Range of Excited Electrons and Holes in Metals and Semiconductors

The relaxation frequency for electron-electron scattering of an electron having energy more than a few k B T above the Fermi level in a metal is calculated in the Born approximation by assuming a phenomenological Yukawa potential. The same method is then used to calculate the relaxation frequency of a hole having energy more than a few k B T below the Fermi level in a metal and to calculate the relaxation frequency of an electron in a semiconductor having spherical energy bands. For electrons in a metal our result is compared with the result obtained in a dielectric constant calculation.