Finite optical spot size and position corrections in thermal spring constant calibration

TLDR

The thermal noise method is a widely used technique for calibrating the spring constant of AFM cantilevers. This study measured how the spring constant changes with the optical spot position along the cantilever. The authors recorded thermal motion while moving the focused laser spot along the cantilever and used a model that incorporates spot diameter and position, together with the equipartition theorem, to calculate the spring constant. The spring constant varied systematically with spot position and disagreed with Sader and Cleveland calibrations, but applying the spot‑size‑and‑position model reduced the discrepancies to better than 10%.

Abstract

One of the most popular methods for calibrating the spring constant of an atomic force microscope cantilever is the thermal noise method. The usual implementation of this method has been to position the focused optical spot on or near the end of the cantilever, acquire a force curve on a hard surface to characterize the optical lever sensitivity and to then measure the thermal motion of the cantilever. The equipartition theorem then allows the spring constant to be calculated. In this work, we measured the spring constant as a function of the spot along the length of the cantilever. The observed systematic variation in the spring constant as a function of this position ranged from for a short 60 µm cantilever up to for a 225 µm cantilever we examined. In addition, the thermally calibrated spring constants systematically disagreed with spring constants calibrated using the Sader and Cleveland methods: by for the short 60 µm cantilever and by for the longest, 225 µm cantilever. By using a model that accounts for the spot diameter and position on the cantilever, the thermally measured spring constants were brought into better than 10% agreement with the other methods.