LIMIT OF DETECTION

The smallest signal you can trust

LOD: signal = 3σ

The limit of detection is the concentration whose signal just clears three times the noise σ of a blank measurement. Below it, you cannot tell the target from random fluctuation. A lower LOD needs a bigger signal, less noise, or both.

LOD is set by signal size and noise together.

WORKED EXAMPLE

From noise to concentration

c_LOD ≈ 0.026 K_D

Take ΔV_max = 60 mV and noise σ = 0.5 mV. Then 3σ = 1.5 mV, so θ = 1.5/60 = 0.025. Solving θ = c/(c + K_D) gives c ≈ 0.026 K_D. With K_D = 1 nM, the LOD is about 26 pM.

A tight binder and a quiet transistor reach low concentrations.

THE NOISE FLOOR

Where the curve meets the noise

On a log axis, the binding curve is an S shape. The dashed line marks 3σ. The concentration where the curve crosses it is the LOD, and everything to its left is lost in the noise.

Lowering the noise slides the crossing point to the left.

NOISE SOURCES

What limits a transistor

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Flicker noise

1/f noise from charge traps at the oxide; it grows at low frequency

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Thermal noise

Random motion of charges in the channel and contacts

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Drift

Slow changes that look like signal, as seen with ISFETs

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Gate area

Flicker noise falls as the gate area grows

Traps at the oxide surface are usually the main source of noise.

TRADE-OFFS

Sensitivity versus noise

Bigger gate Lower flicker noise, but the targets spread over more surface

Nanowire Tiny area, so each bound charge matters more, but the noise is higher

Subthreshold Current changes about 10× per 60 to 100 mV, so a small shift is easy to read

Averaging Repeated readings cut random noise, at the cost of time

Gains in one place usually cost something in another.

UNIT 23 STUDY COMPLETE

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Ready for the Fab Challenge?

You've covered how small a concentration a BioFET can see, and what limits it.