We report an observation of a single-optical-phonon emission by monoenergetic hot electrons traversing thin n + -type GaAs and thin undoped AlGaAs layers in times much shorter than the classical phonon period. This was done by injecting ballistic electrons into the thin layers with energy around the threshold for optical phonon emission and monitoring their exit energy. We estimate a scattering time of -200 fsec for electrons with energy of about 85 meV in « + -type GaAs, and -550 fsec for 40-meV electrons in undoped AlGaAs.PACS numbers: 73.50. Gr, 63.20.Dj Among the variety of phonons in GaAs, the longitudinal optical (LO) phonons are coupled most strongly to low-energy electrons. Electrons with wave vector k will scatter via phonons with wave vector q to k' (q=k -k') with a probability proportional to | q | ~~2 in unscreened material, thus preferring to maintain their original direction. The q=0 LO phonon energy in GaAs has been measured via neutron scattering 1 and inelastic tunneling, 2 and is fto)LO~36 meV. At low temperatures, when the phonon occupation number is small, scattering events are mostly due to phonon emission which is possible only when the electron energy exceeds the lowest unoccupied energy state by at least 36 meV. Using energy spectroscopy, Dimaria et al. 3 have observed phonon replicas in SiC>2 in electron distributions emerging into vacuum. Multiphoton emission in GaAs was observed by Shaw 4 via photoconductivity experiments, and more recently by Hickmott et al. 5 in tunneling experiments. We report here a direct observation of monoenergetic, ballistic, hot electrons that emitted a single LO phonon when traversing very thin layers of n + -type GaAs and insulating AlGaAs. It is particularly interesting that the transit time of the electrons through the layers is smaller than the phonon classical period (27T/&>LO)-To observe the emission of a phonon by a hot electron, a potential barrier (spectrometer) was constructed; its height was considerably lower than hca^o to enable electrons with energy less than hco^o to pass, but sufficiently high to prevent those hot electrons that lost hco^o from passing. A quasi monoenergetic hot-electron beam was produced by a tunnel barrier (injector), which was made especially wide in order to achieve an energetically narrow hot-electron beam. Our hot-electron structures, described in Fig. 1, were grown by molecular-beam epitaxy, were composed of n + -type GaAs emitter, undoped AlGaAs tunnel barrier injector, n "'"-type GaAs transport region (base), undoped AlGaAs spectrometer barrier, and « + -type GaAs collector layer. 6,7 The spectrometer barrier, 70 nm thick, with AlAs mole fraction x=7%, had a conduction-band discontinuity of 63 meV. Because of some lxl0 16 -cm~3 unintentional negative charges in all our molecular-beam-epitaxy layers, the measured barrier height was about 73 meV (the additional 10-meV bowing is expected to have a potential maximum at the center of the barrier). With doping of 8x 10 17 cm "~3 in all n + -type GaAs layers and Fermi ene...