本研究結和太陽能-熱電晶片複合式發電系統(Photovoltaic - Thermoeletric Hybrid System)以及太陽熱電能產生器(Solar Thermoelectric Generator) 的優點，欲設計出更高效率的鈣鈦礦太陽能熱電晶片 (Perovskite Photovoltaic - Thermoeletric Chip)，並用第一原理 (First Principles) 計算模擬塊材氯碘有機鈣鈦礦 (MAPbI3-xClx) 半導體材料的電性、熱性和光學性質，分析不同氯 (Cl) 摻雜濃度 (x) 的光熱電性質，並找出最佳熱電優值。(ZT)
三維塊材無氯有機鈣鈦礦(MAPbI3)是深具潛力的礦石半導體材料，可應用於太陽能電池與熱電晶片等，其具有良好導電性但低熱傳導率，且容易製備。本研究先模擬塊材MAPbI3以確定理論模式與實驗結果相符，再進行MAPbI3-xClx的模擬。建立單位晶胞(Unit Cell)模型後，先以平面波基底(Plane Wave Basis)、Kohn-Sham定理、PBE(Perdew-Burke-Ernzerhof )交換勢能、自洽場(Self Consistent Field, SCF)方法進行幾何結構最佳化，接著在倒晶格空間(Reciprocal Space)進行電子和聲子的計算。電子計算上，以密度泛函理論(Density Functional Theory, DFT)計算能帶結構圖和電子態密度圖求得能隙之光電性質，再搭配波茲曼傳輸方程式(Boltzmann Transport Equation, BTE)求得電導率σ、載子熱傳導率 κ_el、Seebeck係數S；聲子計算上，以密度泛函微擾理論(Density Functional Perturbation Theory, DFPT)計算聲子頻散圖和聲子態密度圖，搭配德拜模型(Debye Model)求聲子熱傳導率 κ_ph。
在熱電性質的研究上，本研究率先研究塊材MAPbI3-xClx 做為熱電晶片材料的價值及可行性，並使用二階微擾理論計算MAPbI3熱電性質，結果和實際值大致吻合，證實了理論及計算方法的適用性和可靠度。研究中發現熱傳的貢獻主要來自聲子，其中又以光頻聲子貢獻較多，電子熱傳微乎其微。摻雜Cl不僅提升電導率，同時因軟模態的發生以及平均質量降低也導致聲子熱傳導率不斷升高。所幸在極低濃度摻雜時 (x=0.25)，電導率提升但聲子熱傳導率無明顯上升的情況下，本質狀態MAPbI3 (x=0)的ZT值可從 1.41×〖10〗^(-7) 升至 8.26×〖10〗^(-7)，成長6倍。當重摻雜電子或電洞使濃度達到 〖10〗^20 cm^(-3)，可分別從 2.00×〖10〗^(-5) 升至 2.09×〖10〗^(-4)， 2.21×〖10〗^(-4) 升至 2.09×〖10〗^(-3)，約為本質狀態下的1000倍。
在光學性質的研究上，本研究瞭解到MAPbI3-xClx主要吸收的光波段為40nm < λ < 400nm的紫外線和400nm < λ < 700nm的可見光，光吸收範圍廣，但吸收率會隨著Cl濃度增加而下降，因此未來設計太陽能熱電晶片，在熱吸收層的設計上應主要加強 λ ≥ 400 nm的熱輻射吸收，即為可見光到紅外線區域。最後本研究發現不論是在太陽能電池光吸收層或熱電晶片上的應用，Cl濃度x=0.25的MAPbI2.75Cl0.25是最佳的配比濃度，作為光吸收層可維持和MAPbI3相仿的光吸收，作為熱電晶片有著和 MAPbI3 一樣低的熱傳導率κ ~ 0.3 W/mK，但有更高的電導率和席貝克係數，因此可提升太陽能電池和熱電晶片的表現。

