我們使用了第一原理分子動力學（first-principles molecular dynamics calculation）以及電子結構的計算方法，來討論 [0001] 方向的奈米線狀結晶的原子位置和電子結構。我們計算得到的結果顯示，由於懸空鍵效應，在奈米線表面上的鎵原子會往內位移，使得鎵原子與氮原子的鍵結傾斜。因此，相較於截取於大塊結晶，此奈米線半徑較小，這是由於表面張力效應所造成的影響。由於奈米線結晶模型中，表面原子數目與內層原子的比值不再很小，使得奈米線結晶的電子結構與大塊結晶及薄膜的電子結構明顯的不同，這是由於大量的表面態所造成。因此沒有明確的類似大塊結晶的能隙。

The atomic arrangements and electronic structures of [0001] oriented GaN nanowires with different side surfaces have been studied by the first-principles molecular dynamics (MD) method and the conventional first-principles electronic structure calculation method. It is found that due to the dangling bond effects, the Ga-N bonds on the side surfaces of the nanowire tilt with Ga surface atoms moving inward. The radius of the nanowire is found to be reduced with respect to the wire truncated from a bulk GaN solid, which can be attributed to the surface tension effect. Due to the large ratio between the numbers of surface atoms and bulk atoms, the electronic structures of these nanowires are very different from those of bulk and films due to the large number of surface atoms or dangling-bond states, so that a bulk-like energy gap can not be clearly defined.

I. Introduction………………………………………...6
II. Theory
2-1 Introduction…………………………………………8
2-2 Density Functional Theory (DFT) with Local Density Approximation (LDA)………………….....10
2-3 The first-principles pseudofunction (PSF) method ..15
2-4 The first-principles molecular-dynamics method .....24
III. Structural models……………………………...34
IV. Results and Discussion ………………………….38
V. Summary ………………………………………..41
References …………………………………………..42
Tables ……………………………………………...45
Figure Captions ……………………………….46

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