The Calculation of Free-Energies in Semiconductors: Defects, Transitions and Phase Diagrams

In this chapter we review a series of novel techniques that make possi- ble the efficient calculation of free energies in condensed-matter systems, without resorting to the quasiharmonic approximation. Employing these techniques, it is possible to obtain the free energy of a given system not just at a predefined tem- perature, but in a whole range of temperatures, from a single simulation. This makes possible the study of phase transitions, as well as the determination of equilibrium concentrations of defects as a function of temperature, as will be illustrated by examples of specific applications. The same techniques, coupled with a scheme to integrate the Clausius-Clapeyron equation, can lead to the efficient determination of phase diagrams, a capability that will be illustrated with the calculation of the phase diagram of silicon.