Time dependence of rate-dependent photomultiplier gain and its implications

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Abstract
Time dependences of rate‐dependent photomultiplier gain were measured precisely in two particular tubes for various count rate changes. Most of the measured time dependences are shown to be well described by three exponential components. While the corresponding time constants remain unchanged for different count rate changes except the one of the first component, the relative population of each component varies considerably according to duration of the measurement immediately before the count rate change. Since the time dependence is considered to reflect the charge buildup on the dynode, a charge buildup model based on electron and hole trapping is proposed to explain the measured time dependences. An abrupt rise or fall in gain, which is clearly seen immediately after a count rate change, is interpreted as a manifestation of a large difference in value between the detrapping constants for trapped electrons and holes. It is shown that in order to be consistent with the measured time dependences the observed tendency of trapped holes to settle into deeper levels at larger times should be attributed to physical processes similar to those of polaron hopping. The proposed charge buildup model should not only indicate possible factors affecting the time dependence, but also give an insight into the physical mechanism involved in charge buildup on thin oxide films.