where R is a reciprocal lattice vector. Umklapp processes (or U-processes) change the momentum of the particle after scattering and are therefore limiting the conduction in semiconductor crystals. Physically, U-processes occur when the final momentum of the particle points out of the first Brillouin zone. Once one knows the scattering probability per unit time from a state k to a state k', it is interesting to determine the scattering rate for a given scattering process. The scattering rate gives the probability per unit time to scatter from a state k to any other state in the reciprocal space. Therefore, the scattering rate is