Theoretical modeling of thermal expansion of crystalline silicon by using the strain phonon spectra

A simple and accurate model has been developed to study the thermal expansion of crystalline silicon based on the lattice dynamics. It is the first time to calculate thermal expansion of crystalline Si by using the strain phonon spectra. A modified Keating model, as the interactional potential, has been adopted to describe the elastic strain energy of Si lattice. This model includes four interactions and needs four force constants. The phonon dispersion relations with and without strain have been calculated. Combining the modified Keating model with the strain phonon dispersion relations, the analytical expressions for the thermal expansion coefficient a has been obtained. It is found that the value of α is 2.43×10^-6 K^-1 at the room temperature. The approach could be expected to be used further in nano silicon beam.