Thermal radiation dominated heat transfer in nanomechanical silicon nitride drum resonators

Piller, Markus; Sadeghi, Pedram; West, Robert G.; Luhmann, Niklas; Martini, Paolo; Hansen, Ole; Schmid, Silvan

doi:10.1063/5.0015166

Cited by 22 publications

(19 citation statements)

References 34 publications

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“…Similar simulations of uniform membranes of equal size are made, in which case the frequency shift remained linear for all power values shown in Fig. 3(b) [27]. As such, this nonlinearity turns out to be a result of a heating-induced detuning of the fundamental defect mode to frequencies outside of the band gap, which delocalizes the mode to the entire PnC membrane.…”

Section: B Responsivity Of Defect Modesmentioning

confidence: 58%

“…From this equation, no dependence on lateral dimensions are expected. However, recent investigations into heat transfer in SiN have shown a non-negligible contribution from emission of thermal radiation [26,27]. This effect becomes more pronounced as the lateral size of the membrane increases and results in a reduction of responsivities compared to that predicted using Eq.…”

Section: B Responsivity Of Defect Modesmentioning

confidence: 99%

“…As such, all simulations take emission into account with an emissivity = 0.05, calculated using optical data of 50-nm SiN membranes [28]. Further investigation into the effect of thermal radiation on the responsivity of membrane resonators can be found in Piller et al [27]. It should be noted that the model presented in Eq.…”

Section: B Responsivity Of Defect Modesmentioning

confidence: 99%

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Thermal Transport and Frequency Response of Localized Modes on Low-Stress Nanomechanical Silicon Nitride Drums Featuring a Phononic-Band-Gap Structure

et al. 2020

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Development of broadband thermal sensors for the detection of, among others, radiation, single nanoparticles, or single molecules is of great interest. In recent years, photothermal spectroscopy based on the shift of the resonance frequency of stressed nanomechanical resonators has been successfully demonstrated. Here, we show the application of soft-clamped phononic crystal membranes made of silicon nitride as thermal sensors. It is experimentally demonstrated how a quasi-band-gap remains even at very low tensile stress, in agreement with finite-element-method simulations. An increase of the relative responsivity of the fundamental defect mode is found when compared to that of uniform square membranes of equal size, with enhancement factors as large as an order of magnitude. We then show phononic crystals engineered inside nanomechanical trampolines, which results in additional reduction of the tensile stress and increased thermal isolation, resulting in further enhancement of the responsivity. Finally, defect-mode and band-gap tuning is shown by laser heating of the defect to the point where the fundamental defect mode completely leaves the band gap.

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Section: B Responsivity Of Defect Modesmentioning

confidence: 58%

Section: B Responsivity Of Defect Modesmentioning

confidence: 99%

Section: B Responsivity Of Defect Modesmentioning

confidence: 99%

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Thermal Transport and Frequency Response of Localized Modes on Low-Stress Nanomechanical Silicon Nitride Drums Featuring a Phononic-Band-Gap Structure

et al. 2020

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“…By solving eq 1 , we can obtain the time dependency of the temperature difference and therefore the frequency dependency with time, as shown in Figure 3 a in the upper chart. The frequency sensitivity 30 − 32 can be calculated as where E is the Young’s modulus, σ is the initial stress, and f is the resonance frequency of the membrane, which can be calculated as where L is the length of the square, and ρ is the mass density of the structural material of the membrane, silicon nitride in this case.…”

Section: Resultsmentioning

confidence: 99%

Micro-Kelvin Resolution at Room Temperature Using Nanomechanical Thermometry

et al. 2021

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Ultrahigh sensitivity temperature measurement is becoming increasingly relevant for different scientific and technological fields from fundamental physics to high-precision engineering applications. Here, we demonstrate the use of a nanomechanical resonator—free standing silicon nitride membranes with thicknesses in the nanoscale—for room temperature thermometry reaching an unprecedented resolution of 15 μK. These devices were characterized by using an interferometric system at high vacuum, where there are only two possible mechanisms for heat transfer: thermal conductivity and radiation. While the expected behavior should be to decrease the frequency of the mechanical resonance due to the thermoelastic effect, we observe that the nanomechanical response can be both positive and negative depending on the thermal flux: a heat point source always shifts the mechanical resonance to lower frequencies, while a distributed heat source shifts the resonance to higher frequencies.

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“…Hence, during post-processing, the raw frequency fluctuations data is low-pass filtered with a pass frequency f pass = 1/(2πτ th ). The thermal time constant was measured at high vacuum in a similar way as described by Piller et al [33]. A blue vertical dash-dotted line in Fig.…”

Section: A Influence Of Signal-to-noise Ratio In Open-loop Configurationmentioning

confidence: 94%

Frequency fluctuations in nanomechanical silicon nitride string resonators

et al. 2020

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High quality factor (Q) nanomechanical resonators have received a lot of attention for sensor applications with unprecedented sensitivity. Despite the large interest, few investigations into the frequency stability of high-Q resonators have been reported. Such resonators are characterized by a linewidth significantly smaller than typically employed measurement bandwidths, which is the opposite regime to what is normally considered for sensors. Here, the frequency stability of high-Q silicon nitride string resonators is investigated both in open-loop and closed-loop configurations. The stability is here characterized using the Allan deviation. For open-loop tracking, it is found that the Allan deviation gets separated into two regimes, one limited by the thermomechanical noise of the resonator and the other by the detection noise of the optical transduction system. The point of transition between the two regimes is the resonator response time, which can be shown to have a linear dependence on Q. Laser power fluctuations from the optical readout are found to present a fundamental limit to the frequency stability. Finally, for closed-loop measurements, the response time is shown to no longer be intrinsically limited but instead given by the bandwidth of the closed-loop tracking system. Computed Allan deviations based on theory are given as well and found to agree well with the measurements. These results are of importance for the understanding of fundamental limitations of high-Q resonators and their application as high performance sensors.

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Thermal radiation dominated heat transfer in nanomechanical silicon nitride drum resonators

Cited by 22 publications

References 34 publications

Thermal Transport and Frequency Response of Localized Modes on Low-Stress Nanomechanical Silicon Nitride Drums Featuring a Phononic-Band-Gap Structure

Thermal Transport and Frequency Response of Localized Modes on Low-Stress Nanomechanical Silicon Nitride Drums Featuring a Phononic-Band-Gap Structure

Micro-Kelvin Resolution at Room Temperature Using Nanomechanical Thermometry

Frequency fluctuations in nanomechanical silicon nitride string resonators

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