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Modelling of frequency response of optomechanical thermal microsensors  

Authors
 Kozlov A.G.
Date of publication
 2016

Abstract
 An analytical method is developed to determine the frequency response of optomechanical thermal microsensors. The optomechanical thermal microsensors concern to thermal microsensors and are made with using surface micromachining. The basic elements of these microsensors are: the plate with absorbing layer; the beams which support the plate over a substrate; the bi-material sections which are the part of the beams and induce the deflection of the plate as result of the bi-material effect.
The three types of the microsensors are considered: microsensor with the two supporting beams in adjacent corners of the plate; microsensor with the two supporting beams in opposite corners of the plate; microsensor with the four supporting beams.
Taking into account the features of each type of the microsensors, in their structures, the domains of modelling are marked out. The size of this domain is determined by the symmetry of the microsensor structure (mirror or axial symmetry). The domains are divided into the regions with homogeneous parameters. For each region the non-steady-state heat conduction equation is obtained that is solved by using the time Fourier transform and eigenfunction method. The heat flux densities between the regions are determined using adjoint boundary conditions in the frequency domain. The analytical expression for the frequency responses of the microsensors is obtained.
The presented method is applied to find the frequency responses, cutoff frequencies and time constants for the three types of optomechanical thermal microsensors. Among the microsensors the design variant with the plate supported by the two beams in adjacent corners has the most sensitivity. The variant with the plate supported by the four beams has the lowest sensitivity. The frequency dependences of the argument for the three variants of the optomechanical thermal microsensors are almost identical. The values of the cutoff frequency and the time constant for the various variants of the microsensors are close. However, among them the microsensor based on the rectangular plate supported by four beams has the slightly better dynamic characteristics. The dependencies of the sensitivity and the time constant of the microsensor with the two supporting beams in adjacent corners on the length of the bi-material section of the beams and on the thickness of the Al-layer of the bi-material section are obtained. The sensitivity increases and the time constant decreases with increasing the length of the bi-material section. With increasing the thickness of Al-layer the sensitivity decreases and the time constant increases.
The present model allows one to determine the dynamic characteristics of optomechanical thermal microsensors: frequency response, time constant, cutoff frequency.
Keywords
 optomechanical thermal microsensor, temperature distribution, frequency response, Fourier transform, eigenfunction method, cutoff frequency, time constant.
Library reference
 Kozlov A.G. Modelling of frequency response of optomechanical thermal microsensors // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part4. P. 112-119.
URL of paper
 http://www.mes-conference.ru/data/year2016/pdf/D163.pdf

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