The sensor has a sweet spot
Graphene Hall Sensor Lab · Multiphysics
A graphene Hall sensor detects a magnetic microbead by the tiny voltage its stray field induces. You'd think more gate voltage always means more signal — it doesn't. The best operating point is somewhere in the middle.
FIG. 1 — The mechanism
One knob moves two things
The back-gate voltage sets the graphene’s 2D carrier density n₂D. The Hall voltage is V_H = I·⟨Bz⟩ / (n₂D·e) — so a lower carrier density gives a biggersignal, which pushes you toward the Dirac point. But go too far and a second effect takes over: near the Dirac point the carrier density is no longer uniform — it breaks into charge “puddles” that fluctuate by about n₀, and because V_H ∝ 1/n those fluctuations land straight in your reading. At high density the signal shrinks into the Johnson–Nyquist thermal noise √(4kT·R·Δf); at low density puddle noise explodes. What you actually care about — SNR — peaks in between.
FIG. 2 — Find the operating point · interactive
Find the operating point
Drag the gate voltage and watch the Hall voltage, the noise, and the SNR move together. The curve is the SNR across the whole gate range; the dot is where you are.
SNR vs gate voltage — peak near 17 V
Simplified companion model. The full simulator implements nine governing equations across 21 device parameters, with heatmaps, field maps, and CSV export.
FIG. 3 — Why it matters
Why it matters
Fabricating and characterizing one graphene device takes weeks and a cleanroom. Being able to sweep geometry, bias, and gate voltage in the browser — and see the SNR surface before committing to a mask — is the difference between one fabrication run and five. That’s what GHSL is for.
Working on magnetic biosensing or graphene devices? I’d love to compare notes.
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