²²We will assume that there is no contact potential difference between the gate material and the semiconductor. Taking this into account is actually quite easy: $v_{\mathit{gb}}^{\prime }=v_{\mathit{gb}}+{\phi }_{\mathit{contact}}$ , but doing so only makes this discussion needlessly complex. For the interested: a contact potential is the difference in voltages between two different materials, just as the ones you would encounter in redox reactions. You can try this yourself by placing a piece of tin foil against an amalgam tooth filling and experience the “contact potential”.