Density Functional Theory (DFT) calculations allow the accurate determination of ground state and transition state energies but require thousands of processing hours for each structure. Monte-Carlo (MC) calculations allow the determination of initetemperature thermodynamic and kinetic properties of disordered systems but require energy evaluations for millions or billions of structures. In a Center for Integrated Nanotechnologies (CINT) project, we have collaborated with users at several universities to combine these seemingly incompatible methods to obtain statistical properties with DFT accuracy. The “glue” that we use to bind DFT and MC together is the Cluster Expansion (CE) formalism. In the CE approach, the system of interest is mapped onto a generalized Ising-like model. For example, a variable in a CE might represent the occupation of a site in an alloy, the formation of a dimer on a surface, or the presence of a vacancy at an interface. These variables parameterize the

possible configurations of the system. Once the CE is fit to a training set of DFT energies that sample these configurations, it allows very rapid evaluation of the energy for an arbitrary configuration, while maintaining the accuracy of the underlying DFT calculations. These energy evaluations can then be used to drive statistical or kinetic MC calculations to obtain finite-temperature properties. As part of CINT projects and three Laboratory Directed Research and Development projects arising from this CINT work, our DFT/CE/MC approach has been or is being applied to obtain bulk, surface, interface, and point defect properties in III-V semiconductors and their alloys.

Contact: Normand Modine namodin@sandia.gov

 

Calculated GaAs surface reconstruction phase diagram (upper left) as a function of inverse temperature and normalized partial pressure. Circles indicate the thermodynamic parameters corresponding to the instantaneous MC snapshots shown in the other three panels.

Calculated GaAs surface reconstruction phase diagram (upper left) as a function of inverse temperature and normalized partial pressure. Circles indicate the thermodynamic parameters corresponding to the instantaneous MC snapshots shown in the other three panels.