The Hakoniwa method, an approach to predict material properties based on statistical thermodynamics and ab initio calculations

Abstract An approach based on statistical thermodynamics and ab initio calculations to predict properties of materials composed of different types of atoms is presented. The key point of what the authors called the “Hakoniwa” method, is to take into account all possible structural supercells constructed by the fixed number of atoms of each species according to the composition of the target material. The conservation of the total number of atoms enables calculating the average value of a material property for a given temperature by applying statistical thermodynamics to the material property values obtained for each of the possible supercells. The application of the Hakoniwa method is illustrated by calculating the average energy gain by mixing Sn and Si atoms in a Ge matrix, as function of the Ge 1− x − y Sn x Si y composition. The relative stability of each composition is compared allowing predicting the impact of Si doping on the stability of Ge 1− x − y Sn x Si y films epitaxially grown on a Ge substrate. In addition, the average bandgap is calculated for a given Ge 1− x − y Sn x Si y composition as a function of the temperature.