Wavefunction engineering of layered semiconductors: theoretical foundations

We present the theoretical basis of wavefunction engineering. We show that a Lagrangian formulation for the valence bands of bulk semiconductors in the k(.)P model provides a direct approach to determining derivative operator ordering in the multiband description of electronic states in semiconductors in the envelope function approximation. The current continuity condition is also obtained through a gauge variation on the Lagrangian. This naturally leads into a finite element approach for the discretization of Schrodinger's equation. Furthermore, by including the Poisson Lagrangian a self-consistent treatment of the Schrodinger-Poisson band-bending in arbitrarily doped structures can be calculated. The theory is developed for both the zinc blende and wurtzite structured compound semiconductors and their heterostructures. Calculations for quantum wells and superlattices are presented to illustrate wavefunction engineering of these structures and the control achieved in obtaining desirable wavefunction localization. We show that when combined with optimization methods, wavefunction engineering provides a powerful new methodology for the optimized design of optoelectronic devices.