THEORETICAL INVESTIGATIONS OF THERMOELECTRIC EFFECTS IN ADVANCED LOW DIMENSIONAL MATERIALS HUANG WEN (B.Sc., National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. _________________ Huang Wen 14 February 2014 ACKNOWLEDGEMENTS Acknowledgements I would like to express my most sincere gratitude and deepest appreciation to my supervisor, Assoc. Prof. Liang Gengchiau, for his guidance and support throughout the course of my PhD at NUS. It is because of his expertise, understanding and patience that help me overcome the difficulties during my graduate study. Without his supervision and encouragement, this research work would not be possible. I would also like to thank Prof. Wang Jian-Sheng from Department of Physics, Dr. Lan Jinghua, Dr. Gan Chee Kwan, Dr. Quek Su Ying and Dr. Luo Xin from the Institute of High Performance Computing for their lively discussions and valuable advices during the collaboration. I am also grateful to my qualifying exam committee, Assoc. Prof. Mansoor Bin Abdul Jalil and Assoc. Prof. Lee Chengkuo, for their insightful comments and suggestions. It is a pleasure to thank all my colleagues in the Computational Nanoelectronics and Nanodevices Laboratory who made my research life memorable with their help and friendship. In particular, thanks to Dr. Lam Kai-Tak, Dr. Da Haixia, Dr. S. Bala Kumar, Dr. Zeng Minggang, Dr. Chen Ji, Mr. Qian You, and many others for their helpful inputs and discussions. My heartfelt thanks go to my parents for their unconditional support, faith, and love. Finally, my special thanks to my husband, Yu Honghai, for the constant encouragement and always staying by my side. i TABLE OF CONTENTS Table of Contents Acknowledgements . i Summary . v List of Tables viii List of Figures ix List of Symbols xvi Chapter Introduction 1.1 Background 1.2 Objectives . 10 1.3 Organization of Thesis . 10 Chapter Methodology . 12 2.1 Energy Dispersions 13 2.1.1 Tight-binding model 13 2.1.2 Fourth-nearest-neighbour force constant approach . 18 2.1.3 First principles density functional theory 21 2.2 Transport Properties . 22 2.2.1 NEGF approach . 22 2.2.2 Ballistic method based on Landauer approach 25 Chapter Thermoelectric Properties of Ge nanowire s . 29 3.1 Introduction 29 3.2 Simulation Set-up . 30 3.3 Results and Discussions . 30 3.3.1 Geometry effects on thermoelectric performance of Ge NWs 30 3.3.2 Comparison between Ge and Si NWs . 35 3.3.3 Temperature effect on thermoelectric performance 38 3.3.4 Packing effect on thermoelectric performance 39 3.4 Summary 42 Chapter Thermoelectric Properties of Graphene Nanoribbons . 43 ii TABLE OF CONTENTS 4.1 Introduction 43 4.2 Simulation Set-up . 44 4.3 Results and Discussions . 45 4.3.1 Thermoelectric properties of perfect GNRs 45 4.3.2 Thermoelectric properties of chiral GNRs 47 4.3.3 Characterizations of energy dispersions for kinked GNRs . 49 4.3.4 Thermoelectric properties of kinked AA-GNRs . 52 4.3.5 Thermoelectric properties of kinked ZZ-GNRs 54 4.3.6 Thermoelectric properties of various kinked GNRs 57 4.4 Summary 59 Chapter Thermoelectric Performance of MX2 Monolayers . 61 5.1 Introduction 61 5.2 Simulation Set-up . 62 5.3 Results and Discussion . 64 5.3.1 Electronic and phononic band structures of monolayer MX2 64 5.3.2 Thermoelectric properties of monolayer MX2 . 66 5.3.3 Temperature effects . 70 5.4 Summary 75 Chapter Thermoelectric Properties of Few-layer MoS2 and WSe2 76 6.1 Introduction 76 6.2 Simulation Set-up . 77 6.3 Results and Discussions . 80 6.3.1 Choice of exchange-correlation functional for electronic band structure calculations 80 6.3.2 Electronic band structures and transport properties 82 6.3.3 Phonon dispersion and transport properties . 86 6.3.4 Thermoelectric performance 87 6.3.5 Temperature effects . 90 6.5 Summary 94 iii TABLE OF CONTENTS Chapter Conclusion and Future Works . 96 7.1 Conclusions 96 7.2 Future works . 97 7.2.1 Transport properties of graphene with grain boundaries . 97 7.2.2 Thermoelectric performance of topological insulators 100 References . 102 List of Publications 108 iv SUMMARY Summary For the continued realization of scaling down in minimum feature size according to Moore’s law, nanostructure devices have attracted growing attentions due to higher capability and integration. At the nanoscale, quantum confinement effects can be observed, and the conventional theory is no longer valid for the energy carriers, therefore, the theoretical assessment of the carrier transport properties is essential for nanostructured materials. Moreover, the topic of thermoelectric effect, which is the conversion between heat and electric voltage based on both electron and phonon transport, becomes increasingly important as people strive to develop technologies to improve energy efficiency. Hence, this thesis theoretically studies the intrinsic ballistic electron and phonon transport