The tip sits at the end of a springy cantilever (stiffness k). As it nears the sample, a Lennard-Jones-like force acts between tip and surface: weak long-range van der Waals attraction pulls the tip down, while strong short-range electron-shell repulsion pushes it back up once atoms nearly touch. The cantilever bends until its spring force balances that tip-sample force, and a laser reflecting off the cantilever's back onto a split photodetector reads that bend as a voltage — the raw AFM signal.
F(z) = 4ε[ 12σ¹²/z¹³ − 6σ⁶/z⁷ ] (attractive for z > z_min, repulsive below)
k·x = F(z_base − x) (cantilever spring balance)
- Contact mode drags the tip directly across the surface at a fixed repulsive setpoint — fast and high-resolution, but the constant lateral drag can scratch soft samples.
- Tapping mode oscillates the cantilever near resonance so the tip only grazes the surface for a fraction of each cycle, cutting lateral force dramatically — gentler on fragile samples at some cost to scan speed.
- Force curve mode drives the base down toward a fixed point: attraction grows until it overcomes the spring stiffness and the tip snaps into contact; pulling back out requires extra force to break adhesion before the tip springs free — the hysteresis loop used to measure surface adhesion.
- A stiffer cantilever (higher k) resists snap-in longer and is less sensitive per unit force, trading sensitivity for stability.