Dislocation density evaluation using dislocation kinetics model

A dislocation kinetics model called the Haasen-Alexander-Sumino (HAS) model is applicable to the quantitative estimation of dislocation density in semiconducting single crystals. In this model, creep strain rate is related with the dislocation density as well as stress components, together with a time-evolution equation of the dislocation density. This model is originally provided under a uniaxial stress state. Then the HAS model was expanded to a multiaxial stress state by neglecting crystal anisotropy and assuming that a crystal is isotropic. Such constitutive equation enables an axisymmetric finite element analysis of dislocation density evaluation. However, single crystals have anisotropy in the elastic constants and specific slip directions. Therefore, we expanded the HAS model to a multiaxial stress state based on the theory of crystal plasticity in order to take account of the crystal anisotropy. Such a constitutive equation requires a three-dimensional finite element analysis of dislocation density evaluation, even though a single crystal has an axisymmetric shape. We also proposed an approximate method, by which the effect of the crystal anisotropy on the dislocation density can be taken into account in the framework of the axisymmetric analysis. We successfully applied these constitutive equations to dislocation density analysis of crystal growth processes, that of ingot annealing and that of heteroepitaxial growth of a thin film on a substrate.