Method for the calibration of atomic force microscope cantilevers

TLDR

Determining AFM cantilever spring constants is essential for users, yet existing Cleveland et al. (1993) methods require mass attachment. The paper proposes a fast, nondestructive method to evaluate AFM cantilever spring constants using only the unloaded resonant frequency, density or mass, and dimensions. The method relies on measuring the unloaded resonant frequency and accounts for factors such as gold coating, which can dramatically shift the frequency, and air damping, which reduces the frequency by about 4 % compared to vacuum. The study shows that the load point on the cantilever critically affects the spring constant, and provides theoretical results that explain this variation, offering practical value to AFM users.

Abstract

The determination of the spring constants of atomic force microscope (AFM) cantilevers is of fundamental importance to users of the AFM. In this paper, a fast and nondestructive method for the evaluation of the spring constant which relies solely on the determination of the unloaded resonant frequency of the cantilever, a knowledge of its density or mass, and its dimensions is proposed. This is in contrast to the method of Cleveland et al. [Rev. Sci. Instrum. 64, 403 (1993)], which requires the attachment of masses to the cantilever in the determination of the spring constant. A number of factors which can influence the resonant frequency are examined, in particular (i) gold coating, which can result in a dramatic variation in the resonant frequency, for which a theoretical account is presented and (ii) air damping which, it is found, leads to a shift of ∼4% in the resonant frequency down on its value in a vacuum. Furthermore, the point of load on the cantilever is found to be extremely important, since a small variation in the load point can lead to a dramatic variation in the spring constant. Theoretical results that account for this variation, which, it is believed will be of great practical value to the users of the AFM, are given.