The Effective Mass of Electrons in Crystals

The transfer of momentum between a conduction electron and a crystal lattice is examined in detail. By physical considerations we are led to the expression (mm*)ij = δij+ ∑ GGiδδkj|aG(k)|2 for the reciprocal effective mass tensor, where G is 2π times a reciprocal lattice vector and aG(k) is a coefficient in the momentum representation of the Bloch eigenfunction: ψk = ∑ GaG(k) exp[i(G+k)·r]. This expression for the effective mass tensor is shown to be completely equivalent to the usual definition.