Effect of Temperature on Dielectric Constant of Silicon Using FHI-aims

The phonopy program package and its FHI-aims interface (Phonopy-FHI-aims) code was used to perform the simulation of Silicon (Si) in this work. Parameter optimization, determination of the best exchange functional and k-grid convergence test were carried out for Si. The effect of temperature on the dielectric tensor and dielectric constant of Si was determined using the quasi-harmonic approximation to account for the anharmonic effects in the determination of the lattice expansion. The shifts in the dielectric constant of Silicon due to lattice expansion for a temperature range of 0 to 1000 K were investigated. The real components of the linear dielectric tensor and the dielectric constants decrease with increase in temperature; the changes observed were not significant because there is just a different of 0.4 between dielectric constants at 0 K and 1000 K. Discontinuities in the dielectric constants were observed between the 200 K and 250 K and 450 K and 500 K. The dielectric constant of Si at room temperature (300 K) is 11.1 for [100], [010], and [001] crystallographic directions.