Lattice Defects in Semiconductors: Towards a Finite-Temperature Theory

Abstract

The progress of Density Functional (DF) calculations of optical, electrical and structural properties of deep defects in semiconductors has been remarkable over the past ten years. Time seems ripe for the extension of such a theory to finite temperature thermodynamical properties (notably free energies of formation and migration). This paper is a step towards that direction. The quasi-harmonic theory of Lattice Dynamics is proposed as a good candidate for such an extension. One important difficulty is the numerical effort required to extract the full dynamical matrix vs. volume from standard DF band calculations for large systems (30-100 atoms/cell), which are on the other hand needed for a thermodynamically consistent theory. To overcome this serious problem we point out some exact relationships existing between differential properties of trajectories and force constants, which may be used to extract accurate dynamical matrices from low-temperature Molecular Dynamics runs. The formalism is presented and successfully tested for a 32-atom argon crystal with and without a vacancy, for which exact results are available. Such a new formalism is proposed as a powerful tool to evaluate dynamical matrices, and thus phonon spectra and thermodynamical properties, of low-symmetry semiconductor systems like defects and amorphous materials, for which a few Carr-Parrinello Molecular Dynamics trajectories are much cheaper than the huge number of self-consistent calculations traditionally required by frozen-phonon or force-constant techniques.