Through Monte Carlo modeling, it is shown that the statistics of electron–hole pair creation in semiconductors (and by extension, presumably, ion-pair creation in gas proportional counters) are substantially different for fast electrons (and by extension, presumably, alpha particles, ions, etc.) cf. x-ray/γ-ray photons. New variables are introduced to quantify the differences in the statistics: the loss parameter, ζ(E′), which acts on the average e−–h+ pair creation energy; and the broadening factor, B(E′), which acts on the Fano factor. E′ is the initial energy of the fast electron. ζ(E′) and B(E′) are computed for a variety of semiconductor materials. A new equation for the statistically limited energy resolution of a particle counting fast electron spectrometer is established. This new equation supersedes and replaces that for the Fano-limited energy resolution of a particle counting fast electron spectrometer. The implications impact a wide variety of fields wherever fast electrons (or alpha particles, ions, etc.) and/or Fano statistics are used; this includes, inter alia, quantum computing, x-ray excitonics, space science, optoelectronics, nuclear engineering, particle physics, photovoltaics, and even neural response variability in the brain.
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