第一性原理研究Ge和GaAs的弹性常数及位错性质

发布时间：2018-06-15 23:32

本文选题：第一性原理计算 + 弹性性质　；参考：《昆明理工大学》2017年硕士论文

【摘要】：研究半导体材料Ge和GaAs的弹性性质和动力学性质具有重要的科学意义和实际价值。本论文以线性与非线性弹性理论为基础,结合第一性原理的密度泛函理论,采用广义梯度近似和局域密度近似方法,数值计算了Ge和GaAs的二阶和三阶弹性常数。考虑不弛豫和原子弛豫的方法,计算Ge和GaAs中glide部分位错在112{111}滑移系统和GaAs中shuffle位错在110{111}}滑移系统中的广义层错能,并通过拟合得到广义层错能曲线。基于位错晶格理论,结合计算得到的二阶弹性常数和广义层错能,研究Ge和GaAs中glide 90°部分位错和GaAs中shuffle 60°位错的力学性质。获得的研究成果如下:对Ge和GaAs弹性性质研究的主要结果:计算所得Ge和GaAs的晶格常数和二阶弹性常数与实验值及先前的理论结果都符合的很好。当应变超过1.5%时就不能再运用线性弹性理论,这时就需要用到非线性弹性理论。三阶弹性常数除了C456与实验值及理论结果较大偏差,其他都符合的很好,并且当考虑到三阶弹性常数时,能量-应变的关系并不是对称的,正应变的能量总是小于负应变的能量,这也说明了大多数三阶弹性常数都是负值。对Ge和GaAs位错性质研究的主要结果:对于Ge和GaAs中glide部分位错的不稳定层错能,局域密度近似方法计算得到的不稳定层错能略高于用广义梯度近似方法计算得到的结果,考虑弛豫得到的不稳定层错能比不弛豫的低,通过弛豫方法得到的不稳定层错能大约是不弛豫的2/3,考虑到Ge和GaAs中的glide 90°部分位错通过键的旋转来滑动,在滑动过程中,会发生很大程度的弛豫,因此通过原子弛豫得到的广义层错能更合理。计算了GaAs中shuffle 60°位错的不稳定层错能,用局域密度近似计算的不稳定层错能比广义梯度近似计算的略大,且原子弛豫方法计算得到的不稳定层错能略小。对于Ge和GaAs中的glide 90°部分位错,不弛豫的位错宽度比原子弛豫的窄,考虑原子弛豫的位错宽度约为不弛豫的1.4倍,考虑原子弛豫的Peierls应力比不弛豫的小。计算得到的GaAs中shuffle 60°位错的位错宽度和Peierls应力在弛豫和不弛豫的情况下相差不大。可见,不稳定层错能越低,位错越宽,Peierls应力越小,则位错越容易滑动;对于具有金刚石及闪锌矿结构晶体中的glide位错,原子弛豫的结果对位错芯结构及Peierls应力影响较大,因此需考虑原子弛豫;而对于shuffle位错,原子弛豫对结果影响很小,从而可以忽略。
[Abstract]:It is of great scientific significance and practical value to study the elastic and dynamic properties of GE and GaAs semiconductor materials. Based on the linear and nonlinear elastic theory and the first-principle density functional theory, the second and third order elastic constants of GE and GaAs are numerically calculated by using generalized gradient approximation and local density approximation. In this paper, the generalized stacking fault energy of glide partial dislocation in 112 {111} slip system and shuffle dislocation in 110 {111} slip system in GE and GaAs are calculated by considering the method of nonrelaxation and atomic relaxation. The generalized laminated fault energy curves are obtained by fitting. Based on dislocation lattice theory, the mechanical properties of glide 90 掳partial dislocation in GE and GaAs and shuffle 60 掳dislocation in shuffle are studied by combining the second order elastic constant and generalized stacking fault energy. The results obtained are as follows: the main results of the study on the elastic properties of GE and GaAs are as follows: the calculated lattice constants and second-order elastic constants of GE and GaAs are in good agreement with the experimental values and previous theoretical results. The linear elastic theory can not be applied when the strain exceeds 1.5 and the nonlinear elastic theory is needed. The third order elastic constant is in good agreement with the experimental data and theoretical results except C456, and when the third order elastic constant is considered, the relationship between energy and strain is not symmetrical. The energy of positive strain is always smaller than that of negative strain, which indicates that most third-order elastic constants are negative. The main results of the study on the dislocation properties of GE and GaAs are as follows: for the unstable layer fault energy of GE and glide partial dislocations, the local density approximation method is slightly higher than the generalized gradient approximation method. The unstable stacking fault energy obtained by considering relaxation is lower than that by unrelaxation. The unstable stacking fault energy obtained by relaxation method is about 2 / 3 of that of unrelaxation. Considering that the partial dislocation in GE and glide 90 掳glides through the rotation of the bond, during the sliding process, A large degree of relaxation occurs, so the generalized stacking fault energy obtained by atomic relaxation is more reasonable. The unstable stacking fault energy of shuffle 60 掳dislocation in GaAs is calculated. The unstable layer fault energy calculated by local density approximation is slightly larger than that calculated by generalized gradient approximation, and the unstable layer fault energy calculated by atomic relaxation method is slightly smaller. For the partial dislocation of glide 90 掳in GE and GaAs, the width of unrelaxation dislocation is narrower than that of atomic relaxation. The width of dislocation considering atomic relaxation is about 1.4 times that of non-relaxation, and the Peierls stress considering atomic relaxation is smaller than that of non-relaxation. The calculated dislocation width of shuffle 60 掳dislocation and Peierls stress have little difference in the case of relaxation and non-relaxation. It can be seen that the lower the unstable stacking fault energy, the smaller the Peierls stress of the dislocation, the easier it is to slide the dislocation, and for the glide dislocation with diamond and sphalerite structure, the effect of atomic relaxation on the dislocation core structure and Peierls stress is greater. Therefore, atomic relaxation should be considered, while for shuffle dislocations, atomic relaxation has little effect on the results, so it can be neglected.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN304

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