Measurement of forces and spring constants of microinstruments

Abstract

Micromachines, including micro scanning tunneling microscope and high force (≈0.1 mN and higher) actuators, are examples of a new class of silicon-based microinstruments for atomic scale surface imaging and modification, as well as submicrometer scale material investigations. A large class of such microinstruments and sensors consist of actuators, such as interdigitated comb drives, that generate force, F, in the form F=βV2, where β is a constant and V is the applied voltage. Such actuators often move a large distance during actuation so that the restoring force, R, of the springs varies nonlinearly with x, i.e., the springs behave as hard springs, and R=K1x+K3x3+… (restoring force is similar for +ve and −ve x due to symmetry). β and Ki, i=1,3,…, of the micro-actuators usually differ from their design values due to processing nonuniformities. Hence, evaluation of these constants becomes necessary for each actuator, and is essential for the instruments that are employed to study materials’ behavior on a small scale. In this article, a methodology is developed to calibrate microinstruments, i.e., to evaluate the values of β and Ki, i=1,3,… . The method is based on buckling of a long slender beam of known dimensions, and made of a material with known property (elastic modulus). Buckling is achieved by an axial compressive force on the beam applied by the actuator of the microinstrument. β and Ki are derived from the relation between the applied voltage on the actuator, and the post buckling deformation of the beam. The beam is designed and cofabricated with the actuator, and hence the calibration mechanism is integrable with each microinstrument. An analysis is provided to estimate the possible errors in calibration due to errors in the measured dimensions of the calibrating beam. It is shown that the calibration error increases linearly with the error in the measured linear dimensions. The applicability of the method is demonstrated by fabricating microinstruments, which, prior to their calibration, are employed to apply torque on single crystal silicon bars (in the form of pillars), until the bars fracture. The instruments are then calibrated, and the calibrated values of β and Ki are used to evaluate the torques applied on the bars at different voltages. Stresses to fracture of the bars are also estimated. The torsion experiment is an example of the application of integrated microinstruments for small scale material studies.