Compact model for non-local avalanche effect in advanced bipolar transistors: An assessment of the relaxation length and its temperature dependence

We present a physics based compact model formulation for non-local avalanche effects. It is explicit and in terms of elementary functions, hence suitable for implementation in existing compact transistor models. The formulation has only two material coefficients as parameters: the energy relaxation length and its temperature coefficient. We present a detailed verification of our model against measured avalanche characteristics, as a function of both bias and temperature, for Si and SiGe industrial bipolar transistors. We demonstrate that the model is complete and accurate enough for the parameter extraction to be taken as an in situ measurement for both the electron energy relaxation length and its temperature coefficient: values obtained correspond to the values published earlier in the semiconductor literature.