Ultrathin Cu films were evaporated on Si(111) surfaces at substrate temperatures of 175 K. By use of a microfabricated device structure, zero-force electrical contacts were formed on the thin Cu layers during evaporation. They allowed current/voltage measurements of diodes with Cu films between 40 and 60 Angstrom. Although the rectifier properties are improved with increasing thickness, the 60 rf diode still exhibits a large inhomogeneous interface with a low barrier height of 0.47 eV and an ideality factor of 2.1. Annealing the diode to room temperature leads to significant changes in the barrier height which increases to 0.65 eV and the ideality factor which decreases to unity, suggesting a modification of the interface. The annealed thin-metal diodes may be used as atomic hydrogen sensors. A chemicurrent is observed in the diode when exposed to H atoms. The current is based on a nonadiabatic electron-hole pair creation which occurs during exothermic adsorption of hydrogen on Cu surfaces.