在鐵電氧化陶瓷材料中，BiFeO3(BFO)材料以高居禮溫度與較小之直接能隙之優勢得以應用在光伏元件。輔仁大學杜繼舜教授團隊在BiFeO3陶瓷中摻雜微量之Nd(BFONd)，可以讓伏轉換效率提升約56倍。本研究以第一原理計算來探討光伏轉換效率提升之緣由，從能隙、吸收係數以及氧空缺影響之角度切入。
以高解析穿透式電子顯微鏡(HRTEM)影像分析BFO陶瓷樣品並建立相符之結構；並由X-ray Rietveld refinement方法以及掃描式穿透式電子顯微鏡(STEM)影像分析，得到Nd原子為取代Bi原子以及Nd摻雜之濃度。
由於BFO為強關聯系統，必須對Fe 3d電子進行L(S)DA+U方法修正，優化其能帶結構，得到U為7.5eV以及J=0.89eV，Ｕ為effective on-site Coulomb interaction 參數，Ｊ為effective on-site Exchange interaction 參數。在電子結構計算得到反鐵磁性的BFO與BFONd直接能隙數值分別為2.254eV與2.227eV，與輔仁大學杜繼舜教授團隊利用穿透光譜測到之BFO與BFONd能隙為2.24eV(與計算誤差為0.63%)、2.204eV (與計算誤差為1.04%)。加入氧空缺之電子結構計算，氧空缺states分別在BFO以及BFONd在導帶下方0.425eV與0.3332eV形成sub-bandgap defect讓光轉換效率變差。除此之外，氧空缺也使Fermi energy移動到導帶並讓載子濃度增加，在摻雜Nd後會抑制氧空缺效應，讓載子濃度變少，而降低光激發載子與載子複合機率，進而讓光伏轉換效率提升。由Glass Law經驗式知道光電流正比於吸收係數，從光學性質計算得到BFONd之吸收係數比BFO高而得以讓BFONd之光電流提升。再來我們做定量分析:在不同入射光強度、相同之樣品厚度條件下，從開路電壓以及能隙數值可以在入射光強度超過800W/m2以上估算光電流變化之比率:增加約30倍。

The BiFeO3 (BFO) materials have received intensive interests in the photovoltaic effect due to the high Curie temperature and the smaller direct band gap than other ferroelectric oxide ceramics. The group of Prof. Tu Chi-Shun has shown the enhanced photovoltaic effect 56 times higher in neodymium doped BFO. Using first-principles calculations, we offered physical insights into the origins of the enhanced photovoltaic effect. The doping effect of Nd in reducing the movable charge density due to oxygen vacancies in BiFeO3 was confirmed by shifting down of Fermi level of electronic structure, resulting in more electrons or holes accumulated on the two sides of p-n junction to enhance Voc and Jsc for increasing photovoltaic effect.
The Rietveld analysis showed the concentration Nd around 1.24%. Besides,the scanning transmission electron microscopy image simulation analysis of BFONd and first-principles calculations of total free energy suggested that the Nd atom replaced the Bi atom on the A site of perovskite ABO3.The electronic structure showed that the calculated direct band gaps are respectively about 2.257 and 2.227 eV for BFO and BFONd. We considered that the oxygen vacancy due to the fabrication at high temperature around 870℃, forming the sub-bandgap defect states which lowered the photovoltaic effect. The doped Nd caused the sub-bandgap defect states shifted closer to conduction band easier to overcome the trap states by thermal perturbation, and reduced the movable charge density by shifting down of Fermi level to enhance photovoltaic power conversions. In addition, the optical calculations showed that the absorption coefficient of BFONd was higher than BFO to enhance the photocurrent density, which was proportional to absorption coefficient based on Glass Law.
In the quantitative analysis,we can estimated the ratio of Jsc of BFONd and BFO at the laser intensity above 800W/m2 with wavelength 405nm, which was around 30 times higher from the Voc and band gap values for same thickness of BFO and BFONd samples.

