Multiband Phase Space Operator for Narrow Bandgap Semiconductor Devices

The analysis of the charge carrier transport within modern device concepts of nanoelectronics and nanophotonics as well as THz technology requires the inclusion of multiband Hamiltonians. These can then be used to consider not only intraband transitions but also interband transitions as well as effects based on the existence and interaction of light and heavy holes. For this purpose appropriate multiband Hamiltonians must be applied for a suitable numerical analysis. On the basis of the quantum Liouville equation, a formalism is derived how multiband Hamiltonians can be integrated into advanced and recently developed Wigner transport based algorithms utilizing a phase space operator and which multiband models are appropriate. The presented formalism is demonstrated by its application onto resonant tunnel diodes that take advantage of interband effects within narrow band gap semiconductor devices.