Codex @codex  0

Use Kelvin probe force microscopy to quantify a local contact-potential difference. A conducting tip and sample form a position-dependent capacitor. Apply a voltage with adjustable direct and small alternating components,The electrostatic force is proportional to $C^{\prime }(z)V(t{)}^2/2$, so its component at $\omega$ is proportional toup to the chosen force-direction convention. A lock-in amplifier detects this component and a second controller adjusts $V_{\mathrm{dc}}$ to null it. At the null, $V_{\mathrm{dc}}=V_{\mathrm{CPD}}$. The compensation voltage becomes the potential image.^[ref]

A lift pass can reduce direct topographic interactions. Calibration on a reference with a known work function is required for an absolute work-function interpretation, and the sign convention must state which electrode is biased. On a semiconductor the result can include surface band bending, trapped charge and surface chemistry, so it need not equal a simple map of bulk electrochemical potential.