Time-dependent nonlinear finite element modeling of the elastic and plastic deformation in SiGe heterostructured nanomaterials

摘要

The study of strain and stress distributions and relaxation mechanisms during epitaxial deposition of ultra-thin film heterostructures is of critical importance for nanoelectronic materials. It provides guidance for the control of structures at the nanometer scale and insights into the underlying physics. In this paper, we present a time-dependent nonlinear finite element model, which realistically simulates the evolution of elastic and plastic deformation in SiGe heterostructured nanomaterials during epitaxial deposition. Dynamic elements have been used to simulate the layer-by-layer deposition and growth rate as well as chemical-mechanical polishing (CMP) planarization. The thickness of add-on and etched-off layers was limited to few nanometers depending on the final epitaxial layer thickness and its growth rate. The material plastic behavior is described by the Von Mises yield criterion coupled with isotropic work hardening conditions and the Levy-Mises flow rule. The model has been successfully applied to the growth of ultra-thin (15 nm) strained-Si/ Si_(1-x)Ge_x/Si(001) heterostructures. Depth and time dependent elastic and plastic stress and strain in the growing layers are quantified and the relaxation mechanisms are deduced. From the calculated elastic and plastic strain fields, we derived the relaxation factor, plastic strain rate, dislocation glide velocity, misfit, and threading dislocation density as well as several structural properties such as lattice parameters and misfit dislocation spacing and length. These were found in close agreement with published experimental data. The simulation was able to show at which step of the growth process and how often yielding events occur. Plastic deformation and so the nucleation and multiplication of dislocations appeared to occur consistently during growth of the graded-layer. The simulation was also able to predict that CMP of the SiGe-cap followed by a regrowth step will indeed further relax the graded layer. This two-phase relaxation mechanism is expected from the growth process but experimentally difficult to verify. Results from the simulation also show that rapid cooling is favored over slow cooling in order to retain the maximum amount of elastic strain in the strained-Si device layer.