Intervalley-Scattering Induced Electron-Phonon Energy Relaxation in   Many-Valley Semiconductors at Low Temperatures
  We report on the effect of elastic intervalley scattering on the energy transport between electrons and phonons in many-valley semiconductors. We derive a general expression for the electron-phonon energy flow rate at the limit where elastic intervalley scattering dominates over diffusion. Electron heating experiments on heavily doped n-type Si samples with electron concentration in the range $3.5-16.0\times 10^{25}$ m$^{-3}$ are performed at sub-1 K temperatures. We find a good agreement between the theory and the experiment. 
M. Prunnila, P. Kivinen, A. Savin, P. Torma and J. Ahopelto