摘要 I
Abstract II
總目錄 III
圖目錄 VI
表目錄 IX
第一章 緒論 1
1-1前言: 1
1-2複鐵性材料(Multiferroics materials): 1
1-3鐵電: 2
1-4鐵電陶瓷 3
1-4-1壓電效應(piezoelectric effect): 3
1-4-2焦電效應(pyroelectric effect) : 3
1-5鐵磁條件 4
1-6動機 5
參考文獻 7
第二章 文獻回顧與原理 9
2-1鐵酸鉍 9
2-1-1鈣鈦礦(perovskite)結構 9
2-2鐵酸鉍摻雜釹(Bi1-xNdx)FeO3 13
2-2-1鐵酸鉍摻雜釹(Bi1-xNdx)FeO3結構 13
2-3能隙(band gap) 15
2-4吸收係數 16
2-4-1直接能隙半導體: 17
2-4-2間接能隙半導體 17
2-5光伏效應 18
2-6再結合與漏電流 22
2-6-1Shockley-Read-Hall recombination 22
2-6-2漏電流 23
2-7 BiFeO3之光伏效應 25
2-8 Rietveld refinement—XRD精算理論 31
2-8-1 XRD實驗之繞射峰強度 31
2-8-2 Rietveld refinement與GSAS/EXPGUI軟體 33
2-9第一原理 35
2-9-1 Hartree approximation 35
2-9-2 Hartree-Fock approximation 37
2-9-3 密度泛函理論(Density functional theorem, DFT) 38
2-9-4局部密度近似(Local-density approximation, LDA) 39
2-9-5 LDA應用在實例上的優缺點 41
2-9-6強關聯的電子系統 42
2-9-7 廣義梯度近似(generalized gradient approximation, GGA) 43
2-9-8局部密度近似+電子相關能(L(S)DA+U) 45
2-9-9 Hybrid functional混合泛函 46
2-9-10虛位勢法(pseudo potential method) 51
2-9-11自洽(self-consist scheme) 53
2-9-12第一原理計算應用 54
2-9-13 VASP(Vienna Ab-initio Simulation Package)軟體 57
2-10 Multislice method 理論 58
參考文獻 62
第三章　實驗步驟與方法 72
3-1陶瓷製程 73
3-1-1臥式球磨 73
3-1-2鍛燒(calcining) 74
3-1-3高能球磨(high energy ball milling) 74
3-1-4壓錠(pressing) 74
3-1-5燒結(sintering) 75
3-2 XRD量測 75
3-3光伏效應量測 76
3-4 Plane view TEM試片 77
3-5建立結構 78
3-5-1Hexagonal convert to rhombohedral 79
3-6 Rietveld 精算方法 80
3-7電子顯微鏡試片影像模擬 84
3-8VASP模擬 87
參考文獻 94
第四章 結果與討論 96
4-1 BFO 結構分析 96
4-2摻雜Nd結構分析 99
4-2-1 Rietveld 精算方法 100
4-2-2微觀結構分析 107
4-3 理論計算 109
4-3-1結構選擇 109
4-3-2 L(S)DA+U方法 111
4-3-3空缺位置: 112
4-3-4氧空缺與Bi空缺精算 113
4-3-5電子結構計算 113
4-3-6吸收係數 122
4-4摻雜Nd之提升光伏轉換效率機制之探討 124
參考文獻 132
第五章 結論 135
參考文獻 138
附錄 140

1. A. Filippetti,and N. A. Hill, First principles study of structural, electronic and magnetic interplay in ferroelectromagnetic yttrium manganite. J. Magn. Magn. Mater., 2001. 236: p. 176-189.
2. J. Wang, J.B.N., H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D.Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K.M. Rabe, M. Wuttig, and R. Ramesh, Epitaxial BiFeO3 Multiferroic Thin Film Heterostructures. Science, 2003. 299(1719).
3. M. Fiebig, T.L., D. Frohlich, A. V. Goltsev, and R. V. Pisarev, Observation of coupled magnetic and electric domains. Nature, 2002. 419(818).
4. Naganuma, H., Ferroelectrics - Physical Effects :Multifunctional Characteristics of B-site Substituted BiFeO3 Films. 2011: In Tech.
5. Zeches, R.J., et al., A Strain-Driven Morphotropic Phase Boundary in BiFeO3. Science, 2009. 326(5955): p. 977-980.
6. 范振豐, 鐵酸鉍鐵電薄膜的電性與光伏效應. 清華大學材料科學工程學系碩士論文, 2010.
7. S. Y. Yang, L.W.M., S. J. Byrnes, T. E. Conry, S. R. Basu, D. Paran, L. Reichertz, J. Ihlefeld, C. Adamo,A. Melville, Y.-H. Chu, C.-H. Yang, J. L. Musfeldt, D. G. Schlom, J. W. Ager III, and R. Ramesh, Photovoltaic effects in BiFeO 3. Appl. Phys. Lett. , 2009. 95(6): p. 062909.
8. Choi, T., Lee, S., Choi, Y. J., Kiryukhin, V., and Cheong, S.-W., Switchable Ferroelectric Diode and Photovoltaic Effect in BiFeO3. Science, 2009. 324(5923): p. 63-66.
9. S. Y. Yang, L.W.M., S. J. Byrnes, T. E. Conry, S. R. Basu, D. Paran, L. Reichertz, J. Ihlefeld, C. Adamo, A. Melville,Y.-H. Chu, C.-H. Yang, J. L. Musfeldt, D. G. Schlom, J. W. Ager and R. Ramesh, Photovoltaic effects in BiFeO3. Appl. Phys. Lett., 2009. 95(062909).
10. Ji, W., K. Yao, and Y.C. Liang, Bulk Photovoltaic Effect at Visible Wavelength in Epitaxial Ferroelectric BiFeO3 Thin Films. Advanced Materials, 2010. 22(15): p. 1763-1766.
11. Hauser, A.J., et al., Characterization of electronic structure and defect states of thin epitaxial BiFeO3 films by UV-visible absorption and cathodoluminescence spectroscopies. Appl. Phys. Lett., 2008. 92(22): p. 222901.
12. W. Eerenstein, N. D. Mathur and J. F. Scott, Multiferroic and magnetoelectric materials. Nature, 2006. 442: p. 759-765.
13. 江明達, 複鐵性BFO陶瓷之光伏效應與分析. 天主教輔仁大學物理學系碩士論文, 2014.
14. Chikazumi, S., Physics of Ferromagnetism. 1997: Oxford University Press.
15. Janak, J.F., Uniform susceptibilities of metallic elements. Phys. Rev. B 1997. 16(255).
16. http://ec.europa.eu/environment/waste/rohs_eee/index_en.htm, European Commission.
17. Bhatt, R., et al., Urbach tail and bandgap analysis in near stoichiometric LiNbO3 crystals. physica status solidi (a), 2012. 209(1): p. 176-180.
18. Saha, S., T.P. Sinha, and A. Mookerjee, Electronic structure, chemical bonding, and optical properties of paraelectric BaTiO3. Phys. Rev. B, 2000. 62(13): p. 8828-8834.
19. Wei Ji, K.Y., and Yung C. Liang, Evidence of bulk photovoltaic effect and large tensor coefficient in ferroelectric BiFeO3 thin film. Phys. Rev. B, 2011. 84(9): p. 094115.
