Critical thickness and strain relaxation in high-misfit heteroepitaxial systems:PbTe1−xSexon PbSe (001)

Abstract

Strain relaxation and misfit dislocation formation is investigated for the high-misfit ${\mathrm{PbTe}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x}/\mathrm{PbSe}$ (001) heteroepitaxial system in which the lattice mismatch varies from 0% to 5.5%. Because a two-dimensional (2D) layer growth prevails for all ${\mathrm{PbTe}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x}$ ternary compositions, the lattice mismatch is relaxed purely by misfit dislocations. In addition, it is found that strain relaxation is not hindered by dislocation kinetics. Therefore, this material combination is an ideal model system for testing the equilibrium Frank--van der Merwe and Matthews--Blakeslee strain relaxation models. In our experiments, we find significantly lower values of the critical layer thickness as compared to the model predictions. This discrepancy is caused by the inappropriate description of the dislocation self-energies when the layer thickness becomes comparable to the dislocation core radius. To resolve this problem, a modified expression for the dislocation self-energy is proposed. The resulting theoretical critical thicknesses are in excellent agreement with the experimental data. In addition, a remarkable universal scaling behavior is found for the strain relaxation data. This underlines the breakdown of the current strain relaxation models.