In addition, the favorable scaling of the electromagnetic forces enables efficient capacitive actuation that would not be possible on the macroscale. Furthermore, you have the option to use the electromechanics interface to include the effects of isotropic electrostriction. Piezoelectric forces also scale well as the device dimension is reduced. Furthermore, piezoelectric sensors and actuators are predominantly linear and do not consume DC power in operation. Quartz frequency references can be considered the highest volume MEMS component currently in production — over 1 billion devices are manufactured per year.
The physics interfaces of the MEMS Module are uniquely suitable for simulating quartz oscillators as well as a range of other piezoelectric devices. One of the tutorials shipped with the MEMS Module shows the mechanical response of a thickness shear quartz oscillator together with a series capacitance and its effect on the frequency response. Thermal forces scale favorably in comparison to inertial forces. That makes microscopic thermal actuators fast enough to be useful on the microscale, although thermal actuators are typically slower than capacitive or piezoelectric actuators.
Thermal actuators are also easy to integrate with semiconductor processes, although they usually consume large amounts of power compared to their electrostatic and piezoelectric counterparts. The MEMS Module can be used for Joule heating with thermal stress simulations that include details of the distribution of resistive losses. Thermal effects also play an important role in the manufacture of many commercial MEMS technologies with thermal stresses in deposited thin films that are critical for many applications.
The MEMS Module includes dedicated physics interfaces for thermal stress computations with extensive postprocessing and visualization capabilities, including stress and strain fields, principal stress and strain, equivalent stress, displacement fields, and more. There is also tremendous flexibility to add user-defined equations and expressions to the system.
For example, to model Joule heating in a structure with temperature-dependent elastic properties, simply enter in the elastic constants as a function of temperature — no scripting or coding is required. When COMSOL compiles the equations, the complex couplings generated by these user-defined expressions are automatically included in the equation system. The equations are then solved using the finite element method and a range of industrial strength solvers.
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Once a solution is obtained, a vast range of postprocessing tools are available to interrogate the data, and predefined plots are automatically generated to show the device response. COMSOL offers the flexibility to evaluate a wide range of physical quantities, including predefined quantities like temperature, electric field, or stress tensor available through easy-to-use menus , as well as arbitrary user-defined expressions.
The Fluid-Structure Interaction FSI multiphysics interface combines fluid flow with solid mechanics to capture the interaction between the fluid and the solid structure. Solid Mechanics and Laminar Flow user interfaces model the solid and the fluid, respectively. The FSI couplings appear on the boundaries between the fluid and the solid, and can include both fluid pressure and viscous forces, as well as momentum transfer from the solid to the fluid — bidirectional FSI. The MEMS module has specialized thin film damping physics interfaces which solve the Reynolds equation to determine the fluid velocity and pressure and the forces on the adjacent surfaces.
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These interfaces can be used to model squeeze film and slide film damping across a wide range of pressures rarefaction effects can be included. Thin-film damping is available on arbitrary surfaces in 3D and can be directly coupled to 3D solids. 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 physics interfaces for piezoresistivity in solids or shells.
The Solid Mechanics physics interface is used for stress analysis as well as general linear and nonlinear solid mechanics, solving for the displacements. The MEMS Module includes linear elastic and linear viscoelastic material models, but you can supplement it with the Nonlinear Structural Materials Module to also include nonlinear material models. You can extend the material models with thermal expansion, damping, and initial stress and strain features.
In addition, several sources of initial strains are allowed, making it possible to include arbitrary inelastic strain contributions stemming from multiple physical sources. The description of elastic materials in the module includes isotropic, orthotropic, and fully anisotropic materials. The Thermoelasticity physics interface is used to model linear thermoelastic materials. It solves for the displacement of the structure and the temperature deviations, and resulting heat transfer induced by the thermoelastic coupling.
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Thermoelasticity is important in the modeling of high-quality factor MEMS resonators. Consequently, software specifically designed for MEMS simulation and modeling has never been more important. Physics such as electromechanics, piezoelectricity, piezoresistivity, thermal-structure, and fluid-structure interactions can be modeled with the software. Design engineers can easily create models of common devices such as actuators, sensors, oscillators, filters, ultra sonic transducers, BioMEMS, and much more.
Get a free 2-week trial by signing up for a workshop in a location near you. Micromachines as Tools for Nanotechnology Hiroyuki Fujita. Emphasis is placed on the application of the Arnoldi method for effective order reduction of thermal systems.
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Table of contents Dynamic Electro-thermal Simulation of Microsystems. Her research interests include the application of model order reduction to MEMS problems and their efficient system-level simulation. He received the Candidate of Science equiv. He is actively involved in the application of model reduction to MEMS problems. Korvink is author or co-author of more than publications in the field of microsystems and joint-editor of "Advanced Micro and Nanosystems" [http: Korvink is a member of the technical programe committees of several conferences and is a member of ASME.
His research activities focus on the development of ultra low-cost methods of MEMS production and the modeling for and simulation of micro- and nanosystems. Christmas posting dates Learn more. As MEMS are often composed of interconnected subsystems, array structures for example, it is desirable to reduce each subsystem on its own and then to couple them back together, following e.
