利用緊密束縛法計算半導體奈米晶體電子結構

Abstract

因為緊密束縛法(Tight-Binding method)的物理想法本身就是從原子的觀點出發，描述的是原子自身的原子軌域和近鄰原子的軌域交互作用，所以依循著這樣子的想法只要程式上給予輸入奈米晶體不管什麼結構的原子座標和緊密束縛法的參數，就應該要能寫出Hamiltonian的矩陣。因此在本篇論文中主要做的是為如何整合緊密束縛法並建立程式到能計算不只以往ZincBlende、Wurtzite、Rocksalt、Diamond結構單一材料奈米晶體的電子結構，還要能計算多元材料，例如InGaAs，或複合材料，例如core/shell結構，甚至像是缺陷摻雜或其它任意晶體結構等等奈米晶體的電子結構，而且這個程式所選擇要考慮的原子軌域還要是能讓使用者可以任意選取並非固定的。 而硬體的記憶體非常有限，所以必須創造稀疏矩陣來取代完整的矩陣，且在創造稀疏矩陣之前還必須先預估非零項的個數才能去跟電腦要那樣的空間，因此在本論文中也會就這個技術上的問題做討論。

Tight-binding method describe atomic orbital itself and the nearest neighbors' atomic orbital interaction.If we input the atomic coordinates and tight-binding parameters, regardless of the structure of nanocrystal, the tight-binding Hamiltonian matrix can be written down and the accurate electronic structure can be obtained. So in this thesis, we integrate tight-binding theory and create the computer code to calculate the electronic structure of different type of nanocrystals, including not only ZincBlende、Wurtzite、Rocksalt but also Honeycomb or multi-element material、core/shell structure and so on. Because of the computer memory restriction, we must create sparse matrix to replace full matrix.But before creating sparse matrix, we have to estimate the number of nonzero element.So we will discuss this technical problem in the thesis too.