20. S. Y. Yang, J.S., J. F. Scott,S.J. Byrnes,J.W.Ager,L.W.Martin,P.Shafer, C.-H. Yang and R. Ramesh, Above-bandgap voltages from ferroelectric photovoltaic devices. Nat Nano, 2010. 5(2): p. 143-147.
21. Li, H., Jin, K. X., Yang, S. H., Wang, J., He, M., Luo, B. C., Wang, J. Y., Chen, C. L., and Wu, T., Ultraviolet photovoltaic effect in BiFeO3/Nb-SrTiO3 heterostructure. Journal of Applied Physics, 2012. 112(8): p. 083506.
22. C. S. Tu, C.-M.H., Z.-R. Xu, V. H. Schmidt, Y. Ting,R. R. Chien, Y.-T. Peng,J. Anthoninappen, Calcium-doping effects on photovoltaic response and structure in multiferroic BiFeO3 ceramics. J. Appl. Phys., 2013. 114(124105).
23. Pabst, G.W., Martin, Lane W., Chu, Ying-Hao, and Ramesh, R., Leakage mechanisms in BiFeO3 thin films. Appl. Phys. Lett., 2007. 90(7): p. 072902.
24. Farokhipoor, S. and B. Noheda, Conduction through 71oDomain Walls in BiFeO3 Thin Films. Phys. Rev. Lett., 2011. 107(12): p. 127601.
25. Zhang, S.B., S.H. Wei, and A. Zunger, Intrinsic n-type versus p -type doping asymmetry and the defect physics of ZnO. Phys. Rev. B, 2001. 63(7): p. 075205.
26. Paudel, T.R., S.S. Jaswal, and E.Y. Tsymbal, Intrinsic defects in multiferroic BiFeO3 and their effect on magnetism. Phys. Rev. B, 2012. 85(10): p. 104409.
27. A. S. Bhalla, R.G., and R. Roy, The perovskite structure - a review of its role in ceramic science and technology. Material Research Innovations, 2000. 4(1): p. 3-26.
28. Kubel F., S.H., Structure of a Ferroelectric and Ferroelastic Monodomain Crystal of the Perovskite BiFeO3. Acta Crystallogr., Sec. B: Struct. Sci. , 1990. 46(698).
29. T. Zhao, A.S., F. Zavaliche, K. Lee, M. Barry, A. Doran, M. P. Cruz, Y. H. Chu,C. Ederer, N. A. Spaldin, R. R. Das, D. M. Kim, S. H. Baek, C. B. Eom ,and R. Ramesh, Electrical control of antiferromagnetic domains in multiferroic BiFeO3 films at room temperature. Nature materials, 2006. 5.
30. Claude Ederer and Nicola A. Spaldin, Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite. Phys. Rev. B, 2005. 71(6): p. 060401.
31. Pradhan, A.K., Zhang, Kai, Hunter, D., Dadson, J. B., Loiutts, G. B., Bhattacharya, P., Katiyar, R., Zhang, Jun, Sellmyer, D. J., Roy, U. N., Cui, Y., and Burger, A., Magnetic and electrical properties of single-phase multiferroic BiFeO3. J. Appl. Phys., 2005. 97(9): p. 093903.
32. 李翊豪, Mn-Sn-M系合金薄帶磁卡效應之研究 (M=B, Al, Ga, C, Si, Fe, Co, Ni). 國立中正大學物理研究所碩士論文, 2011: p. 24.
33. Kornev, I.A., et al., Finite-Temperature Properties of Multiferroic BiFeO3. Phys. Rev. Lett., 2007. 99(22): p. 227602.
34. Wang, Y., et al., First-principles lattice dynamics and heat capacity of BiFeO3. Acta Materialia, 2011. 59(10): p. 4229-4234.
35. Ederer, C. and N.A. Spaldin, Influence of strain and oxygen vacancies on the magnetoelectric properties of multiferroic bismuth ferrite. Phys. Rev. B, 2005. 71(22): p. 224103.
36. S. J. Clark and J. Robertson, Band gap and Schottky barrier heights of multiferroic BiFeO3. Appl. Phys. Lett. , 2007. 90(132903).
37. Ju, S., Cai, Tian-Yi, and Guo, Guang-Yu, Electronic structure, linear, and nonlinear optical responses in magnetoelectric multiferroic material BiFeO3. The Journal of Chemical Physics, 2009. 130(21): p. 214708.
38. J. B. Neaton, C.E., U. V. Waghmare,N. A. Spaldin,and K. M. Rabe, First-principles study of spontaneous polarization in multiferroic BiFeO3. Phys. Rev. B, 2005. 71(014113).
39. Goffinet, M., Hermet, P., Bilc, D. I., and Ghosez, Ph, Hybrid functional study of prototypical multiferroic bismuth ferrite. Phys. Rev. B, 2009. 79(1): p. 014403.
40. Ihlefeld, J.F., Podraza, N. J., Liu, Z. K., Rai, R. C., Xu, X., Heeg, T., Chen, Y. B., Li, J., Collins, R. W., Musfeldt, J. L., Pan, X. Q., Schubert, J., Ramesh, R., and Schlom, D. G., Optical band gap of BiFeO3 grown by molecular-beam epitaxy. Appl. Phys. Lett., 2008. 92(14): p. 142908.
41. Basu, S.R., Martin, L. W., Chu, Y. H., Gajek, M., Ramesh, R., Rai, R. C., Xu, X., and Musfeldt, J. L., Photoconductivity in BiFeO3 thin films. Appl. Phys. Lett., 2008. 92(9): p. 091905.
