Nucleation rate and glide velocity of misfit dislocations in Si1−xGex/(100) Si heterostructures

Abstract

Expressions are presented for the rate of strain relaxation, misfit dislocation nucleation, and propagation in strained Si_1−xGe_x/(100)Si heterostructures. Independent measurements of misfit dislocation nucleation and 60° type a/2 〈110〉 dislocation glide velocity in the temperature range 450–1000 °C have led to a model which characterizes the kinetics of strain relaxation for 0<xeff, which drives strain relaxation, is defined for an arbitrary strain profile and strained‐layer geometry. New experimental data for misfit dislocation glide velocity (V in cm s⁻¹) have been fitted to a semi‐empirical relation found to be appropriate for all Si_1−xGe_x/(100)Si heterostructures, V=(4±2)⋅10¹³(τ_eff /μ)² exp−[(2.25±0.05)/kT]. An analogous expression for the nucleation rate of new misfit dislocation segments was determined from experimental data, dN(t)/dt=BN₀(τ_eff /μ)^2.5 exp−[2.5±0.2)/kT], where N₀ is the density of heterogeneous nuclei and B is a material constant ∼10¹⁸ s⁻¹ for Si_1−xGe_x. These expressions are combined in a kinetic model which is then used to predict the rate of strain relaxation in Si_1−xGe_x/Si heterostructures.