本論文利用壓電力顯微鏡(Piezoelectric Force Microscopy, PFM)觀測多鐵性鐵酸鉍(BiFeO3, BFO)薄膜在奈米尺度下的電域結構與電域成長。可同時觀察樣品的表面形貌、水平(In-Plane, IP)與垂直(Out-of Plane, OP)方向之電域。對多晶與磊晶薄膜進行量測，顯示晶界上有較高的空間電荷(Space Charge)，此空間電荷在微觀中能有效減少束縛電荷所造成的去極化能，此發現提供BFO薄膜中電域大於理論尺寸的解釋。其IP-PFM與OP-PFM觀測到的條紋狀電域，應為考量鐵電有序、磁電耦合與去極化能後，其本質傾向的穩定分佈狀態。對晶軸方向(111)的磊晶BFO薄膜動態量測結果顯示，在外加電壓較小的情形下，其域壁(Domain Wall)為非線性的緩慢爬行移動(Creep Motion)。在外加電壓接近飽和電壓的情形下，域壁擴散則達平衡狀態，受能量項影響包含(1)域壁上束縛電荷所造成的退極化能；(2)域壁的表面能；(3)探針與薄膜表面之靜電能。滿足影響電域的能量總和達到最小值時即為電域穩定的平衡尺寸。計算其反向脈衝的位準電場(0.81~0.91 MV/cm)略小於正向脈衝的位準電場(1.71~1.93 MV/cm)，與其本身的自發極化皆為垂直向下吻合。

In this study, I observe the domain structure and growth at nanoscale by the piezoresponse force microscopy (PFM) in the multiferroic BiFeO3 thin films. The topography, in-plane (IP) and out-of-plane (OP) components of domains for BFO thin films can be revealed simultaneously. The effects of free carriers exist at grain boundaries, where free carries are assumed to screen the depolarization fields in rough epitaxial and polycrystalline samples. The effect of free carriers also provide the explanations for that BFO ferroelectric domains are usually larger than theory expected. The stripe-like domains formed as normal states by considering ferroelectric ordering, magnetoelectric coupling, and the depolarization energy. When applying lower voltage pulses, the domain grows logarithmically with time, which suggests the observed domain wall follows the creep motion in (111) epitaxial sample. When applying higher voltage pulses (close to the macroscopically saturation voltage), the observed states are in equilibrium so that the domain size is determined by minimizing the domain free energies, which include the contributions from (1) the depolarization energy from the bound charges on the domain wall; (2) the surface energy of the domain wall and (3) interaction energy between the domain and the tip fields. The threshold electric field of nonequlibrium creep wall for negative bias (~0.81-0.91 MV/cm) is smaller than that (~1.71-1.93 MV/cm) for positive bias. It is reasonable since the original polarizations of the films tend to direct toward the bottom electrodes.

1. Gene H. Haertling, J. Am. Ceram. Soc. 82, 4 797–818 (1999).
2. W. Eerenstein, N. D. Mathur and J. F. Scott, Nature 442, 17 (2006).
3. T. Zhao, A. Scholl, 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, Nature Materials 5, 825-829 (2006).
4. R. Ramesh and Nicola A. Spaldin, Nature Materials 6, 21-29 (2007).
5. T. Zhao, A. Scholl, F. Zavaliche, H. Zheng, and M. Barry, A. Doran, K. Lee, M. P. Cruz and R. Ramesh, App. Phys. Lett. 90, 123104 (2007).
6. Ying-Hao Chu, Lane W. Martin, Mikel B. Holcomb, Martin Gajek, Shu-Jen Han, Qing He, Nina Balke, Chan-Ho Yang, Donkoun Lee, Wei Hu, Qian Zhan, Pei-Ling Yang, Arantxa Fraile-Rodríguez, Andreas Scholl, Shan X. Wang and R. Ramesh, Nature Materials 7, 478-482 (2008)
7. F. Zavaliche, R. R. Das, D. M. Kim, C. B. Eom, S. Y. Yang, P. Shafer, and R. Ramesh, App. Phys. Lett. 87, 182912 (2005).
8. Ying-Hao Chu, Qian Zhan, Lane W. Martin, Maria P. Cruz, Pei-Ling Yang, Gary W. Pabst, Florin Zavaliche, Seung-Yeul Yang, Jing-Xian Zhang, Long-Qing Chen, Darrell G. Schlom, I.-Nan Lin, Tai-Bor Wu, and Ramamoorthy Ramesh, Adv. Mater. 18, 2307-2311 (2006).
9. P. Shafer, F. Zavaliche, Y.-H. Chu, P.-L. Yang, M. P. Cruz and R. Ramesh, APPLIED PHYSICS LETTERS 90, 202909 (2007).
10. S. V. Kalinin, B. J. Rodriguez, S. Jesse, Y. H. Chu, T. Zhao, R. Ramesh, S. Choudhury, L. Q. Chen, E. A. Eliseev and A. N. Morozovska, PNAS 10, 51 (2007).