42. Bin, C., Mi, Li, Yiwei, Liu, Zhenghu, Zuo, Fei, Zhuge, Qing-Feng, Zhan, and Run-Wei, Li, Effect of top electrodes on photovoltaic properties of polycrystalline BiFeO3 based thin film capacitors. Nanotechnology, 2011. 22(19): p. 195201.
43. Singh, S.K., Maruyama, K., and Ishiwara, H., Reduced leakage current in La and Ni codoped BiFeO3 thin films. Appl. Phys. Lett., 2007. 91(11): p. 112913.
44. Yohei, U., Shuhei, Yamazaki, Takeshi, Kawae, and Akiharu, Morimoto, Polarization-Induced Photovoltaic Effects in Nd-Doped BiFeO3 Ferroelectric Thin Films. Japanese Journal of Applied Physics, 2012. 51(9S1): p. 09LE10.
45. Arnold, D.C., Composition-Driven Structural Phase Transitions in Rare-Earth-Doped BiFeO3 Ceramics: A Review. IEEE tranasctions on ultrasonics, ferrorlrctrics, and frequencyvcontrol, 2015. 62(1).
46. C. S. Tu, C.-M.H., Z.-R. Xu, V. H. Schmidt, Y. Ting, R. R. Chien, Y.-T. Peng, and J. Anthoninappen, Calcium-doping effects on photovoltaic response and structure in multiferroic BiFeO3 ceramics. J. Appl. Phys., 2013. 114(12): p. 124105.
47. Tu, C.-S., Chen, Cheng-Sao, Chen, Pin-Yi, Wei, Hsiu-Hsuan, Schmidt, V. H., Lin, Chun-Yen, Anthoniappen, J., andLee, Jenn-Min, Enhanced photovoltaic effects in A-site samarium doped BiFeO3 ceramics: The roles of domain structure and electronic state. Journal of the European Ceramic Society, 2016. 36(5): p. 1149-1157.
48. Choi, H., Jeong, Jaeki, Kim, Hak-Beom, Kim, Seongbeom, Walker, Bright, Kim, Gi-Hwan, and Kim, Jin Young, Cesium-doped methylammonium lead iodide perovskite light absorber for hybrid solar cells. Nano Energy, 2014. 7: p. 80-85.
49. G. L. Yuan, S.W.O., J. M. Liu, and Z. G. Liu, Structural transformation and ferroelectromagnetic behavior in single-phase Bi1-xNdxFeO3 multiferroic ceramics. Appl. Phys. Lett, 2006. 89(052905).
50. Razumovskaya, L.A.R., and L. A. Shilkina, Magnetoelectric interactions in BiFeO3, Bi0.95Nd0.05FeO3 and Bi0.95La0.05FeO3 multiferroics. Tech. Phys. Lett., 2008. 34(9): p. 760-762.
51. J. Schiemer, R.L.W., M. A. Carpenter, Y. Lin, J. L. Wang,L. Nore, O. Li, and W. Hutchison, Temperature-dependent electrical,elastic and magnetic properties of sol-gel synthesized Bi0.9 Ln0.1FeO3 (Ln = Nd, Sm). J. Phys. Condens. Matter, 2012. 24(12).
52. Y .-P. Jiang, X.-G.T., Q.-X. Liu, D.-G. Chen, and C.-B. Ma, Improvement of electrical conductivity and leakage current in coprecipitation derived Nd-doping BiFeO3 ceramics. J. Mater. Sci. Mater. Electron., 2014. 25(1): p. 495-499.
53. P. Thakuria and P. A. Joy, High room temperature ferromagnetic moment of Ho Substituted nanocrystalline BiFeO3. Appl. Phys.Lett., 2010. 7(162504).
54. G. L. Yuan, S.W.O., J. M. Liu, and Z. G. Liu, Structural transformation and ferroelectromagnetic behaviours in single-phase Bi1-xNdxFeO multiferroic ceramics. Appl. Phys. Lett., 2006. 89(052905).
55. P. Siriprapa, A.W., and S. Jiansirisomboon, Electrical properties of Nd-doped BiFeO3 ceramics. Ferroelectrics, 2008. 451(1): p. 103-108.
56. J. Dzik, H.B., K. Osinska, A. Lisinska-Czekaj, and D. Czekaj, Synthesis, structure and dielectric properties of Bi1-xNdxFeO3. Arch. Metall. Mater., 2011. 56(4): p. 1119-1125.
57. J. Dzik, A.L.-C., A. Zarycka, and D. Czekaj, Study of phase and chemical composition of Bi1-xNdxFeO3 powders derived by presssureless sintering. Arch. Metall. Mater., 2013. 58(4): p. 1371-1376.
58. T. Pikula, J.D., A. Lisinska-Czekaj, D. Czekaj, and E. Jartych, Structure and hyperfine interactions in Bi1-xNdxFeO3 solid solutions prepared by solid-state sintering. J. Alloys Compd., 2014. 606: p. 1-6.
59. Fox, M., Optical properties of solids. 2001, Oxford,New York: Oxford university press.
60. Lin Penga, H.D., Jianjun Tiana, Qing Rena, Cheng Penga, Zhipeng Huanga, Pingxiong Yanga,and Junhao Chua, Influence of Co doping on structural, optical and magnetic properties of BiFeO3 films deposited on quartz substrates by sol–gel method. Applied Surface Science, 2013. 268(1): p. 146–150.
61. N. Kumar, A.K., C. Bhardwaj, and D. Kaur, Effect of La doping on structural, optical and magnetic properties of BiFeO3 thin films deposited by pulsed laser deposition technique. Optoelectronics and advanced materials - rapid communications. 4(10).
