IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 41 (2008) 125306 (8pp) doi:10.1088/0022-3727/41/12/125306 Theoretical analysis of resonance frequency change induced by adsorption Ji-Qiao Zhang, Shou-Wen Yu 1 and Xi-Qiao Feng Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People’s Republic of China E-mail: yusw@tsinghua.edu.cn Received 22 February 2008, in final form 23 April 2008 Published 29 May 2008 Online at stacks.iop.org/JPhysD/41/125306 Abstract Microcantilever-based techniques can be used to explore the autonomy and property of molecules (e.g. DNA and single actin filaments) adsorbed on a surface. A theoretical model is presented here to predict the resonance frequency of a cantilever induced by physically adsorbed atoms/molecules. The cantilever is modelled as a sandwich beam containing two surface layers of a finite thickness and a bulk layer between them. It is found that the resonance frequency shift depends sensitively on both the mass and bending stiffness variations of the cantilever induced by the adsorbed atoms/molecules. The adsorptions of O atoms on Si(1 0 0), of O atoms on Au(1 0 0) and of H atoms on Au(1 0 0) are taken as three representative examples. We demonstrate that physisorption can induce distinctly different resonant responses of cantilevers, depending not only on the adatoms but also on the substrate material. This study is helpful for the optimal design of microcantilever-based measurement techniques. 1. Introduction Due to their advantages of high sensitivity, enhanced reliability, fast response, reduced size and low costs, microfabricated beams or cantilevers have been widely used as sensors, actuators and transducers in physical, chemical and biological applications [1–5]. Microcantilever-based sensing techniques are based on the changes in physical quantities that are easily measured, e.g. deflection, resonance frequency and quality factor of the beam. They can be used to explore, for example, the autonomy and property of biomacromolecules (e.g. DNA and single actin filaments) [6–8] and to detect the mass of particles deposited onto the cantilever [9–15]. Therefore, a deep understanding of the cantilever’s response upon adsorption is important to optimize the structural parameters and to improve the performance of the sensor devices. Experimental observations have demonstrated that adsorbates on the surface of a microcantilever can cause a shift in its resonance frequency [9–19]. This provides a direct measure of the mass of adsorbates by assuming that the spring constant remains fixed. By measuring the resonance frequency, Cleveland et al [9] detected the nanogram mass of particulates deposited onto a cantilever. Using a 1 Author to whom any correspondence should be addressed. similar method, Thundat and co-workers [10, 11] estimated the relative amount of adsorbates on the cantilever with picogram mass resolution. Another remarkable improvement in this technique comes from the work of Ilic and co-workers [12, 13], who measured the mass of a single Escherichia coli with micromechanical oscillators. Gupta et al [14] fabricated even smaller cantilevers for detecting a single vaccinia virus. Recently, Ilic et al [15] fabricated nanomechanical sensors with subattogram mass detection sensitivity. In many cases, however, adsorption also alters the spring constant of a microcantilever. Early in 1975, Lagowski et al [16] found that the normal mode of vibration of thin crystals depends strongly on the surface preparation and on the ambient atmosphere and attributed this change to the effects of surface stresses. Chen et al [17] and Cherian and Thundat [18] showed that the resonance frequency of a cantilever depends on both the mass increase and the spring constant change induced by surface adsorption of chemicals. Wang et al [19] studied the nanomechanical properties of ultra-thin single-crystal silicon resonators, with emphasis on their surface effects associated with thermal treatments and gas adsorption. Lu et al [20] analysed the influence of pure surface stresses and adsorption-induced surface stresses on the vibration frequency of a cantilever sensor. As an extension of Dareing and Thundat’s work [21], Huang et al [22] investigated the 0022-3727/08/125306+08$30.00 1 © 2008 IOP Publishing Ltd Printed in the UK