A numerical investigation of the effects of laser heating on resonance measurements of nanocantilevers




Kutturu, Padmini

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Nanomechanical resonators (NR) are cantilevers or doubly clamped nanowires (NW) which vibrate at their resonance frequency. These nanowires with picogram-level mass and frequencies of the order of MHz can resolve added mass in the attogram (10-18 g) range, enabling detection of a few molecules of cancer biomarkers based on the shift in resonance frequency. Such biomarker detection can help in the early stage detection of cancer and also aid in monitoring the treatment procedure in a more advanced stage. Optical transduction is one of the methods to measure the resonance frequency of the cantilever. However, there is a dependence of measured resonance frequency on the polarization of light and the laser power coupled as thermal energy into the cantilever during the measurement. This thesis presents a numerical model of the nanocantilever and shows the variation in resonance frequency and amplitude due to varied amounts of energy absorption by the NW from the laser during resonance measurements. This thesis answers questions on the effects of laser heating by calculating the temperature distribution in the NW, which changes the Young’s modulus and stiffness, causing a resonance downshift. It also shows the variation of resonance amplitude, affecting signal strength in measurements, by considering the effects of structural damping. In this work, a numerical model of the nanowire was analyzed to determine the temperature rise of the NW due to laser heating. The maximum temperature was calculated to be about 500 K with 1 mW of laser power absorbed in Silicon NWs and it is shown that the nanowire tip would reach its melting point for about 2.6 mW of laser power absorbed by it. The resonance shift due to attained temperature of the NW was calculated. The frequency is predicted to decrease by 24 kHz for a 11.6 MHz resonator, when 2mW of laser power is absorbed. However, the frequency shift is mode-dependent and is larger for higher modes. The variation in vibration amplitude around the resonance peaks is calculated based on the effects of structural damping. This can be used to decide on the suspension height of the NW above the substrate, before fabrication. This calculation also provides a method to study the variation in material damping due to temperature. Finally, a semi-analytical method for calculating the frequency of a cantilever beam with varying Young’s modulus is derived to examine the validity of the results calculated above. An effective Young’s modulus value for the laser heated NW is given, which serves as a correction factor for the resonance shift. The derivation is then extended to calculate the resonance shift with an addition of a mass to the beam of varying Young’s modulus.



Nanomechanical resonators (NR), Doubly clamped nanowires (NW), Cantilevers, Optical transduction, Temperature distribution, Young’s modulus