Hall Effect and Impurity Levels in Phosphorus-Doped Silicon

An experimental study has been made of the energy level structure of a phosphorus donor impurity in silicon, using Hall coefficient and Hall mobility measurements on six samples of widely varying impurity content and compensation. The main purpose was to test the Kohn-Luttinger theoretical model which predicts a splitting of the sixfold degenerate (excluding spin) ground "$1s$" level, with a single state being depressed in energy by between 0.009 and 0.015 ev relative to the remaining fivefold degenerate level. The splitting energy can be measured by comparing carrier concentration vs temperature curves corresponding to this energy level scheme with experimental curves derived from Hall data. The curves for our samples all agree well with the Kohn-Luttinger model for splitting energies of between 0.009 and 0.012 ev, in agreement with the theoretical prediction.