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

Abstract

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.

Electrothermal Characterization of Doped-Si Heated Microcantilevers Under Periodic Heating Operation

“…While most of the aforementioned applications operate thermal cantilevers at steady-state or with short electrical pulses, the periodic heating (ac) operation could realize precision scientific measurements that are not feasible with the steady-state cantilever operation. By implementing the 3x method [37], thermal cantilevers can measure local temperature with a resolution of $1 mK [38,39], opening the possibility of nanoscale thermophysical property measurement. The photothermomechanical actuation of cantilever probes is another example of the periodic heating operation [40][41][42][43].…”

“…However, understanding the full spectrum 3ac signal of the doped-Si heated cantilever still remains challenging, mainly due to the inherent complexities of the cantilever, such as the presence of two doped regions, a nonlinear temperature dependence of the cantilever resistance, and the complicated geometry. While previous studies have attempted to predict the ac behaviors of the microcantilever with a simple 1D model [38,39,[49][50][51][52][53], they observed serious deviations of the 1D model from experimental data at high frequencies [51,52]. FEA was applied for the transient modeling of the cantilever during pulse and periodic heating operations [54].…”

“…An ac input current of 112 lA-rms was applied to the bridge circuit by a Keithley 6221 ac/dc source meter over a range of frequencies spanning 10 Hz-34 kHz. The direct use of a current source obviates the signal adjustment that is required to correct a measurement error when using a voltage source [39,55]. While the cantilever was operated under periodic current flow in a vacuum environment, the inphase and out-of-phase 3x voltage signals across the cantilever were measured by a differential lock-in scheme [37].…”

Temperature measurements of heated microcantilevers using scanning thermoreflectance microscopy

“…18 However, AC thermal characterization of heated microcantilevers to date mostly relies on theoretical modeling and indirect measurement. [19][20][21] Although transient temperature measurements of a heated microcantilever was performed by acquiring temperature-dependent reflectance, 22 measurements were limited to the pulsed operation in time domain at a fixed point and detailed discussion on temperature, spatial, and temporal resolutions was not provided. Therefore, it is crucial to measure the temperature distribution of heated microcantilevers during AC operation.…”

DC and AC electrothermal charicterization of heated microcantilevers using scanning thermoreflectance microscopy

“…Therefore, it hardly becomes a cost-effective thermometry. Although AC operation of heated microcantilevers offers unique applications, including thermomechanical actuation [10,11], thermal topographic imaging [12], and local thermal analysis [13], AC thermal characterization of heated microcantilevers mostly relies on theoretical modeling [14] or indirect measurement [15] of which precision is under question. Especially, when heated microcantilevers operating under AC heating are applied to nanoscale thermal metrology, it is prerequisite to perform AC thermal characterization with high precision.…”