During the hypothetical contact transient of the three layers of the four MOS structures in problem below, are electrons transferred from the gate conductor to the Si or vice versa? Explain the detailed sequence in the same way as in given Figure.

Problem

Polycrystalline silicon has been used as the gate material in Si MOS transistors. It is also used as a barrier layer for making contact to thin Si layers to prevent a metal conductor from penetrating and short-circuiting the thin Si layer. But in MOS, poly-Si gate also gives one more parameter to control the threshold voltage (see next problem).

Thus, construct the equilibrium energy band diagram of a polycrystalline silicon gate MOSC on n-type Si at V_G = 0. Do this for four cases.

(a) The Si-gate is doped to the same donor concentration at the n-type Si bulk.

(b) The Si-gate is so heavily doped that its Fermi level is at E_C.

(c) The Si-gate is doped to p-type with its acceptor concentration equal to the donor concentration in the n-Si bulk.

(d) The Si-gate is doped to degenerate p-type with E_F = E_v.