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one energy. It is not necessary that dg r&g Bk J J s j with the integral performed over a surface of constant energy, be positive for some such surface. The necessary condition for negative resistance in the i direction only demands that Bg/dE along some line in the i direction be positive. In Ge and Si with warped heavy-hole bands, the necessary reversal may only correspond toIn this Letter we describe direct observations of bimolecular band-to-band transitions at rectifying junctions in single crystals of gallium phosphide and indium phosphide.The presence of bimolecular recombination kinetics is deduced from the nearly square dependence of the emitted radiation on the injection current. Additional evidence for band-toband electroluminescence is supplied by an analysis of the spectral distributions of the absorption coefficient, the electroluminous emittance, and the photovoltaic response of gallium phosphide crystal rectifiers. These band-to-band radiative transitions differ in a number of ways from those occurring via localized levels. 1 The above-mentioned square dependence has been discussed by van Roosbroeck and Shockley 2 and looked for without success in germanium by Newman 3 who found a linear dependence. So far only Aigrain and Benoit 4 observed a square dependence in germanium, when a very sensitive detection technique was used. Braunstein, 5 who investigated band-to-band radiative transitions of injected carriers in Ge-Si alloys, GaAs, GaSb, and InP, found a linear dependence in all cases, in agreement with Newman's observations. 3 Our GaP samples were grown by I. Hegyi of these Laboratories from gallium solution by the method of Wolff, Keck, and Broder 6 using a 5day programmed heat-cool cycle with a peak temperature of about 1200°C. The crystals were flat hexagonal platelets with major faces parallel a redistribution from the thermal equilibrium distribution along constant-energy surfaces.Most of these conclusions were simultaneously and independently reached by Dr. C. Kittel. I am very grateful to him for making his results available. I would also like to thank Dr. F. Herman for several discussions. ^ousmanis, Duncan, Thomas, and Williams, Phys. Rev. Letters 1, 404(1958). 2 H. Kromer, Phys. Rev. 109., 1856 (1958); Proc. Inst. Radio Engrs. 47, 397 (1959).to (111) planes and an area of a few square millimeters. They were a few tenths of a mm thick. The crystal structure, determined by J. White, was that of sphalerite with a lattice constant of 5.449 A. The impurity with the highest concentration was copper with approximately 5-50 parts per million. Care was taken to avoid using crystals that had inclusions of free gallium or free phosphorus.Undoped GaP crystals appear to contain grown junctions beneath the surface, which resemble somewhat those found in single crystals of silicon carbide grown by commercial processes. 7 A highly w-type conducting layer is separated from the bulk by a rectifying junction and most likely also by a nearly intrinsic layer. Ohmic contacts to the crystal bulk can be mad...