Image made using the COMSOL Multiphysics® software and is provided courtesy of COMSOL.
A pressure sensor gives the pressure based on capacitance change, which is related to the deformation of the structure. Deformation depends on the ambient pressure and temperature, on the materials used, and on any initial stresses in the material.
The design and modeling of microelectromechanical systems (MEMS) is a unique engineering discipline. At small length scales, the design of resonators, gyroscopes, accelerometers, and actuators must consider the effects of several physical phenomena in their operation. Consequently, COMSOL Multiphysics is ideally suited for MEMS applications. To this end, the MEMS Module provides predefined user interfaces with associated modeling tools, referred to as physics interfaces, for a variety of coupled physics, including electromagnetic-structure, thermal-structure, or fluid-structure interactions. You can include a variety of damping phenomena in your model: thin-film gas damping, anisotropic loss-factors for solid and piezo materials, anchor damping, and thermoelastic damping. For elastic vibrations and waves, perfectly matched layers (PMLs) provide state-of-the-art absorption of outgoing elastic energy.
Best-in-class piezoelectric and piezoresistive modeling tools allow for simulations where composite piezo-elastic-dielectric materials can be combined in any imaginable configuration. The MEMS Module includes analyses in the stationary and transient domains, as well as fully-coupled eigenfrequency, parametric, quasi-static, and frequency response analyses. You can easily perform lumped parameter extraction of capacitance, impedance, and admittance, and connect to external electrical circuits via SPICE netlists. Built upon the core capabilities of COMSOL Multiphysics®, the MEMS Module can be used to address virtually any phenomena related to mechanics at the microscale.
The thermal stress in a layered plate is studied in this example. A plate consisting of two layers, a coating and a substrate layer is stress and strain free at 800 degrees C. The temperature of the plate is reduced to 150 degrees C and thermal stresses are induced. A third layer, the carrier layer, is added and the thermal stresses in the coating and a substrate layer are added as an initial stress and the temperature is finally reduced to 20 degrees C.
The model performs a static analysis on a piezoelectric actuator based on the movement of a cantilever beam, using the Piezoelectric Devices predefined multiphysics interface. Inspired by work done by V. Piefort and A. Benjeddou, it models a sandwich beam using the shear mode of the piezoelectric material to deflect the tip.
A surface acoustic wave (SAW) is an acoustic wave propagating along the surface of a solid material. Its amplitude decays rapidly, often exponentially, through the depth of the material.
SAWs are utilized in many kinds of electronic components, including filters, oscillators, and sensors. SAW devices typically apply electrodes to a piezoelectric material to convert an electric signal into a SAW, and then back again. The SAW response provides the information that the device is used to collect.
This model investigates the resonance frequencies of a SAW gas sensor. The sensor consists of an interdigitated transducer etched onto a piezoelectric substrate, covered with a thin film. The mass of the film increases as its material selectively adsorbs a chemical substance from the air. This causes a shift in resonance to a slightly lower frequency and thus information about the amount of species in the air.
This example illustrates the ability to couple thermal, electrical, and structural analysis in one model. This particular application moves a beam by passing a current through it; the current generates heat, and the temperature increase leads to displacement through thermal expansion. The model estimates how much current and increase in temperature are necessary to displace the beam. Although the model involves a rather simple 3D geometry and straightforward physics, it provides a good example of multiphysics modeling.
This example shows how to set up a piezoelectric transducer problem following the work of Y. Kagawa and T. Yamabuchi.
The composite piezoelectric ultrasonic transducer has a cylindrical geometry that consists of a piezoceramic layer, two aluminum layers, and two adhesive layers. The system applies an AC potential on the electrode surfaces of both sides of the piezoceramic layer.
The goal is to compute the admittance for a frequency range around the four lowest eigenfrequencies of the structure.
This is a benchmark model for ultrasonic transducer simulation but also a good starting point for simulations of SAW and BAW filters.
AT cut quartz crystals are widely employed in a range of applications, from oscillators to microbalances. One of the important properties of the AT cut is that the resonant frequency of the crystal is temperature independent to first order. This is desirable in both mass sensing and timing applications. AT cut crystals vibrate in the thickness shear mode—an applied voltage across the faces of the cut produces shear stresses inside the crystal. This example considers the vibration of an AT cut thickness shear oscillator, focusing on the mechanical response of the system in the frequency domain. Setting up a COMSOL model using the various standards set up to define piezoelectric material orientation is covered in detail (note that the details of the standards are covered in a COMSOL blog post). The effect of a series capacitor on the mechanical resonance is also considered. Adding a series capacitance is a technique frequently employed to tune crystal oscillators.
An electrostatically actuated MEMS resonator is simulated in the time and frequency domains. The device is driven by an AC + DC bias voltage applied across a parallel plate capacitor. The dependence of the resonant frequency on DC bias is assessed, and frequency domain and transient analyses are performed to investigate the device performance.
A capacitive pressure sensor is simulated. This model shows how to simulate the response of the pressure sensor to an applied pressure, and also how to analyze the effects of packing induced stresses on the sensor performance.
Microresistors allow for quick and accurate actuation or structural movement directly related to the electricity that is applied to them. Microresistors can be used in many applications where small perturbations or deflections are required to be applied to devices, almost instantaneously.
The Microresistor Beam app illustrates the importance of fully coupled, multiphysics simulations. An electric potential is applied across a small resistor and the deformation, temperature, and electric potential within the beam are computed.
This application allows for the geometric dimensions to be varied, along with the material properties, electrical conductivity, and applied voltage. Based on the results, you can design the right microresistor for your device.
The elastic cantilever beam is one of the elementary structures used in MEMS designs. This model shows the bending of a cantilever beam under an applied electrostatic load. The model solves the deformation of the beam under an applied voltage.
