Electronic structure of semiconductor surface inversion layers at finite temperature. The Si(100)-SiO2system

The electronic structure of an $n$-channel inversion layer in the Si-Si${\mathrm{O}}_2$ metal-insulator-semiconductor system is investigated at finite temperatures for the (100) surface. The subband energies for the ground state and the low-lying excited states are calculated (i) within a Hartree self-consistent-field formulation and with exchange-correlation corrections treated perturbationally in the plasmon-pole approximation and (ii) by employing a finite-temperature version of the local density functional (LDF) technique. Many-body effects are found to be important even at room temperature. A comparison of results of the two methods shows that the LDF works quite well also at finite temperatures for the unprimed subband ladder. Our results for the unprimed subbands are in good quantitative agreement with recent experimental results. For the primed subbands our results agree only qualitatively with the experiments and the two methods give considerably different results. Finally the critical temperature for the two-valley to one-valley transition is calculated to be about 4.5 K for electron densities around ${10}^{11}$ ${\mathrm{cm}}^{-2\mathrm{}}$.