THE DEPLETION LAYER

How deep does it reach?

Exposed ions The depletion layer is the region of uncovered dopant ions under the gate

Charge balance Gate charge equals depletion charge plus inversion charge

Maximum depth Once inverted, extra gate voltage adds electrons, not depth

A number For N_A = 10¹⁶ cm⁻³ the maximum depth is about 0.3 µm

Heavier doping means a shallower depletion layer, and a higher threshold.

THE SWITCH POINT

What Vth means

VGS = Vth

The threshold voltage is the gate-to-source voltage at which a conducting inversion channel forms. In an enhancement-mode NMOS, it's positive, commonly 0.3 to 1 V. Well below it the transistor is essentially off.

Vth is the gate voltage where the switch turns on.

THE RECIPE

Three ingredients of Vth

Vth = VFB+2φF+Qd/Cox

The flat-band voltage V_FB accounts for the work-function difference and any oxide charge. The 2φF term supplies the band bending for inversion. Q_d / C_ox is the extra voltage needed to support the depletion charge across the oxide.

Every knob that sets Vth acts on one of these three terms.

WHAT MOVES Vth

Six knobs

Doping N_A More doping raises Vth

Oxide thickness A thinner oxide lowers the depletion term

Gate material Its work function shifts the flat-band voltage

Oxide charge Trapped or nearby charge shifts Vth by −Q / Cox

Body bias A reverse-biased source-body junction raises Vth

Temperature Vth falls as the device heats up

Oxide charge is the knob that biosensors will turn.

CHARGE SHIFTS THE THRESHOLD

The transistor as a charge detector

ΔVth = −Q / Cox

Put positive charge Q per unit area at the oxide-silicon interface, and the gate needs less positive voltage to invert the surface, so Vth drops by Q/C_ox. Negative charge raises it. Example: 10¹² elementary charges per cm² on a 0.345 µF/cm² oxide moves Vth by about 0.46 V.

Sensing with a FET means measuring how far a surface charge moves the threshold.

TWO MODES

Enhancement and depletion

Enhancement mode Normally off: an NMOS has Vth > 0 and needs gate voltage to form a channel

Depletion mode Normally on: a channel exists at VGS = 0 and a gate voltage pinches it off

Where each is used Logic uses enhancement mode; some sensors, like doped nanowires, use depletion mode

Both respond to charge the same way: the threshold shifts.

UNIT 5 STUDY COMPLETE

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Ready for the Fab Challenge?

You've covered what sets the switch-on voltage, and how charge shifts it.