Work Function Difference between Gate Metal and Silicon.
This is one source of the voltage difference between the Si channel and the gate metal which create band bending in Si. This band-bending of, or the voltage-drop in, silicon must be first compensated by the applied bias and then an additional voltage has to be applied to bend further the Si energy band so as to induce a charge inversion layer.
In the following applet, you may change condition in the text field or in the choice box, or mouse drag the Fermi level ( ____ Ef )of silicon. [Warning: The mouse-drag needs your patience. If your mouse moves away from the Fermi level without dragging it, then try again ]
Best is a combination where the gate metal and the silicon have the smallest work function difference.