Electronic and thermoelectric transport in semiconductor and metallic superlattices

A detailed theory of nonisothermal electron transport perpendicular to multilayer superlattice structures is presented. The current–voltage $\mathrm{(I–V)}$ characteristics and the cooling power density are calculated using Fermi–Dirac statistics, density-of-states for a finite quantum well and the quantum mechanical reflection coefficient. The resulting equations are valid in a wide range of temperatures and electric fields. It is shown that conservation of lateral momentum plays an important role in the device characteristics. If the lateral momentum of the hot electrons is conserved in the thermionic emission process, only carriers with sufficiently large kinetic energy perpendicular to the barrier can pass over it and cool the emitter junction. However, if there is no conservation of lateral momentum, the number of electrons participating in a thermionic emission will increase. This has a significant effect on the $\mathrm{I–V}$ measurements as well as the cooling characteristics. Theoretical calculations are compared with the experimental dark current characteristics of quantum well infrared photodetectors and good agreement over a wide temperature range for a variety of superlattice structures is obtained. In contrast with earlier studies, it is shown that lateral momentum is conserved for the case of electron transport in planar semiconductor barriers.