properties, especially with a focus on the thermoelectric performance for novel nanostructured materials beyond silicon. Firstly, semiconducting one-dimensional Ge nanowires are studied. In the ballistic regime, their transport and thermoelectric properties are greatly influenced by geometry effects. The Ge nanowires along [100] direction have better thermoelectric performance in terms of power factor. For extremely small nanowires, the effect of cross-sectional shape is also significant. Comparing the results between triangular Ge and Si nanowires with nm side length, n-type Si nanowires outperform Ge nanowires due to higher number of subband valleys contributing to the electron transport. v SUMMARY Secondly, the investigations of various graphene nanoribbon (GNR) structures show that the thermoelectric performances of kinked GNRs are greatly improved comparing to their straight counterparts. The structures with smaller width have better performance. The first peak value of ZT (ZT1st peak) is larger for the structures with two zigzag GNR (ZGNR) segments but smaller for the structures with only one ZGNR segment, since two ZGNR segments connected by 120◦ can open up a band gap, whereas one ZGNR segment alone still preserves the metallic behavior. Thirdly, two-dimensional transition-metal dichalcogenide layered structures are also studied. The transport and thermoelectric properties are compared among different monolayer structures: MoS2, MoSe2, WS2, and WSe2. The results show that transport properties are not very sensitive to the crystal orientation. As temperature increases, ZT1st peak increases almost linearly except for monolayer n-type WSe2, n-type MoSe2 and p-type WS2, which have higher increasing rates when temperature is high due to the electron transport contribution from an additional valley. Finally, the thermoelectric performances are also investigated for multilayer MoS2 and WSe2. The results show that the thickness dependence is different for different doping types. For MoS2, ZT1st peak decreases as the number of layers increases, with the exception of bilayer in n-type doping, which has a slightly higher ZT1st peak vi value than monolayer. However, for SUMMARY WSe2, bilayer has the largest ZT1st peak in both n-type and p-type doping. At high temperature of 500 K, ZT1st peak can reach remarkably large values for ntype monolayer MoS2 and bilayer WSe2. vii LIST OF TABLES List of Tables Table1-1 Thermoelectric properties of typical low-dimensional materials in past two decades. . Table 2-1 Force-constant parameters for 2D graphene in units of 104 dyn/cm=10 N/m. The term n refers to the nth nearest neighbour atom. . 20 Table 3-1 Energy difference between subband valleys in conduction and valence band E-k (Unit in eV) for Ge NWs with different sizes. 33 Table 3-2 The number of circular Si NWs can be packed into the square device of the side length of µm. The packing distance between NWs increases from nm to 10 nm, where nm is large enough to assume negligible interactions between Si NWs. 40 Table 5-1 Lattice constants, electronic energy band gaps and effective masses (unit in m0) at K point (kx along K→Γ and ky along K→M) for electrons (n-type) and holes (p-type) for monolayer MX2 (M=Mo,W; X=S,Se). 66 Table 6-1 Comparison of the calculated band gaps with different functionals.  is defined as the k-point close to mid-way alongthe Γ-K. 78 viii CHAPTER In general, the high ZT values at high temperature are also related with the relatively large band gaps of MoS2 and WSe2, so that the bipolar effect is not significant. On the other hand, the ratio of Ke to Kph increases with increasing temperature, which suggests the Ke has a larger influence at higher T. We note that very high ZT1st peak values of 1.6 and 2.1 are obtained for n-type 1TL-MoS2 and 2TL-WSe2 at 500K. We also note that a recent study show that our assumption of unchanged electronic band structure is valid for MoS2 in the temperature range of 100-500 K due to the well-separated indirect and direct gaps in bulk and thin film MoS2, but there may be some deviations in WSe2, which need further study for the details. 6.5 Summary This chapter studies thermoelectric performance and electron and phonon properties of bulk and thin film MoS2 and WSe2, using a ballistic transport approach based on electronic band structures and phonon dispersions obtained from first-principles calculations. It is found that the electronic band gaps and thermal conductance per thickness approach to the bulk when the thickness increases. At room temperature, the value of ZT1st peak decreases with increasing thickness when the thickness exceeds 2TL for both MoS2 and WSe2. The 1TL shows the largest ZT1st peak only in n-type MoS2, but are smaller than 2TL in other cases. Our calculations suggest that the competition between G and Kph dominates the thickness dependence of ZT1st peak at room temperature, 94 CHAPTER and the transport direction has little effect on the thermoelectric performance. As temperature increases, ZT1st peak generally increases at a slower rate at low temperature and faster rate at high temperature due to the different changes in S, G, Kph and Ke. The ZT1st peak can reach remarkably large values of 1.6 and 2.1 for n-type 1TL-MoS2 and 2TL-WSe2, suggesting these transition-metal dichalcogenides are promising thermoelectric materials. 