非对称双轴张应变对锗能带的影响

First-principle study of effect of asymmetric biaxial tensile strain on band structure of Germanium

采用第一性原理方法系统地研究了沿(001)、(101)和(111)面施加晶面内各方向应变不相等的双轴张应变,即非对称双轴张应变对锗能带结构的影响.结果表明:对于沿(001)面施加非对称双轴张应变,至少某一个方向应变大于2.95%,间接-直接带隙转变才能发生;对于沿(101)面施加非对称双轴张应变,至少某一个方向应变大于3.44%,间接-直接带隙转变才能发生;然而,沿(111)面施加非对称双轴张应变,不发生间接-直接带隙转变.另外,研究还发现无论是施加对称双轴应变还是非对称双轴应变,间接-直接带隙转变得到的应变Ge带隙值都与应变前后拉伸面面积变化大小成反比.

The strain engineering is an effective method to modulate the optical properties of germanium. The biaxial tensile strain has been extensively studied, most of the investigations focusing on biaxial tensile strain with equal in-plane strain at different crystal orientations, namely symmetric biaxial tensile strain. However, the effect of biaxial tensile strain with unequal in-plane strain at different crystal orientations, namely asymmetric biaxial tensile strain, has not been reported. In this paper, we systematically investigate the effect of asymmetric biaxial tensile strain on the band structure of Ge by using first-principle calculation. We firstly calculate and analyze the dependence of band gap on strain for Ge with asymmetric biaxial tensile strain along three low Miller index planes, i.e., （001）, （101） and （111）. Then, we present the values of band gap and strain for some typical indirect-to-direct bandgap-transition-points under asymmetric biaxial tensile strain. Finally, we analyze the influence of biaxial tensile strain on the valance band structure. For the asymmetric biaxial tensile strain along the （001） plane, the indirect-to-direct band gap transition only occurs when the strain of one orientation is larger than 2.95%. For asymmetric biaxial tensile strain along the （101） plane, the indirect-to-direct band gap transition only occurs when the strain of one orientation is larger than 3.44%. Asymmetric biaxial tensile strain along the （111） plane cannot transform Ge into direct band gap material. For asymmetric biaxial tensile strains along the （001） and （101） plane, the indirect-to-direct band gap transition points can be adjusted by changing the combination of in-plane strain at different crystal orientations. The value of bandgap of direct-band-gap Ge under biaxial tensile strain is inversely proportional to the area variation induced by application of strain. The asymmetric biaxial tensile strain along the （001） plane is the most effective to transform Ge into direct band gap material among the three types of biaxial strains, which are similar to the symmetric biaxial tensile strains. In addition, the symmetric biaxial tensile strain will remove the three-fold degenerate states of valance band maxi-mum, leading to a removal of the degeneracy between one heavy hole band and the light hole band. For biaxial tensile strain along the （001） and （101） plane, the asymmetric biaxial tensile strain could further remove the degeneracy between another heavy hole band and the light hole band.