substrate. This effect could potentially have led to the deposition of tellurium on the surface of the sample. From our AFM characterization of the sample in Figure 2-3 a), we decided to monitor the surface temperature in-situ using a pyrometer and raised the substrate temperature accordingly as the superlattice continued to grow. The result is the smooth sample surface in Figure 2-3 b).

29 2.3 X-Ray Diffraction 21 The next step in characterizing our samples is x-ray diffraction (XRD). XRD provides valuable data on the structure of the film, rather than the surface. From XRD, we can ascertain the species present in the film, the preferred orientation, lattice constants, the presence of any superlattice reflections, and any stress/strain in the film. When this path-length difference corresponds to an integer number of wavelengths (n), then constructive interference will occur and the detector will show higher intensities. This requirement is known as the Bragg reflection criteria and is given by: nλ = 2d sin θ, (2.1) where λ is the x-ray wavelength (1.54 Å for copper Kα1 lines), d is the lattice spacing, and θ is the diffraction angle. In the standard Bragg-Brentano geometry, the detector is positioned at an angle of 2θ. In this particular source-detector geometry, only crystal planes parallel to the sample surface will cause diffraction peaks to appear. From the Bragg reflection criteria, one can calculate the spacing between these crystal planes. It is apparent from Equation 2.1 that the additional periodicity of the superlattice could produce reflections not present in an alloy sample. Using d = 60 Å and the Kα1 wavelength, for first-order diffraction (n = 1) we would expect to see a superlattice reflection at 2θ 1.5. Our XRD scans begin at 2θ = 5 to avoid exposing the detectors the direct beam, so we were unable to observe any superlattice reflections in our samples. We analyze our XRD scans using computer software to match collected data with what would be expected for a particular species. In our case, we can confirm that both Bi2Te3 and Sb2Te3 are present from XRD from a simple Bragg-Brentano scan, as seen in Figure 2-4.

30 22 Figure 2-4. X-ray diffraction spectrum in the Bragg-Brentano scan geometry (10/50 superlattice sample). Peaks matched with known Miller indices for Sb2Te3, Bi2Te3, and InP are denoted in blue, green, and purple text, respectively. This scan confirms the presence of all expected species. Most peaks not identified can be explained by secondary radiation lines. From the data in Figure 2-4, we can confirm that Bi2Te3, Sb2Te3, and InP are all present in this sample. Since the concentration of Bi2Te3 is so small compared to the other species, the intensity of those reflections is miniscule in comparison. The width of Bragg reflections is also of interest, as a perfect crystal will produce a sharper peak than a real crystal with imperfections. As mentioned above, only crystal planes parallel to the sample surface will produce diffraction peaks. The parallel crystal planes in an imperfect that appear in a Bragg-Brentano will have some degree of imperfection in their parallelism. To measure such an imperfection, we Figure 2-5. Omega "rocking curve" scan of the Sb2Te3 (0 0 6) peak. The red curve is the collected data and the black dashed curve shows a Gaussian fit with a FWHM of.227, which is typical for these films. The FWHM of the InP (111) rocking curve is about.020, which places the lower limit on the FWHM that we can obtain for films on these substrates. fix the detector position a diffraction maximum and tilt the sample. This measurement is known

31 as a rocking curve, and can provide information on mosaicity, dislocations, and any other 23 irregularities in the orientation of that particular crystal plane. For our films, we collect rocking curves on the (006) peak of Sb2Te3 (Figure 2-5). The full width at half maximum (FWHM) of these curves can be used as a quick measure of the purity or epitaxy of the sample, but the real value of these rocking curves is reciprocal space maps. In this scan geometry we scan the 2θ/ω axis as well as the ω axis, allowing us to determine variation in the width of the peak along both of these axes. Variation along the 2θ/ω axis stems from variation in the spacing of the lattice (see Equation 2.1), while the variation along the ω axis provides information on any strain or dislocations (as mentioned above). Figure 2-6 shows the raw 2θ/ω and ω scan data as well as the calculated reciprocal space map. a) b) Figure 2-6. Raw scan data (a) and the calculated reciprocal space map (b). The reciprocal space map is plotted in terms of reciprocal lattice units. The second, less-intense peak in the reciprocal space map could possibly be due to the aluminum cradle that holds the sample during these scans. The main peak in the reciprocal space map has significant spread in both Qx and Qy directions, indicating there is a considerable amount of strain in these films. This result is not so surprising,

