Description:
A velocity-randomizing collision integral is constructed to describe electron-hole pair production by energetic electrons in the (000) valley of InSb. The Boltzmann equation is solved numerically by a variational-iterative method, and the electron-hole pair generation rates at high fields are obtained for a set of values of an over-all constant factor appearing in the collision integral. One of the cases solved is that in which this factor is chosen so as to give a pair-production scattering probability close to that calculated from the electron wave functions in InSb. Also studied is the hypothetical case in which the pair-production probability is significantly greater than the electron-phonon scattering probability at energies less than the threshold for electron transfer to the L1 minima. It is shown that in this case a single-valley negative differential mobility (NDM) can result at fields in which no significant transfer of electrons to the L1 minima occurs, but this hypothetical situation probably does not occur in InSb. The generation rates calculated in each of the cases solved are not inconsistent with experiments. Only polar optical-type phonon scattering is considered, and the calculations are for a lattice temperature of 77°K. The Kane band structure is used, and the band overlap integral is included in the electron-phonon scattering matrix elements.