Electron and phonon energy spectra in a three-dimensional regimented quantum dot superlattice

Abstract

We report on theoretical investigation of the electron and phonon energy spectra in a three-dimensional regimented quantum dot superlattice. Our results are obtained by numerical solution of the Schr\"odinger and elasticity equations using the finite-difference method. The calculations are performed for a Ge/Si material system taking into account characteristic band-gap offsets, elastic stiffness constants, and other relevant parameters. Coupling among quantum dots in such a regimented structure results in formation of extended electron states and minibands, provided that the disorder in the system is small. Electron and phonon densities of states of these artificial quantum dot crystals are also calculated. We demonstrate that the acoustic-phonon dispersion in the quantum dot superlattice undergoes strong modification, which leads to emergence of quasioptical branches. These branches are much lower in energy than optical phonons in bulk semiconductors and thus may strongly affect energy relaxation processes. Other phenomena that originate from the specific electron and phonon spectra in quantum dot superlattices, such as negative differential conductivity and carrier scattering anisotropy, are also discussed.