Ionized-Impurity Scattering Mobility of Electrons in Silicon

Curves have been obtained of the temperature dependence of the electron mobility in a set of n-type silicon samples of varying impurity content and compensation between about 30^∘{} and 100^∘{}K by combining data from electrical resistivity and Hall effect measurements. The curves have been used in an experimental test of the applicability of the Brooks-Herring formula to the ionized-impurity scattering of electrons in silicon under conditions for which the Born approximation is valid. Impurity concentrations in the samples were determined by analysis of the Hall vs temperature data. It was necessary to correct for the lattice-scattering contribution to the observed mobility in comparing the Brooks-Herring formula with the experimental results. It is found that the formula gives a good quantitative description of the results when an electron effective mass of 0.3 of the true mass is used, provided that the ion scattering is not too strong. When ion scattering is dominant, however, such as at low temperatures in relatively impure samples, there is a discrepancy between formula and results which may be due to electron-electron interactions.