A transient solution of the Boltzmann equation exposes energy overshoot in semiconductor devices

A method is developed to analyze the transient response of semiconductor devices in phase space. This is achieved by solving the space and time dependent electron Boltzmann transport equation self-consistently with the Poisson and transient hole-current-continuity equation. The result gives the details of the time evolution of the distribution function. The method is applied to analyze a bipolar junction transistor. The model predicts the limits in which the steady-state response approximation can be applied. The model exposes a transient overshoot in the high energy tail of the distribution function.