The main problem thereby is that the thermal flow is not lumped by nature as, for example, the electrical flow is along metallic wire interconnects. The ratio of electrical conductivity of metals and that of insulators is of the order of Hence, the electrical current flow takes place almost solely in metal paths. This is not the case with heat flow because the ratio of thermal conductivities in microtechnology is only of the order of Therefore, it is unclear how to lump the thermal fluxes at shared surfaces between two finite element models in order to form the thermal ports which would serve to couple together several compact models.
Note that, if one would keep all the surface nodes as ports, i. Step response of the full-scale and reduced order models for the microhotplate array based upon a gas sensor device from [4]. Reduction is done by block Arnoldi from [5], in case when two heat sources of 40mW each are switched on.
General technique of coupling two reduced thermal models gained by Krylov-subspace-based projection is discussed in [1]. In this respect, the structure-preserving model reduction techniques [6] should be further investigated. A silicon-nitride membrane with integrated heater and sensing element was fabricated by low-frequency plasma enhanced chemical vapor deposition. The microstructured hotplate consists of a thin film membrane composed of silicon nitride suspended over a silicon frame.
Thin film metal resistors are fabricated on top of the membrane for heating and temperature sensing. In order to achieve a preferably circular symmetric and homogenous temperature distribution at the center of the square membrane, both resistors are arranged as shown in Fig. Schematic view of the thin-film resistors for heating and temperature sensing.
Heating resistor is operated at constant voltage. The sensing resistor is configured for four-point measurement. The characterization of the static and transient thermal properties of the membrane is performed on a temperature controlled mount. The electrical resistance depends linearly on the temperature over the investigated temperature range and is modeled by 4. The transient thermal response of the membrane is characterized by applying a rectangular voltage signal to the heating resistor using a function generator.
The thermal response over a whole period is presented in Fig. One can recognize the drop in the heating power shortly after the voltage is applied. This is due to the fact that also the heating resistor depends on temperature nonlinearity of the right hand side in 3.
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An increase in temperature causes the heating resistance to grow which leads to slightly smaller heating power. This temperature is defined as the steady-state value.
Thus, the temperature drops down to its initial value. FE mesh of the three-dimensional model with It considers the heat conduction through the solid material and the air beneath the membrane as well as convection to the air above the membrane. The latter is considered in the form of convection boundary condition: Radiation mechanism has not been considered with respect to MOR, but it can be included via defining an additional temperature-dependant input as explained in section 5. Heat loss mechanisms considered by the FE model.
System-level model of microstructure and electrical components. Resistors are modeled as temperature dependent. A step input function is applied to a controlled voltage source which drives the heating resistor. Two different applications are presented in the following sections.
Simulation results of full scale FE model of silicon-nitride membrane from Fig. Based on reduced model, it is possible to efficiently determine the control parameters while preserving the accuracy of the device simulation. The absolute temperature of the membrane should be independent of variations in ambient temperature and changes in convection boundary conditions.
Furthermore, adjustments to new temperature set points should be performed by the thermal microsystem as quick as possible. In [18] two application scenarios for operation of the micro hotplate case study under temperature control were investigated, constant-value set-point temperature control and tracking control. In the first case a fast thermal response, which leads to the prescribed temperature value, is desired with minimum overshoot. The second scenario requires the temperature profile to track a prescribed function of time. In both cases the resistance values of the heating and sensing resistor depend on their respective temperatures according to the equation 4.
With suitable values for the proportional and integral gain parameters of the control unit, this loop can efficiently eliminate the effects of ambient temperature variations and will also allow the membrane temperature to follow time-varying set point temperatures. The heating resistor acts as an actuator onto the process, by transferring the control signal to the membrane in form of a heat generation rate, which in turn changes its temperature.
The sensing resistor supplies the temperature information which is compared to an external set value. The resulting difference is passed to the controller whose output is used to set a voltage source which drives the temperature-dependant heating resistor we have the nonlinear input function in 3. System-level model of microstructure and control loop. A PI-controller is used in the control loop.
No assurance can be given to the overall quality of the adjusted parameter set. However, in case when the control should fulfill specific goals, standard procedures are not applicable and further adjustments of the control parameters are required. In this case, an optimization strategy, based on the reduced order model, can be applied.
Several goal functions with different weighting factors can be defined. For example, to achieve a fast thermal response, the integral deviation between set point temperature and actual system response can be defined as goal function. Optimization aims at reducing this value to zero. If the goal is to prevent overshooting, the minimum value of the difference between set point and response is a suitable parameter, which should be minimized to zero as well.
If both goals are to be achieved, a weighted combination of above goal functions can be defined. In the first application scenario a step function acts as the set point. Proportional and integral gain parameters are 0. The time constant of the cooling process on the other hand side, is inherent to the thermal microsystem and cannot be influenced with the current scheme.
Active cooling or operation at elevated temperatures would accelerate the cooling process.
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Controlled membrane temperature reaching set-point value with a rise time of 0. The rise time of the uncontrolled system is 4. The drastic improvement of the rise time during the heating phase is achieved by excessive over heating during the initial phase. Secondly, a saw tooth signal is applied to the control loop.