We consider a one-dimensional periodic potential, or "superlattice," in monocrystalline semiconductors formbeyd a periodic variation of alloy composition or of impurity density introduced during epitaxial growth. If the period of a superlattice, of the order of 100Å, is shorter than the electron mean free path, a series of narrow allowed and forbidden bands is expected duet o the subdivision of the Brillouin zone into a series of minizones. If the scattering time of electrons meets a threshold condition, the combined effect of the narrow energy band and the narrow wave-vector zone makes it possible for electrons to be excited with moderate electric fields to an energy and momentum beyond an inflection point in the E-k relation; this results ina negative differential conductance in the direction of the superlattice. The study of superlattices and observations of quantum mechanical effects on a new physical scale may provide a valuable area of investigation in the fieId of semiconductors.