95 CHAPTER Chapter Conclusion and Future Works 7.1 Conclusions In this thesis, the background of thermoelectrics is introduced, followed by a summary of the computational method to evaluate it. Then, using the ballistic transport model based on electron and phonon energy dispersions, the thermoelectric performance are investigated theoretically for some advanced low-dimensional materials. Firstly, one-dimensional potential thermoelectric materials are considered. For Ge nanowires, [100] direction have better thermoelectric performance compared to [110] and [111] directions. The transport and thermoelectric properties are greatly influenced by geometry effects, especially for extremely small nanowires, cross-sectional shape effect is very significant. Comparing between triangular Si and Ge nanowires, n-type Si can outperform n-type Ge for nanoscale cases. The temperature and packing effects are also investigated. For graphene nanoribbons, the thermoelectric performances of kinked GNRs are greatly improved compared to their straight counterparts. With the presence of kink structures, thermoelectric properties are less sensitive to edge geometries, which may be preferable in fabrication. The thermoelectric properties of various hybridized kinked GNRs with different connecting segments and angles are investigated as well. Same as in the straight cases, structures with smaller width of the connecting segments have better performance. Then, for 96 CHAPTER two-dimensional materials, monolayer and multilayer transition-metal dichalcogenide layered structures are studied. The transport and thermoelectric properties are compared between MoS2, MoSe2, WS2, and WSe2 monolayers. The results show that transport properties are not very sensitive to crystal orientations. The results of multilayer MoS2 and WSe2 show that the thickness dependence is different for n-type and p-type doping types. The temperature effects are also investigated. To conclude, these physical understanding of the electron and phonon transport properties in ballistic regime can serve as a guideline for experimentalists on the new direction for low-dimensional thermoelectric materials. 7.2 Future works There are also some interesting topics that can be extended from the works presented here. The following sections introduce some possible directions. 7.2.1 Thermoelectric properties of graphene with grain boundaries For graphene, structural defects appeared during growth or processing are of practical significance on the performance, such as point and line defects. Grain boundaries are line defects separating single-crystalline domains with preferably periodic structure due to minimum formation energy. After individual dislocation is first imaged in free-standing graphene layer by 97 CHAPTER transmission electron microscopy (TEM) [118], recently, more reports have shown grain boundaries in graphene produced by chemical vapor deposition (CVD) [119, 120], opening an opportunity for studies on the structure, properties and control of grain boundaries in graphene. Theoretically, first principles calculations are used to study the electronic properties of graphene with grain boundaries [121-123]. The structure is dictated by the misorientation angle of two crystallites. For any possible misorientation angle, it is possible to construct a grain boundary structure in which all carbon atoms maintain their three-fold coordination. The grain boundaries can be classified into class I (symmetric) and class II (asymmetric). The electronic properties are different for graphene with different classes of grain boundaries from metallic to semiconducting based on the theory of transverse momentum conservation, and class II grain boundaries can introduce large transport gaps. These transport gaps and electrical conductance can be modulated by strains on grain boundaries [123]. The effect of grain boundaries on the thermal conductivity of graphene is also studied theoretically using NEGF approach [124, 125]. Unlike the structural dependence on electronic transport, graphene with all types of grain boundaries have excellent thermal conductivity, and among which, symmetric zigzag grain boundaries show the highest thermal conductance, yielding about 80% transmission of the pristine graphene. As the temperature increases, the thermal conductance of grain boundaries