Theoretical approach to the energy resolution of semiconductor detectors

There is a number of processes in semiconductor detectors that lead to peak broadening. In many papers, semi-empirical approach is used to take into account the contribution of one or another factor to the signal variance of a semiconductor detector. The correct formula for the signal variance cannot be semiempirical at the researcher's option. It must result strictly from the exact mathematical description of the particle registration by a detector. In this work, using the theory of branching cascade processes the general expression for the energy resolution of semiconductor detectors was derived. It was shown that the general formula encloses all specific contributions of the peak broadening published in literature and has additional contributions to the energy resolution fluctuations of the electron and hole lifetimes caused by nonuniformity of the trap density, and fluctuations of the electronic gain.