Velocity-field characteristics of selectively doped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum-well heterostructures

Recent experimental observations indicating poor correlation between the saturation velocity and Ohmic mobility lead us to propose a theory for a velocity-limiting mechanism in quantum-well heterostructures. The theory is based on the distribution function which takes into account the electron-drift anisotropy introduced by the high electric field for a degenerately doped quantum well. The drift velocity is shown to be limited by the Fermi velocity; a result which indicates that the saturation velocity is independent of the low-field mobility which is strongly controlled by momentum-randomizing scattering events. The dominance of optical-phonon emission at high electric field lowers the saturation velocity below the Fermi velocity. Excellent agreement is obtained between the theoretical and experimental results on the velocity-field characteristics of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum-well heterostructures.