We have developed a microscopic model to study the hot-electron- spectroscopy method which uses GaAs planar-doped barrier transistors. Our simulation is based on the Monte Carlo method and includes the effects of ionized impurity scattering, pair electron-electron scattering, long-range plasmon scattering, and coupled plasmon/phonon scattering. The nonparabolicity of the band structure and the Pauli exclusion principle are also taken into account in the highly doped base region. The numerical results show that the experimental method of Hayes will indeed reflect the overall momentum distribution of injected hot electrons if the planar-doped barriers are ''ideal." Ideal means that the self-consistent potential (due to conduction electrons and ionized impurities) is well described by the continuum approximation. We demonstrate that potential fluctuations arising from the discrete natue of the charges and reflection of electrons at the base-collector junction make it impossible to obtain the precise distribution function from the experiments.