Electron-electron scattering: Collision integral and relaxation rate

We derive a simple formula for the nonequilibrium, electron-electron relaxation rate 1/te-e in nondegenerate semiconductors, starting from the collision integral Ie-e(k). Numerical evaluation of the rate of quadrupole-moment relaxation confirms the magnitude and dependence of 1/te-e on carrier temperature and density. For highly elongated distributions, the thermal current relaxes more slowly than the quadrupole moment, indicating a limitation of the relaxation-time approach. Exchange scattering makes a negligible contribution to 1/te-e in the low-density limit.