A Thermoelastic Model for Interface Strain Effects in Microscale and Nanoscale Heterostructures

Abstract

We propose a thermoelastic model for strain effects in microscale planar and nanoscale cylindrical and spherical core/shell heterostructures, which takes into account the difference between lattice constants, linear thermal expansion coefficients, free thermal expansion of lattice constants and elastic stiffness constants of constituent semiconductors. Using the stress-strain relations for thermoelastic bodies, coupled with lattice mismatch induced discontinuity in elastic strain at heterointerface so called shrink fit condition, explicit analytical expressions are derived for interface strain in microscale heterolayers and nanoscale cylindrical and spherical core/shell heterostructure nanowires and quantum dots.  Proposed model predicts that the room temperature values of in plane linear thermal expansion coefficient of GaAs thin film is identical to that of silicon substrate ( , but smaller than in bulk GaAs ( , while the out of plane linear thermal expansion coefficient exceeds the bulk value by Poisson ratio ( , which are in excellent agreement with high resolution x-ray scattering measurements. Furthermore, lattice vibration, lattice mismatch and thermal expansion coefficients mismatch effect on core band gaps of CdSe/CdZnS and ZnSe/CdZnS QDs are calculated as a function of temperature, which are in good agreement with experimental optical absorption data. Results suggests that the proposed thermoelastic strain model can be a good predictive tool for the design of highly mismatched microscale and nanoscale heterostructure devices operating at high temperatures.