ABSTRACT
Thermal expansion of a string couples its resonance frequency to its temperatures, which can be utilized for temperature sensing. Low-frequency instability, s(1s) ≈ 5.9 × 10-8, leads to an estimated temperature resolution of 2.5 × 10-4°C. String-based photo-thermal spectroscopy, utilizing the high temperature sensitivity, allows for spectroscopy analysis of picogram samples. 8.1 IntroductionRoom temperature quality factors of more than one million1,2makes micro-and nanomechanical string resonators interesting for fundamental studies as well as for a variety of applications. String resonators have been utilized for fundamental studies of, e.g., damping mechanisms1-7 and nanomechanical classical two-level systems.8 The use of string resonators for material characterization9,10 and gas,11 mass12,13 and thermal sensing14-18 has also been demonstrated.The string-like behavior of a beam is caused by a high built-in level of tensile stress. In this case, the bending rigidity can be neglected and the resonance frequency becomes a function of the tensile stress. Therefore, the resonance frequency can be tuned without changing beam material or dimensions. The tensile stress increases the stored energy, and thus the resonance frequency, while its influence on the intrinsic damping (energy loss) is typically small. The quality factor is defined by the ratio of stored to lost energy during one cycle of vibration. The tensile stress thus leads to high Q values in string resonators. The influence of the tensile stress seen for string resonators has also been observed for membrane resonators.19-21Despite the similarities between string and membrane resonators, we will only treat string resonators in this chapter. The content of this chapter is organized in the following way: The beam equation for a tensile stressed beam and an approximated solution to it is described in Section 8.2. In Section 8.3, the damped vibration of string resonators is described. The use of string resonators for mass sensing, temperature-sensing and photothermal spectroscopy is described in Section 8.4. Section 8.5 is used for conclusions.
