臺灣博碩士論文加值系統

在本篇論文中我們以第一原理方法計算參雜3d 過度金屬元素的二氧化錫的物理性質，其中最令我們感興趣的就是電子結構以及磁學的性質。一般的半導體並不具有磁性，例如Si、As、還有GaAs 等。而這類的半導體利用帶電載子的電性以及濃度來控制其傳輸性質，近來令學者們感興趣的磁性半導體是希望能夠再利用額外的磁性得到更多廣泛的應用。
二氧化錫具有導電性以及透明的光學性質，一般來說導體大多都是非透明的，而透明的物質絕大部分是屬於絕緣體。近來的研究發現在二氧化錫當中參雜鈷可得到相當大的磁矩。因此我們便利用第一原理的方法來研究是否其餘3d 過度金屬參雜在二氧化錫能得到相同有趣的性質。
在我們的研究中發現參雜鈷的時候能得到當參雜的濃度當參雜的濃度越稀薄的時候會發現其具有磁性半金屬的性質，對於參雜鐵的時候則只展現出磁性金屬的性質，關於參雜錳的時候則有磁性半導體的特性，最後一種參雜鎳的二氧化錫則不具有任何的磁性且是屬於半導體。
在此希望能將所發現的研究成果貢獻於全人類，並進一步改善人的生活。

The discovery of the ferromagnetic semiconductor has stimulated a great deal of interests in the origin or its ferromagnetism because of its potential applications in the spintronics, a rapidly developing research area, in which the electron spin play an important role in addition to the usual charge degree of freedom. Semiconductor devices generally take advantage of the charge of electrons, whereas magnetic materials are used for recording information involving electron spin. SnO2 exhibits interesting electrical and optical properties and is widely used as a transparent conductor. More recently, Ogale et al. found that the thin films of Sn1−xCoxO2− (x < 0.3) not only exhibit ferromagnetism with a Curie temperature close to 650 K, but also a giant magnetic moment of (7.5±0.5) µB/Co, which is much larger than the value for small Co clusters ( 2.1µB/Co). Thus we have investigated electronic structures of 3d-metal doped rutile SnO2 (Mn, Fe, Co, and Ni) by first principle calculations. And we found the Co, Fe, and Mn-doped SnO2 indeed exhibit ferromagnetic properties, while Ni-doped cases are non magnetic. I hope these theoretical studies are helpful for the development of spintronic and DMS system to improve the humanity life.

1 Introduction 6
2 Energy Band Theory of Solids 7
2.1 Born-Oppenheimer Approximation . . . . . . . . . . . . . . . 7
2.1.1 The Sch¨odinger equation of many-body system . . . . . 7
2.1.2 The separation of the dynamics of electrons and nuclei 8
2.2 Hartree-Fock Equation . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Hartree theory . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Fock approximation . . . . . . . . . . . . . . . . . . . . 11
2.3 Density Functional Theory . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Hohenberg-Kohn theorem . . . . . . . . . . . . . . . . 13
2.3.2 The Kohn-Sham equations . . . . . . . . . . . . . . . . 18
2.3.3 Local density approximation . . . . . . . . . . . . . . . 20
2.3.4 Muffin-tin potential . . . . . . . . . . . . . . . . . . . . 21
2.3.5 The augmented plane wave method . . . . . . . . . . . 22
2.3.6 The linearized augmented plane wave method . . . . . 25
3 Electronic Structure andMagnetic Properties of Sn1−xMxO2− (M=Mn,
Fe, Co, Ni) 28
3.1 Overview of Interesting Properties of SnO2 . . . . . . . . . . . 28
3.2 Calculation details . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Results of Sn1−xCoxO2 . . . . . . . . . . . . . . . . . . . . . . 35
3.4 Results of Sn1−xFexO2 . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Results of Sn1−xMnxO2 . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Results of Sn1−xNixO2 . . . . . . . . . . . . . . . . . . . . . . 70
3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Conclusion 77

[1] H. Ohno, Science. 281, 951 (1998).
[2] Y. D. Park et al., science. 295, 651 (2002).
[3] C. Kilic and A. Zunger, Phy. Rev. Lett. 88, 095501 (2002).
[4] S. B. Ogale et al., Phy. Rev. Lett. 91, 077205 (2003).
[5] G. Grosso and G. Parravicini, Solid State Physics (Elsevier Science,
USA, 2000).
[6] N. Ashcroft and N. Mermin, Solid State Physics (Brooks/Cole, USA,
1976).
[7] R. M. Martin, Electronic Structure (Cambridge, UK, 2004).
[8] S. Cottenier, Density Functional Theory and the Family of (L)APW-
methods: a step-by-step introduction ( Belgium, 2004).
[9] H. Weng et al., Phy. Rev. B 69, 125219 (2004).
[10] J. M. D. Coey et al., Appl. Phy. Lett. 84, 1332 (2004).
[11] H. Kimura et al., Appl. Phy. Lett. 80, 94 (2002).
[12] J. M. D. Coey, J. Appl. Phys. 97, 10D313 (2005).
[13] C. B. Fitzgerald et al., J. Appl. Phys. 64, R29 (2004).
[14] L. Bergqvist et al., Phy. Rev. Lett. 93, 137202 (2004).
79