1D thermal characterization of micro/nano-cantilevers for Suspended ThermoReflectance measurements

Sarkar, Dipta; Brady, Jeffrey; Baboly, Mohammadhosein Ghasemi; Xu, Leidong; Singh, Gurpreet; Leseman, Zayd Chad

doi:10.1063/1.5115512

Cited by 3 publications

(4 citation statements)

References 28 publications

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“…The thermophysical parameter values needed to evaluate Equations (8),- (11) , (20), and (22) ) is depicted in Figure 3. The pulsing parameters used here are similar to those of [4] who consider heating at a slightly lower rates ( 0.0625 mW/μm 3…”

Section: Case Studymentioning

confidence: 99%

“…The heat transfer coefficient of this study has been modified from that of previous work and its value is presented in the context of previous works as follows. In some early studies, for example [11], the heat transfer from the cantilever to the air is not explicitly modelled and the authors instead opt for a prescribed periodic temperature at the base of the cantilever. However it has been experimentally shown that the heat transfer from the surface is significant in the self heated cantilever [34].…”

Section: Case Studymentioning

confidence: 99%

“…The subject of this study is to consider the effect that such inhomogeneity in thermal conductivity has upon the resulting temperature distribution of a multi-layer cantilever operated in oscillatory mode. Understanding the deflection of the self-heated micro-cantilever requires an understanding of the thermal profile [6] and previous thermal models include both exact mathematical solutions [11] [12] [13] and numerical simulations [14] [15] [4] [16] though none investigate the effects of variation in thermal conductivity across the cantilever thickness (across the different layers).…”

Section: Introductionmentioning

confidence: 99%

“…These generally all represent the exact solution using the 1-D fin (extended surface) model [13] [11] [12]. In [11] the fin approximation is used to model heat transfer along the length of the cantilever, but the problem is further approximated by representing periodic heating using a simple boundary condition at one end of the fin. In the study [12] the self-heated cantilever is modelled analytically in a 1-D steady problem that effectively also uses the solution to the problem of heat transfer along extended surface.…”

Section: Introductionmentioning

confidence: 99%

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Pulsed heating of the self-actuated cantilever: an exact solution investigation of non-axial temperature gradients

Becker,

Gutschmidt,

Boyd

et al. 2023

Preprint

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Self-actuated bimorph cantilevers are implemented in a variety of micro-electro-mechanical systems. Their tip deflection relies on the unmatched coefficients of thermal expansion between layers. The thermal bimorph phenomenon is dependent on the temperature rise within the cantilever and while previous studies have investigated variations in the thermal profile along the cantilever length, these have usually neglected variations in the thermal profile along the cantilever thickness. The current study investigates the thermal distribution across the thickness of the cantilever. The exact closed form solution to the problem of heat conduction in the composite (layered) domain subjected to transient volumetric heating is developed using the appropriate Green’s function. This solution is applied to a 3-layer cantilever with an Aluminium heater, a Silicon Dioxide resistive layer, and a Silicon base layer. The Aluminum heater experiences volumetric heating at a rate of 0.2 mW/μm3 of 5μs duration at 100 μs intervals. Benchmark solutions of the temperature at select times and positions are provided. It is shown that there are non-negligible temperature gradients across the cantilever thickness during the heating and the first 5μs afterwards. These short-lived temperature differences are significant in magnitude and are positively biased with the unmatched thermal expansion coefficients between the layers. These temperature differences, which have previously been neglected, are important because they will act to enhance bending.

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Section: Case Studymentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pulsed heating of the self-actuated cantilever: an exact solution investigation of non-axial temperature gradients

Becker,

Gutschmidt,

Boyd

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Pulsed heating of the self-actuated cantilever: a one-dimensional exact solution investigation of non-axial temperature gradients

Becker,

Gutschmidt,

Boyd

et al. 2024

J Eng Math

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Self-actuated bimorph cantilevers are implemented in a variety of micro-electro-mechanical systems. Their tip deflection relies on the unmatched coefficients of thermal expansion between layers. The thermal bimorph phenomenon is dependent on the temperature rise within the cantilever and, while previous studies have investigated variations in the thermal profile along the cantilever length, these have usually neglected variations in the thermal profile along the cantilever thickness. The current study investigates the thermal distribution across the thickness of the cantilever. The exact closed form solution to the one-dimensional problem of heat conduction in the composite (layered) domain subjected to transient volumetric heating is developed using the appropriate Green’s function. This solution is applied to a one-dimensional case study of a 3-layer cantilever with an Aluminium heater, a silicon dioxide resistive layer, and a silicon base layer. The aluminium heater experiences volumetric heating at a rate of 0.2 mW/μm3 of 5 μs duration at 100 μs intervals (10 kHz with a 1/20 duty cycle). Benchmark solutions of the temperature at select times and positions are provided. It is shown that there are negligible temperature gradients across the cantilever thickness during the heating and the first ~ 5 μs afterward. These short-lived temperature differences are positively biased with the unmatched thermal expansion coefficients between the layers, though their relative influence on bending is not clear. A simple parametric analysis indicates that the relative magnitude of the temperature differences across the cantilever (compared to the overall temperature) decreases substantially with increasing duty cycle.

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In-plane thermal conductivity measurements of Si μ-cantilevers using the suspended thermo-reflectance (STR) technique

Sarkar,

Singh,

Yilbas

et al. 2024

Review of Scientific Instruments

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The Suspended Thermoreflectance (STR) technique is described in this paper. This optoelectronic measurement tool performs thermal characterization of freestanding micro-/nanoscale materials. STR performs thermal mapping at the submicron level and produces unconstrained thermal conductivity unlike other optical measurement techniques where independent conductivity measurement is not possible due to their reliance on heat capacity. STR works by changing the temperature of a material and collecting the associated change in light reflection from multiple points on the sample surface. Reflection is a function of the material being tested, the wavelength of the probe light, geometry, and the composition of the specimen for transparent and quasi-transparent materials. In this article, Si μ-cantilevers are studied. In addition, a thermal analytical model is developed and incorporated with optical equations to characterize the conductivity of the Si μ-cantilevers. The analytical model is compared with a finite element model to check its applicability in the STR experiment and data analysis. To validate the technique, the thermal conductivity of 2 and 3 µm thick Si μ-cantilevers was determined using STR at a temperature range of 20–350 K and compared to simulations using the equation of phonon radiative transfer and literature values.

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1D thermal characterization of micro/nano-cantilevers for Suspended ThermoReflectance measurements

Cited by 3 publications

References 28 publications

Pulsed heating of the self-actuated cantilever: an exact solution investigation of non-axial temperature gradients

Pulsed heating of the self-actuated cantilever: an exact solution investigation of non-axial temperature gradients

Pulsed heating of the self-actuated cantilever: a one-dimensional exact solution investigation of non-axial temperature gradients

In-plane thermal conductivity measurements of Si μ-cantilevers using the suspended thermo-reflectance (STR) technique

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