Michael James Martin Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 e-mail: martinm2@asme.org Simulation of Micromechanical Measurement of Mass Accretion: Quantifying the Importance of Material Selection and Geometry on Performance Micro- and nanomechanical resonators operating in liquid have been used to measure the change in the mass of either cells or functionalized surfaces attached to the resonator. As the system accretes mass, the natural frequency of the system changes, which can be measured experimentally. The current work extends methods previously developed for simulation of an atomic force microscope operating in liquid to study this phenomenon. A silicon cantilever with a 10 micron width, an 800 nm thickness, and a length of 30 microns was selected as a baseline configuration. The change in resonant frequency as the system accretes mass was determined through simulation. The results show that the change in natural frequency as mass accretes on the resonator is predictable through simulation. The geometry and material of the cantilever were varied to optimize the sys- tem. The results show that shorter cantilevers yield large gains in system performance. The width does not have a large impact on the system performance. Selecting the optimal thickness requires balancing the increase in overall system mass with the improvement in frequency response as the structure becomes thicker. Because there is no limit to the max- imum system stiffness, the optimal materials will be those with higher elastic moduli. Based on these criteria, the optimum resonator for mass accretion measurements will be significantly different than an optimized atomic-force microscopy (AFM) cantilever. [DOI: 10.1115/1.4025842] Keywords: biodetection, nano-electro-mechanical-systems, resonators 1 Introduction Resonant micro- and nanosystems are employed in atomic- force microscopy (AFM), a basic tool of experimental nano- science [1–3]. These systems have been successfully operated as feedback control systems in liquid, allowing the study of cells in a liquid medium [4,5]. Similar systems have also been used to measure the evaporation rate of small droplets [6]. Recently, researchers have merged the two measurement tech- nologies to attempt mass measurements in liquid. In these sys- tems, the added mass of the resonator is determined through by measuring the change in resonant frequency of the system. This method has been attempted for two challenging applications: determining the mass of a cell as it grows [7,8], and detection of DNA at low concentrations [9]. In both of these applications, the heavy damping of the resonator as it operates in liquid lowers the resolution of the system. To allow optimization of future designs, it is desirable to have a method to simulate the change in the frequency response of the system as mass is absorbed. In all of these systems, the resolution is determined by the qual- ity factor, Q [10,11], which is the ratio of the device’s vibrational energy U i to the loss per cycle U d , Q ¼ 2pU i =U d (1) In systems operating in liquid, or gas at atmospheric pressure, the energy lost to the surrounding fluid generally dominates the mechanical and structural losses inside the resonator [12]. These losses must then be computed, and incorporated into any predic- tion of the sensor performance. Three approaches have been taken to computing the impact of these losses on the performance of resonators. The first approach is to assume that the resonator is operating close to its natural fre- quency, and calculate the flow around a rectangular cross section of the resonator vibrating at the resonant frequency. The resonator motion is assumed to be yðtÞ¼ A sin xt ð Þ (2) where A is the amplitude of vibration. The total damping per cycle is then U d ¼ ð 2p=x 0 F d t ðÞ _ yðtÞdt (3) where F d (t) is the drag as a function of time. Because the drag at low Reynolds numbers is generally proportional to the velocity, U d is generally proportional to amplitude squared. For a resonator cross section, the vibrational energy is equal to the peak kinetic energy, U i ¼ 0:5m xA ð Þ 2 (4) where m is the cross-sectional mass. Combining these results means that Q will be independent of the amplitude of vibration. This has two implications. First, it implies that the quality fac- tor will be independent of the mode shape of the system. Second, Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 11, 2012; final manuscript received September 25, 2013; published online November 26, 2013. Assoc. Editor: Steven W Shaw. Journal of Vibration and Acoustics APRIL 2014, Vol. 136 / 021003-1 Copyright V C 2014 by ASME Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/31/2014 Terms of Use: http://asme.org/terms