Thermodynamic modeling of elastic mismatch strain energy on epitaxial growth of GaInN thin films

The effect of mismatch elastic strain energy between GaInN epitaxial film and GaN (0001) substrate is investigated by classical thermodynamics combining with classical elastic mechanics and first-principles calculations. The mismatch elastic strain energies in different indium content are calculated by classical mechanics with stiffness coefficients determined by the first-principles calculations. A negative excess term is discovered in the mismatch strain energy of GaInN epitaxial films. The negative excess term largely counteracts the positive mixing enthalpy of GaInN solution compound, suppressing the large miscibility gap of GaInN alloy. The calculations well explain the successful growth of GaInN epitaxial films with high indium content. This work provides an easy and logical approach to evaluate the thermodynamics of lattice mismatch in various material systems, such as heteroepitaxial growth, second-phase precipitation, etc.