Electron mobility of heavily doped semiconductors including multiple scattering by ionized impurities

A theoretical treatment of the multiple scattering problem for electrons in heavily doped semiconductors is developed for the purpose of resolving a long-standing discrepancy between theory and experiment on electron transport in semiconductors and semimetals. The scattering strength term in the traditional Brooks-Herring formula for ionized impurity scattering is modified to take into account the effect of the spatial proximity of ionized donors leading to an additional scattering term proportional to the cube of ionized impurity concentration, whereas the Brooks-Herring theory varies strictly linearly with the ionized impurity concentration. Comparisons between theory and experiment for GaAs, GaN, ZnO, and a-Sn are presented, showing significant improvement overall. In some cases, improvements greater than an order of magnitude are achieved. The agreement between theory and experiment for heavily doped ZnO over the temperature range of 21-322 K is within about 1%, depending on temperature.