Theory of Defects in Semiconductors

Volume 104 of the series Topics in Applied Physics pp 115-140


The Calculation of Free-Energiesin Semiconductors: Defects, Transitionsand Phase Diagrams

  • E. R. HernándezAffiliated withCampus de Bellaterra
  • , A. AntonelliAffiliated withUniversidade Estadual de Campinas
  • , L. ColomboAffiliated withUniversity of Cagliari
  • , P. OrdejónAffiliated withCampus de Bellaterra

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In this chapter we review a series of novel techniques that make possible 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 temperature, 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.


71.10.-w 71.17.-m 71.23.-k 71.55.-i 63.20Mt