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As you know, the physics of MOS capacitor is not simple. I have tried here to create a tool that may help simplify the 'situation'. But it seems, after all the effort, that it did not improve the situation much. If at first the applet appears too busy, it may help hiding the "charge" profile by cliking on the button.

This applet is to illustrate the equilibrium condition of MOS structure in the charge profile and the energy band diagram. You can try various gate metals, oxide thickness, and Si doping type and level.

As with the equilibrium band diagram of PN junction diode, the thermal equilibrium in MOS is dictated by the constant Fermi level (in metal and in semiconductor). As the equilibrium band diagram is achieved, an additional constraint to be met is the charge neutrality.

Sources of space charge are: