Warm and hot carriers in silicon surface-inversion layers

A study of the hot-carrier effects for electrons in silicon inversion layers is reported. Measurements of the warm-electron coefficient $\beta$ at 77 °K give - 2 × ${10}^{-8\mathrm{}}$ ${\mathrm{cm}}^2$/${\mathrm{V}}^2$ in the 〈110〉 and - 5 × ${10}^{-8\mathrm{}}$ ${\mathrm{cm}}^2$/${\mathrm{V}}^2$ in the 〈100〉 direction on a (110) silicon surface. A theory of $\beta$ is given for the two-dimensional carrier gas model. The two-dimensional Boltzmann equation is solved in the diffusion approximation. Explicit results for the distribution function are given for scattering of the electrons by acoustic phonons, surface roughness, and optical phonons as well as for scattering by combined acoustic phonons and surface charges. The current-voltage characteristics is also calculated for high electric fields using a Maxwellian distribution with electron temperature $T_e$. These results are compared with experimental values obtained in this paper and those given by Fang and Fowler.