Sensors and Actuators 82 Ž2000. 30–39 www.elsevier.nlrlocatersna
A system-level simulation of complex multi-domain microsystems by using analogue hardware description languages M. Jakovljevic a,) , P.A. Fotiu b, Z. Mrcarica c , H. Detter a a
c
Vienna UniÕersity of Technology, Institute for Precision Engineering, Floragasse 7, A-1040 Vienna, Austria b UniÕersity of Nis, Faculty of Electronic Engineering, Department of Electronics, 18000 Nis, YugoslaÕia UniÕersity of Applied Sciences (FH) Wiener Neustadt, Department of Mechatronics, A-2700 Vienna, Austria Received 7 June 1999; received in revised form 29 November 1999; accepted 5 January 2000
Abstract A simulation approach is presented, which permits the simulation of spatially distributed fields with behavioral models of other physical effects and accompanying electronics within a single simulator environment. The final system-level model is a blend of finite-element, analytical, semi-analytical and parametric behavioral models with complex analogue and digital circuit networks. Previously evaluated calculations revealed successful simulation of finite element models with more than 25 000 nodes by using analogue simulators with hardware description language. The relative error of static calculations in comparison with commercial finite element simulators is better than 0.002% and 0.08% for 2D and 3D models, respectively. The results obtained in transient model verification proved the accuracy of the method. The simulation of the flow sensor system, whose functionality is governed by coupled fluidic-thermal-electric domains, is employed to show the feasibility of the method for complex microsystem modeling. q 2000 Elsevier Science S.A. All rights reserved. Keywords: System-level simulation; FEA; Space-continuous modeling
1. Introduction Microsystems consist of devices or subsystems, which employ different physical principles for achieving a required functionality. The simulation is necessary to accelerate a development cycle and reduce the costs of a trial-and-error procedure. The process of microsystem development begins with validation of the system design at higher levels of abstraction through the use of idealized model descriptions. It progresses through the simulation of complex subsystems and ends with simulation and optimization of the system, or system-level simulation. In general, system-level simulation is a way to simulate complete systems consisting of the subsystems where several physical domains must be taken into account. The objective of the system-level simulation is a fast simulation of several hundreds or thousands of components, which is done by using accurate, but mostly idealized Žparametric, analytical or semi-analytical. models of sub) Corresponding author. Tel.: q43-1-58801-35821; fax: q43-1-5880135899. E-mail address:
[email protected] ŽM. Jakovljevic..
systems. In contrast, the device simulation handles complex physical models with only one or a few devices described by partial differential equations ŽPDE.. The typical commercial device simulator software employs finite difference, finite element w1x or boundary element methods. Apart from those general-purpose software codes, several microsystem simulators have been developed w2,3x with an emphasis on coupling effects based on finite elements or mixed boundary-finite element techniques. These simulators cannot be termed system-level simulation tools, because they actually belong to the field of specialized device simulation dedicated to problemspecific coupled field calculations. Unfortunately, those simulators are not capable of simulating complete smart systems, which consist of mixed Ždigital and analogue. electronics in interaction with electrostatic, electromagnetic and structural fields. The relationships at the system-level can be very complicated, and the modeling with idealized subsystems is, in many cases, appropriate only for the first-order estimation of the system-level behavior. Very small deviations in the subsystem modeling will result in unreliable simulations of the behavior of smart microsystems. Finally, the lack of
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 0 0 . 0 0 3 4 9 - 6
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appropriate tools will limit the ability of the designer to develop previously inconceivable microsystems with defensible costs. Provided an appropriate level of technology can be accomplished, simulation tools are important factors in order to predetermine and limit the properties of the final design. The objective of this paper is to present a method for accurate system-level modeling consisting of device, behavioral and circuit models in event-driven analogue simulator environments. It is applicable for system-level simulation of closely coupled space-continuous systems. For a better understanding of the subject, we start with a brief description of the most common terms and obstacles that emerge in both modeling and coupling of subsystems.
