SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.3. METAL-OXIDE-SEMICONDUCTOR CAPACITOR 441

Ec

EFi

EF

Ev

Oxide Semiconductor

z

Vs = 2 φF at inversion

Vs

Channel with electrons

++++

eφF =EF–EFi:

positive for p -substrate

negative for n-substrate

Surface

potential

eφF

e

Figure 9.9: Band bending of the semiconductor in the inversion mode. The interface poten-
tial isψs. A simple criterion for inversion is thatψs=2φF. The electron density changes
monotonically near inversion.

semiconductor near the interface has electrical properties of ann-type semiconductor. This is
shown in figure 9.8c. The device can be switched between depletion (OFF) and inversion (ON)
and as a result current flow can be modulated by a gate bias.
Due to the importance of the inversion regime in the MOSFET, let us examine it in quantita-
tive detail. In figure 9.9 we show the band bending of the semiconductor on the onset of strong
inversion. The band bending is described by the quantityeψ,whichmeasuresthepositionof
theintrinsicFermilevelwithrespecttothebulkintrinsicFermilevel. The surface band bend-
ing at the oxide-semiconductor interface is described in terms of the potentialeψsas shown in
figure 9.9.
The onset of inversion is a gradual process as a function of gate bias. We will first use the
criterion that strong inversion occurs when the electron concentration at the interface is equal to
the bulkp-type concentration.ThustheintrinsiclevelEFishouldbeatapositioneφFbelow
theFermilevelattheinterface. Thus the surface band bending is given by

ψs(inv)=2φF (9.3.1)

Note that for an NMOS FET, the substrate isp-type andφFis positive and a positive biasψs
is needed to cause inversion. For a PMOS FET the substrate isn−type andφFis positive. A