Hopping conduction in semiconductor superlattices in a quantized magnetic field

Abstract

Hopping conduction between localized Stark states in superlattices in longitudinal electric and magnetic fields is investigated. Electron scattering with acoustic phonons, short-range impurities, and with polar-optic phonons are taken into consideration. The expression for hopping current formally exhibits a series of maxima at the points p${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$=n\ensuremath{\theta} [Stark-cyclotron resonance (SCR)] or at p${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$=\ensuremath{\Vert}n\ensuremath{\theta}\ifmmode\pm\else\textpm\fi{}${\mathrm{\ensuremath{\omega}}}_{\mathrm{ol}}$\ensuremath{\Vert} [Stark-cyclotron-phonon resonance (SCPR)] (${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ and \ensuremath{\theta} are cyclotron and Bloch frequencies, respectively, ${\mathrm{\ensuremath{\omega}}}_{\mathrm{ol}}$ are optic-phonon frequency modes in superlattices, and p and n are integer numbers). However, the SCR's are strongly suppressed due to finite collisional broadening and are not easily detected experimentally. Within the framework of the dielectric continuum model, numerical calculations show that the amplitude of SCPR is much weaker than the amplitude of SCR and it does not give contributions to the hopping current. These observations are in good qualitative agreement with recent experiments. \textcopyright{} 1996 The American Physical Society.