Charge density at the Al$_{2}$O$_{3}$/Si interface in Metal-Insulator-Semiconductor devices: semiclassical and quantum mechanical descriptions

In this paper, a quantum correction computation of the inversion layer of charge density was investigated. This study is carried out for a one-dimensional Metal-Insulator-Semiconductor (MIS) structure with (100) oriented $P$-type silicon as substrate. The purpose of this paper is to point out the differences between the semiclassical and quantum-mechanical charge description at the interface Al$_{2}$O$_{3}$/Si, and to identify some electronic properties of our MIS device using different thickness of the high-k oxide and diverse temperature with different carrier statitics (Fermi–Dirak statitics and Boltzmann statitics). In particular, the calculations of capacitance voltage ($C$–$V$), sheet electron density, a relative position of subband energies and their wave functions are performed to examine qualitatively and quantitatively the electron states and charging mechanisms in our device.