Analytic model of thermal runaway in silicon detectors

Usually the thermal behavior of silicon detectors is predicted from numerical methods (FEA or finite difference methods). However, these results are specific to the modelled structure and the input parameter set. Here we pursue the complementary, analytic, approach which offers some general (if approximate) results that allow relatively simple extrapolation of the performance of a specific detector design.We present simple network models to calculate analytically the limit of thermal stability in silicon detectors. In particular we use a minimal model, which ignores the thermal resistance within the sensor in comparison with the off-detector resistance. We further discuss an extension of this model to study the effects of a finite sensor thermal resistance.