increases. Similarly to the pristine graphene discussed above, the out-of-plane acoustic 98 CHAPTER mode is dominant in thermal conductivity of graphene with grain boundaries at low temperatures [124]. Therefore, in future works, we can investigate the details of electron and phonon transport of graphene with various grain boundary structures using NEGF. Fig. 7-1 shows two typical structures of graphene with grain boundaries. For graphene with grain boundary misorientation angel θ = 30 and other asymmetric types, two possible connection orders can be formed for device with two grain boundaries in the channel. Fig. 7-1 Structures of graphene with grain boundary of (a) misorientation angle θ = 21.8 and (b) misorietation angel θ = 30. (c) Structures of a device with graphene with two reversely positioned grain boundaries as the transport channel. For asymmetric grain boundaries, two connections AZA and ZAZ are possible. The distance between the grain boundaries is d. 99 CHAPTER 7.2.2 Thermoelectric performance of topological insulators Recent theoretical and experimental works have demonstrated that some of the traditional thermoelectric materials are topological insulators [126-130], which have opened up a new direction for ZT enhancement. A topological insulator (TI) behaves as an insulator in the interior and contains conducting surface states protected by the particle number conservation and time-reversal symmetry topologically [131]. TI and thermoelectric materials have similar requirements of heavy elements and small band gaps. For TIs, they can generate large spin-orbit coupling to form topological surface states, and modify the band structure with an inverted band. For thermoelectric materials, they can reduce thermal conductivity while maintaining large power factor. An example is Bi2Te3 whose bulk forms have been used commercially for decades [4]. It is predicted that a tunable hybridization-induced band gap of surface states can be generated to improve low temperature thermoelectric performance in Bi2Te3 thin films in nanoscale. This technique can also be applied to other materials in the same class [132]. Mechanically exfoliated stacks of Bi2Te3 thin films have demonstrated the reduction of thermal conductivity with preserved electrical properties in the topological-insulator surface transport regime [133]. The preliminary study on Bi2Te3 single quintubles has shown that ZT can increase to 140%~250% mainly due to the reduction in the lattice thermal conductivity. 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Liang, "Theoretical study on thermoelectric properties of Ge nanowires based on electronic band structures," IEEE Electron Device Lett. 31, 1026 (2010). 3. W. Huang, J.-S. Wang, and G. Liang, "Theoretical study on thermoelectric properties of kinked graphene nanoribbons," Phys. Rev. B 84, 045410 (2011). 4. M. Zeng, W. Huang, and G. Liang, “Spin dependent thermoelectric effects in Graphene-based spin valves,” Nanoscale 5, 200 (2013). 5. W. Huang, H. Da, and G. Liang, "Thermoelectric performance of MX2 (M=Mo,W; X=S,Se) monolayers," J. Appl. Phys. 113, 104304 (2013). 6. K. L. Low, W. Huang, Y.-C. Yeo, G. Liang, “Ballistic Transport Performance of Silicane and Germanane Transistors,” IEEE Trans. Electron Devices 61, 1590 (2014). 7. W. Huang, X. Luo, C. K. Gan, S. Y. Quek, and G. Liang, “Theoretical study of thermoelectric properties of few-layer MoS2 and WSe2,” Phys. Chem. Chem. Phys. 16, 10866 (2014). Book Chapters 1. W. Huang, A. Nurbawono, M. Zeng, G. Gupta, and G. Liang, “Electronic structure of graphene based materials and their carrier transport properties,” Chapter 21, Volume (Nanostructure and Atomic Arrangement) of Graphene Science Handbook, CRC, in press. 2. G. Gupta, M. Zeng, A. Nurbawono, W. Huang, and G. Liang, “Applications of Graphene Based Materials in Electronic Devices,” Chapter 20, Volume (Applications and Industrialization) of Graphene Science Handbook, CRC, in press. 108 PUBLICATIONS Conference Publications 1. W. Huang, C. S. Koong, and G. Liang, "Theoretical Study on Thermoelectric Properties of Ge and Si Nanowires," 2009 International Conference on Solid State Devices and Materials (SSDM 2009), Sendai Kokusai Hotel, Miyagi, Japan, Oct. 7-9, 2009. 2. W. Huang, and G. Liang, "Size and Chirality Dependence on Thermoelectric Properties of Graphene Nanoribbons," 2010 International Conference on Solid State Devices and Materials (SSDM 2010), Tokyo, Japan, Sep. 22-24, 2010. 3. W. Huang, C. S. Koong, and G. Liang, "Theoretical Study on Geometry and Temperature Effects of Thermoelectric Properties of Si and Ge Nanowires," International Conference on Solid-State and Integrated Circuit Technology (ICSICT 2010), InterContinental, Pudong, Shanghai, China, Nov. 1-4, 2010. 