Relaxation of hot electrons in a degenerate two-dimensional electron system: transition to one-dimensional scattering

The energy relaxation channels of hot electrons far from thermal equilibrium in a degenerate two-dimensional electron system are investigated in transport experiments in a mesoscopic three-terminal device. We observe a transition from two dimensions at zero magnetic field to quasi--one-dimensional scattering of the hot electrons in a strong magnetic field. In the two-dimensional case electron-electron scattering is the dominant relaxation mechanism, while the emission of optical phonons becomes more and more important as the magnetic field is increased. The observation of up to 11 optical phonons emitted per hot electron allows us to determine the onset energy of LO phonons in GaAs at cryogenic temperatures with a high precision, $\eph=36.0\pm0.1\,$meV. Numerical calculations of electron-electron scattering and the emission of optical phonons underline our interpretation in terms of a transition to one-dimensional dynamics.