能源短缺是當今所面臨的一個重要課題，因此人們迫切地尋找新的替代能源，其中鋰離子電池扮演著重要的角色。電極材料為決定鋰離子電池基本特性的主因，目前商品化的陽極材料多以選用碳材為主，陰極材料則以LiCoO2為主，目前的研究重點為對環境無汙染的無鈷材料，其中LiFePO4為相當有潛力的陰極材料，本研究目的為改善其導電性不佳的缺點，達到實用性、商品化的可能 。
本研究主要是利用摻雜金屬離子來改善LiFePO4的導電性，以第一原理為理論基礎，利用VASP量子化學計算軟體模擬LiFePO4摻雜金屬離子（Mg2+、Al3+、Ti4+、Zr4+、Nb5+）前後電性結構的變化，藉由能帶結構圖和電子狀態密度圖來探討LiFePO4的導電性；另外，模擬不同摻雜濃度與導電性優劣的關係，並計算其形成能來判斷摻雜時結構形成所需能量的多寡，以便決定構形的可行性。
從能帶結構圖發現LiFePO4為半導體性質，摻雜高價金屬離子能減少LiFePO4的能隙，由此證明摻雜金屬離子能有效改善其導電性；由電子狀態密度圖可以了解摻雜過後各個原子的能量分布情形，發現改善導電性的主因在於摻雜的原子在費米能附近有局域性的能量分布，及其鄰近的Fe原子在費米能附近的能量貢獻。摻雜不同濃度金屬離子會造成不同混合比例的Fe2+/Fe3+，產生不同的導電程度，其中以摻雜[Zr4+]＝12.5%效果最佳，若將形成能列入製程的考慮，Ti原子和Nb原子不適合高濃度的摻雜。

It is an important issue of energy shortage in recent years. People want to find alternative energy sources, especially lithium-ion batteries. Since the commercialization of lithium-ion batteries, cathode materials have been extensively studied because of its attractive properties such as energy density and rate capability. LiFePO4 is a very promising choice of cathode materials for electric vehicles or hybrid electric vehicles. The objective of this study was to improve the electronic conductivity of LiFePO4.
We use doping metal ions into LiFePO4 to increase the intrinsic electronic conductivity in this study. The electronic structures of LiFePO4 after doping metal ions were performed by using first-principles calculation. We investigate electronic conductivity of LiFePO4 by band structure and density of states. Furthermore, we discuss the relation between the doping concentration and electronic conductivity. Moreover, we calculate the formation energy to determinate the energy for fabricating doped LiFePO4.
From the analysis of the band structure, it could be seen that doping metal ions into LiFePO4 result in the decrease of energy gap. The narrower energy gap indicates that the electronic conductivity of LiFePO4 could be significantly enhanced by replacement of Li atom with metal ions. From the analysis of the density of states, it was found that the energy attributed of each atom. Further, it showed that the narrow band near the Fermi level were mainly attributed to the substituted atom and its neighboring Fe atom. It plays an important role in enhancing conductivity. It is accompanied by the transformation of Fe atoms from the Fe3+ into Fe2+. The different ion-doping concentration on it will have an effect on the electronic conductivity. There exists an optimum doping concentration about [Zr4+]=12.5%. However, the excessive formation energy should be considered in practical fabrication.

[1] 黃可龍、王兆翔、劉素琴, "鋰離子電池原理與技術," 五南圖書出版股份有限公司, 2010.
[2] Y. Shao-Horn, L. Croguennec, C. Delmas, E. C. Nelson, and M. A. O'Keefe, "Atomic resolution of lithium ions in LiCoO2," Nature Materials, vol. 2, pp. 464-467, 2003.
[3] V. A. Streltsov, E. L. Belokoneva, V. G. Tsirelson, and N. K. Hansen, "Multipole analysis of the electron density in triphylite, LiFePO4, using X-ray diffraction data," Acta Crystallographica Section B, vol. 49, pp. 147-153, 1993.
[4] Y. Zhang, Q. Huo, P. Du, L. Wang, A. Zhang, Y. Song, et al., "Advances in new cathode material LiFePO4 for lithium-ion batteries," Synthetic Metals, vol. 162, pp. 1315-1326, 2012.