This research starts with the computational quantum mechanics, using first principles to simulate the chlorine doping effect with different concentration (x value) on the optical and thermoelectric properties of 3D mixed halide methylammonium lead perovskites (MAPbI3-xClx). Finding the highest thermoelectric figure of merit (ZT) and suitable solar absorbance range are our major targets.
The 3D bulk MAPbI3 is considered as a potential mineral semiconductor material for future solar cells and thermoelectric chips. It has good electrical properties, low thermal conductivity, and only needs low cost to produce. This research employed the Khon-Sham theory, PBE (Perdew–Burke–Ernzerhof) exchange correlation energy functional, and self-consistent field (SCF) method, to calculate the plane wave in the reciprocal space. In the electron simulation, we used the density functional theory (DFT) to evaluate the band structure and electron density of states to calculate the optical band gaps. Then applying Boltzmann transport equation (BTE) to calculate the electrical conductivity σ, carrier thermal conductivity κ_el, and Seebeck coefficient S. In the phonon simulation, we used density functional perturbation theory (DFPT) to evaluate the phonon dispersion relation and phonon density of states, and applied the Debye model to calculate the phonon thermal conductivity κ_ph.
This research has found that the main contribution to the heat transfer is mainly from phonons, especially the optical parts, the contribution from electrons is little. In addition, doping Cl will increase not only electrical conductivity, but also phonon thermal conductivity. The latter is because of the production of soft modes and the reduction of averaged weight. At the very low Cl doping concentration, e.g. x=0.25, electrical conductivity increases while the thermal conductivity almost remain the same values as MAPbI3, ZT value rises up from 1.41×〖10〗^(-7) to 8.26×〖10〗^(-7). The latter is about 6 times greater than the former. Doping carriers, such as electrons or holes, ZT value can grow up to 10 times the value of MAPbI3, at the same carrier concentration condition. When electron or hole doping concentration reaches 〖10〗^20 cm^(-3), the ZT value of MAPbI3 would achieve 2.00×〖10〗^(-5) and 2.21×〖10〗^(-4) respectively, which is 1000 times the value of the intrinsic condition, and it’s 2.09×〖10〗^(-4) and 2.09×〖10〗^(-3) for condition x=0.25.
In the study of the optical property, we obtained that the main absorbance wavelength located in the ultraviolet light region (40nm < λ < 400nm) and visible light region (400nm < λ < 700nm). MAPbI3-xClx has wider absorption range, but its absorption coefficient decreases with the Cl concentration. The design of the heat absorber of the solar thermoelectric chips must enhance the thermal radiation absorption in the range of λ ≥ 400 nm, which is the region from visible to infrared light. Finally, the conclusion of this research is that the MAPbI2.75Cl0.25 is the best tuning for the light absorption layer in the solar cell, and highest ZT value for the thermoelectric chip. Hence it can improve the performance of future solar thermoelectric chips.

摘要……………………………………………………………………………………………………….…I
圖表目錄…………………………………………………………………………………………………IX
符號及專有名詞………………………………………………………………………………………XI
第一章 緒論……………………………………………………………………………………………..1
1.1 太陽能熱電晶片發展簡介………………………………………………….…........1
1.2 熱電晶片簡介………………………………………………………………………........4
1.3 研究方法與目的………………………………………………………………………...6
1.4 氯碘有機鈣鈦礦太陽能電池文獻回顧………………………………………...7
1.5 氯碘有機鈣鈦礦熱電晶片文獻回顧………………………………………........8
第二章 計算量子力學與固態物理理論……………………………………………………...9
2.1 微擾理論…………………………………………………………………………………10
2.1.1 一階能量修正…………………………………………………………….........12
2.1.2 一階波函數修正……………………………………………………....………12
2.1.3 二階能量修正………...………………………………………………...………13
2.2 Born–Oppenheimer近似…………………………………………………..……..14
2.3 密度泛函理論……………………………………………………………………….…15
2.3.1 Kohn-Sham定理……………………………………………………………...15
2.3.2 自洽場計算……………………………………………………………………...16
2.3.3 Bloch定理…………………………………………………………………........17
2.4 密度泛函微擾理論…………………………………………………………….…….19
2.5 原子振盪與聲子傳播……………………………………………………………….20
2.6 動態矩陣與聲子頻散關係………………………………………………………..23
2.7 二階聲子熱傳導率…………………………………………………………………..25
2.8 電子波茲曼傳輸方程式…………………………………………………………....28
第三章 模擬方法與模型建構…………………………………………………………………..32
3.1 模擬方法與計算流程………………………………………………………………32
3.2 氯碘有機鈣鈦礦模型建立…………………………………………………….…33
第四章 結果與討論………………………………………………………………………………...37
4.1 無氯有機鈣鈦礦的熱電性質……………………………………………………37
4.2 氯碘有機鈣鈦礦的光學性質……………………………………………………39
4.3 氯碘有機鈣鈦礦的熱電性質……………………………………………………41
4.3.1 氯摻雜…………………………………………………………………………….41
4.3.2 載子摻雜…………………………………………………………………………48
第五章 結論與未來工作建議………………………………………………………………..…52
5.1 結論…………………..………………………………………………………………......52
5.2 未來工作建議.………………………………………………………………………..53
參考文獻……………………………………………………………………………………………......54

[1] N. Wang, L. Han, H. He, N. H. Park, & K. Koumoto. A novel high-performance photovoltaic–thermoelectric hybrid device. Energy & Environmental Science, 4(9), 3676-3679, 2011

[2] A. Makki, S. Omer, Y. Su, & H. Sabir. Numerical investigation of heat pipe-based photovoltaic–thermoelectric generator (HP-PV/TEG) hybrid system. Energy Conversion and Management, 112, 274-287, 2016

