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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.© 1999 American Institute of Physics.