2. Subsystem coupling and system-level modeling 2.1. Heterogeneous simulation enÕironments Two physical domains might be coupled in either a unidirectional or a bi-directional way. For unidirectional coupling, it is not necessary to develop special simulation methods, because the simulation procedure is straightforward. It is based on coupling of standard device simulators specialized for one physical domain and synchronized by the simulation manager, which is able to schedule and synchronize simulator inputroutput values among homogenous or heterogeneous hardware systems w4x. If commercial finite element simulators are used for solutions in different specific domains, bi-directional coupling is treated by iterative methods. In this case, the simulation manager has to iterate all interconnected variables and supervise time step control in order to achieve convergence. Nevertheless, in tightly coupled problems convergence of such a procedure cannot be guaranteed and, in fact, is lost in many cases w5x. Moreover, even if convergent, solutions may be significantly slowed down by a considerable communication overhead w6x. 2.2. Homogenous simulation enÕironments An alternative approach consists of techniques for simulation and coupling in a single simulation environment. Hence, the governing equations can be assembled in a single matrix scheme and reliable convergence can be accomplished. Such a procedure provides additional freedom in the design process and avoids possible problems with different data exchange formats and software interconnections. Therefore, the application of universal simulation systems capable of simulating almost all physical domains seems attractive. The simulation tool of choice in this case may be an analogue simulator. After going through a number of developments, the SPICE-like circuit simulators have been an industry standard for the last 25
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years. This class of analogue simulators has limited modeling capabilities using simple functional behavioral models and circuit networks. Easy coupling with other physical fields is hardly feasible in this case, even though the representation of different physical domains by using equivalent circuit networks is feasible w7–9x. Circuit simulators lack definable tolerances Žresolution. for particular physical quantities, since they deal only with electrical quantities such as charge, voltage, current, etc. The scalability and applicability of system-level simulation is improved by using analogue simulators with analogue hardware description languages ŽHDL., which are generalized extensions of circuit simulators. 2.3. Analogue simulators and modeling In addition to superb electronic modeling, such simulators contain the programming syntax needed for controlling all aspects of analogue numerical modeling, providing the design and the coupling of non-electric domains by means of ‘‘through’’ Žcurrent, heat flow, force etc.. and ‘‘across’’ Želectric potential, temperature, velocity, etc.. quantities. Furthermore, the control over temporal and iterative steps is provided. In comparison to device simulators, where the designer needs to define only the boundary conditions and the geometry of the device, modeling and validation of appropriate HDL models remains an exacting process. Existing modeling techniques differ by scope and goals, inasmuch as they have an impact on the velocity and the reliability of the calculation. Fortunately, analogue simulators support simulations at different levels of abstraction, i.e. the components in system-level model can be simplified at the beginning of the design process and improved in later phases. Such a flexibility is not available within device simulators. It is necessary to find the best possible operating principle for the designed device, based on numerous tests and fast simulations with idealized models. Subsequent stages of design require final refinements of the system-level model in a smaller set of simulations by employing more complex and slow, but very accurate sub-system models. Concerning the interconnections between models, a distinction should be made among compact, distributed, and space-continuous coupling. Space-continuous interconnections couple device models of participating domains intending to implement accurate space-continuous interactions of device ŽPDE. models. Compact interactions deal with only one physical quantity, while distributed interconnections tend to improve the quality of compact modeling by enabling reduced forms of spatially distributed functionality. This is shown in Fig. 1. 2.4. HDL modeling methods The behavioral modeling provides a generic ‘‘framework’’ where parameters indicating technology, dimen-
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developing reduced-order models of different fields and their interactions slows its application in a wide range of research and industrial projects. 2.5. Summary
Fig. 1. System-level model consisting of compact, distributed and spacecontinuous models.
