Influence of the ionized impurities on the cooling effect

Abstract

In polar semiconductors the electron temperature T can become smaller than E This "cooling effect" has been studied by many authors the lattice temperature T (1, 2) neglecting the effect of impurity scattering. L'Paranjape and de Alba (1) expanded the distribution function to second order in the drift momentum p They obtained monotonically decreasing T with increasing 0' E electric field E which indicates the insuffiency of this approximation. However, if one expands the momentum and energy balance equation up to second order in p the results for the J-E-characteristics a r e in good agreement with those obtained without expansion (2). 0 Throughout this work the following assumptions a r e made: isotropic material, parabolic band structure, combined scattering by polar optical modes and ionized impurities, drifted Maxwell-Boltzmann distribution ( P -P J 3/2 [ -' n f(p) = ( 2 r m* kBTE) 2m" kgTE Conservation of momentum and energy yields two equations to determine the J-E-characteristic. To evaluate the collision integral the matrix elements of Frohlich and Paranjape (3) and Brooks (4) were used.Fig. 1 shows the dependence Tv'e. E for various impurity concentrations % E for n-type InSb at 77 OK. An increase of r+, results in a larger ratio of the randomized 3 2 energy (-k T ) to the drift energy (p /(2m*)). At a certain concentration n = 2 B E 0 D = I$ the cooling effect does not appear anymore. To determine I$ we set TE = T, , .This value I$ depends strongly on the lattice temperature (Fig. 2).1) This work was sponsored by the Ludwig-Boltzmann-Gesellschaft.