本研究以多尺度方式分析有機與無機材料奈米線熱電晶片之電子與聲子傳輸現象，從計算量子力學(Computational Quantum Mechanics)出發，模擬奈米尺度純矽奈米線其聲子頻散圖與電子態密度圖後，以Boltzmann傳輸方程式計算介觀尺度的電子傳導率、Seebeck係數與熱傳導係數，與文獻微奈米尺度實驗數據比較其電性、熱性與熱電優值(Figure of Merit)。確定模擬正確性後，再以相同方法推估矽鍺合金與有機導電高分子聚合物奈米線的鬆弛時間(Relaxation Time)與平均自由徑(Mean Free Path)，估計其熱傳導率、電導率、Seebeck係數與熱電優值。最後以系統動態模擬巨觀尺度下以有機與無機熱電材料作為電動車熱電晶片之空調系統設計，在最低能量消散控制策略下，其冷凍空調性能係數COP (Coefficient of Performance)與現行汽車壓縮機冷媒空調效率比較並做未來可行性分析。
理論方面，首先以密度泛函理論（Density Functional Theory, DFT）中的PBE(Perdew–Burke–Ernzerhof)模型找出奈米線結構的最小能量，計算出無機矽鍺奈米線與有機導電高分子聚合物奈米線的電子態密度圖等電性相關物理量後，再以Boltzmann Equation計算奈米線電子傳導率與Seebeck係數。在聲子熱性方面，我們以密度泛函微擾理論（Density Functional Perturbation Theory, DFPT）計算出奈米線的聲子態密度圖、聲子頻散圖，分析得到其熱容(Heat Capacity)、聲子群速度(Group Velocity)與平均自由徑(Mean Free Path)後，計算出奈米線的熱傳導係數。再以相同的方法建立其他有機與無機奈米線原子結構，以第一原理評估各固態物理性質。最後在Euler-Lagrange架構下優化非線性動態系統的升壓器(Boost Converter)與降壓器(Buck Converter)能量轉換效率，模擬以創新型有機與無機熱電材料作為電動車熱電晶片空調之COP與空調性能。
結論為理想聚對亞苯聚合物奈米線熱電晶片空調有可能超越目前車用傳統壓縮機式空調系統之性能(冷氣模式下"COP ≥ 2.5" ，暖氣模式下"COP ≥ 3" )，進而達到電動車輛的動力系統至空調系統全面電動化的目的。

The thermoelectric chips can convert heat into electricity and vice versa. So they can be used as power generators, waste heat recovery systems, refrigerators and air conditoners. The nowadays commercial thermoelectric materials are rare and expensive. Therefore, in this thesis we choose common materials like silicon, germanium and conductive polymer as thermoelectric chips in which we use computational quantum mechanics to find their DOS (Density of States) and band structures. BTE (Boltzmann Transport Equation) is then introduced to calculate the electrical properties of the nanostructures, such as Seebeck coefficient, electrical conductivity and electron thermal conductivity.
DFPT (Density Functional Perturbation Theory) is used to simulate the phonon DOS and dispersion relation of the semiconductor and conductive polymer nanowires, which can be used to calculate the phonon group velocity, heat capacity and mean free path. Next, we obtain the phonon thermal conductivity of the nanostructures under phonon gas model. After we predict the electrical and thermal properties of the nanowires, we can calculate their figure of merit (ZT). Improved doping poly-p-phenylene (PPP) nanowire is then chosen to design the thermoelectric chip air conditioner because it has the highest ZT. The coefficient of performance (COP) and temperature dynamics of an electric vehicle’s cabin is calculated. The energy losses of power converters we used are minimized under the Euler-Lagrange (EL) framework.
In conclusion, novel PPP-based thermoelectric chip air conditioner will be a potential air conditioner candidate for future electric vehicles since it is able to increase mileage and improve climate control.

