In general, the mobility of a charge carrier, like an electron, is directly proportional to the electric field it experiences. However, this velocity cannot increase indefinitely and at some point, it saturates and the electron reaches a terminal velocity. The reason the velocity saturates is that between collisions of the electron with other elements in the material, the high electric field accelerates the electron to the point where it gains enough kinetic energy that it emits energy in the form of an optical phonon. The emission decelerates the electron and the process repeats all over again. To a first approximation:

\[v_{\text {sat }}=\sqrt{\frac{E_{\text {phonon }}}{2 m_{e f f}}}\]

Where \(E_{\text {phono }}\) is the energy of the emitted phonon (characteristic of the material) and \(m_{\text {eff }}\) is the effective mass of an electron in the material.

\(E_{\text {phonon }}\) and \(m_{e f f}\) for \(\mathrm{Si}\) is \(0.063 \mathrm{eV}\) and \(1.09 m_{e}\) while in GaAs, it is \(0.034 \mathrm{eV}\) and \(0.067 m_{e}\). Calculate the terminal velocities for electrons in both semiconductors. \(m_{e}\) is the rest mass of an electron.