2-ω and 3-ω temperature measurement of a heated microcantilever

This article describes temperature measurement of a heated atomic force microscope cantilever using the 2ω and 3ω harmonics of the cantilever temperature signal. When the cantilever is periodically heated, large temperature oscillations lead to large changes in the cantilever electrical resistance and also lead to nonconstant temperature coefficient of resistance. We model the cantilever heating to account for these sources of nonlinearity, and compare models with experiment. When the heating voltage amplitude is 17.9 V over the driving frequency range 10 Hz-34 kHz, the cantilever temperature oscillation is between 5 °C and 200 °C. Over this range, the corrected 2ω method predicts cantilever temperature to within 16% and the corrected 3ω method predicts the cantilever temperature within 3%. We show a general method for predicting the periodic cantilever temperature, sources of errors, and corrections for these errors.