MOSFET: Depletion Region Maximum Depth Vt Transition Voltage and Fermi Level

(1)When voltage is first applied it is too low to attract many additional carrier electrons.  As the voltage rises hole carriers flee the gate exposing more fixed negative charges to balance out the charge on the gate. A circle with – is a fixed acceptor dopant atom with captured electron.

(2) (3) Additional fixed charges exposed

(4) When the threshold voltage Vg = Vt each additional increase in Vg and gate charge is balanced by carrier electrons.  In the image you have to imagine the electrons overlapping the first row of fixed charges.  At this point the depletion region depth Xd does not grow much.  A – is a mobile carrier electron.

This occurs where intrinsic Fermi level moves from Ef above Efi to Ef below Efi. This is a change of 2Ef.  See page 4 of Introduction to Solid State Devices: Chapter 10.

The depletion width up to and including the maximum depletion width given by:

Substituting:  

See page 17 of Introduction to Solid State Devices: Chapter 10

Electron inversion charge density as a function of surface potential

• Note how the curve starts at 2*Ef.  That corresponds with Vt mentioned previously above.
• The curve is exponential in comparison with the depletion region relation which is quadratic. Thus inversion charge dominates.
• See page 10 of Introduction to Solid State Devices: Chapter 10

Figure: Maximum depletion width versus doping

• See page 8 of Introduction to Solid State Devices: Chapter 10

Identity Table

Research Links

• Introduction to Solid State Devices: Chapter 10    ( The whole book is here Local copy here )
• PHP Math Publisher Syntax