Fig a: Band diagram for ideal MOS structure at equilibrium.

In this figure $q\phi_m$ it measured from metal fermilevel to the conduction band of the oxide. Similarly, $q\phi_s$ is the modified work functionat the semiconductor oxide interface. In the ideal case we assume that $\phi_m=\phi_s$, so there is no difference in the two work functions.

MOS Capacitor in Accumulation:

As negative voltage is applied between the metal and the semiconductors a negative charge is deposited on metal. Due to this an equal net positive charge accumulation at the surface of the semiconductor. In the case of a p-type substrate this occurs by hole accumulation at the semiconductor-oxide interface. Since the applied negative voltage depresses the electro static potential of the metal relative to the semiconductor, the elctron energies are raised in the metal relative to the semiconductor.

MOS Capacitor in depletion:

As positive voltage is applied from metal to the semiconductor. This raises the potential of the metal lowering the metal Fermi level by qv relative its equilibrium position. As a result the oxide conduction band is tilted. The positive voltage depose positve charge on the metal and calls for a corresponding net negative charge at the surface of semiconductor. Such a +ve charge in p-type material arises from deplexing of holes from the region near the surface, leaving behind uncompensated ionized acceptors.

MOS Capacitor in Inversion:

As a positive voltage is continued to increase, the bands at the semiconductor surface band down more strongly. In fact, a sufficiently large voltage can band Ei below EF. The region near the semiconductor surface in this case has conduction properties typical of n-type material, with an electron concentration. This n-type surface layer is formed not by doping, but instead by inversion of the originally p-type semiconductor due to the applied voltage. The best criterion for strong inversion is that the surface should be as strongly n type as the substrate the surface as it is above EF far from the surface. This occurs below when $\phi_s(inv.)=2\phi_F$