sions or materials are required. The framework is given in either analytical or semi-analytical form with the respect to physical laws. Semi-analytical models are used in cases, when some aspects of the physical device cannot be represented analytically or require a certain level of simplification. The ‘‘tailored’’ modeling w10x proposes application-oriented behavioral modeling in early stages of the microsystem design for providing facts about operational principles and interactions in the system. This helps in the management of design complexities and shortens the time for redesigning during system optimization. It requires significant expertise in the problem’s physical background, simulator technology, system identification and programming techniques. The level of needed expertise increases with the complexity of the problem to be solved. As a consequence, automatic modeling tools have been developed w11,12x. They extract crucial physical parameters for behavioral models or produce abstract parametric Žblack-box, curve-fitting. representations. For the parameter extraction, measured data or results of finite element calculations may be used. Pure parametric models do not require details about the problem domain or physical dependencies. By parameter extraction, satisfactory results can be accomplished for a modest number of variables and parameters. It will work well for compact Žlumped. models with a sufficiently small number of parameters, but not for closely coupled, space-continuous and nonlinear systems. Reports w12x also indicate that examples involving deadband-functions or hysteresis cannot be solved yet. Parameter extraction can be a time-consuming job, if the results originate from codes like finite element programs. Prior to parameterization, the model must be built, validated and simulated for different input data in a transient mode. Problems in system-level modeling occur also as a result of the compact nature of employed subsystem-models and their interactions. In many cases, sub-systems are coupled on space-continuous boundaries or volumes. Advances have been made in the field of so-called reducedorder modeling for space-continuous structural and electrostatic interaction w5x. The lack of systematized approach for
Summarizing these brief descriptions of modeling problems found in the system-level simulation, we state that the modeling of space-continuous domains and their interactions in complex microsystems still represents a tough objective with available modeling techniques. The reduction of space-continuous subsystem-level models into compact models in a system-level simulation could have significant consequences: Ø The application of compact models in many cases is limited to one part of operating characteristics, depending on the particular device. Ø The reliability of the calculated system-level behavior decreases. Ø The lack of appropriate modeling techniques for spacecontinuous multi-domain subsystems limits the development of innovative microsystems. This leads to conservative design strategies. Obviously, the accuracy and the level of abstraction in the modeling of complex systems are opposing objectives. A compromise is hard to find, but the modeling process could be accelerated. Therefore, a method for easy and fast development of complex models is presented, avoiding the introduction of additional complications or new tools into the process of microsystem development.
3. Description of the modeling method Our approach consists of techniques for the extension of analogue simulators by finite elements ŽFE. w13x, which can be programmed using hardware description languages ŽHDL.. Analogue simulators calculate systems assembled from ordinary differential equations, but the simulation of microsystems require the solution of partial differential equations. This is accomplished by discretizing the spacecontinuous system into finite elements and subsequently applying a variational principle w14x. This method may be considered in the analogue simulation by programming finite element libraries for a particular hardware description language. The finite elements can be incorporated into the system matrix by using a standard formulation of the HDL model with ‘‘through’’ and ‘‘across’’ quantities. For instance, tetrahedral finite elements can be implemented in the form shown in Fig. 2. The local matrix of general finite elements is expressed by
w Kx q 4 s Fb 4 q Fs 4 q Fn 4
Ž 1.
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Fig. 2. Finite element model for tetrahedral shape functions with four nodes Ža. HDL model structure Žb. physical structure.
This equation can be solved in any advanced analogue simulator using HDL. In Eq. Ž1. wKx denotes a local matrix of finite element constants, q4 represents the vector of unknowns and Fb 4 , Fs 4 and Fn 4 denote vectors of body, surface, and nodal loads, respectively. A finite element is programmed as a generic library model. The constants and load vectors are attached depending on the particular problem setup. An interim translation into the system matrix by circuit equivalents of finite elements is avoided. The global matrix system is assembled from finite elements and compact Žlumped, discrete. models and solved by the simulator Alecsis w15x. The architecture of this simulator is similar to other commercial analogue simulators w16,17x, but also includes capabilities for the descrip-
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Fig. 4. System-level interactions and modeling Žflow sensor..
tion of space-continuous models in an object-oriented HDL and syntax for cloning and connecting arbitrary models. Fig. 3. describes the principle of model design. With the help of a preprocessor Ždata translation block., FE models can be imported from commercial simulators such as ANSYS Ž.lis files.. Afterwards, boundary conditions and loads may be altered. The preprocessor translates the mesh and model geometry into finite element description for Alecsis HDL Žsee Eq. 1.. This implies the reproduction of ANSYS PDE models in the analogue simulator without any reduction. The parameters Ž femodel file. are attached to finite element models ŽAleC q q FE module library.. The quality of the model is verified by comparing the results from both simulators Žerror estimation utility, FEcomparison file.. In addition, the model may be coupled to
Fig. 3. The principle of model design.
