Quantum mechanical determination of the potential and carrier distributions in the inversion layer of metal—oxide—semiconductor devices

The mobile carrier distribution within the inversion layer of a metal—oxide—semiconductor device is obtained by solving Schroedinger's equation and Poisson's equation conjunctively, using the variational method of Rayleigh-Ritz and a Picard iteration technique. The tunneling of carriers into the gate oxide is taken into account. Both equilibrium and nonequilibrium situations are treated. The quantized energy subbands in which the majority of the carriers (99%) resides are obtained for various degrees of inversion; the level spacing increases as the inversion becomes stronger. The self-consistent results are compared with the conventional solutions and the significance of their differences is discussed.