Chapter 2 · Animation 1 of 4 · Sections 2.2 and 2.3
Why the Bands Bend at Zero Gate Voltage
Connect the gate to the body and watch electrons flow through the wire until the Fermi levels line up. The charge left behind bends the bands; the flatband voltage undoes it.
electron in the wire / inversion layerhole⊖ acceptor ion+oxide charge
What to look for
Before the connection the Fermi levels differ; after it they are level, and the vacuum-level step has turned into band bending in the silicon plus a voltage across the oxide.
The electrons that flowed through the wire are exactly the + charge left on the gate, matched by the − ions (and electrons) in the silicon.
With VGB = VFB the silicon is neutral and the bands are flat, whatever the gate material or oxide charge.
The physics behind it
ΦMS = φw,gate − φw,body: about −0.98 V for n⁺ polysilicon on p-type silicon with NA = 10¹⁷ cm⁻³ (Section 2.2).
VFB = ΦMS − Q′o/C′ox (eq. 2.3.10), where Q′o is the effective interface charge per unit area.
In general VGB = VFB + ψox + ψs: the part of VGB beyond VFB divides between the oxide and the silicon.