[3] W. Zhu, Y. Deng, Y. Wang, S. Shen, & R. Gulfam. High-performance photovoltaic-thermoelectric hybrid power generation system with optimized thermal management. Energy, 100, 91-101, 2016

[4] J. Zhang, Y. Xuan, & L. Yang. A novel choice for the photovoltaic–thermoelectric hybrid system: the perovskite solar cell. International Journal of Energy Research, 40(10), 1400-1409, 2016

[5] D. Kraemer et al. High-performance flat-panel solar thermoelectric generators with high thermal concentration. Nature Materials, 10(7), 532-538, 2011

[6] A. Kojima, K. Teshima, Y. Shirai and T. Miyasaka. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. Journal of the American Chemical Society, 131, 6050, 2009

[7] J. H. Noh, S. H. Im, J. H. Heo, T. N. Mandal, and S. I. Seok. Chemical Management for Colorful, Efficient, and Stable Inorganic–Organic Hybrid Nanostructured Solar Cells. Nano Letters, 13, 1764–1769, 2013

[8] J. H. Heo et al. Efficient Inorganic–Organic Hybrid Heterojunction Solar Cells Containing Perovskite Compound and Polymeric Hole Conductors. Nature Photon. 7, 486–491, 2013

[9] J. Burschka, N. Pellet, S. J. Moon, R. H. Baker, P. Gao, M. K. Nazeeruddin1 and M. Gratzel. Sequential Deposition as A Route to High-Performance Perovskite-Sensitized Solar Cells. Nature 499, 316–319, 2013
[10] A. Pisoni, J. Jaćimović, O. S. Barišić, M. Spina, R. Gaál, L. Forró, and E. Horváth. Ultra-Low Thermal Conductivity in Organic–Inorganic Hybrid Perovskite CH3NH3PbI3. The Journal of Physical Chemistry Letters, 5, 2488–2492, 2014

[11] X. Mettan, R. Pisoni, P. Matus, A. Pisoni, J. Jacimovic ́, di, B. ́Nafrá, M. Spina, D. Pavuna, L. Forro ́, and E. Horva ́th. Tuning of The Thermoelectric Figure of Merit of CH3NH3MI3 (M = Pb, Sn) Photovoltaic Perovskites. The Journal of Physical Chemistry C, 119, 11506−11510, 2015

[12] S. D. Stranks, G. E. Eperon, G. Grancini, C. Menelaou, M. J. P. Alcocer, T. Leijtens, L. M. Herz, A. Petrozza, and H. J. Snaith. Electron–Hole Diffusion Lengths Exceeding 1 Micrometer in An Organometal Trihalide Perovskite Absorber. Science 342, 341–344, 2013

[13] J. Liu, and O. V. Prezhdo. Chlorine Doping Reduces Electron-Hole Recombination in Lead. The Journal of Physical Chemistry Letters, 6, 4463−4469, 2015

[14] N. Onoda-Yamamuro, T. Matsuo, and H. Suga. Calorimetric and IR Spectroscopic Studies of Phase Transitions in Methylammonium Trihalogenoplumbates (II). Journal of Physics and Chemistry of Solids, 51, 1383, 1990

[15] M. Ibáñez, Z. Luo, A. Genç, L. Piveteau, S. Ortega, D. Cadavid, O. Dobrozhan, Y. Liu, M. Nachtegaal and M. Zebarjadi. High-Performance Thermoelectric Nanocomposites from Nanocrystal Building Blocks. Nature Communications, 7, 10766, 2016

[16] D. C. Langreth and J. P. Perdew. Theory of Nonuniform Electronic Systems. I. Analysis of the Gradient Approximation and A Generalization that Works. Physical Review B, 21(12), 5469, 1980

[17] Perdew, J. P., Burke, K., & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical Review Letters, 77(18), 3865, 1996

[18] J. H. Im, J. Luo, M. Franckevicius, N. Pellet, P. Gao, T. Moehl, S. M. Zakeeruddin, M. K. Nazeeruddin, M. Gratzel, and N. G. Park. Nanowire Perovskite Solar Cell. Nano Letters, 15, 2120, 2015

[19] M. Liu, M. B. Johnston, H. J. Snaith. Efficient Planar Heterojunction Perovskite Solar Cells by Vapour Deposition. Nature, 501, 395–398, 2013

[20] Y. P. He, and G. Galli, Perovskites for Solar Thermoelectric Applications: A First Principle Study of CH3NH3Al3 (A=Pb and Sn). Chemistry of Materials, 26, 5394–5400, 2014

[21] M. Wang and S. Lin. Anisotropic and Ultralow Phonon Thermal Transport in Organic-Inorganic Hybrid Perovskites: Atomistic Insights into Solar Cell Thermal Management and Thermoelectric Energy Conversion Efficiency. Advanced Functional Materials, 26, 5297–5306, 2016

