Electron-electron angular relaxation in a two-dimensional electron gas

The relaxation of a low-energy electron beam in a two-dimensional electron gas (2DEG) due to electron-electron scattering is studied. The solution of the Boltzmann equation shows that the scattering is characterized by two different relaxation times for the energy and angular relaxation. The estimates of the electron-electron relaxation time previously obtained were related to the energy relaxation time τ. The characteristic time for the angular relaxation of the electron distribution function is longer than τ by a factor of ln[${\mathit{E}}_{\mathit{F}}$/(E-${\mathit{E}}_{\mathit{F}}$)], where E is the electron energy and ${\mathit{E}}_{\mathit{F}}$ is the Fermi energy of the 2DEG. The fact of small-angle scattering in electron-electron collisions is important for distinguishing truly ballistic regimes in experiments with electron beams.