摘要 I
誌謝 II
符號表 VI
第一章 緒論 1
1.1奈米結構提升材料之熱電優值 5
1.2矽鍺與其奈米導線熱電材料文獻回顧 6
1.3有機導電高分子熱電材料文獻回顧 6
1.4研究動機與目標 7
第二章 計算量子力學與固態物理理論 10
2.1 微擾理論 11
2.1.1 一階能量修正 13
2.1.2 一階波函數修正 13
2.1.3 二階能量修正 14
2.2 Born-Oppenheimer近似假設 15
2.3密度泛函理論 15
2.3.1 Kohn-Sham定理 16
2.3.2 Bloch定理 17
2.3.3自洽場計算 18
2.4密度泛函微擾理論 19
2.5原子震盪與聲子傳播 21
2.6動態矩陣與聲子頻散關係 23
2.7聲子熱傳導率 25
2.8 Boltzmann傳輸方程式 28
2.9冷凍空調性能係數 31
第三章 模擬方法與模型建構 33
3.1模擬方法與計算流程 33
3.2矽鍺奈米線的建立 35
3.3有機高分子聚合物奈米線的建立 37
第四章 結果與討論 43
4.1塊材矽的熱相關性質 43
4.2矽鍺奈米線的熱性與電性 44
4.3有機導電高分子奈米線的熱性與電性 50
4.4電動車用熱電晶片空調系統性能分析 57
第五章 結論與未來工作建議 61
5.1結論 61
5.2未來工作建議 62
參考文獻 63

[1] V. Rama, S. Edward, C. Thomas, O. Brooks, Thin-film thermoelectric devices with high room-temperature figures of merit. Nature, 413, p.597-602, 2011.
[2] Mildred S. Dresselhaus, Gang Chen, Ming Y. Tang, Ronggui Yang, Hohyun Lee, Dezhi Wang, Zhifeng Ren, Jean-Pierre Fleurial and Pawan Gogna, New directions for low-dimensional thermoelectric materials. Advanced Materials, 19, p.1043-1053, 2007.
[3] G. J. Snyder and E. S. Toberer, Complex thermoelectric materials. Nature Materials, 7, p.105-114, 2008.
[4] Allon I. Hochbaum, Renkun Chen, Rau Diaz Delgado, Wenjie Liang, Erik C. Garnett, Mark Najarian, Arun Majumdar and Peidong Yang, Enhanced thermoelectric performance of rough silicon nanowires. Nature, 451, p.163-167, 2008.
[5] Akram I. Boukai, Yuri Bunimovich, Jamil Tahir-Kheli, Jen-Kan Yu, William A. Goddard III and James R. Heath, Silicon nanowires as efficient thermoelectric materials. Nature, 451, p.168-171, 2008.
[6] G-H. Kim, L. Shao, K. Zhang and K. P. Pipe, Engineered doping of organic semiconductors for enhanced thermoelectric efficiency. Nature Materials, 12, p.719-723, 2013.
[7] Li-Dong Zhao, Shih-Han Lo, Yongsheng Zhang, Hui Sun, Gangjian Tan, Ctirad Uher, C. Wolverton, Vinayak P. Dravid and Mercouri G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature, 508, p.373-377, 2014.
[8] M. C. Steele and F. D. Rosi, Thermal Conductivity and Thermoelectric Power of Germanium-Silicon Alloys. Journal of Applied Physics, 29, p.1517-1520, 1958.
[9] L. D. Hicks and M. S. Dresselhaus, Effect of Quantum-Well Structures on the Thermoelectric Figure of Merit. Physical Review B, 47, p.12727-12731, 1993.
[10] L. D. Hicks and M. S. Dresselhaus, Thermoelectric Figure of Merit of a One-Dimensional Conductor. Physical Review B, 47, p.16631-16634, 1993.
[11] L. D. Hicks, T. C. Harman, X. Sun, and M. S. Dresselhaus, Experimental study of the effect of quantum-well structures on the thermoelectric figure of merit. Physical Review B, 53, p.10493-10496, 1996.
[12] Eun Kyung Lee, Liang Yin, Yongjin Lee, Jong Woon Lee, Sang Jin Lee, Junho Lee, Seung Nam Cha, Dongmok Whang, Gyeong S. Hwang, Kedar Hippalgaonkar, Arun Majumdar, Choongho Yu, Byoung Lyong Choi, Jong Min Kim, and Kinam Kim, Large Thermoelectric Figure-of-Merits from SiGe Nanowires by Simultaneously Measuring Electrical and Thermal Transport Properties. Nano Lett., 12, p.2918−2923, 2012.
[13] H. Shirakawa, E. J. Louis, A. G. Macdiarmid, C. K. Chiang, and A. J. Heeger, Synthesis of Electrically Conducting Organic Polymers - Halogen Derivatives of Polyacetylene. Journal of the Chemical Society-Chemical Communications, 16, p.578-580, 1977.
