TECHNICAL PAPER Exact analysis of antibody-coated silicon biological nano-sensors (SBNSs) to identify viruses and bacteria Reza Hosseini-Ara 1 • Amir Hossein Karamrezaei 2 • Ali Mokhtarian 2 Received: 28 April 2019 / Accepted: 1 July 2019 / Published online: 8 July 2019 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract In this paper, the vibration analysis of a Silicon Biological Nano-sensor (SBNS) with full coverage of Myosin as bio- logically adsorbent layer is investigated based on modified nonlocal Euler–Bernoulli beam model. This SBNS works based on calculating the shift of resonant frequency in the presence of Myosin layer and adsorbed viruses and bacteria. For this end, the effects of surface stresses, nonlocal parameter, and rotary inertia as well as the mass and stiffness of the adsorbent layer are taken into account, which can play a major role in changing the resonant frequency and the precision of SBNSs at nano-scale. The results illustrate that the effects of adsorbent layer, surface stresses, nonlocal parameter and rotary inertia may reduce resonant frequency of SBNS, which is significant especially at nano-scale. Finally, for the purpose of verification assessment, the numerical results were compared with the results of other studies and showed complete agreement. The present study can provide helpful insights for the design and characterization of accurate biological Nano- sensors. 1 Introduction Nanotechnology has revolutionized the diagnosis and treatment of cancer, cardiovascular and infectious dis- eases. In this regard, one of the most important appli- cations of nanotechnology is mechanical nano-sensors used to identify pathogenic agents based on the shift of resonant frequency (Burg and Manalis 2003). There are strong links between structures with mechanical, elec- trical or chemical properties on a micro/nano-scale, and the slightest mechanical changes can be detected using this very high sensitivity. For this end, one of the most important computational characteristics of the beams is resonant frequency variation, and as the beam has a micro or nano dimension, it has a much higher sensi- tivity compared to the beam with a macro structure (Knobel 2008), so that even with the presence of a vital molecule (Burg et al. 2007), a cell (Grover et al. 2011), a virus (Gupta et al. 2004), a protein (Hanay et al. 2012; Chaste et al. 2012) or a gold atom (Jensen et al. 2008), resonant frequency changes. To this end, the nano-beam is impregnated with a biological material as an adsorbent layer in nano-sensors, which can be a type of antibody (Lavrik et al. 2004; Cherian and Thundat 2002). Hence, when the nano-beam is exposed to a solution or a specific environment, the target molecules may attach to it, leading to some variations in the mass and stiffness of the beam, which can cause resonant frequency variation in the nano-sensor. In this regard, Gupta et al. (2004) investigated smallpox virus and determined its mass using micro-sensors, which contained a mass of about 9.5 femtogram. Moreover, Ramos et al. examined the adsorption of E. coli bacteria on cantilever micro-beams and showed that the added mass alone could not be the main cause of the sensor response. Their experiments showed that the size and resonant frequency depend on the distribution of adsorbed bacteria cells on the beam surface. Thus, resonant frequency reduces owing to the added mass caused by the adsorption of bacteria, whereas the increase in resonant frequency is associated with the effect of the flexural stiffness of the beam due to the bacterial stiffness (Fritz et al. 2000). Tamayo et al. presented a theoretical model for predicting resonant frequency variation due to the adsorption of molecules & Reza Hosseini-Ara HosseiniAra@pnu.ac.ir 1 Department of Mechanical Engineering, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran 2 Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, Khomeinishahr/Isfahan, Iran 123 Microsystem Technologies (2020) 26:509–516 https://doi.org/10.1007/s00542-019-04533-w