Get e-book Fast Simulation of Electro-Thermal MEMS: Efficient Dynamic Compact Models (Microtechnology and MEMS)

Contents:

Fast Simulation of Electro-Thermal MEMS : Efficient Dynamic Compact Models

This tutorial is written for MEMS engineers and is enriched with many case studies which equip readers with the know-how to facilitate the simulation of a specific problem. The Best Books of Check out the top books of the year on our page Best Books of Product details Format Paperback pages Dimensions x x Looking for beautiful books? Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Other books in this series. Piezoceramic Sensors Valeriy Sharapov. Silicon Microchannel Heat Sinks L.

Micromechanical Photonics Hiroo Ukita.

SearchWorks Catalog

However, the advanced user can access and modify low-level solver settings as needed. Electrostatic forces scale favorably as the device dimensions are reduced, a fact frequently leveraged in MEMS.

The MEMS Module provides a dedicated physics interface for electromechanics that, for MEMS resonators, is used to compute the variation of the resonant frequency with applied DC bias — the frequency decreases with applied potential, due to the softening of the coupled electromechanical system.

The small size of the device results in a MHz resonant frequency even for a simple flexural mode. 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 MIRACLE OF THE PEOPLE OF THE SEA: EL MILAGRO de la GENTE del MAR;
.
Holding to the Ground!
.
Introduction to Computer Fundamentals.

The equations are then solved using the finite element method and a range of industrial strength solvers. 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.

Top Authors

Fast Simulation of Electro-Thermal MEMS provides the reader with a complete methodology and software environment for creating efficient dynamic compact models for electro-thermal MEMS devices. It supplies Microtechnology and MEMS. Editorial Reviews. From the Back Cover. Fast Simulation of Electro-Thermal MEMS provides Fast Simulation of Electro-Thermal MEMS: Efficient Dynamic Compact Models (Microtechnology and MEMS) - Kindle edition by Tamara Bechtold, Evgenii B. Rudnyi, Jan G. Korvink. Download it once and read it on your Kindle.

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. 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.

Thermoelasticity is important in the modeling of high-quality factor MEMS resonators. 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.

Account Options

He received the Candidate of Science equiv. We have further demonstrated the applicability of reduced order models for an efficient system- level simulation of the device together with the control circuitry while preserving the accuracy of the device simulation. A silicon-nitride membrane with integrated heater and sensing element was fabricated by low-frequency plasma enhanced chemical vapor deposition. 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. It is further possible to use parametric model order reduction pMOR [13] for constructing reduced models which preserve material properties as parameters.

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.

Bestselling Series

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.

Stanford Libraries

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.

Fast Simulation of Electro-Thermal MEMS : Efficient Dynamic Compact Models

Controlled membrane temperature reaching set-point value with a rise time of 0. The rise time of the uncontrolled system is 4.

MEMS Module.
Biblical Workbook II.
.

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. This shall lead to a likewise increase in membrane temperature. Optimization yields a different set of parameters to fulfill this task proportional and integral gain equal 0.

Small oscillations occur in the initial phase and decay after the first milliseconds. For comparison, we include results from an uncontrolled heating setup as shown in Fig. Data is normalized to the respective maximum values.

Flow controlled Bartels micropump mp6 - Bartels Mikrotechnik

The response of the uncontrolled setup lacks behind the set point. A already mentioned above, the cooling process cannot be influenced by the present setup. Temperature response to a linearly increasing heating power of an uncontrolled scheme and to a linearly increasing set point value of a controlled system. The difference between actual membrane temperature and the set point value is determined in OP1; no gain is added here. OP2 performs the time integration while simultaneously adding a gain factor. The heating resistor is driven by a unity gain buffer to decouple the electrical load of the heating resistor from the integrating operational amplifier.

The dissipated electrical power is passed to the reduced model, which describes the dynamic behavior of the membrane. The temperature value at the location of the sense resistor is used to set the resistance value of the temperature sensing resistor.

A constant current is fed through the sense resistor which yields in a temperature dependent output voltage to be compared with the set point value.

OP3 model sepoint diff. Reduced order model implemented for co-simulation with a control circuit. Difference to the configuration of Fig. The reduced order model is implemented as a state-space system 3. Please note that the presented setup reduced order model of the MEMS device and the control circuitry can be easily extended by coupling other physical domains and further analog and digital circuitry.

This information is well known for most bulk materials. Monocrystaline silicon is the dominant material for MEMS fabrication and has been extensively studied so that its mechanical, thermal and electrical characteristics are well known [9].

Fast simulation of electro-thermal MEMS : efficient dynamic compact models in SearchWorks catalog.
Las estepas de España y su vegetación (Spanish Edition)!
?

Devices which are purely made from silicon, like e. However, the fabrication of most MEMS devices involves the deposition of thin films, which are employed to fulfill specific functions, like sensing, actuation, passivation, etc. Unfortunately, the material properties of thin films depend strongly on the fabrication parameters and subsequent process steps of the MEMS structure. In order to build an accurate MEMS model, the material properties of thin films have to be determined. In case of electro-thermal MEMS, the material thermal properties of thin film materials are of special interest, as the transient characteristic of the device are determined by thermal conductivity and specific heat parameters r and c p r in 1 of the employed materials.

These two parameters determine how fast and to what extent e. A conventional way to determine unknown thermal properties is to build and characterize dedicated test structures, which employ the thin film material of interest as a functional component. A review of the state of the art in determining material thermal properties of thin films is given in [10]. Mentioned test structures preferably feature simple geometries [11], [12] and hence, can be described by analytical models.

If the applied heat and temperature distribution are measured, one can determine the material thermal properties of the employed thin films from analytical models. The main drawback of such an approach is that the heat flow is mostly assumed to be one-directional, although heat conduction is a distributed phenomenon. Therefore, for higher accuracy more precise numerical models are required, which however, require considerable computational effort.

In the previous sections we have seen that computational effort for simulation linear thermal models can be reduced by applying model order reduction. Once again, we consider model to be linear, if material properties can be assumed temperature independent. It is further possible to use parametric model order reduction pMOR [13] for constructing reduced models which preserve material properties as parameters. Such parameterized small-size models can be used within a data fitting procedure to efficiently obtain those material parameters.

However, the main at present is to speed up the simulation of the numerical model in order to enable a time-efficient optimization. Hence, in the following we will assume the adequacy of the numerical model.