Semi-Empirical Pseudopotential Calculations (SEPM)
SEPM calculations use the in the following steps:
- Assume the size, shape and composition of the nanostructure: 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".
- 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.
- Construct empirical psuedopotentials: SEPM pseudopotentials are fit to produce LDA quality wavefunctions as well as experimental bad gaps. These potentials are fit to a continuous functional form in reciprocal space. Typically, experimental band gaps, effective masses and deformation potentials are included in the fit. To reduce the size of the basis set we fit to a low cutoff (e.g. a cut-off of 5 Ry).
- Solve the single particle Schroedinger equation: A
single particle Hamiltonian is constructed by superposing the atomic
pseudopotenials for each atom in the system. This Hamiltonian is then
solved using either the Folded Spectrum method and the Linear Combination
of Bulk Bands method.
- Many particle properties: Using the single-particle
levels and inter-particle interactions, many particle properties such
as exciton-exciton interactions can be obtained using the configuration-interactions
methods.
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