METHOD FOR THE CALIBRATION OF ATOMIC-FORCE MICROSCOPE CANTILEVERS

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 unloa ded resonant frequency of the cantilever, a knowledge 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 t he 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 resu lt in a dramatic variation in the resonant frequency, for which a theo retical account is presented and (ii) air damping which, it is found, leads to a shift of similar to 4% in the resonant frequency down on it s value in a vacuum. Furthermore, the point of load on the cantilever is found to be extremely important, since a small variation in the loa d point can lead to a dramatic variation in the spring constant. Theor etical results that account for this variation, which, it is believed will be of great practical value to the users of the AFM, are given. ( C) 1995 American Institute of Physics.