Superlattice space-charge-wave analyses in a modified drift-diffusion model and in a simplified balance-equation formulation

Unstable space-charge-waves in superlattice miniband transport are investigated using a modified drift-diffusion model and using a simplified one-dimensional hydrodynamic balance-equation formulation with a relaxation-time approximation. We point out that the earlier widely accepted notion, that in the small wavevector limit the space-chargewave (SCW) propagates at a phase velocity equal to the carrier drift velocity and with an amplitude-growth rate equal to the negative value of the mobility frequency, -ω _c, was crucially based on the implicit assumption that the system momentum relaxation time τ_m is extremely small. Taking account of a finite momentum relaxation time, we find that even the drift-diffusion model would yield results significantly different from the above predictions: the phase velocity of a long-wavelength traveling SCW can be much slower than the carrier drift velocity and its amplitude-growth rate much smaller than -ω_c. A hydrodynamic balance-equation formulation, which properly treats energy dissipation and further reduces the amplitude-growth rate, provides a convenient tool for improved qualitative analyses in SCW-related problem in semiconductor superlattices.