Electron ground state in the semiconductor inversion layer and low frequency MIS capacitance

By varying the total energy and electrostatic energy functionals which represent an approximate self-consistent solution of Schrödinger's and Poisson's equation, the ground state of electrons is determined in a semiconductor inversion layer. It was assumed that all the electrons in the semiconductor inversion layer are in the ground state.The low frequency capacitance metal-insulator-semiconductor (MIS) capacitors is calculated by the proposed theory and the results are compared with classically calculated capacitance. Numerical results are given for a silicon (111) p-type bulk at 77°K.