We present Monte Carlo simulations of the transient behavior of electrons injected into GaAs at high energies and accelerated (decelerated) by constant electric fields. Our calculations differ from previous calculations due to the inclusion of a realistic band structure (empirical pseudopotential) and the injection of electrons at high energies (e.g., via a heterobarrier). The results show that a narrow "collision-free window" (CFW) exists with respect to parameters such as the external electric field, the injection energy, the external voltages, and the semiconductor dimensions. Within this window average electron velocities of\sim 8 \times 10^{7}cm/s can be achieved over distances of 10-5cm in emitter (source)- and base-like structures. Voltage (field) parameters typical for the collector (drain) are far outside the CFW and allow only for much reduced (by a factor of ∼ 10) electron velocities. We also discuss thermal noise in "ballistic devices" and show that the noise equivalent temperature can be exceedingly high.