我們利用第一原理(first-principle)的方法來討論以陣列方式排列的四層原子厚的氮化鎵(GaN)奈米盤(nanodisk)，並計算隨著分開距離變化的每一氮化鎵奈米盤總能量與偶極矩。我們發現隨著奈米盤彼此之間距離的增加，每一奈米盤的偶極矩會上升，當鄰近兩奈米盤的邊緣相互距離約為11Å時，偶極矩會達到飽和。此結果可以歸因於電荷轉移的效應；當奈米盤之間的距離足夠靠近時，由於電荷轉移而產生一個反向偶極矩，此反向偶極矩與鎵¬-氮雙層所形成的偶極矩方向相反。當奈米盤之間的距離增加，經由電荷轉移修正過後的奈米盤總能量會隨之下降。這個結果說明了奈米盤固有的電偶極會使奈米盤之間產生排斥作用。

The first-principles calculation method has been used to calculate the total energy and the dipole moment per disk of an array of four-atomic-layers thick GaN nanodisks as functions of their separation. The dipole moment per disk is found to increase with the separation of the disks and saturates at a separation between the edges of neighboring disks of about 11Å. This trend indicates that there exists a charge transfer effect, which gives rise to a dipole moment in opposite direction to the dipole moment associated with the two Ga-N bilayers when disks are close enough. The approximate total energy after the adjustment of the charge transfer effect is found to decrease with the increase of the separation of disks, which indicates that the intrinsic dipoles of the nanodisks gives rise to repulsive interactions among them.

I. Introduction 5
II. Theory
2-1 Introduction 7
2-2 Density Functional Theory (DFT) with
Local-Density Approximation (LDA) 8
2-3 The Pseudofunction (PSF) Method 13
III. Structural model and calculation details 22
IV. Results and Discussion 25
V. Summary 29
References 30
Table Caption 33
Figure Caption 34
Tables 35
Figures 38

[1] Bukowski T J and Simmons J H 2002 Crit. Rev. Solid State Mater. Sci. 27 119
[2] Weisbuch C, Benisty H and Houdr´e R 2000 J. Lumin. 85 271
[3] Lauhon L J, GudiksenM S, Wang D and Lieber C M 2002 Nature 420 57
[4] J. I. Pankove, E. A. Miller, and J. E. Berkeyheiser 1971 RCA rev. 32 383
[5] A.R. Smith, R.M. Feenstra, D.W. Greve, J. Neugebauer, J.E. Northrup, Phys. Rev. Lett. 79 (1997) 3934
[6] A.R. Smith, R.M. Feenstra, D.W. Greve, M.S. Shin, M. Skowronski, J. Neugebauer, J.E. Northrup, J. Vac. Sci. Technol. B16 (1998) 2242
[7] J. Fritsch, O.F. Sankey, K.E. Schmidt, J.B. Page, Phys. Rev. B57 (1998) 15360
[8] K. Rapcewicz, M.B. Nardelli, J. Bernholc, Phys. Rev. B56 (1997) R12725
[9] F. Berardini, V. Fiorentini, Phys. Rev. B57 (1998) R9427
[10] K. Karch, J.-M. Wagner, F. Bechstedt, Phys. Rev. B57 (1998) 7043
[11] A. Pavlovska, V.M. Torres, E. Bauer, R.B. Doak, I.S.T. Tsong, D.B. Thomson, R.F. Davis, Appl. Phys. Lett. 75 (1999) 989
[12] J.E. Northrup, R.D. Felice, J. Neugebauer, Phys. Rev. B55 (1997) 13878
[13] J.E. Northrup, J. Neugebauerm, Phys. Rev. B53 (1996) R10477
[14] E.J. Tarsa, B. Heying, X.H. Wu, P. Fini, S.P. DenBaars, J.S. Speck, J. Appl. Phys. 82 (1997) 5472
[15] L. W. Tu, C. L. Hsiao, T. W. Chi and I. Lo 2003 Appl. Phys. Lett. 81 1601
[16] P. Hohenberg and W. Kohn, Phys. Rev. B864, 136 (1964)
[17] L. Hedin and B. I. Lundqvist, J. Phys. C: Solid State Phys. 4, 2064 (1971)
[18] L. Hedin, Phys. Rev. A796, 139 (1965)
[19] A. D. Becke, Phys. Rev. A38, 3098 (1988)
[20] C. Lee, W. Yang and R. G. Parr, Phys. Rev. B37, 785 (1988)
[21] D. M. Ceperley and G. J. Alder, Appl. Phys. Lett. 45, 566 (1980)
[22] O.K. Andersen, Phys. Rev. B12, 3060 (1976)
[23] Solid State Physics, vol.15 , edited by F. Seitz and D. Turnbul, p.224
[24] K. Kambe, Z. Naturforsch 22, 322 (1967); 22, 422 (1967); 23, 1280 (1968)
[25] J. B. Pendry, Low Energy Electron Diffraction, Academic Press, London, 1974 p.137
[26] H. J. Monkhorst and J. D. Pack, Phys. Rev. B13, 5188 (1976)
[27] D.R. Lide (Ed.), CRC Handbook of Chemistry and Phtsics, 73rd edn., Boca Raton, Ann Arbor, Lodon,Tokyo, 1992-1993
[28] Otto F. Sankey and David J. Niklewski, Phys. Rev. B40, 3979 (1989)
[29] M. –H. Tsai and K. C. Hass, Phys. Rev. B52, 16420 (1995)
[30] D. D. Johnson, Phys. Rev. B 38, 12807 (1988)
[31] S. L. Cunningham, Phys. Rev. B10, 4988 (1974)
[32] W. A. Harrison, Phys. Rev. B10, 1860 (1974)
[33] Jackson J D 1975 Classical Electrodynamics 3nd edn (New York: Wiley) 147
[34] Jackson J D 1975 Classical Electrodynamics 3nd edn (New York: Wiley) 151
[35] M. –H. Tsai, O. F. Sankey, K. E. Schmidt, and I. S. T. Tsong, Materials Science and Engineering B88, 40 (2002)