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electronic or digital components ŽAleC q q electronic device library. together with behavioral models of different physical domains using the Alecsis HDL. Finally, the design of the system-level model consisting of several subsystems modeled at various levels of abstraction is complete, and the model is ready for use in the analogue simulator. The advantages of such approach are demonstrated by the following facts: Ø The model is designed by defining the geometry with boundary conditions, and applying material data, as in commercial device ŽFE. simulators. Ø The model may be defined in a well-known FE environment and imported into the analogue simulator Ø The quality of the model and the performance of the analogue simulator may be quickly compared to the results from FE simulators Žsee Fig. 11. Ø Space-continuous systems from various physical domains may be simulated in detail, coupled with other submodels consisting of discrete models of electronic devices, digital components and behavioral models of any kind. Therefore, it is possible to perform a simultaneous simulation of a fully coupled multi-domain system consisting of subsystems, which may be modeled at various levels of abstraction. The governing equations are assembled in one system matrix and are calculated within a single simulator environment. Such a task can be performed by commercially available standard analogue simulation environments. It appears not to be necessary to develop entirely new simulation tools for this purpose. 4. Simulation example As an example, the simulation of a home-appliance flow sensor is illustrated. This device is similar to the one
Fig. 6. Positions of the subsystems and the nodes of interest with triangular mesh Ž2D model..
described in Ref. w18x. The system contains multi-domain models for turbulent fluid flow, digital electronics Žtimediscrete., analog electronics Žtime-continuous. and temperature field calculations Žtime and space-continuous. designed at various levels of abstraction. The interconnections between subsystems are shown in Fig. 4. The system is built on a silicon substrate with two silicon beams etched in the bulk ŽFig. 5.. The structure is assumed to be glued in an epoxy resin and the heat dissipation is neglected on all surfaces except on the lower boundary with an ideal heat sink and constant ambient temperature T s 2978K. Forced convective heat transfer to the fluid will cool down the beam. The change in the temperature is mea-
Fig. 5. Structure of the flow sensor.
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can be estimated by counting pulses from the D-FF using standard microprocessor technology. The thermal flow model is described as a finite-element model based on the heat transfer equation ET kDT y r P c
Fig. 7. Electro-thermal sigma-delta converter w19x with thermal interactions in the fluidic-thermal-electrical system.
Et
q qv s 0
Ž 2.
where T is the temperature and k, c, r , qV denote the thermal conductivity, heat capacity, material density, and the volumetric heat flow, respectively. In most cases, boundary conditions are such that either temperature or heat flux are prescribed at the surface S of the body. Accordingly, ET
sured on the S H temperature sensing device. The beam with an accompanying temperature sensor S C is used as a reference. Both temperature-sensing elements are connected to the inputs of the comparator. Together with the clock circuitry and the D-FF, this comparator unit comprises a part of the electro-thermal sigma-delta converter w19x. The output of the flip-flop switches the heater over the FET transistor. The heat flows into the bulk Žconductive flow. and into the fluid Žconvective flow. depending on the flow velocity. Therefore, the temperature will rise until the limit is reached, which is defined by the sensing circuitry and the reference S C . The temperature difference between the heater and the sensor must be held above some level depending on the mismatch between resistor values in the sensing circuitry. The thermal system in a feedback-loop behaves as a low-pass filter. The flow speed
T s T S on ST , qn s k
En
s q S on S q ,
Ž 3.
where ST and S q , respectively, denote the surface with prescribed temperature or heat flux. In Eq. Ž3. ETrEn is the directional derivative of the temperature field along the outward normal vector n on the boundary S. Finite element libraries developed for the Alecsis simulator can be used for solving this class of problems. The forced turbulent fluid flow QCF is designed as an array of behavioral Žcompact. models, coupled with each finite element of the silicon beams. For this reason, the distributed interaction between two subsystems is modeled. Its behavior is expressed by w18x: QCF s K C P Õ 0.8 P Ž THPLATE y TF .
Ž 4.
In Eq. Ž4., K c denotes a constant depending on geometry and fluid properties and Õ denotes the velocity of the fluid.
Fig. 8. Two-dimensional thermal field calculated by the ANSYS5.4 finite element simulator.
M. JakoÕljeÕic et al.r Sensors and Actuators 82 (2000) 30–39
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Fig. 9. The result of the 2D simulation with traces Žsee Fig. 6. of o101, o201, o200, o301, o300, heater rate, pulse of the D-FF, fluid velocity, and the clock signal vs. time in seconds Žoriginal Alecsis output..