32 as strain between the superlattice layers is expected in spite of the small lattice mismatch 24 between Bi2Te3 and Sb2Te3. There is also some variation in the lattice spacing, as indicated by the finite spread along the 2θ/ω axis (Qx direction). 2.4 X-Ray Reflectivity X-ray reflectivity (XRR) measures the intensity of reflected x-ray beams at a grazing incidence angle to determine the film thickness, density, and surface roughness. Total reflection of x-rays will occur when the incident angle is less than some critical angle, which is related to the refractive index of the material, and therefore the electron density. Above this critical angle, the reflection intensity will decrease as the x-rays begin to penetrate the material and begin to interfere with the reflected wave. The interference patterns generated by the XRR measurement are known as reflection fringes (see Figure 2-7). To obtain information about the density, thickness, surface roughness and superlattice interfaces, we model the reflection pattern using values for these film parameters and adjust these values until the model matches the collected data. This measurement is particularly useful as a second measurement of the surface roughness and superlattice Figure 2-7. XRR data for a 10/50 superlattice sample. The blue curve is the measured data and the red curve is the fitted data up to the angle at which the reflection fringes begin to disappear. period without performing a costly transmission electron microscopy measurement. From the

33 25 data in Figure 2-7, we were able to determine the film thickness was around 61 nm, and the fitted model corresponded to a 10/50 period superlattice. However, since it is possible to have an incorrect model coincidentally fit the collected data, we must collect more transmission electron microscopy data to confirm this conclusion. 2.3 Raman Spectroscopy Raman spectroscopy is a method to probe the film lattice vibrations, or phonons. Incident photons from a monochromatic laser source can undergo two scattering processes: Rayleigh scattering and Raman scattering. About 1 in every 10,000 photons will undergo Rayleigh scattering. These photons are scattered by phonons or crystal defects with no energy loss and reach the photodetector with the same frequency as the incident photons. Raman scattering occurs much less frequently; about 1 in every 10,000,000 photons undergoes Raman scattering. These photons excite a phonon to a higher vibrational state and scatter with an energy equal to the difference between this higher vibrational state and the incident photon energy. Both energy and momentum are conserved in Raman scattering processes. In the Raman setup, laser light is incident on the sample and the scattered light is collected by a spectrometer. Using the spectrometer to scan through wavelengths, we can probe the phonon energy spectrum. Figure 2-8 shows a depiction of the Raman-active modes in Bi2Te3 (or Sb2Te3) as well as a Raman spectrum.

34 a) b) 26 E 1 g E 2 g A 1 1g A 2 1g Figure 2-8. Raman-active modes and Raman spectrum. In Figure 2-8 a), bismuth (or antimony) atoms are represented by the larger blue spheres with tellurium being represented by green spheres. The arrows indicate the direction of vibration for each phonon mode (modified from [17]). The Raman spectrum in Figure 2-8 b) displays all of these modes as well as a mode for tellurium [18]. We observe all expected Raman modes in our spectrum. The relatively low intensity of the A 1 1g phonon mode could indicate confinement in the superlattice as predicted in Transmission Electron Microscopy Transmission electron microscopy (TEM) operates on similar principles as the traditional light microscope, only using electrons in place of photons. Electrons have a shorter de Broglie wavelength than photons, and can therefore provide much higher resolution than a light microscope. The de Broglie wavelength of an electron with a typical TEM energy of 150 kev has a wavelength of 3.2 pm, compared to a photon in the visible spectrum with a wavelength of about 600 nm. Using an electromagnetic lens, electrons emitted from a filament source are focused onto the sample. TEM provides internal structural information by relying on electrons that are transmitted through the sample, rather than scattered by the surface. Samples with a higher density will scatter more electrons than those with a lower density, and will therefore appear lighter.