62. Vurgaftman, I., J.R. Meyer, and L.R. Ram-Mohan, Band parameters for III–V compound semiconductors and their alloys. J. Appl. Phys., 2001. 89(11): p. 5815-5875.
63. Dobrovolsky, A., Stehr, J. E.,Chen, S. L., Kuang, Y. J., Sukrittanon, S., Tu, C. W., Chen, W. M., and Buyanova, I. A., Mechanism for radiative recombination and defect properties of GaP/GaNP core/shell nanowires. Appl. Phys. Lett., 2012. 101(16): p. 163106.
64. Cheng, T.-H., Peng, K.-L., Ko, C.-Y., Chen, C.-Y., Lan, H.-S., Wu, Y.-R., Liu, C. W., and Tseng, H.-H., Strain-enhanced photoluminescence from Ge direct transition. Appl. Phys. Lett., 2010. 96(21): p. 211108.
65. Fox, M., Optical properties of solids. Oxford master series in condensed matter physics. 2001, New York: Oxford University Press.
66. Neamen, D.A., Semiconductor Physics and Devices Basic Principles. 2012, New York: Raghu Srinivasan.
67. Xu, Y. and M. Shen, Structure and optical properties of nanocrystalline BiFeO3 films prepared by chemical solution deposition. Materials Letters, 2008. 62(20): p. 3600-3602.
68. Lee, S.M.S.a.M.K., Semiconductor Devices Physics and Technology. 1985: John wiley & Sons, inc.
69. Proctor, C.M., and Nguyen, Thuc-Quyen, Effect of leakage current and shunt resistance on the light intensity dependence of organic solar cells. Appl. Phys. Lett., 2015. 106(8): p. 083301.
70. Morfa, A.J., Nardes, Alexandre M., Shaheen, Sean E., Kopidakis, Nikos, and van de Lagemaat, Jao, Time-of-Flight Studies of Electron-Collection Kinetics in Polymer:Fullerene Bulk-Heterojunction Solar Cells. Advanced Functional Materials, 2011. 21(13): p. 2580-2586.
71. Breeze, A.J., Schlesinger, Z., Carter, S. A., and Brock, P. J., Charge transport in TiO2/MEH-PPV polymer photovoltaics. Phys. Rev. B, 2001. 64(12): p. 125205.
72. Qi, B. and J. Wang, Fill factor in organic solar cells. Physical Chemistry Chemical Physics, 2013. 15(23): p. 8972-8982.
73. Meillaud, F., Shah, A., Droz, C., Vallat-Sauvain, E., and Miazza, C., Efficiency limits for single-junction and tandem solar cells. Solar Energy Materials and Solar Cells, 2006. 90(18–19): p. 2952-2959.
74. King, R.R., Sherif, R. A., Kinsey, G. S., Kurtz, S., Fetzer, C. M., Edmondson, K. M., Law, D. C., Cotal, H. L., Krut, D. D., Ermer, J. H., and Karam, N. H., Bandgap Engineering in High-Efficiency Multijunction Concentrator Cells. 2005.
75. Glass, A.M., D. von der Linde, and T.J. Negran, High‐voltage bulk photovoltaic effect and the photorefractive process in LiNbO3. Appl. Phys. Lett., 1974. 25(4): p. 233-235.
76. Alexe, M., Local Mapping of Generation and Recombination Lifetime in BiFeO3 Single Crystals by Scanning Probe Photoinduced Transient Spectroscopy. Nano Letters, 2012. 12(5): p. 2193-2198.
77. Seidel, J., Fu, Deyi, Yang, Seung-Yeul, Alarcón-Lladó, Esther, Wu, Junqiao, Ramesh, Ramamoorthy, and Ager, Joel W., Efficient Photovoltaic Current Generation at Ferroelectric Domain Walls. Physical Review Letters, 2011. 107(12): p. 126805.
78. Chen, Z., He, Long, Zhang, Fan, Jiang, Jun, Meng, Jianwei, Zhao, Boyuan, and Jiang, Anquan, The conduction mechanism of large on/off ferroelectric diode currents in epitaxial (111) BiFeO3 thin film. J. Appl. Phys., 2013. 113(18): p. 184106.
79. Peng, C.J. and S.B. Krupanidhi, Structures and electrical properties of barium strontium titanate thin films grown by multi-ion-beam reactive sputtering technique. Journal of Materials Research, 1995. 10(03): p. 708-726.
80. Yang, H., Jain, M., Suvorova, N. A., Zhou, H., Luo, H. M., Feldmann, D. M., Dowden, P. C., DePaula, R. F., Foltyn, S. R., and Jia, Q. X., Temperature-dependent leakage mechanisms of Pt∕BiFeO3∕SrRuO3 thin film capacitors. Appl. Phys. Lett., 2007. 91(7): p. 072911.
81. You, L., Chua, Ngeah Theng, Yao, Kui, Chen, Lang, and Wang, Junling, Influence of oxygen pressure on the ferroelectric properties of epitaxial BiFeO3 thin films by pulsed laser deposition. Phys. Rev. B, 2009. 80(2): p. 024105.
82. Wang, Y.P., Zhou, L., Zhang, M. F., Chen, X. Y., Liu, J.-M., and Liu, Z. G., Room-temperature saturated ferroelectric polarization in BiFeO3 ceramics synthesized by rapid liquid phase sintering. Appl. Phys. Lett., 2004. 84(10): p. 1731-1733.
