ICME Multiscale Modeling of MEMs Pressure Sensors Operating at High Temperature

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Nowadays, the diaphragms based Micro-Electro-Mechanical Systems (MEMs) pressure sensors are widely used to measure pressure in automotive, industrial, aerospace, and even in medical applications because of small size, lightweight, high resolutions, and ability to integrate to the integrated circuit (IC) fabrication process. A diaphragm (thin membrane), which is often made of polycrystalline silicon, is one of the most important mechanical parts in MEMs pressure sensors because it acts as a sensing element. The pressure sensor works on the basis of mechanical deflection of a thin diaphragm. In general, in order to achieve high sensitivity of the sensors, the diaphragm is usually fabricated in nano-thickness.

Fig.1 pressure sensor

Piezoresistive sensing and capacitive sensing are two main types of MEMs pressure sensors. In this research, capacitive sensing is analyzed. Capacitive sensing is based on the distance between a thin diaphragm and a substrate. When the diaphragm deflects due to external pressure, a decrease of the distance between the substrate and the diaphragm makes the capacitance increase. An electrical circuit is applied to measure the capacitance[1]. After calibration, the applied pressure can be determined.

However, most MEMs pressure sensors in industries and aerospace applications are usually operated under pressure cycling at high temperature. Silicon is brittle at room temperature, but at high temperature (more than 800 K), silicon becomes a ductile material[2]. Therefore, a poly-Si diaphragm, is susceptible to dislocations and may suffer from creep. Moreover, since a diaphragm is cycled several times, the stress-strain behavior in a diaphragm is possible to change. Both pressure cycling and high temperature may have a huge effect on the change in deflection, which leads to unreliable results. Understanding of mechanical behavior of the diaphragm is of critical importance in achieving high reliability of the MEMs sensors. Since doing experiments on the nanometer thickness materials is difficult to perform and costly, doing computational simulation is preferable. Consequently, multiscale modeling is applied to study mechanical properties and to predict deflection of the diaphragm under pressure cycling at high temperature.

Multiscale modeling approach

To predict deflection of the diaphragm, Finite Element Analysis (FEA) is performed by utilizing information from Internal State Variable (ISV) and semi-continuum approach for plate-like nanomaterials, which is proposed by Haitao Zhang, C.T.Sun [3][4], This semi-continuum approach predicts mechanical behaviors of a thin plate with nano-thickness accurately, so it replaces conventional continuum theory. ISVs can be developed by collecting all information from downscaling bridges as shown in Fig.2.

Fig.2 Multiscale modeling for a diaphragm in MEMs pressure sensors under pressure cycling at high temperature.


In the microscale, Crystal Plasticity(CP) in Finite Element Analysis (FEA) is performed to provide polycrystal stress-strain behavior to the ISVs and semi-continuum approach; however, to run the simulations, hardening rules from the mesoscale must be obtained.


In the mesoscale, all hardening constants must be calculated by using dislocation dynamics simulations and passed to the higher level, crystal plasticity simulation. In addition, dislocations in polycrystalline silicon are likely to occur due to high temperature, so dislocation dynamics must be simulated to provide dislocation density to the ISVs and semi-continuum approach. However, to run this simulations, the dislocation mobility from the atomistic scale is needed.

Atomistic scale

At the atomistic scale, Dislocation Mobility coefficients can be calculated by using Embedded Atom Method (EAM) model, and Modified Embedded Atom Method (MEAM) model, and passed to dislocation dynamics simulations in the mesoscale. Besides nanocrystal structures and boundary energy can be predicted in this length scale and are given to the ISVs and semi-continuum approach. However, to determine the MEAM potential, energy-volume curve and generalized stacking fault energy (GSFE) must be obtained from the electronics scale.

Electronic scale

At the electronics scale, the elastic moduli, lattice parameters, energy-volume curve and the GSFE are estimated by using Density Functional Theory (DFT). The information would be passed to the atomistic scale and also passed to the ISV and semi-continuum approach.


  1. Eswaran P, Malarvizhi S, MEMS Capacitive Pressure Sensors: A Review on Recent Development and Prospective, International Journal of Engineering and Technology (IJET), Vol 5 No 3 pp2734-2746 Jun 2013
  2. Seyed M. Allameh, Silicon-Based, Microelectronmechanical Systems (Si-MEMS) in: W. O. Soboyejo and T. S. Srivatsan, Advanced structural materials: properties, design optimization, and applications. CRC Press, Taylor & Francis Group (2006)
  3. Zhang HT, Sun CT, Semi-continuum model for plate-like nanomaterials, AIAA/ASME/ASCE/AHS structures, structureal dynamics, and materials conference, Denver, Colorado, April 2002
  4. Zhang HT, Sun CT, Nanoplate model for plate-like nanomaterials, AIAA Journal 2004;42:2002-9
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