35 27 Sample preparation for TEM measurements is paramount, as we need to make the sample thin enough to be transparent to electrons. To thin the sample sufficiently, we use a focused ion beam (FIB) after protecting the film with a metal coating. The ions used in the milling process have energies around 5keV. After milling, the sample is polished with less energetic ions (~.1keV). After this extensive sample preparation process, we can mount the sample for the TEM measurements. For this work, we use TEM to precisely determine the period of the superlattice and the constituent thicknesses, as seen in Figure 2-9. a) b) c) d) Figure 2-9. TEM data for two growths of a 10/50 superlattice. Figure 2-9 a) and c) provide surface and interface data from the same growth, respectively. The same is true for b) and d) for a different growth. Bi2Te3 layers appear as a lighter gray than Sb2Te3, as the heavier Bi atoms scatter the electrons at a higher angle. In Figure 2-9 a), we see an unwanted amorphous growth on the surface of the sample, which was reflected in the spotty RHEED pattern at the end of the growth. The only possible source of this material is tellurium, which is only deposited when the surface of the sample becomes sufficiently cool for tellurium to condense. While this may appear to be an issue with

36 the growth process, it is actually a promising sign that our films have a relatively low thermal 28 conductivity for the film surface to be at a much lower temperature than the substrate. To correct this issue, we monitored the surface temperature in situ using a pyrometer. If the surface temperature dropped sufficiently, we increased the substrate temperature to prevent the condensation of tellurium on the sample surface. In subsequent growths we observe a cleaner surface, such as that shown in Figure 2-9 b). Additionally, we can see from Figure 2-9 c) that the superlattice period for the first growth was actually closer to 10Å Bi2Te3/70Å Sb2Te3, rather than 10Å Bi2Te3/50Å Sb2Te3. In the second growth, we also adjusted the Sb2Te3 growth time to obtain the 10Å Bi2Te3/50Å Sb2Te3 superlattice period seen in Figure 2-9 d). Although TEM proves to be time-consuming and expensive, it is an invaluable resource for superlattice growth.

37 Chapter 3 29 Electrical and Thermal Transport We conduct electrical transport in the standard Hall bar geometry (Figure 3-1) on our samples. From these measurements, we calculate the conductivity/resistivity, carrier concentration, and mobility as a function of temperature. We also characterize the weak antilocalization in these films, which is a hallmark of transport through topologically protected surface states. The Hall bar is fabricated using standard photolithography techniques including spin coating of SPR 3012 photoresist, exposure to UV radiation from a Karl Süss MA/BA6 contact aligner, and developing of the resist in MF CD-26 developer. After photolithography we etch the film using an ULVAC NE-550 dry Figure 3-1. Etched Hall Bar used for electrical transport measurements. In this case, we make electrical contact directly to the material itself, rather than using contact pads. etcher, leaving the Hall bar protected by the photoresist. We mount the sample using GE varnish, and make electrical contact using indium dots after scratching the photoresist with a pin. All temperature measurements and magnetic field sweeps are performed in a physical property measurement system (PPMS). A detailed description of all device fabrication processes is given in Appendix B. To measure the thermal conductivity of these films in the cross-plane direction, we used the 3ω method. The devices are fabricated with a similar lithography process, but metal

38 evaporation replaces the ULVAC etch. We make electrical contact using indium dots and 30 conduct preliminary measurements at room temperature in a UHV chamber and PPMS. 3.1 Electrical Transport Resistivity as a function of temperature We first measure the parallel resistance as a function of temperature (Rxx) in the absence of a magnetic field. From these data and a) using the Hall bar dimensions, we can convert this resistance to resistivity (ρxx) or conductivity (σxx). Resistivity vs. temperature data for two 60Å period superlattices with b) different constituent thicknesses as well as a BixSb2-xTe3 alloy is given in Figure 3-2. The plots for the superlattice samples exhibit typical metallic transport characteristics. Charge carrier scattering at high temperatures is dominated by collisions with lattice Figure 3-2. Resistivity as a function of temperature for: a) two superlattice samples and b) an alloy sample. vibrations (phonons), and by collisions with impurities at low temperature. These two mechanisms are independent of each other, and so can be summed by Matthiessen s rule: ρtot = ρl + ρi where ρl and ρi denote the resistivity due to collisions with lattice phonons and impurities, respectively. ρi is only dependent on the concentration of defects and impurities, and

