矽(Si)和砷化鎵(GaAs)是半導體領域中最常被應用的兩個半導體材料，因此矽和砷化鎵許多性質對半導體工業而言是非常重要的，只要能夠了解其材料及物理特性，就能夠增加矽和砷化鎵在半導體工業上的應用與發展。本論文是採用密度泛函理論(Density functional theory DFT)的軟體fhi98md，針對矽和砷化鎵的能帶結構探討應變和溫度效應對其能帶結構的影響。密度泛函理論將系統能量用電子密度函數表示，局部密度近似法(Local density approximation LDA)則是假設電子密度是均勻分佈，虛擬勢能(Pseudopotential)簡化離子與價電子間的作用位勢函數。利用上述方法探討應變對能隙的影響，並進一步研究在不同溫度時，應變對能隙所造成的變化幅度。此外，也模擬不同溫度，晶體達平衡時的晶格常數大小。

　The applications of the Si and GaAs have been getting more and more important in the semiconductor industry. With the feature of Si and GaAs, it has been applied more extensively in the semiconductor field. Therefore, knowing the physical properties of these materials in detail becomes the crucial issue to develop the semiconductor industry. The objective of this thesis is to study the effects of strainsand temperature on the band structures of Si and GaAs by the fhi98md, which is built on the density functional theory(DFT). This constitutes a method in which without loss of rigor one work with electron density as the basic varible, instead of the wave function. The local density approximation(LDA) uses the uniform-electron gas formula for exchange and correlation energy. The pseudopotential approximation removes the core electrons and by replacing them and the strong ionic potential by a weaker pseudopotential that acts on a ser of pseudo wave functions rather than the true valence wave functions. By using above methods, we will discuss the effect of energy gap with respect to the strain and temperature in this thesis. Moreover, we will also simulate the variation of the lattice constant from different temperature in equilibrium state.

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