11. I. E. Dzyaloshinskii, Sov. Phys. JETP 10, 628 (1959).
12. I. E. Dzyaloskinskii, Sov. Phys. JETP 11, 708 (1960).
13. J. Wang, J. B. Neaton, 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, Science 299 14 (2003).
14. J. B. Neaton, C. Ederer, U. V. Waghmare, N. A. Spaldin and K. M. Rabe1, Phys. Rev. B 71, 014113 (2005).
15. Claude Ederer and Nicola A. Spaldin, Solid State and Materials Science 9, 128-139 (2005).
16. H. Zheng et al., Science 303, 661 (2004).
17. Ce-Wen Nana, M. I. Bichurin, Shuxiang Dongb, D. Viehland and G. Srinivasan, J. Appl. Phys. 103, 031101 (2008).
18. T. Tybell, P. Paruch, T. Giamarchi and J.-M. Triscone, Phys. Rev. Lett. 89, 9 (2002).
19. Nicola A. Hill, J. Phys. Chem. B 104, 6694-6709 (2000).
20. Srinivasan G, Hayes R and Bichurin M I, Solid State Commun. 128 261 (2003).
21. Smolenskii G. A. and Chupis I. E., Sov. Phys. Usp.25 475 (1982).
22. Schmid H., Int. J. Magn. 4 337 (1973).
23. Hill NA, Filippetti A.J, Magn Mater 976, 242-245 (2002).
24. Baettig P. and Spaldin N. A., Appl. Phys. Lett. 86 012505 (2005).
25. Van Aken B. B. and Palstra T. T. M., Phys. Rev. B 69 134113 (2004).
26. Van Aken B. B., Palstra T. T. M., Filippetti A. and Spaldin N. A., Nat. Mater. 3, 164 (2004).
27. Goto T., Kimura T., Lawes G., Ramirez A. P. and TokuraY., Phys. Rev. Lett. 92 257201 (2004).
28. Efremov D. V., van den Brink J. and Khomskii D. I., Nat.Mater. 3 853 (2004).
29. Robert T. Smith, Gary D. Achenbach, Robert Gerson and W. J. James, J. Appl. Phys. 39, 1 (1968).
30. Xiaoding Qi, Joonghoe Dho, Rumen Tomov, Mark G. Blamire and Judith L. MacManus-Driscoll, App. Phys. Lett. 86, 062903 (2005).
31. W. G. Cady, McGraw-Hill, New York (1946) .
32. Toshio Mitsui, Itaru Tatsuzaki and Eiji Nakamura, Gordon and Breach Science Publishers, New York, (1976).
33. 吳朗, “電子陶瓷-壓電”, 全欣資訊圖書股份有限公司 (1994) .
34. 張凱勛,成功大學,碩士論文, “鋯鈦酸鉛(Pb(ZrTi)O3鐵電材料之奈米電域極化及反轉研究” (2006) .
35. 洪從軒,成功大學,碩士論文, “鎳鐵/鈦酸鍶鋇、鎳鐵/鈦酸鋇雙層膜系統之多鐵性研究” (2007).
36. 鍾維烈, “鐵電體物理學”, 科學出版社,(2000).
37. Kenji Uchino. Ferroelectric Devices, Materials Engineering. Marcel Dekker, 2000, ISBN 0-8247-8133-3.
38. A. F. Devonshire, Advances in Physics, 3 , 10, 85-130.(1954).
39. B. D. Cullity,S. R. Stock, Prentice Hall, New Jersey (2001).
40. P. Papon, J. Leblond, P.H.E. Meijer, Springer-Verlag Berlin Heidelberg, French (2006).
41. “Powder Diffraction File”, http://www.icdd.com/
42. I. Sosnowska, W. Schäfer, W. Kockelmann, K.H. Andersen, I.O. Troyanchuk, Appl. Phys. A 74, S1040-S1042 (2002).
43. V. R. Palkar, J. John, and R. Pinto, APPLIED PHYSICS LETTERS 80, 9, 1628 (2002).
44. H. Béa, S. Fusil, K. Bouzehouane, M. Bibesi, M. Sirena, G. Herranz, E. Jacquet, J.-P. Contour and A. Barthélémy, JJAP 45, 7, L187-L189 (2006).
45. Y. H.Chu, T. Zhao, M. P. Cruz, Q. Zhan, P. L. Yang, L. W. Martin, M. Huijben, C. H. Yang, F. Zavaliche, H. Zheng and R. Remesh, Appl. Phys. Lett. 90,252906 (2007).
46. D. Lebeugle, D. Colson, A. Forget, and M. Viret, Appl. Phys. Lett. 91,022907 (2007).
47. Ying-Hao Chu, Maria P. Cruz, Chan-Ho Yang, Lane W. Martin, Pei-Ling Yang, Jing-Xian Zhang,Kilho Lee, Pu Yu, Long-Qing Chen, and Ramamoorthy Ramesh, Adv. Mater. 19, 2662-2666 (2007).
48. G. Catalan, H. Béa, S. Fusil, M. Bibes, P. Paruch, A. Barthélémy and J. F. Scott, Phys.Rev. Lett. 100, 027602 (2008).
49. Z.W. Xu, Y.C. Liang, S. Dong, L.Q. Guo, T. Sun and Q.L. Zhao, Key Engineering Materials Vols. 315-316 ,758-761 (2006).
50. M. Alexe, A. Gruverman,”Nanoscale Characterisation of Ferroelectric Materials”, Springer (2004).
51. A. F. Devonshire, "Theory of Ferroelectrics," Advances in Physics, 3 ,10 85-130 (1954).
52. R. Liithi, H. Haefke, K.-P. Meyer, a) E. Meyer, L. Howald, and H.-J. Gijntherodt, J. Appl. Phys. 74, 12, 7461-7471 (1993).
53. VEECO “CP-ⅡUser’s Guide Part Ⅰ：Basic Imaging Techniques” 1-7.
54. Seungbum Hong, Jungwon Woo, Hyunjung Shin and Jong Up Jeon, Y. Eugene Pak, Enrico L. Colla, Nava Setter,Eunah Kim and Kwangsoo No, J. Appl. Phys. 89, 2, 1377 (2001).