39 is independent of temperature. ρl is proportional to the concentration of thermal phonons 31 available for collisions, which is proportional to the temperature for temperatures greater than the Debye temperature. Thus, we see linear behavior at intermediate temperatures for the resistivity of the superlattice samples before the resistivity levels off at low temperatures. At low temperatures scattering from lattice phonons becomes negligible, and the constant scattering from lattice impurities becomes apparent [19]. The alloy sample shown in Figure 3-2 exhibits insulating properties. The initial increase in resistivity and bump at 200K can be explained by the rapid change in carrier concentration at this temperature (see Figure 3-3). As the temperature decreases, the bulk carriers begin to freeze out, and the resistivity continues to rise. Once the carrier concentration becomes relatively constant, the continued increase in resistivity down to about 25K is due to increased localization effects (see section 3.1.3). Below 25K the resistivity begins to level off as the carriers begin to transport through metallic topological surface states. If these states were not present, the resistivity would continue to increase somewhat linearly, rather than level off. The small increase in resistivity at extremely low temperature (which is actually present in all samples) can be attributed to electron-electron interaction. At such low temperatures quantum effects become significant and the electrons will become correlated, leading to an increase in resistivity Carrier concentration and mobility When a magnetic field is applied to the sample the charge carriers will drift to one side, causing a voltage to appear perpendicular to the current flow. This phenomenon is known as the Hall effect. By measuring the linear dependence of the resistance in this direction (Rxy) as a

40 function of magnetic field, we calculate the carrier concentration at several temperatures. The 32 slope of the linear relationship (RH) is given by RH = 1/(net) where n is the carrier concentration, e is the carrier charge, and t is the film thickness. The sign of the slope determines which side of the sample the carriers will drift to, and therefore the sign of the charge carriers. From the carrier concentration and resistivity measurement at each temperature, we calculate the carrier mobility as a function of temperature. These quantities are related by ρxx = 1/(neμ) where ρ is the resistivity, n is the carrier concentration, e is the electronic charge of the carriers, and μ is the carrier mobility. We compare the carrier concentrations and mobilities of the same three samples (two superlattices and one alloy) in Figure 3-3. Figure 3-3. Carrier concentrations and mobilities of two superlattice samples and an alloy sample. The carrier concentration of the superlattice samples is mostly constant through the entire temperature range, which is consistent with the conclusion that these materials behave as highly doped degenerate semiconductors. Their mobility dependence on temperature also follows this conclusion, as it steadily rises as temperature decreases and collisions with phonons become less frequent. The slight decrease at low temperatures can again be contributed to electron-electron interaction effects. For the alloy sample, as the temperature decreases, the bulk carriers are frozen out and the carrier density drops rapidly to a relatively constant value.

41 3.1.3 Weak Anti-localization 33 Weak anti-localization (WAL) is a hallmark of transport through topological surface states. In the Drude model, charge carriers undergo ballistic transport through a medium with low scattering. However, in disordered systems (those with lattice defects, boundaries, dislocations, etc.) these carriers will undergo diffusive transport and the wave properties of the carriers can no longer be neglected. Therefore, the probability that a carrier will travel through the medium will have interference terms from the difference in the length of the paths taken. This phenomenon is analogous to interference from a double slit experiment. In low-dimensional systems, it is significantly more likely that charge carriers will scatter through closed paths of the same length than in three dimensional Figure 3-4. Electron scattering in a real material. The length of the red and green paths is the same, and carriers that traverse these paths will have the same phase in the weak localization regime. In the weak anti-localization regime, the time reversed paths cause the carriers to have opposite spins and therefore opposite phases. Reproduced from [20]. systems (see Figure 3-4). Since the length of these two paths is the same the phase of these two waves will be the same, which leads to constructive interference. This constructive interference suggests that backscattering is more likely, and the carriers are localized to these closed paths. The higher probability of backscattering leads to a lower probability of transmission, and an increase in resistivity over the classical value. This phenomenon is known as weak localization. In systems with strong spin-orbit coupling, such as topological insulators, the spin of the carriers

