Langmuir 1994,10, 1003-1004
1003
Experimental Determination of Spring Constants in Atomic Force Microscopy Tim J. Senden**+and William A. DuckertJ Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia, and Materials Department and Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, California 93106 Received April I , 1993. In Final Form: February 10, 1994" A simple method is presented for measuring the spring constant of atomic force microscope (AFM) cantilevers. The spring constant is determined by measuring the static deflection of a cantilever under the force of a known end-mass.
Atomic force microscopes have recently been used to measure colloidaland surface forces.l-12 In this procedure, the force between either a colloidal particle or an AFM tip and another surface is determined from the deflection of a cantilever. One major criticism of use of the AFM for force measurement is error in the magnitude of forces which arises from uncertainty in the cantilever spring constant. In this Letter we present a simple experimental determination of the spring constant based on gravimetry. The spring constant ( k ) for an end loaded, thin beam with rectangular cross section is given by eq 113
where w, t , and 1are the beam width, thickness, and length, respectively. Values of spring constants for microfabricated silicon nitride cantilevers derived using this equation have been used previously to interpret AFM force measurements. Unfortunately, two quantities in this equation are not known accurately: the thickness and Young's modulus. In order to obtain high force resolution, AFM cantilevers are typically very thin (
