FROM CHEMISTRY TO VOLTAGE

pH becomes surface potential

Δψ₀ = −2.3 · (kT/q) · α · ΔpH

Each pH unit moves the surface potential by at most 2.3·kT/q. The factor α, between 0 and 1, says how completely the surface follows the solution, and 1 is an ideal, fully responsive surface. Because Vth = constants − ψ₀, a rising pH raises the threshold of an NMOS ISFET.

Higher pH gives a more negative surface and a higher NMOS threshold.

THE NERNST LIMIT

The ceiling: 59 mV per pH

2.3 kT/q = 59.2 mV per pH

At 25 °C, kT/q is 25.7 mV, so 2.3·kT/q is 59.2 mV per pH unit. That is the Nernst limit for a simple surface, where α = 1. Real insulators fall short, so measured sensitivity is α × 59.2 mV per pH unit.

α tells you how close a real insulator gets to the ceiling.

SENSING INSULATORS

Materials differ a lot

SiO₂ roughly 20–40 mV/pH: a weak response, and it hydrates over time

Si₃N₄ roughly 45–55 mV/pH: a common, reasonable choice

Al₂O₃ roughly 53–58 mV/pH: near the limit

Ta₂O₅ roughly 55–59 mV/pH: near the limit, and stable

Insulators with more active surface sites sit closer to the Nernst limit.

WORKED EXAMPLE

How far does Vth move?

0.9 × 59.2 ≈ 53 mV per pH

An ISFET with α = 0.9 responds at about 53 mV per pH unit at 25 °C. If the solution moves from pH 7.0 to 7.4, that is 0.4 units, so Vth shifts by about 0.4 × 53 = 21 mV.

Multiply the pH change by α × 59.2 mV to predict the shift.

SENSITIVITY LINES

The slope is the sensitivity

Both lines pass through zero shift at pH 7. The ideal surface climbs 59 mV per pH unit. A weaker surface, with α of about 0.5, climbs about half as fast, so the same pH change gives a smaller signal.

A steeper line means a larger signal for the same pH change.

UNIT 11 STUDY COMPLETE

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Ready for the Fab Challenge?

You've covered how much threshold shift you get per pH unit, and why 59 mV is the ceiling.