42 traversing time-reversed the closed orbits will be exactly opposite. This causes destructive 34 interference, and a decrease in resistivity from the classical value. If we now switch on a magnetic field and break time-reversal symmetry, each path will now have opposite phase and when we average over all paths the interference terms will disappear. Mathematically, one path will pick up a phase of +(eba)/ħ and the other path will pick up a phase of -(eba)/ħ, where B is the magnetic field and A is the area of the enclosed paths. The introduction of a magnetic field destroys WAL effects, and the resistivity returns to the classical value. The strength of the field needed to destroy these effects depends on the phase-coherence length of the carriers. A longer phase coherence length implies that the path of the enclosed loops leading to coherent backscattering will be longer, and therefore the phases will grow further apart much quicker when a magnetic field is introduced. This effect causes the resistivity to return to the classical value at a lower magnetic field than that of a system with a shorter phase-coherence length. We measure the coherence length the carriers in our film by fitting the decrease in resistance to the model developed by Hikami, Larkin, and Nagaoka [21]: σ xx (H) σ xx (0) = Δσ xx (H) = α e2 2π 2 ħ [Ψ (1 2 + ħc ħc 2 4el φ H ) ln ( 2 4el φ H )], (3.1) where α = -1/2 per channel for weak anti-localization and 1 per channel for weak localization, and l φ is the phase coherence length. We fit the above equation to magnetoresistance measurements conducted on our alloy sample at T = 2.2K, 5K, 10K, and 25K, as this particular sample at these particular temperatures exhibited the most prominent WAL signature. Raw transport data converted into twodimensional resistivity and Δσxx are given in Figure 3-5.

43 35 a) b) Figure 3-5. Two-dimensional magnetoresistance data collected from the alloy sample. Figure 3-5 a) is raw Rxx data converted to two-dimensional ρxx by using the sample dimension. 3-5 b) plots Δσxx for four temperatures displaying WAL over a smaller magnetic field range. The hallmark of WAL is the cusp in the ρxx and Δσxx data in Figure 3-5. To calculate Δσxx we use σxx (H) = 1/ρxx (H) and then subtract the σxx value at zero magnetic field. We can use this simple relationship between σxx and ρxx rather than the tensor relationship, which takes into account contributions from ρxy, because ρxx dominates ρxy. We fit the cusp in Δσxx out to 1T to determine the phase coherence length in Figure 3-6. l f µ T -.3 Figure 3-6. Phase coherence length as a function of temperature for the alloy sample. Inset: fitting of the Δσxx cusp out to 1T to determine the phase coherence length.

44 3.2 Thermal Transport The 3ω Method To measure the cross-plane thermal conductivity, we employ the 3ω method developed by Cahill [22] [23] [24]. The 3ω method employs a 4-probe geometry similar to that of the Hall bar, and is purely an electrical measurement. When AC current is passed between two current pads in at a frequency ω, temperature fluctuations will appear at a frequency 2ω. This is because the electrical power is related to the current by P = I 2 R. These temperature fluctuations will also cause the resistance to fluctuate at the same frequency, and when these resistance fluctuations at a frequency 2ω couple with the current at a frequency ω, a voltage harmonic appears at a frequency 3ω. By measuring the magnitude of this third voltage harmonic as a function of frequency and knowing how the resistance changes as a function of temperature (from Rxx vs. T) we can calculate the temperature fluctuations, given by [21]: T = 4 R V (dr dt ) 1 V 3ω, (3.2) where R is the resistance of the heater, V is the rms voltage at 1ω, V3ω is the in-phase rms voltage at 3ω, and dr/dt is the derivative of the resistance with respect to temperature obtained from an R vs. T measurement. We can then fit the temperature fluctuations as a function of current frequency to a linear model and calculate the thermal conductivity of the film. Since our films are electrically conducting, we cannot simply immediately deposit a gold wire onto the sample. We must use a modified version of the 3ω method [23] [24] where we deposit a 100nm layer of SiO2 to electrically isolate the film from the metal heater. We also fabricate a reference sample consisting of the bare InP substrate, the 100nm SiO2 layer, and the

45 gold heater. A more detailed description of the sample fabrication process is presented in 37 Appendix B. The film acts as a simple thermal resistor in-series with the substrate-insulating structure, and so we expect to see a frequency-independent temperature fluctuation offset between the reference and film samples given by [22]: T = pt κw, (3.3) where ΔT is the temperature fluctuation, p is the power supplied per unit length, w is the width of the heater, t is the thickness of the film, and κ is the thermal conductivity of the film. By using these two samples, we are essentially able to subtract out the insulating layer s contribution to the temperature fluctuations and determine the thermal conductivity of the film. The two samples along with the predicted calculated temperature fluctuations as a function of current frequency is given in Figure 3-7. Figure 3-7. Predicted temperature fluctuations for our reference and superlattice samples. The constant temperature difference between the two samples allows us to calculate the thermal conductivity. The experimental setup for the 3ω measurement is quite simple. After wiring our devices using indium dot contacts, we place them under UHV to prevent any thermal dissipation from blackbody radiation. We use a Keithley 3390 function generator to sweep the current frequency

