Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 1 / Section A(i) / 2 / ii / Solution

Measure cantilever torsion with the lateral channel of a four-quadrant optical detector. An in-plane surface displacement perpendicular to the cantilever axis twists the cantilever. The reflected laser spot moves sideways, so the left-minus-right detector signal, demodulated at $\omega$ by a lock-in amplifier, gives the amplitude and phase of the lateral piezoresponse. The top-minus-bottom signal primarily records bending.

Displacement along the cantilever axis can instead cause buckling and leak into the nominally vertical channel. Rotate the specimen by $90^{\circ }$ and repeat the measurement to sample the other in-plane component; use a reference specimen and sensitivity calibration before converting a voltage into displacement or force. A torsional spring constant and lever-arm calibration are additionally needed for an actual lateral-force value. Thus lateral piezoresponse is not automatically a calibrated force measurement.