Energy exchange in single-particle electron-electron scattering

Electron-electron scattering has been of interest in the treatment of hot carriers for several decades. Recently, the details of this scattering process have become much more important with regard to the degradation of Si MOS transistors, where it is suggested that intercarrier scattering excites electrons well above 3 eV, even with only 2 V bias. On the other hand, it is generally found that the energy exchange found in the electron-electron interaction is quite small. As a consequence, we have examined the detailed energy loss (gain) through the electron-electron interaction for carriers in Si. This is evaluated assuming a thermal Maxwellian hot carrier distribution at 2500 K and the parameters for Si. We find that the energy exchange is highly peaked around small energies (less than 20 meV), and falls off rapidly with energy.