46 38 and two SRS 830 lock-in amplifiers to record the 1 st and 3 rd voltage harmonics. We measure the in-phase component of the third voltage harmonic at several current frequencies, and use these measurements to calculate the temperature fluctuations. Our data for the 3ω measurement are shown in Figure 3-8. Figure ω data taken at T = 10K. It is apparent from these measurements that we were unable to successfully use the 3ω method to calculate the cross-plane thermal conductivity of these superlattices. We did not observe linear behavior of the third voltage harmonic as a function of the frequency, and when we convert the 3ω data into temperature fluctuations at the second harmonic, we do not see the predicted frequency-independent temperature offset between the reference and superlattice sample. One possible reason for this setback is the thickness of the film. 3ω measurements on conducting films are typically performed for film thicknesses on the scale of 1 μm. Our thickest films were 60 nm, so it is possible that the heat generated from the gold wire overwhelmed the film and passed directly into the substrate. If this is the case we would not observe the frequencyindependent ΔTfilm as seen in Figure 3-8, however we would still observe the linear behavior of

47 39 the temperature fluctuations as a function of current frequency from the substrate and SiO2 layer. This could be due to the weaker 3ω signal in materials with a relatively high thermal conductivity. A high substrate thermal conductivity in film measurements presents the advantage of having most of the temperature drop occur across the film itself. However if there is no film present, then a substrate with a low thermal conductivity produces a larger 3ω signal [25]. At present, it seems the best option for obtaining higher quality 3ω data is to increase the thickness of our films. This solution will invariably introduce growth issues, as MBE growths require long periods of time to achieve such pristine samples. The 60 nm superlattice samples required 4-5 hours of II-VI growth alone, and it is possible for the growth rates to become unstable in the time it takes to increase the film thickness to.5-1 μm.

48 Chapter 4 40 Future Investigations: Toward a Figure of Merit The purpose of this work was to grow and begin the process of thermoelectrically characterizing Bi2Te3/Sb2Te3 superlattices. Due to our experimental difficulties measuring the cross-plane thermal conductivity, we were unable to obtain a value for ZT in this work. Additionally, our measurements for the electrical properties were all performed in the in-plane direction. Cross-plane measurements are almost always more complicated than in-plane measurements, and this is certainly the case for measuring the electrical conductivity and Seebeck coefficient. To measure the cross-plane electrical conductivity one needs to utilize a transmission line model (TLM), similar to the process of measuring contact resistance in semiconductor devices. By spacing out electrical contacts and performing 2-point resistance measurements one can obtain the contact resistance of the sample, which includes the resistance of the electrical contacts and the cross-plane resistance of the superlattice. Venkatasumbramanian et al. used this method in their seminal paper [1], and assumed an isotropic carrier concentration to calculate the mobility anisotropy between the cross-plane and in-plane directions. However, one criticism of this paper is that the mobility anisotropy approaches unity as the superlattice period is increased, meaning that the films become isotropic! This result is intuitively surprising because superlattices are inherently anisotropic and the constituent materials themselves are highly anisotropic. While simple in theory, measurement of the cross-plane Seebeck coefficient is a significantly more difficult measurement that requires an incredibly complicated device fabrication process that was beyond the scope of this work. The method presented by Yang et al.

49 [26] also requires an experimental protocol to 41 consistently obtain high-quality 3ω data, so this procedure must be perfected first. The prescribed device is presented in Figure 4-1. The inset voltage probe measures the voltage fluctuations at the second harmonic, which are related to the Seebeck coefficient. This devices allows for simultaneous measurement of the thermopower and thermal conductivity, but is exceedingly complicated to fabricate and Figure 4-1. Device to measure the thermal conductivity and Seebeck coefficient in the cross-plane direction. Similarly to the 3ω measurement, it is also necessary to fabricate a reference sample without the superlattice present. The Seebeck coefficient is then defined as α = ΔV2ω / ΔT2ω. Reproduced from [26]. requires a large amount of experimental finesse and familiarity, both of which are beyond the scope of this work. We have grown and characterized Bi2Te3/Sb2Te3 superlattices with smooth surfaces and high-quality interfaces. With a comprehensive understanding of the 3ω method and a careful fabrication process it will be quite possible to test the validity of the claims made by Venkatasubramanian et al. of the high thermoelectric figure of merit, however due to time and skill limitations we were unable to complete this process.