83. Arca, F., Tedde, Sandro F., Sramek, Maria, Rauh, Julia, Lugli, Paolo, and Hayden, Oliver, Interface Trap States in Organic Photodiodes. Scientific Reports, 2013. 3: p. 1324.
84. Lin, Y.S., Y.W. Lain, and S.S.H. Hsu, AlGaN/GaN HEMTs With Low Leakage Current and High On/Off Current Ratio. IEEE Electron Device Letters, 2010. 31(2): p. 102-104.
85. Seidel, J., Martin, L. W., He, Q., Zhan, Q., Chu, Y. H., Rother, A., Hawkridge, M. E., Maksymovych, P., Yu, P., Gajek, M., Balke, N., Kalinin, S. V., Gemming, S., Wang, F., Catalan, G., Scott, J. F., Spaldin, N. A., Orenstein, J., and Ramesh, R., Conduction at domain walls in oxide multiferroics. Nat Mater, 2009. 8(3): p. 229-234.
86. Zhao, P., Bian, Liang, Wang, Lei, Xu, Jinbao, and Chang, Aimin, Enhanced open voltage of BiFeO3 polycrystalline film by surface modification of organolead halide perovskite. Appl. Phys. Lett., 2014. 105(1): p. 013901.
87. Fan, Z., K. Sun, and J. Wang, Perovskites for photovoltaics: a combined review of organic-inorganic halide perovskites and ferroelectric oxide perovskites. Journal of Materials Chemistry A, 2015. 3(37): p. 18809-18828.
88. Fan, Z., K. Yao, and J. Wang, Photovoltaic effect in an indium-tin-oxide/ZnO/BiFeO3/Pt heterostructure. Appl. Phys. Lett., 2014. 105(16): p. 162903.
89. C. S. Tu, C.M.H., V. H. Schmidt, R. R. Chien, M. D. Jiang, and J. Anthoninappen, The origin of photovoltaic responses in BiFeO3 multiferroic ceramics. Journal of Physics: Condensed Matter, 2012. 24(49): p. 495902.
90. Griffiths, D.J., Introduction to Electrodynamics (4th Edition). 2012: Pearson.
91. Queisse, W.S.a.H.J., Detailed Balance Limit of Efficiency of p‐n Junction Solar Cells. J. Appl. Phys., 1961. 32(510).
92. Dreele, A.C.L.a.R.B.V., General Structure Analysis System (GSAS). Los Alamos National Laboratory Report LAUR, 2004. 86-748.
93. H.M.Rieveld, A Profile Refinement Method for Nuclear and Magnetic Structures J. Appl. Cryst., 1969. 2(65).
94. 吳泰伯、許樹恩, X光繞射原理與材料結構分析. 1992: 中國材料科學學會.
95. 楊仲準, 粉末繞射分析技術與實例應用講義.
96. CaRIne Crystallography http://carine.crystallography.pagespro-orange.fr/.
97. McCusker, L.B., Von Dreele, R. B., Cox, D. E., Louer, D., and Scardi, P., Rietveld refinement guidelines. Journal of Applied Crystallography, 1999. 32(1): p. 36-50.
98. Neil W. Ashcroft, N.D.M., Solid State Physics. 1976, New York, 1sted: Holt, Rinehart and Winston Inc.
99. Marder, M.P., Condensed matter physics. 2000: John Wiley and Sons.
100. 謝希德、陸棟, 固態能帶理論. 1998: 復旦大學出版社.
101. P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas. Phys. Rev. B, 1964. 136(B864).
102. W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev., 1965. 140(A1133 ).
103. 江進福, 波函數與密度泛函. 物理雙月刊, 2001. 廿三卷五期: p. p.549~553.
104. D. R. Hamann, M.S., and C. Chiang, Norm-Conserving Pseudopotentials. Phy. Rev. Lett., 1979. 43(1494).
105. M. C. Payne, M.P.T., D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys, 1992. 64(4)(1045).
106. S. H. Vosko, J.P.P., and A. H. MacDonald, Ab Initio Calculation of the Spin Susceptibility for the Alkali Metals Using the Density-Functional Formalism. Phys. Rev. Lett., 1975. 35(1725).
107. Pearson, R.G., Absolute electronegativity and absolute hardness of Lewis acids and bases. J. Am. Chem. Soc., 1985. 107 (24)(6801).
108. 第一原理材料計算科學2011暑期進階課程講義. 2011: 國家理論科學研究中心.
109. 馮端、金國鈞, 凝聚態物理學(上卷). 2003: 高等教育出版社. p.363~387.
110. J. P. Perdew, K.B., and M. Ernzerhof, 77, 3865, 1996., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett., 1996. 77(3865).
111. Gironcoli, M.C.a.S.d., Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B, 2005. 71(035105).
112. I. V. Solovyev, P.H.D., and V. I. Anisimov, Corrected atomic limit in the local-density approximation and the electronic structure of d impurities in Rb. Phys. Rev. B 1994. 50(16861).
113. V. I. Anisimov, I.V.S., M. A. Korotin, M. T. Czyzyk, and G. A. Sawatzky, Density-functional theory and NiO photoemission spectra. Phys. Rev. B, 1993. 48(16929).
114. V. I. Anisimov, J.Z., and O. K. Andersen, Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B, 1991. 44(943).
115. Gunnarsson, V.I.A.a.O., Density-functional calculation of effective Coulomb interactions in metals. Phys. Rev. B, 1991. 43(7570).
116. V. I. Anisimov, F.A., and A. I. Liechtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method. J. Phys.: Condens. Matter 1997. 9(767).
117. A. I. Lichtenstein, M.I.K., Ab initio calculations of quasiparticle band structure in correlated systems: LDA++ approach. Phys. Rev. B, 1998. 57(6884).
