砷化鎵與砷化銦異質結構之第一原理計算

Abstract

近幾年來，量子點被廣泛的應用在半導體雷射之中，因為它有低臨界電流以及能在高溫下穩定操作的優點。它的應用包括了光碟的讀寫頭、遠紅外線感應器和光纖通訊。但是將一般的量子點應用到光纖通訊上面會有一些問題，例如它在高驅動電流密度下，其微分增益將受到限制。為了解決這些問題，因此有了Sub-monolayer quantum dot (SMLQD) 的產生。透過低臨界電流密度以及高微分增益，它可以解決一般傳統量子點所產生的問題。SMLQD 是將兩個晶格常數不同的材料沉積在一起得到。因此在材料的接面處，必然會有應力及應變的產生。本篇論文主要是研究由砷化鎵(GaAs)和銦化鎵(InAs)所構成的SMLQD中的應變分佈。我們透過第一原理的計算來預測在SMLQD中的應變分佈，並且將我們的結果跟一般彈性力學所得到的結果作比較。我們的理論基礎是建構在密度泛函理論之上，由此出發的所得到的計算結果將得到比彈性力學來的更加精準。如此一來，我們也可以驗證彈性力學在描述應變時的可靠性。除此之外，我們還想了解在有應變的情況下，能隙會如何改變。為了克服局部密度近似法在計算半導體能隙上的缺陷，我們分別應用了 GW 修正以及 modified Becke-Johnson potential。

Quantum dot has been widely used in semiconductor laser for the recent years. It has the advantages of low threshold current density and being stable under high temperature. Its applications include the header of read-write CD-ROM, infrared sensor and optical communication. However, there are still some problems while applying the traditional quantum dots in optical communication such as the limitation of differential gain under high drive current density. Submonolayer deposition of quantum dot (SMLQD) has been proposed as a solution to these problems. It can overcome the problem of traditional QD by reaching higher differential gains and lower threshold current density. SMLQD is formed by deposition of lattice mismatched materials. Therefore, there will be an intrinsic strain between the interfaces of these materials. In this thesis, we are interested in strain distribution of SMLQD composed of GaAs and InAs. We perform ab-initio calculations to predict the strain in SMLQD and compare the results with the strain calculated in continuum elasticity. Our research is based on density functional theory (DFT). The results from DFT should in principle gives be more accurate then continuum elasticity. In this way, we can verify the reliability of continuum elasticity while describing the strain. Besides, we also want to know how the band gap varies under the strain. To overcome the problem that local density approximation (LDA) fails to give the correct band gaps for semiconductors, we apply both modified Becke-Johnson potential and GW correction in our calculation.