50 Appendix A 42 MBE Growth Procedure Desorption in the III-V Chamber: 1) Mount InP (11)A substrate onto molybdenum block with pure indium melted on a hot plate at 210 C 2) Load block into buffer chamber, pump down, and transfer to III-V chamber 3) Set the substrate temperature to 625 C and rotate at 12 RPM 4) Open the arsenic shutter when the cell reaches 500 C 5) Desorb the substrate under arsenic for 12 minute while using RHEED to monitor the substrate surface. 6) Turn the substrate temperature to 200 C, turn arsenic off when the substrate temperature reaches 336 C 7) Unload the substrate from the III-V chamber and transfer to the II-VI chamber via the buffer chamber. Growth of Superlattices in the II-VI Chamber: 1) Set the Te, Bi, and Sb cell temperatures to 301 C, 509 C, and 416 C, respectively. 2) Set the substrate temperature to 295 C and rotate at 12 RPM. Monitor the surface temperature using the pyrometer until it reaches 230 C. 3) After substrate has been at temperature for 1 hour, turn on Te cell for 10s. 4) Turn on Sb for 12 minutes and 22 seconds (17 minutes and 48 seconds) to grow 50Å (40Å) of Sb2Te3.

51 5) Check the pyrometer temperature after every Bi2Te3 layer and raise the 43 substrate temperature if the pyrometer temperature falls below 220 C. 6) Turn on Bi for 5 minutes and 40 seconds (11 minutes and 20 seconds) to grow 10Å (20Å) of Bi2Te3. 7) Collect RHEED data after every Bi2Te3 layer to monitor the surface of the film. 8) Repeat steps 4-6 until 10 periods of the superlattice have been grown. 9) Cool the substrate to room temperature and unload the sample to the buffer chamber. Growth of BixSb2-xTe3 Alloy in the II-VI Chamber: 1) Set the Te, Bi, and Sb cell temperatures to 302 C, 509 C, and 418 C, respectively. 2) Set the substrate temperature to 315 C and rotate at 12 RPM. Monitor the surface temperature using the pyrometer until it reaches 230 C. 3) After substrate has been at temperature for 1 hour, turn on Te cell for 10s. 4) Turn on Sb and Bi for 2 hours 13 minutes and 20 seconds. 5) Frequently check the pyrometer temperature and raise the substrate temperature if the pyrometer temperature falls below 220 C. Also collect RHEED data frequently to monitor the sample surface. 6) Cool the substrate to room temperature and unload the sample to the buffer chamber.

52 Appendix B 44 Device Fabrication Processes Hall Bar for Electrical Transport Measurements: 8) Spin coat SPR 3012 photoresist onto sample at 4500 rpm (5000 rpm on smaller samples to prevent edge beads). Bake for 60 seconds at 100 C. 9) Expose photoresist using Karl Suss MA/BA6 contact aligner and Hall bar mask for 8 seconds. 10) Develop resist for 60 seconds in MF CD-26 developer to dissolve exposed resist. 11) Etch in ULVAC NE-550 dry etcher to remove film not protected by photoresist. Spin-coat 3012 Expose and Develop Etch Figure B-1. Hall bar device fabrication process. The end result of this process is a superlattice in the shape of the Hall bar covered in photoresist. We then scratch the resist to expose the film and make electrical contact. Metal Heater for Thermal Transport Measurements: 7) Spin coat LOR 2A lift-off resist onto sample at 3000 rpm. Bake for 180 seconds at 170 C

53 45 8) Spin coat nlof 2020 photoresist onto sample at 4500 rpm. Bake for 60 seconds at 100 C 9) Expose photoresist using Karl Suss MA/BA6 contact aligner and Hall bar mask for 10 seconds. Bake for 60 seconds at 100 C 10) Develop for 60 seconds in MF CD-26 developer to dissolve unexposed resist. Check under microscope to confirm all LOR 2A has been dissolved, and develop for another 30 seconds if necessary. 11) Deposit 100 nm SiO2, 5 nm Ti, and 95 nm Au using electron beam evaporator 12) Lift-off resist and metal layer in Remover 1165 at 80 C Figure B-2. Device fabrication for the 3w devices. The end result is a layer of SiO2 and Ti/Au in the shape of a Hall bar. The device pictured is the superlattice sample, for the reference sample we perform the same process on a bar substrate.