When a metal is brought into contact with a semiconductor (n-type) a depletion layer is formed at the metal-semiconductor interface on which band bending occurs. In the full-depletion model it is assumed that all donors are positively charged (withi this layer). What happens if a back-gate (with a insulating thin layer) at the back-side of the semiconductor is placed with a negative polarity? Similar to pnp MOSE FETs I would expect that for a sufficient large voltage the chemical potential is driven into the valence band so that right under this gate an accumulation of holes is created, i.e. inversion. But what happens with the repelled electrons? Can they affect the depletion layer width at the metal-semiconductor junction through recombination with the ionized donors?