WHEN THE MODEL BREAKS

Shrink the channel, change the rules

Long channel The gate alone sets the barrier, and the drain barely matters once the device is saturated

Short channel Source and drain are so close that they tug on the same barrier the gate controls

Today Production channels are tens of nanometers long, against the micrometers of early textbooks

The square law I_D ∝ (V_GS − V_th)² assumes a long channel and carriers that keep speeding up

Four things change when L shrinks: the speed limit, the slope, the barrier and the threshold.

VELOCITY SATURATION

Electrons hit a speed limit

v = μE, until v_sat ≈ 10⁷ cm/s

One volt across a 50 nm channel is a field of 200,000 V/cm. At that strength electrons lose energy to the lattice as fast as the field gives it, so they stop speeding up. The current then grows roughly in step with the gate overdrive, not with its square.

In a short channel the carriers run at the speed limit, and extra voltage buys less and less.

CHANNEL-LENGTH MODULATION

Saturation is not flat

I_D = I_sat(1 + λV_DS)

Past pinch-off, more drain voltage moves the pinch-off point toward the source and shortens the effective channel. The current creeps up. λ grows as L shrinks, so a short device makes a poorer current source and a lower-gain amplifier.

A short transistor never quite saturates, and its output resistance falls.

DRAIN-INDUCED BARRIER LOWERING

The drain reaches across

DIBL = ΔV_th ÷ ΔV_DS (mV per volt)

In a short channel the drain's field reaches the source end and lowers the barrier the gate is trying to hold up. The threshold drops as the drain voltage rises, and so does the control the gate has over leakage. Separately, V_th also rolls off as L shrinks, because source and drain share the charge under the gate.

Short channels leak more, and they leak more at high drain voltage.

TAKING BACK CONTROL

Four effects, four fixes

Thinner gate dielectric The gate couples more strongly to the channel

Shallow, abrupt junctions Source and drain reach less far under the gate

Halo implants Extra doping near the ends holds back the drain's field

Better geometry FinFETs and nanosheets wrap the gate around the channel (Part 4)

Every fix for short-channel effects is a way of giving the gate more say than the drain.

UNIT 8 STUDY COMPLETE

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Ready for the Fab Challenge?

You've seen four ways a short channel breaks the textbook, and why the gate has to fight to stay in charge.