Off-zone-center or indirect band-gap-like hole transport in heterostructures

Unintuitive hole transport phenomena through heterostructures are presented. It is shown that for large bias ranges the majority of carriers travel outside the $\Gamma$ 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.