MEMS Module

Built-In User Interfaces and Results

The MEMS Module provides built-in user interfaces that are tailored to the type of device and multiphysics interaction being analyzed. These interfaces define sets of domain equations, boundary conditions, initial conditions, predefined meshes, and predefined studies with solver settings as well as predefined plots and derived values. All of these features can be accessed within the COMSOL Multiphysics^® environment.

Values for the electric field, stress, strain, quality factors, damping, resonant frequencies, dissipation, and scattering parameter (S-parameter), as well as values for capacitance, admittance, and impedance matrices, can be calculated and exported to the Touchstone file format. Any mathematical expression can be plotted or evaluated in terms of the computed quantities.

Electrostatics

The capacitive effects in MEMS devices can be analyzed with electrostatics computations where the fields are determined by the electric potential and charge distribution. Both the finite element method (FEM) and boundary element method (BEM) are available for solving the electric potential and can be combined for a hybrid boundary-element–finite-element method (BEM–FEM). Based on the computed potential field, a number of quantities can be calculated, such as the capacitance matrices, electric fields, charge density, and electrostatic energy.

The electrostatics functionality can be extended with built-in options for multiphysics effects like piezoelectricity, electrostriction, and ferroelectricity. Debye dispersion and dielectric loss material models are available for both frequency-domain and time-dependent analysis.

Fluid–Structure Interaction (FSI)

The Fluid-Structure Interaction (FSI) multiphysics interface of the MEMS Module combines fluid flow with solid mechanics to capture the bidirectional interactions between fluids and solid structures. The flow can be either laminar or turbulent. For including specific microfluidic phenomena, the MEMS Module can be combined with the Microfluidics Module. Turbulent flow requires the CFD Module or Heat Transfer Module. The CFD Module also allows two-phase and three-phase flow to be coupled with solid mechanics.

Piezoresistivity

The piezoresistive effect refers to the change in a material’s conductivity in response to an applied stress. The ease of integration of small piezoresistors with standard semiconductor processes, along with the reasonably linear response of the sensor, has made this technology particularly important in the pressure sensor industry. For modeling piezoresistive sensors, the MEMS Module provides several dedicated interfaces for piezoresistivity in solids or shells. When combining the MEMS Module with the Structural Mechanics Module, a piezoresistivity user interface for thin shells is available.

Thermomechanical Couplings

The Thermoelasticity interface combines the Solid Mechanics and Heat Transfer in Solids interfaces, which includes coupling terms for thermoelastic damping. Thermoelastic damping is particularly important in smaller MEMS structures, in which regions of compression and expansion are in close proximity. The cyclic deformation of resonators creates local temperature variations and thermal expansion of the material, which appears as damping. The thermoelastic coupling terms result in the material being cooled when under tension and heated when under compression. The resulting irreversible heat transfer between warm and cool regions of the solid produces mechanical losses that may be important at the microscopic level.

Damping in MEMS Resonators

A number of different damping phenomena can be modeled using the MEMS Module, including squeeze-film damping; isotropic and anisotropic loss-factors for dielectric, elastic, and piezoelectric materials; and thermoelastic damping. For computing anchor damping, perfectly matched layers (PMLs) provide state-of-the-art absorption of outgoing elastic waves for both elastic and piezoelectric solids. A fully coupled eigenfrequency, frequency-response, or transient analysis can be performed.

By combining the MEMS Module with the Acoustics Module, the effects of acoustic damping from a surrounding fluid, including pressure acoustic and thermoviscous damping, can be included.

Prestressed and Biased Devices

The MEMS Module can be used to study devices that are prestressed with mechanical and thermal loads. The built-in harmonic perturbation analysis allows for computing the frequency response as well as the eigenfrequencies and eigenmodes of such models.

In a similar way, electrostatically biased MEMS resonators, including micromechanical filters, can be analyzed. For instance, since these devices are biased by a DC voltage and driven by an alternating current, it is possible to analyze how damping and biasing effects cause the resonance frequencies to shift.

