NEM Relay: Electrostatic Pull-In & Contact Hysteresis

Gate Drive

Gate voltage V 8.0 V

Beam & Contact

Spring stiffness k 8.0 N/m

Rest gap g₀ 60 nm

Contact adhesion F_adh 80 nN

Relay State

OPEN — circuit broken

Gap remaining

60.0 nm

Switch cycles

Pull-in V_PI

— V

Release V_PO

— V

F_es (electrostatic)

0 nN

F_s (spring)

0 nN

gap / g₀ vs gate voltage — blue = closing, red = stuck closed

How it works

A NEM relay is a nanoscale electromechanical switch: a spring-suspended cantilever electrode sits a gap g₀ above a fixed contact. A gate voltage V pulls the beam down electrostatically; once it touches the contact, current flows exactly like a mechanical relay — but with near-zero OFF-state leakage, unlike a CMOS transistor.

Electrostatic force:  F_es = ε₀ A V² / (2 d²)
Spring restoring:     F_s  = k x       (d = g₀ − x)
Equilibrium:          F_es(x) = F_s(x)

This equilibrium is only stable for x < g₀/3. Beyond that point F_es grows faster than F_s can compensate — a runaway pull-in instability snaps the beam the rest of the way to contact. The threshold is:

V_PI = √( 8 k g₀³ / (27 ε₀ A) )

Releasing the contact is not the mirror image of closing it. Once touching, the beam sits at a much smaller residual gap where F_es is huge, and van der Waals / capillary adhesion (F_adh) adds extra holding force. The beam only springs back open once k·g₀ exceeds F_es(V) + F_adh — which happens at a release voltage V_PO well below V_PI. That gap between "snap closed" and "spring open" is the hysteresis loop traced on the chart, and it is exactly what real NEM relay papers measure to characterize a device.

Gate voltage — drive it up past V_PI to snap the relay shut; drive it back down past V_PO to release it.
Auto-sweep — ramps V up and down automatically so the pull-in/release loop traces itself on the chart.
Stiffness / gap / adhesion sliders — push adhesion high enough relative to k·g₀ and the beam can get permanently stiction-locked: a real reliability failure mode that limits NEM relay switching endurance.

Real-world relevance: NEM relay logic is studied (Berkeley, Stanford, and others) as a near-zero-leakage complement to CMOS for extreme-low-power and radiation-hard circuits, precisely because the ON/OFF states are literal mechanical contact — not a leaky depletion region.

Cantilever beam Circuit closed E-field between plates

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.