Relation of drift velocity to low-field mobility and high-field saturation velocity

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Abstract
From an investigation of the behavior of the momentum distribution function of electrons or holes under scattering rate and momentum scaling transformations, a number of interesting results are derived concerning the parameterization of drift‐velocity–vs–electric‐field relations in terms of mobility and saturation velocity. Indeed it is determined that saturation velocity is invariant under scaling of the magnitude of the scattering rates, which alters mobility, while mobility is invariant under scaling of the magnitude of the momentum, which alters saturation velocity. This independence between mobility and saturation velocity is utilized to generalize to interfaces velocity‐field relations valid the the bulk. Using the transformation of drift velocity under both rate and momentum scaling, partial experimental data can be used to predict high‐field saturation velocities. These velocities need not be reduced due to higher scattering rates as much as their low‐field counterparts. Nonzero magnetic fields and nonuniform scaling are also considered.