Electronic effect on the elastic constant c44 of n-type silicon

The change of the elastic constant c44 of Si is theoretically investigated in the presence of both free electrons and bound electrons. While in p-type semiconductors the bound-hole contribution to the change of the elastic constant c44 is qualitatively different from the free-hole contribution, the bound-electron contribution in n-type Si is essentially identical to the free-electron contribution. It is shown that this phenomenon results from the facts that the donor ground state of silicon is a singlet and that the six conduction valleys of silicon are uniformly lowered by a shear acoustic wave.