Finite Element Analysis of Elastic and Plastic Deformation during Growth of Si_1−xGe_x/Si Heterostructures

Abstract

The elastic and plastic stress distribution in strained Si_1−xGe_x heterostructure (x=0.2 and x=0.5), was investigated during the growth process using a nonlinear transient finite element modeling. The material plastic behavior is described by the von Mises yield criteria coupled with isotropic work hardening conditions. The calculated stress distribution during growth of the SiGe cap layer shows that the von Mises stress fluctuates strongly within the layers and at the interfaces. The surface of constant composition Si_1−xGe_x layer is found under compressive stress in both cases. Within that layer the normal stress in the growth direction remains compressive for x=0.2, while it changes from compressive to tensile for x=0.5. In the graded layer the stress goes from tensile to compressive for x=0.5 and in the opposite way for x=0.2. High plastic deformation is observed in the layers, with the maximum von Mises plastic stress being higher for x=0.5 and localized in the SiGe graded region. The plastic strain vanishes monotonically up to 8 μ deep into the Si bulk substrate, in agreement with TEM images that revealed dislocation loops penetrating into the substrate. The time dependent analysis shows that elastic and plastic deformation appear almost instantaneously in the sublayers, while in the Si substrate it is delayed up to 300 s.