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We report on an efficient numerical technique for directly locating transmission resonances and zeros in semiconductor heterostructures using tight-binding multiband models. The quantum transmitting boundary method is employed to generate the inverse of the retarded Green's function ${\mathit{G}}^{\mathit{R}}$(E) in the tight-binding representation. The poles of ${\mathit{G}}^{\mathit{R}}$(E) are located by solving a nonlinear non-Hermitian eigenvalue problem. The eigenvalues are calculated using a shift and invert nonsymmetric Lanczos algorithm followed by Newton refinement. We demonstrate that resonance line shapes are accurately characterized by the location of the poles and zeros of ${\mathit{G}}^{\mathit{R}}$(E) in the complex energy plane. The real part of the pole energy corresponds to the resonance peak and the imaginary part corresponds to the resonance width. A Fano resonance is characterized by a zero-pole pair in the complex energy plane. In the case of an isolated Fano resonance, the zero always occurs on the real energy axis. However, we demonstrate that for overlapping Fano resonances the zeros can move off of the real axis in complex conjugate pairs. This behavior is examined using a simple analytic model for multichannel scattering.

Nanoscale heterostructures are generally characterized by local strain variations. Because the atoms in such systems can be irregularly positioned, theroretical models and parameterizations that are restricted to hydrostatic and uniaxial strain are generally not applicable. To address this shortcoming, a method that enables the incorporation of general distortions into the empirical tight binding model is presented. The method shifts the diagonal Hamiltonian matrix elements due to displacements of neighboring atoms from their ideal bulk positions. The new, efficient, and flexible method is developed for zincblende semiconductors and employed to calculate gaps for GaAs and InAs under hydrostatic and uniaxial strain. Where experimental and theoretical data are available our new method compares favorably with other methods, yet it is not restricted to the cases of uniaxial or hydrostatic strain. Because our method handles arbitrary nearest-neighbor displacements it permits the incorporation of diagonal parameter shifts in general, three-dimensional nanoscale electronic structure simulations, such as the nanoelectronic modeling tool (NEMO 3D).

Unintuitive hole transport phenomena through heterostructures are presented. It is shown that for large bias ranges the majority of carriers travel outside the $\ensuremath{\Gamma}$ zone center (i.e., more carriers travel through the structure at an angle than straight through). Strong interaction of heavy-, light-, and split-off hole bands due to heterostructure interfaces present in devices such as resonant tunneling diodes, quantum-well photodetectors, and lasers are shown to be the cause. The result is obtained by careful numerical analysis of the hole transport as a function of the transverse momentum k in a resonant tunneling diode within the framework of a $\mathrm{sp}3s*$ second-nearest-neighbor tight-binding model. Three independent mechanisms that generate off-zone-center current flow are explained: (1) nonmonotonic (electronlike) hole dispersion, (2) lighter quantum well than emitter effective masses, and (3) strongly momentum-dependent quantum-well coupling strength due to state anticrossings. Finally a simulation is compared to experimental data to exemplify the importance of a full numerical transverse momentum integration versus a Tsu-Esaki approximation.