Joule Heating and Thermal Stress

Thermal, electric, and structural effects can be easily combined. Predefined multiphysics couplings for Joule heating and thermal expansion enable modeling of electric current conduction in a structure, the subsequent electric heating caused by the ohmic losses, and the thermal stresses induced by the temperature field. Typical applications include thermal actuators and fuses. All material properties can be nonlinear and temperature dependent. Modeling of mechanical contact can be extended to include contact resistance for both heat and electric currents. Thin conducting layers can be modeled using specialized tools for layered shells.

Piezoelectricity

Uniquely advanced piezoelectric modeling tools allow for static, frequency-domain, coupled eigenfrequency, and time-domain simulations. Designs are allowed to have materials combined in any imaginable configuration and can easily include coupled piezoelectric, metallic, dielectric, and fluid parts.

Both the direct and inverse piezoelectric effects can be modeled, and the piezoelectric coupling can be formulated using the strain-charge or stress-charge forms. The MEMS Module includes a library of common piezoelectric material properties, including lead zirconate titanate (PZT) and quartz. Many piezoelectric materials exhibit nonlinear ferroelectroelastic behavior at large applied electric fields. It is also possible to model thin-layered dielectric and piezoelectric structures with shells, which can be accessed by combining the MEMS Module and Composite Materials Module.

Damping in piezoelectric devices can be represented with loss factors for the piezoelectric as well as the elastic and dielectric domains. Dielectric heating can be computed and coupled with heat transfer analysis to investigate the effects of dispersion.

When analyzing piezoelectric behavior using the Piezoelectricity interface, results can be obtained for the electric potential and electric field, displacement, strain, stress, capacitance, losses, admittance, impedance, and S-parameters.

Wave Dynamics in Elastic and Piezoelectric Materials

Vibrations and propagation of elastic and piezoelectric waves can be modeled in the frequency domain as well as in the time domain. This enables analysis of, for example, acoustic transducers and resonators, including bulk acoustic wave (BAW) and surface acoustic wave (SAW) devices.

For time-domain simulations, a choice between implicit and explicit methods is available. In all cases, different material types can be combined in the same model, including functionally graded materials.

The frequency-domain and implicit time-domain simulations are based on the finite element method, whereas the explicit time-domain simulations are based on the discontinuous Galerkin (dG or dG-FEM) method. The dG-FEM method uses a time-explicit solver to ensure a computationally efficient hybrid method that can solve very large models with many millions of degrees of freedom (DOFs). This method shows excellent parallel computing performance, including when running it on clusters.

For modeling waves leaving the computational domain, a variety of boundary conditions and absorbing layers are available, including nonreflecting boundary conditions, sponge layers, perfectly matched layers (PMLs), and elastic port boundary conditions.

Electromagnetic–Structure Interaction

The Electromechanics multiphysics interface combines solid mechanics and electrostatics with a moving mesh to model the deformation of electrostatically actuated structures, such as inertial sensors. The interface is also compatible with ferroelectroelastic and electrostrictive materials and has options for both FEM and BEM. A similar multiphysics interface for magnetomechanics is available when the MEMS Module is combined with the AC/DC Module.

Electrostrictive and Ferroelectroelastic Materials

Electrostriction is a form of electromechanical interaction where an electric field applied to an electrostrictive material generates a deformation of the material (direct effect), and a stress applied to the material changes its polarization (inverse effect). To model this phenomenon, the Electrostriction interface can be used, which includes a multiphysics coupling between the Solid Mechanics and Electrostatics interfaces.

The Ferroelectroelasticity interface can be used for modeling the coupling of Solid Mechanics and Electrostatics. This enables modeling of nonlinear electromechanical interactions in ferroelectric and piezoelectric materials. Electric polarization in such materials, including possible hysteresis and saturation effects, depends nonlinearly on the applied electric field. In addition, the polarization and mechanical deformations in such materials can be strongly coupled.

Electrical Circuits

The MEMS Module enables the combination of 2D and 3D models with SPICE circuits. In the combined simulation, parts of the model will have circuit representation. This can be used to evaluate the effect of a series capacitor on a quartz crystal oscillator, for example.

For any model or combination of models, the Electrical Circuit interface can be used to solve for the voltages, currents, and charges associated with the circuit elements. Circuit models can contain passive elements like resistors, capacitors, and inductors as well as active elements such as diodes and transistors. Circuit topologies can be imported or exported in the SPICE netlist format.