A non-Markovian model of avalanche gain statistics for a solid-state photomultiplier

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Abstract
A solid‐state photomultiplier (SSPM) capable of continuously detecting individual photons of wavelength between 0.4 and 28 μm has recently been disclosed [Petroff et al., Appl. Phys. Lett. 5 1, 406 (1987)]. The initial response of the SSPM to a single photon is a fast, high‐amplitude current pulse of between 104 and 105 electrons. The distribution of the pulse amplitudes possesses a strikingly and unexpectedly narrow dispersion. We present a phenomenological model of the SSPM avalanche process which successfully predicts the shape of the observed pulse‐amplitude distribution by including small history‐dependent effects on the carrier transport, effects heretofore ignored in the traditional (Markovian) treatments. The model clarifies the consequences of the electric field strength and the scattering of the electrons for the development of the avalanche in the SSPM.