[22] T. Ye, X. Wang, X. Li, A. Q. Yan, S. Ramakrishna, & J. Xu. Ultra-high Seebeck Ccoefficient and Low Thermal Conductivity of A Centimeter-sized Perovskite Single Crystal Acquired by A Modified Fast Growth Method. Journal of Materials Chemistry C, 5(5), 1255-1260, 2017

[23] P. Atkins and R. Friedman. Molecular Quantum Mechanics 4th ed. pp. 168-175, 2005

[24] M. Born, and J.R. Oppenheimer. On the Quantum Theory of Molecules. Annalen der Physik 389,20, 457–484, 1927

[25] P. Hohenberg and W. Kohn. Inhomogeneous Electron Gas. Phys. Rev. 136, 3864, 1964
[26] W. Kohn and L. Sham. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. A 140, 1133, 1965

[27] D. Liang and J. E. Bowers. Recent Progress in Lasers on Silicon. Nature photonics, 4(8), 511-517, 2010

[28] F. Bloch. Über die Quantenmechanik der Elektronen in Kristallgittern. Zeitschrift für Physik A Hadrons and Nuclei, 52, 555, 1929

[29] 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

[30] S. Baroni, S. Gironcoli, and A. D. Corso. Phonons and Related Crystal Properties from Density-Functional Perturbation Theory. Reviews of Modern Physics, 73, 2001

[31] X. Gonze. First-Principles Responses of Solids to Atomic Displacements and Homogeneous Electric Felds: Implementation of A Conjugate-Gradient Algorithm. Physical Review B, 55, 1997

[32] P. Debye. Zur Theorie der spezifischen Waerme. Annalen der Physik Leipzig. 39, 789–839, 1912

[33] G. A. Slack, and S. Galginaitis. Thermal Conductivity and Phonon Scattering by Magnetic Impurities in CdTe. Physical Review, 133, A253, 1964

[34] L. Boltzmann. On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium. reprinted in
Wissenschaftliche Abhandlungen von Ludwig Boltzmann, Vol. II pp. 164–223

[35] T. M. Tritt. Thermal Conductivity - Theory, Properties, and Applications. Plenum Publishers, New York, 2004

[36] R. Franz, and G. Wiedemann. Ueber die Wärme-Leitungsfähigkeit der Metalle. Annalen der Physik, 165, 497–531, 1853

[37] http://accelrys.com/resource-center/downloads/updates/license-pack/index.html

[38] M. D. Segall et al. First Principles Simulation: Ideas, Illustrations and the CASTEP code. Journal of Physics: Condensed Matter, 14(11), 2717, 2002

[39] S. J. Clark et al. First Principles Methods Using CASTEP. Zeitschrift für Kristallographie-Crystalline Materials, 220(5/6), 567-570, 2005

[40] https://github.com/WMD-Bath/Hybrid-perovskites

[41] H. Zhang, Q. Liao, X. Wang, K. Hu, J. Yao, and H. Fu. Controlled Substitution of Chlorine for Iodine in Single-Crystal Nanofibers of Mixed Perovskite MAPbI3– xClx. Small, 12, 28, 3780–3787, 2016
[42] T. Baikie et al. Synthesis and Crystal Chemistry of the Hybrid Perovskite (CH3NH3)PbI3 for Solid-state Sensitised Solar Cell Applications. Journal of Materials Chemistry A, 1(18), 5628-5641, 2013

[43] W. Kong et al. Characterization of An Abnormal Photoluminescence Behavior upon Crystal-phase Transition of Perovskite CH3NH3PbI3. Physical Chemistry Chemical Physics, 17(25), 16405-16411, 2015

[44] R. A. Jishi, O. B. Ta, & A. A. Sharif. Modeling of Lead Halide Perovskites for Photovoltaic Applications. The Journal of Physical Chemistry C, 118(49), 28344-28349, 2014

[45] C. Quarti et al. Structural and Optical Properties of Methylammonium Lead Iodide Across the Tetragonal to Cubic Phase Transition: Implications for Perovskite Solar Cells. Energy & Environmental Science, 9(1), 155-163, 2016

[46] J. H. Noh et al. Chemical Management for Colorful, Efficient, and Stable Inorganic–organic Hybrid Nanostructured Solar Cells. Nano letters, 13(4), 1764-1769, 2013

[47] J. P. Perdew. Density Functional Theory and the Band Gap Problem. International Journal of Quantum Chemistry, 28(S19), 497-523, 1985

[48] M. K. Y. Chan and G. Ceder. Efficient Band Gap Prediction for Solids. Physical Review Letters, 105(19), 196403, 2010

[49] File:Solar Spectrum.png. Wikimedia Commons, the free media repository. https://commons.wikimedia.org/w/index.php?title=File:Solar_Spectrum.png&oldid=203946392