4. W. Huang, and G. Liang, “Effects of vacancy and magnetic field on thermoelectric properties of straight and kinked graphene nanoribbons,” 15th International Workshop on Computational Electronics, University of Wisconsin, Madison, USA, May 22-25, 2012. 109 [...]... to the increasing world’s demand and the crisis of running out of fossil fuel reserves To meet this crucial challenge, great attention has been focused on thermoelectric 1 CHAPTER 1 materials, which can convert heat directly into electricity providing costeffective green energy conversion This chapter gives a review of the status of the emerging field of advanced low- dimensional thermoelectric materials, ... PbTe and SiGebased nanocomposites, mainly due to the reduced thermal conductivity with the introduction of nanometer-sized grains [26-32] Thermoelectric performance of typical examples of the nanocomposties and other lowdimensional materials are summarized in Table 1-1 Table 1-1 Thermoelectric properties of typical low- dimensional materials in past two decades Materials Carrier Type ZT Temperature... corresponding bulk form The low- dimensional materials benefit from the quantum confinement of the electron charge carrier The electron energy bands are narrower with increased confinement and decreased dimensionality, resulting in high effective masses and large Seebeck coefficients Meanwhile, engineered heterostructures can maintain a high electrical conductivity due to electron filtering [15] In addition,... various interface scatterings in small length 6 CHAPTER 1 scale can effectively reduce the lattice thermal conductivity Hence, the quantum confinement effect can be used to increase S and control S and σ independently while minimizing κph, and therefore enhance ZT [14] Using the above principles, a variety of low- dimensional materials have been proposed and studied recently The first demonstration of a low- dimensional. .. doping and introduce point defects in solid solutions, which has limitations due to the decrease of carrier mobility while reducing the thermal conductivity From 1960 to 1990, there has been little progress on enhancement of ZT However, in mid 1990s, the interest in advanced thermoelectric materials was renewed due to the realization of complexity at multiple length scales Since then, the field of thermoelectrics... thermoelectric properties The results of this thesis should reveal the physical insights of these advanced low- dimensional thermoelectric materials and their potential in energy management applications 1.3 Organization of thesis In this thesis, the main research focus is on the computational investigations on carrier transport properties and thermoelectric performance of Ge nanowires, GNRs and transition-metal... obtaining the eigenvalues of the periodic Hamiltonian Hp at different k points, the electronic band structures of 5-AGNR can be found as shown in Fig 2-2(a) In the simulation, the hopping integral of t = 2.7 eV is used If considering edge effects for AGNR, t corresponding to the edge points should be modified to 1.12t [47] so that the results will be more close to the trends observed in first principal... achieved in their films [43, 44] Hence, in this 9 CHAPTER 1 work, the above-mentioned novel 1D and 2D materials are studied on their thermoelectric performance and the intrinsic transport properties 1.2 Objectives The objectives of the research work in this thesis are to understand the material properties of advanced low- dimensional materials: Ge nanowires, GNRs and transition-metal dichalcogenides, investigate...LIST OF FIGURES List of Figures Fig 1-1 Illustration of thermoelectric effects: (a) energy generation and (b) heat cooling (c) State -of- the-art thermoelectric devices 3 Fig 2-1 The geometry of a 5-AGNR The rectangle box denotes the unit cell for π-orbital tight-binding method The atoms are numbered corresponding to the Hamiltonian 14 Fig 2-2 (a) The electronic band structure of 5-AGNR... absorption and dissipation of a current-carrying conductor with a temperature gradient It is only significant when the temperature difference is large Fig 1-1 Illustration of thermoelectric effects: (a) energy generation and (b) heat cooling (c) State -of- the-art thermoelectric devices With thermocouples as the building blocks as shown in Fig 1-1(c), the thermoelectric effects can be applied in several applications . THEORETICAL INVESTIGATIONS OF THERMOELECTRIC EFFECTS IN ADVANCED LOW DIMENSIONAL MATERIALS HUANG WEN (B.Sc., National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF. Characterizations of energy dispersions for kinked GNRs 49 4.3.4 Thermoelectric properties of kinked AA-GNRs 52 4.3.5 Thermoelectric properties of kinked ZZ-GNRs 54 4.3.6 Thermoelectric properties of various. like to thank Prof. Wang Jian-Sheng from Department of Physics, Dr. Lan Jinghua, Dr. Gan Chee Kwan, Dr. Quek Su Ying and Dr. Luo Xin from the Institute of High Performance Computing for their