Critical Lateral Dimension For A Nanoscale-patterned Heterostructure Using The Finite Element Method

摘要

The finite element method (FEM) is used to simulate the combined strained In_xGa_(1-x)As epitaxial layer and the interfacial dislocation on a nanoseale-patterned GaAs substrate. The critical thickness is calculated based on the overall energy balance approach. Three-dimensional models show that there exists a lateral dimension-dependent critical thickness below which no misfit dislocation is generated. Moreover, this critical thickness becomes infinite for a lateral dimension less than some critical value. The result indicates that an arbitrarily thick coherent epilayer is obtained when the substrate is patterned to a dimension smaller than the critical lateral dimension. The possibility of the dislocation-free growth derives from the three-dimensional stress relief mechanisms.