A rigorous theory of the difference frequency mixing of two signals, one with frequency ω and the other with frequency near 2ω, in semiconductors is presented. It is shown that a lower-frequency (DC ~ 10THz) directional photocurrent and voltage are generated as a result of this nonlinear interaction. This result conclusively links the 'directional photogalvanic effect' with the third-order nonlinearity. The magnitude of the difference frequency response is evaluated as a function of frequency and the efficiency of the method is examined for various energy coupling techniques. Comparison with alternative methods for difference frequency generation using the second order nonlinearities is made and the practical applications are considered.