Hot Electron Effects in Landau Levels of MOS Inversion Layers

A hot electron theory is applied to Landau levels of MOS inversion layers as the first example of the theory for extremely quantized systems. The energy gain from drain fields and the energy loss to phonons are formulated in the self-consistent Born approximation. A difference between the electron temperature and the lattice temperature in Landau levels is calculated by balancing these two energy terms. A larger temperature difference is expected for a larger Landau index and is almost independent of the position where the Fermi level lies. The typical temperature rises are 1.4 K for N =0, 3.0 K for N =1, 4.1 K for N =2 and 5.0 K for N =3, when the applied electric field is 20 V/cm, the applied magnetic field is 140 kOe and the lattice temperature is 1.4 K. The observed temperature rises are little lower than the theoretical results.