High-field distribution function in GaAs

Use of the drifted Maxwellian distribution is shown to be unjustified for GaAs samples in which the Gunn effect is usually observed, because the carrier concentration is much too low for electron-electron collisions to predominate. It is pointed out that solution of the Boltzmann equation is considerably simpler at fields high enough so that the average electron energy exceeds several times the optical phonon energy. The simplification occurs because the polar optical scattering may then be considered elastic. Relaxation times and rates of energy loss in acoustic, optical, and intervalley scattering are examined in order to determine which scattering processes must be included in the Boltzmann equation. It is found that intervalley scattering is very likely to be more important than polar optical scattering for high-energy electrons in either the central or the outer valleys. Approximate solutions of the Boltzmann equation for electrons in the lower valley are given for a wide range of fields. The number of electrons per unit energy range, calculated from the solution of the Boltzmann equation, is given for electrons in both valleys for a field of 2.4 × 10³volts/cm, where the approximation mentioned should be reasonably good.