The Inverse Band-Structure Problem

Modern crystal-growth techniques, such as molecular beam epitaxy or metallorganic chemical-vapor deposition, are capable of producing prescribed crystal structures, sometimes even in defiance of equilibrium, bulk thermodynamics. Unfortunately, the number of possible combinations is so vast and the electronic properties are so sensitive to the details of the crystal structure that simple trial-and-error methods are unlikely to be successful. We have developed a new computational method that addresses the fundamental problem of finding the atomic configuration of a complex, multi-component system that produces a target electronic-structure property. This method can be viewed as the theoretical counterpart of combinatorial chemistry. Conventional electronic-structure theory proceeds by first specifying the atomic coordinates of a given structure, and then calculating the electronic properties. Our "inverse approach" allows us to determine the crystal structure having pre-assigned electronic and optical properties.

Our method is based on:

  1. a fast-learning simulated annealing algorithm to sample the space of atomic configurations, and
  2. a fast and accurate "Order N" method to calculate the electronic structure of a given configuration.
A typical simulation run is shown below. In this example, we search for the configuration of a GaP/InP superlattice in the [001] direction that maximizes the fundamental band gap. In the figure the band gap is shown as a function of the number of simulated-annealing steps.

Selected References

    A. Franceschetti and A. Zunger, Nature 402, 60 (1999). (This article was reviewed by Inside R&D and Nanotech Alert).

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