= Gate-to-substrate Fermi-level difference
{title2=$\widetilde\mu_g-\widetilde\mu_s=-eV_g$}
An ideal insulating gate blocks particle exchange between the gate and substrate of a <MOSFET>. Their <electrochemical potentials>, represented by their band-diagram <Fermi levels>, therefore need not coincide. An applied gate voltage fixes their difference; with $e>0$ and voltage defined by an electron reservoir, $\widetilde\mu_g-\widetilde\mu_s=-eV_g$. Contact work-function differences also affect <band bending>, so equal Fermi levels do not imply flat bands. Each conducting region can separately have a spatially constant equilibrium electrochemical potential.
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