At cryogenic temperature, the dark rate in a photomultiplier is caused by single electrons, emitted spontaneously from the cathode surface. This "cryogenic" dark rate increases with decreasing temperature down to at least 4 K. The average event rate is proportional to the area of the emitting surface and insensitive to the electric field at that surface. The electrons are emitted in bursts. The bursts are distributed randomly in time, but the events within a burst are highly correlated. The burst durations are distributed according to a power law. As the temperature decreases, the rate of bursts, as well as the number of events per burst, increase. The observed time distributions are indicative of a trap mechanism. So far, there is no physics explanation of the observed phenomenon.