Pseudopotential Calculations of the Electronic Structure of Semiconductor Quantum Nanostructures

The Solid State Theory group is involved in performing state of the art calculations of the electronic structure of a wide range of semiconductor nanostructures, ranging from 2 dimensional quantum wells and superlattices to 0 dimensional quantum dots.

Our theory of quantum nanostructures proceeds in the following steps:

  1. Assume the size, shape and composition of the nanostructure. The nanostructures can be "free-standing" colloidal dots whose surface is passivated, or "embedded dots" such as pyramidal or lens-shaped InAs in a GaAs "cap". One can assume also that the dot is either chemically pure, or that it has a given composition/alloying profile.

  2. Relax the atomic positions to minimize strain. If the dot is embedded in another material, we use the Valence Force Field (VFF) to relax all atomic positions.

  3. Construct empirical psuedopotentials. Since we need to avoid "LDA errors", we must use "realistic" pseudopotentials that not only produce correct band gaps, but also give (unlike LDA) correct effective masses and their anisotropies. Furthermore, since we need to consider very large dots, we need pseudopotentials whose plane wave description can be accomodated with a small basis set (e.g. a cut-off of 5 Ry). We have developed a new generation of empirical pseudopotential methods which satisfy these conditions.

  4. Solve the single particle Schroedinger equation using one of the folowing methods.

  5. Calculate the dielectric screening function and the interparticle Coulomb and exchange integrals.

  6. Using the single-particle levals and inter-particle interactions, solve the configuration-interactions problem.


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