[5] A. K. Padhi, K. S. Nanjundaswamy, and J. B. Goodenough, "Phospho-olivines as positive-electrode materials for rechargeable lithium batteries," Journal of the Electrochemical Society, vol. 144, pp. 1188-1194, 1997.
[6] Z. Li, D. Zhang, and F. Yang, "Developments of lithium-ion batteries and challenges of LiFePO4 as one promising cathode material," Journal of Materials Science, vol. 44, pp. 2435-2443, 2009.
[7] Y. Wang, J. Wang, J. Yang, and Y. Nuli, "High-Rate LiFePO4 Electrode Material Synthesized by a Novel Route from FePO4 • 4H2O," Advanced Functional Materials, vol. 16, pp. 2135-2140, 2006.
[8] C. Lai, Q. Xu, H. Ge, G. Zhou, and J. Xie, "Improved electrochemical performance of LiFePO4/C for lithium-ion batteries with two kinds of carbon sources," Solid State Ionics, vol. 179, pp. 1736-1739, 2008.
[9] S. B. Lee, S. H. Cho, S. J. Cho, G. J. Park, S. H. Park, and Y. S. Lee, "Synthesis of LiFePO4 material with improved cycling performance under harsh conditions," Electrochemistry Communications, vol. 10, pp. 1219-1221, 2008.
[10] Z. y. Chen, H. l. Zhu, S. Ji, R. Fakir, and V. Linkov, "Influence of carbon sources on electrochemical performances of LiFePO4/C composites," Solid State Ionics, vol. 179, pp. 1810-1815, 2008.
[11] H. Liu, G. X. Wang, D. Wexler, J. Z. Wang, and H. K. Liu, "Electrochemical performance of LiFePO4 cathode material coated with ZrO2 nanolayer," Electrochemistry Communications, vol. 10, pp. 165-169, 2008.
[12] F. Croce, A. D'Epifanio, J. Hassoun, A. Deptula, T. Olczac, and B. Scrosati, "A novel concept for the synthesis of an improved LiFePO4 lithium battery cathode," Electrochemical and Solid-State Letters, vol. 5, pp. A47-A50, 2002.
[13] S.-Y. Chung, J. T. Bloking, and Y.-M. Chiang, "Electronically conductive phospho-olivines as lithium storage electrodes," Nat Mater, vol. 1, pp. 123-128, 2002.
[14] H. L. Park, S. C. Yi, and Y. C. Chung, "The electronic structure of LiFe15/16Mg1/16PO4 : Ab initio approach," Journal of Ceramic Processing Research, vol. 7, pp. 271-274, 2006.
[15] J. Xu and G. Chen, "Effects of doping on the electronic properties of LiFePO4: A first-principles investigation," Physica B-Condensed Matter, vol. 405, pp. 803-807, 2010.
[16] J. L. Liu, Z. Z. Wang, G. H. Zhang, Y. Liu, and A. S. Yu, "Size-Controlled Synthesis of LiFePO4/C Composites as Cathode Materials for Lithium Ion Batteries," International Journal of Electrochemical Science, vol. 8, pp. 2378-2387, 2013.
[17] 趙成大, 固體量子化學-材料化學的理論基礎, 2nd ed. 北京:高等教育出版社, 2003.
[18] P. Hohenberg and W. Kohn, "Inhomogeneous Electron Gas," Physical Review, vol. 136, pp. B864-B871, 1964.
[19] W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects," Physical Review, vol. 140, pp. A1133-A1138, 1965.
[20] M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, "Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients," Reviews of Modern Physics, vol. 64, pp. 1045-1097, 1992.
[21] P. E. Blöchl, "Projector augmented-wave method," Physical Review B, vol. 50, pp. 17953-17979, 1994.
[22] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, et al., "Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation," Physical Review B, vol. 46, pp. 6671-6687, 1992.
[23] Z. Zhou, X. Gao, J. Yan, D. Song, and M. Morinaga, "A first-principles study of lithium absorption in boron- or nitrogen-doped single-walled carbon nanotubes," Carbon, vol. 42, pp. 2677-2682, 2004.