kp Theory of Semiconductor Nanostructures

Galeriu, Calin

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kp Theory of Semiconductor Nanostructures

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The objective of this project was to extend fundamentally the current kp theory by applying the Burt-Foreman formalism, rather than the conventional Luttinger-Kohn formalism, to a number of novel nanostructure geometries. The theory itself was extended in two ways. First in the application of the Burt-Foreman theory to computing the momentum matrix elements. Second in the development of a new formulation of the multiband kp Hamiltonian describing cylindrical quantum dots. A number of new and interesting results have been obtained. The computational implementation using the finite difference method of the Burt-Foreman theory for two dimensional nanostructures has confirmed that a non-uniform grid is much more efficient, as had been obtained by others in one dimensional nanostructures. In addition we have demonstrated that the multiband problem can be very effectively and efficiently solved with commercial software (FEMLAB). Two of the most important physical results obtained and discussed in the dissertation are the following. One is the first ab initio demonstration of possible electron localization in a nanowire superlattice in a barrier material, using a full numerical solution to the one band kp equation. The second is the demonstration of the exactness of the Sercel-Vahala transformation for cylindrical wurtzite nanostructures. Comparison of the subsequent calculations to experimental data on CdSe nanorods revealed the important role of the linear spin splitting term in the wurtzite valence band.

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