A simple approach to temperature dependence of strain energy: Application to GaN-based semiconductors

We propose a simple approach to temperature dependence of the strain energy in epitaxial thin films coherently grown on the substrate and apply it to the stability for GaN-based semiconductors. The strain energy is simply described as a function of the bulk modulus and lattice parameters using the continuum elasticity theory. Based on this formula, the temperature dependence of the strain energy is estimated using Mie–Grüneisen equation of state that gives temperature dependence of the bulk modulus and lattice parameter. The versatility of the strain energy formula is confirmed by comparing the calculated strain energy for GaN with that obtained by our empirical potential calculations at 0 K. We also compare the temperature dependence of the bulk modulus and lattice parameter for GaN with experimental results at high temperatures. The calculated results imply that the elastic constants decrease while the lattice parameter increases with increase of temperature. They are consistent with experimental results. Using these calculated results, it is clarified that the strain energy accumulated in zinc blende structured (ZB) GaN coherently grown on ZB–SiC(0 0 1) at 1000 K becomes ∼10% greater than that at 0 K. This gives smaller critical film thickness of misfit dislocation generation at high temperatures.