This Demonstration simulates an ideal NMOS capacitor constructed using silicon, silicon oxide, and an aluminum electrode. The variable
is the thickness of the oxide layer;
are, respectively, the electric fields and the electrostatic potentials applied to the oxide and to the semiconductor;
are the hole and electron densities inside the semiconductor far away from the interface; and
is the concentration of positive dopant ions inside the semiconductor.
is the Fermi level inside the metal and the semiconductor, while
is the position of the Fermi level of the intrinsic semiconductor; hence it lies in the middle of the band gap.
are the conduction and valence bands of the semiconductor.
Several assumptions are made to simplify the model. The electric field is assumed constant inside the oxide and linear in the depletion layer. The carrier density in the metal is assumed to be infinite, so the band profile stays flat inside it. A Boltzmann approximation is assumed for carrier densities in the semiconductor. The voltage bias cannot exceed the threshold voltage, since a simple model for the inversion layer is missing. Also, interface trap states are neglected.