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Current-voltage characteristics have been calculated for a structure consisting of two metal surfaces separated by a thin film of "insulating" material. The analysis includes both tunneling and thermionic emission, and takes account of dielectric constant and image force. Curves of current density vs field strength are presented for various values of barrier height and dielectric constant. Several comparisons of theory with experiment are given, and it is concluded that the theory overemphasizes the thermionic contribution.