In order to better understand energy estimation of electromagnetic showers in segmented calorimeters, detailed Geant4 simulation studies of electromagnetic showers in the energy range 1-100 GeV in CsI have been performed. When sampled in layers of 1.99 cm thickness, corresponding to 1.08 radiation lengths, the energy fluctuations in the samples show distributions that vary significantly with depth. The energy distributions are similar for incident electrons and photons and were found to change systematically along the shower, varying little with the initial energy. Three probability distributions have been fitted to the data: negative binomial, log-normal and Gaussian distributions, none of which gives a good fit over the full shower length. The obtained parameterizations might be useful in the use of the maximum likelihood method for estimating the energy. Two methods for estimating the energy have also been studied. One method is based on fitting individual longitudinal shower profiles with a Gamma-function, the other one corrects the measured energy for leakage by utilizing the energy deposited in the last layer. Our simulations indicate that the last-layer correction method applied to photons and electrons of 1 and 10 GeV gives about a factor of 2 improvement in the energy resolution.

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