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2-ω and 3-ω temperature measurement of a heated microcantilever
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Image of FIG. 1.
FIG. 1.

(a) Schematic of periodic heating of cantilever with serial resistor circuit and SEM picture of the cantilever used in the experiment. (b) Cantilever steady temperature, power, and resistance relation calibrated with Raman spectroscopy.

Image of FIG. 2.
FIG. 2.

(a) Nondimensional current and its major harmonic components when the circuit is driven with a pure harmonic voltage source. (b) Nondimensional resistance oscillation, R/R m , to estimate the correction factor for the large resistance oscillation of cantilever.

Image of FIG. 3.
FIG. 3.

Correction factor F/F V with respect to ΔR/R m for different R s /R m . (a) 2ω method with η = 0.03 and (b) 3ω method with η = 0.

Image of FIG. 4.
FIG. 4.

Measured periodic temperature of the heated cantilever with a periodic voltage source and a maximum power of 8 mW. (a) Total circuit voltage, cantilever voltage, and cantilever resistance. (b) Cantilever resistance at different driving frequencies. (c) Maximum and minimum cantilever temperature as a function of driving frequency ω.

Image of FIG. 5.
FIG. 5.

Amplitude and phase of V 2 ω, raw measured with either V offset = 0 (η = 0) or V offset = 0.5 V (η = 0.03). The plot also shows V 2 ω , which excludes V 2 ω, error according to Eq. (7).

Image of FIG. 6.
FIG. 6.

Correction factor F = T raw/T cantilever for the 2ω and 3ω methods when the cantilever is operated by a periodic voltage source with power amplitude of 8 mW.

Image of FIG. 7.
FIG. 7.

Periodic temperature for driving voltage amplitude 13.4 V and 17.9 V, estimated by oscilloscope measurement as well as the 2ω and 3ω methods.

Image of FIG. 8.
FIG. 8.

Periodic temperature and measured voltage for (a) V 2 ω ,raw and (b) V 3 ω ,raw. The periodic temperatures were measured and corrected using F 2 ω and F 3 ω .


Generic image for table
Table I.

Dominant harmonic components and correction factor.

Generic image for table
Table II.

Procedures of 2ω and 3ω method for temperature measurement.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: 2-ω and 3-ω temperature measurement of a heated microcantilever