Semiconductors and Their Heterostructures: Contributions to the Theory of Electronic and Optical Properties.

We introduce a new scheme to study semiconductor heterostructure electronic states that is more general than common envelope function approaches, allowing full -zone dispersions and often-neglected material differences to be described. This modal scattering formalism offers a "best choice" flux conserving interface connection rule at each energy by identifying a relevant unitary scattering matrix. Calculations of Gamma-X scattering in GaAs/AlAs structures illustrates the technique. We then construct an efficient twelve-mode/eight-band k cdot p theory that exposes a light and heavy -particle coupling absent in many other schemes, as well as new transfer matrix contributions; the latter describe interfacial spin-orbit coupling effects and finite basis corrections. This model is employed to predict new transmission resonances in InAs/GaSb interband tunnel structures. We also offer a novel interpretation of the popular envelope function approximation, which emerges from our theory after simplifying assumptions. We then present a simple prescription for a "length gauge" derivation of the electronic contributions to nonlinear optical susceptibilities of crystals. This provides expressions free from the unphysical zero frequency divergences which often plague susceptibility calculations of clean, cold semiconductors. In contrast to a recently presented alternative formalism, the transparent mathematical details of our approach facilitates physical interpretation and analysis; for example, we can easily identify corrections to the commonly quoted non-interacting-electron semiconductor Bloch equations. We also derive the general second and third order semiconductor susceptibilities, whose zero frequency limits can now reveal novel effects not previously discussed. Further, we present a model calculation of third order semiconductor nonlinearities that corrects previously published dispersions, clarifies various zero frequency limits, and corresponds with several known results. Finally, we offer preliminary considerations of the consequences of our results on theoretical descriptions of semiconductor heterostructure optical properties. This includes describing the advantages of a heterostructure analog to our bulk crystal optical response scheme, as well as the benefits of our heterostructure electronic state formalism.