118. Antoine Georges, G.K., Werner Krauth, and Marcelo J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. , 1996. 68(13).
119. Heyd, J., and Scuseria, Gustavo E., Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional. The Journal of Chemical Physics, 2004. 121(3): p. 1187-1192.
120. Heyd, J., et al., Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional. The Journal of Chemical Physics, 2005. 123(17): p. 174101.
121. Paier, J., Marsman, M., Hummer, K., Kresse, G., Gerber, I. C., and Ángyán, J. G., Screened hybrid density functionals applied to solids. The Journal of Chemical Physics, 2006. 124(15): p. 154709.
122. Paier, J., et al., Screened hybrid density functionals applied to solids. J. Chem. Phys., 2006. 124(154709): p. 249901.
123. John P., E., and Matthias and Burke Kieron, Rationale for mixing exact exchange with density functional approximations. The Journal of Chemical Physics, 1996. 105(22): p. 9982-9985.
124. Adamo, C. and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model. The Journal of Chemical Physics, 1999. 110(13): p. 6158-6170.
125. Ernzerhof, M., Construction of the adiabatic connection. Chemical Physics Letters, 1996. 263(3): p. 499-506.
126. Ernzerhof, M., J.P. Perdew, and K. Burke, Coupling-constant dependence of atomization energies. International Journal of Quantum Chemistry, 1997. 64(3): p. 285-295.
127. Heyd, J., G.E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential. The Journal of Chemical Physics, 2003. 118(18): p. 8207-8215.
128. Paier, J., et al., Screened hybrid density functionals applied to solids. The Journal of Chemical Physics, 2006. 124(15): p. 154709.
129. Marsman, M., et al., Hybrid functionals applied to extended systems. Journal of Physics: Condensed Matter, 2008. 20(6): p. 064201.
130. Goffinet, M., et al., Hybrid functional study of prototypical multiferroic bismuth ferrite. Phys. Rev. B, 2009. 79(1): p. 014403.
131. Becke, A.D., Density‐functional thermochemistry. III. The role of exact exchange. The Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
132. Gill, P.M.W., B.G. Johnson, and J.A. Pople, A standard grid for density functional calculations. Chemical Physics Letters, 1993. 209(5): p. 506-512.
133. Tomić, S. and N.M. Harrison, Electronic structure of III–V’s semiconductors from B3LYP and PBE0 functionals. AIP Conference Proceedings, 2010. 1199(1): p. 65-66.
134. Bilc, D.I., et al., Hybrid exchange-correlation functional for accurate prediction of the electronic and structural properties of ferroelectric oxides. Phys. Rev. B, 2008. 77(16): p. 165107.
135. Becke, A.D., Density‐functional thermochemistry. IV. A new dynamical correlation functional and implications for exact‐exchange mixing. The Journal of Chemical Physics, 1996. 104(3): p. 1040-1046.
136. Himmetoglu, B., Floris, Andrea, de Gironcoli, Stefano, and Cococcioni, Matteo, Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems. International Journal of Quantum Chemistry, 2014. 114(1): p. 14-49.
137. Paier, J., M. Marsman, and G. Kresse, Why does the B3LYP hybrid functional fail for metals? The Journal of Chemical Physics, 2007. 127(2): p. 024103.
138. A. I. Liechtenstein, V.I.A., and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 1995. 52(R5467).
139. Neil W. Ashcroft, N.D.M., Solid State Physics. Vol. chap. 8. 1976, New York, 1sted: Holt, Rinehart and Winston Inc.
140. vasp manual http://wolf.ifj.edu.pl/workshop/work2008/tutorial/vasp.pdf.
141. Furthmuller, G.K.a.J., Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 1996. 54(11169).
142. Russak, I.B., Calculus of Variations MA 4311 Lecture Notes. 2002.
143. 劉代康, 藉由第一原理分析CoSi(核)-SiO2(殼)奈米線界面與內部缺陷所導致的異常鐵磁性質. 國立清華大學材料科學工程研究所碩士論文, 2014.
144. Manual of MacTempas.
145. Stadelmann, P. JEMS http://cimesg1.epfl.ch/CIOL/ems.html.
146. Simon, S.H., The Oxford Solid State Basics. 2013: Oxford University Press.
147. P.A.Stadelmann, http://cimewww.epfl.ch/people/stadelmann/jemsWebSite/jems.html, 2004.
148. Kresse, G. and J. Hafner, Ab initiomolecular dynamics for open-shell transition metals. Phys. Rev. B, 1993. 48(17): p. 13115-13118.
149. Kresse, G. and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 1996. 54(16): p. 11169-11186.
150. Z. X. Cheng, A.H.L., X. L. Wang, S. X. Dou, K. Ozawa, H. Kimura, S. J. Zhang, and T. R. Shrout, Structure, ferroelectric properties, and magnetic properties of the La-doped bismuth ferrite. J. Appl. Phys., 2008. 103(07E507).
151. Qing-hui Jiang, C.-w.N., Yao Wang, Yu-heng Liu, and Zhi-jian Shen,, Synthesis and properties of multiferroic BiFeO3 ceramics. J. Electroceram, 2008. 21(690).
152. Yoshio Waseda, E.M., and Kozo Shinoda, X-Ray Diffraction Crystallography: Introduction, Examples and Solved Problems. 2011: Springer Science & Business Media.
153. Ashish Gautam , K.S., K. Sen , R.K. Kotnala , and M. Singh Crystal structure and magnetic property of Nd doped BiFeO3 nanocrytallites. Materials Letters, 2011. 65: p. 591-594.