[14] H. Yan, N. Ohno, and N. Toshima, Low thermal conductivities of undoped and various protonic acid-doped polyaniline films. Chemistry Letters, 4, p.392-393, 2000.
[15] G-H. Kim, L. Shao, K. Zhang and K. P. Pipe, Engineered doping of organic semiconductors for enhanced thermoelectric efficiency. Nature Materials, 12, p.719-723, 2013.
[16] FAO, WFP and IFAD, The State of Food Insecurity in the World 2012. Economic growth is necessary but not sufficient to accelerate reduction of hunger and malnutrition. FAO, Rome, 2012.
[17] M. J. Verstraete and Z. Zanolli, Density Functional Perturbation Theory. Lecture Notes of the 45th IFF Spring School “Computing Solids - Models, ab initio methods and supercomputing”, Forschungszentrum Julich, 2014.
[18] Chris-Kriton Skylaris, Perturbation Theory. Quantum Chemistry, 2006.
[19] Stefano Baroni, Stefano de Gironcoli, Andrea Dal Corso, and Paolo Giannozzi, Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys., 73, 2001.
[20] Xavier Gonze and Changyol Lee, Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density functional perturbation theory. Phys. Rev. B, 55, 1997.
[21] Steven H. Simon, Lecture Notes for Solid State Physics. Oxford University, 2012.
[22] Masashi Yamaguchi, Time-Resolved Phonon Spectroscopy and Phonon Transport in Nanoscale Systems. Length-Scale Dependent Phonon Interactions, Springer Science+Business Media, p.207-226, 2014.

[23] P. G. Klemens, Thermal Conductivity. Academic London, Vol. 1, 1969.
[24] G. S. Nolas, J. Sharp and H. J. Goldsmid, Transport of Heat and Electricity in Solids. Materials Science, 45, p.15-57, 2001.
[25] Á.G. Miranda, T.S. Chen, C.W. Hong, Feasibility study of a green energy powered thermoelectric chip based air conditioner for electric vehicles. Energy, 59, p.633-641, 2013.
[26] Deyu Li, Yiying Wu, Philip Kim, Li Shi, Peidong Yang and Arun Majumdar, Thermal conductivity of individual silicon nanowires. Applied Physics Letters, 83, p.2934-2936, 2003.
[27] N. Basescu, Z.-X. Lui, D. Moses, A. J. Heeger, H. Naarmann and N.Theophilou, High electrical conductivity in doped polyacetylene. Nature, p.403-405, 1987.
[28] Murat Ates, Tolga Karazehir and A. Sezai Sarac, Conducting Polymers and their Applications. Current Physical Chemistry, 2, p.224-240, 2012.
[29] David Parker, Jan Bussink, Hendrik T. van de Grampel, Gary W. Wheatley, Ernst-Ulrich Dorf, Edgar Ostlinning, Klaus Reinking, Polymers, High Temperature. Wiley-VCH: Weinheim, 2002.
[30] P. D. Desai, Thermodynamic Properties of Iron and Silicon. Journal of Physical and Chemical Reference Data, 15, p.967-983, 1986.
[31] H. R. Shanks, P. D. Maycock, P. H. Sidles and G. C. Danielson, Thermal conductivity of silicon from 300 to 1400 K. Physical Review, 130, p.1743-1748, 1963.
[32] Renkun Chen, Allon I. Hochbaum, Padraig Murphy, Joel Moore, Peidong Yang, and Arun Majumdar, Thermal conductance of thin silicon nanowires. Physical Review Letters, 101, 2008.
[33] Jivtesh Garg, Nicola Bonini, and Nicola Marzari, First-Principles Determination of Phonon Lifetimes, Mean Free Paths, and Thermal Conductivities in Crystalline Materials:Pure Silicon and Germanium. Length-Scale Dependent Phonon Interactions, 2014.
[34] Hosung Lee, Alaa M. Attar and Sean L. Weera, Performance Prediction of Commercial Thermoelectric Cooler Modules using the Effective Material Properties. Journal of Electronic Materials, 44, p.2157-2165, 2015.
[35] R. A. Serway, Principles of physics. 2nd ed. Saunders golden sunburst series, Fort Worth: Saunders College Pub. Xxxii, p.954, 1998.
[36] Bharat Bhushan, Springer Handbook of Nanotechnology. 3rd ed. Springer, p354, 2010.