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Hot electron effects have been observed in semiconductors for many decades; however, until recently, direct experimentally determined spectroscopic information on the hot electron distribution function did not exist. As a result the microscopic basis for hot electron transport could only be inferred. To bridge the gap between theory and experiment we invented hot electron spectroscopy, a technique which enabled us to obtain direct spectroscopic information on the electron momentum distribution, . In this paper we describe the technique and discuss hot electron spectra obtained in GaAs. "Ballistic" electron transport is observed in samples having narrow transit regions (<850 Å) and near diffusive transport for samples having wide transit regions (>1700 Å). In addition, a theoretical model has been developed enabling us to identify all observed features in the spectra.