154. Stefano Curtarolo, W.S., Gus L.W. Hart , Michal Jahnatek , Roman V. Chepulskii ,Richard H. Taylor, Shidong Wang, Junkai Xue,Kesong Yang, Ohad Levy, Michael J. Mehl,Harold T. Stokes, Denis O. Demchenko , Dane Morgan, FLOW: An automatic framework for high-throughput materials discovery. Computational Materials Science, 2012. 58: p. 218–226.
155. Vijayanand, S., H.S. Potdar, and P.A. Joy, Origin of high room temperature ferromagnetic moment of nanocrystalline multiferroic BiFeO3. Appl. Phys. Lett., 2009. 94(18): p. 182507.
156. Kubel, F., and Schmid, H., Structure of a ferroelectric and ferroelastic monodomain crystal of the perovskite BiFeO3. Acta Crystallographica Section B-structural Science, 1990. 46(6): p. 698-702.
157. Lahmar, A., Zhao, K., Habouti, S., Dietze, M., Solterbeck, C. H., and Es-Souni, M., Off-stoichiometry effects on BiFeO3 thin films. Solid State Ionics, 2011. 202(1): p. 1-5.
158. Niizeki, N. and M. Wachi, The crystal structures of Bi2Mn4O10, Bi2Al4O9 and Bi2Fe4O9, in Zeitschrift für Kristallographie - Crystalline Materials. 1968. p. 173.
159. Liechtenstein, A.I., Anisimov, V. I., and Zaanen, J., Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B, 1995. 52(8): p. R5467-R5470.
160. Diéguez, O., González-Vázquez, O. E., Wojdeł, Jacek C., and Íñiguez, Jorge, First-principles predictions of low-energy phases of multiferroic BiFeO3. Phys. Rev. B, 2011. 83(9): p. 094105.
161. S. L. Dudarev, G.A.B., S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B, 1998. 57 (3): p. 1505-1509.
162. Hauser, A.J., Zhang, J., Mier, L., Ricciardo, R. A., Woodward, P. M., Gustafson, T. L., Brillson, L. J., and Yang, F. Y., Characterization of electronic structure and defect states of thin epitaxial BiFeO3 films by UV-visible absorption and cathodoluminescence spectroscopies. Appl. Phys. Lett., 2008. 92(22): p. 222901.
163. 周淑婷, 氮氧化矽絕緣層其光致發光及拉曼光譜與MOS結構電容-電壓量測研究. 國立中山大學物理研究所碩士論文, 2003.
164. Lopatiuk-Tirpak, O., Schoenfeld, W. V., Chernyak, L., Xiu, F. X., Liu, J. L., Jang, S., Ren, F., Pearton, S. J., Osinsky, A., and Chow, P., Carrier concentration dependence of acceptor activation energy in p-type ZnO. Appl. Phys. Lett., 2006. 88(20): p. 202110.
165. Trupke, T., Green, M. A., Würfel, P., Altermatt, P. P., Wang, A., Zhao, J., and Corkish, R., Temperature dependence of the radiative recombination coefficient of intrinsic crystalline silicon. J. Appl. Phys., 2003. 94(8): p. 4930-4937.
166. Lee, J.-H., Choi, Hyoung Joon, Lee, Dongeun, Kim, Min G., Bark, Chung W., Ryu, Sangwoo, Oak, Min-Ae, and Jang, Hyun Myung, Variations of ferroelectric off-centering distortion and 3d-4p orbital mixing in La-doped BiFeO3 multiferroics. Phys. Rev. B, 2010. 82(4): p. 045113.
167. Li, S., et al., Influence of orbital contributions to the valence band alignment of Bi2O3, Fe2O3, BiFeO3, and Bi0.5Na0.5TiO3. Phys. Rev. B, 2013. 88(4): p. 045428.
168. Zang, Y., Xie, Dan, Wu, Xiao, Chen, Yu, Lin, Yuxuan, Li, Mohan, Tian, He, Li, Xiao, Li, Zhen, Zhu, Hongwei, Ren, Tianling, and Plant, David, Enhanced photovoltaic properties in graphene/polycrystalline BiFeO3/Pt heterojunction structure. Appl. Phys. Lett., 2011. 99(13): p. 132904.
169. Cai, W., Fu, Chunlin, Gao, Rongli, Jiang, Weihai, Deng, Xiaoling, and Chen, Gang, Photovoltaic enhancement based on improvement of ferroelectric property and band gap in Ti-doped bismuth ferrite thin films. Journal of Alloys and Compounds, 2014. 617: p. 240-246.
170. Gupta, S., Tomar, Monika, and Gupta, Vinay, Ferroelectric photovoltaic properties of Ce and Mn codoped BiFeO3 thin film. Journal of Applied Physics, 2014. 115(1): p. 014102.
171. Chi-Shun Tu, Z.-R.X., V.H. Schmidt, Ting-Shan Chan, R.R. Chien, and Hyungbin Son, A-site strontium doping effects on structure, magnetic, and photovoltaic properties of (Bi1−xSrx)FeO3−δ multiferroic ceramics. Ceramics International, 2015. 41(7): p. 8417-8424.
172. Chang, L.-Y., Tu, Chi-Shun, Chen, Pin-Yi, Chen, Cheng-Sao, Schmidt, V. H., Wei, Hsiu-Hsuan, Huang, Ding-Jie, and Chan, Ting-Shan, Raman vibrations and photovoltaic conversion in rare earth doped (Bi0.93RE0.07)FeO3 (RE=Dy, Gd, Eu, Sm) ceramics. Ceramics International, 2016. 42(1, Part A): p. 834-842.