Various representations of the dielectric functions of semiconducting materials have been proposed. We compare five different models for representing the dielectric functions of crystalline (c-) Si, amorphous (a-) Si, and c-Ge from 1.5 to 6.0 eV. The four-oscillator critical point with parity plus one-dimensional tight-binding model (CPP-1D) best represents c-Si. Different models best represent a-Si and c-Ge. These representations provided a basis for modeling variations encountered in semiconductor manufacturing.