Finally, TF and THPLATE are the temperatures of the fluid and the particular plate Žbeam. element, respectively. The heat generator is modeled as a behavioral component, while the electronic and digital components are represented with discrete and digital electronic models respectively. The 2D version of the model is described in Fig. 6. It is assumed that the switching FET dissipates the heat into the thermal model Žsee Fig. 7.. The temperature sensor is a diode with temperature dependant operating characteristics. The increase of temperature dependent current I D passing through the diode is expressed by w20x: EI D ET
EIS
s
ET
Us const .
P exp
eU kT
q IS P
eU kT
1
ž /
P y
T
P exp
eU kT
Ž 5. ´
EI D ET
s Us const .
EG 0 y eU kT 2
P ID
Ž 6.
where the temperature-dependant current I D is linearized as I D s f Ž U,T . s IS P exp
eU kT
f ID 0 q
EI D ET
DT q
EI D EU
DU
Ž 7. and adapted in the form, which is appropriate for iterative processes in the HDL, I D y I Dm0 s
EI D ET
ŽTyT m. q
EI D EU
ŽUyU m. .
Ž 8.
The index m denotes the results from the past iteration. The U is the diode voltage, e is the electron charge, k is the Boltzmann’s constant, EG0 is the forbidden-gap voltage and IS is the diode reverse current. The thermal coupling between the sensing element and the heater exists and may be described with gain G s TamplitudeSrTamplitudeH ; 0.1 and delay time constant T ; 0.4 ms. The advantage
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Fig. 10. The 3D simulation result ŽANSYS visualization..
of this approach is that it provides an opportunity to examine the performance of the system depending on different layouts and dissipation-limiting techniques in order to extend and optimize the capabilities of the final design. Obviously, such transient space-continuous analysis cannot be easily conducted in SPICE-like simulators nor evaluated in finite-element simulators either. The spacecontinuous two-dimensional thermal model is designed and meshed by using the ANSYS finite element software ŽFig. 8.. Then, it will be transferred into a form applicable for analogue simulators. The simulation of both model representations in ANSYS and HDL with presumed static loads verifies the model. The results of the analogue solver
Fig. 11. Relative error over nodes in 3D ŽError - 0.08%, 1159 nodes. thermal field calculated by Alecsis and compared to the results of ANSYS.
Ž2D thermal model. deviate no more than 0.002% compared to the ANSYS results. According to the transient simulation results, the frequency of the digital output will change depending on the fluid velocity ŽFig. 9.. In the 2D case, the spatial distribution of the electronic devices is intentionally misrepresented as infinite in the third dimension. This, however, appears to be sufficient for developing an approximate model for the validation of the simulation principle. A more accurate representation may be accomplished by using a 3D thermal system with electronic devices placed on the surface of the wafer. An irregularly shaped 3D geometry can be easily modeled by finite elements but introduces numerical difficulties in finite difference schemes. Simple finite networks w21x may be used as an
Fig. 12. Transient results Ždetail. for the behaviour of the 3D flow sensor ŽAlecsis simulator.. Traced signals are the fluid velocity, the temperature of the heater Žo200., of the cantilever close to the heater Žo201., and the temperature of the reference diode Žo300..
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Fig. 13. Transient calculation times for simulations by Alecsis on a Pentium III PC Ž500 MHz, 128 Mb RAM, Linux OS. for different numbers of nodes and 100 time steps using a frontal solver w22x.
alternative, but in order to reach a comparable accuracy, the system matrix has to be significantly larger. The 3D simulation ŽFig. 10. matches the results calculated by ANSYS with an error less than 0.08% ŽFig. 11.. The evaluation of 3D simulations ŽFig. 12. with Alecsis Ž1159 nodes, in 30 000 time and iterative steps. took 5 h on an Intel Pentium III-500 MHz computer under Linux. Although these models are rather small sized, successful calculations of two-dimensional FE models with more than 25 000 nodes and a relative error smaller than 0.005% in comparison to ANSYS have been reported w18x. In addition, finite element models for beams and electrostatic fields have been developed. In order to understand how to get an idea of computational expenses in analyzing space-continuous models in analogue simulators, several tests on electrostatic models have been performed. In Fig. 13, run-time results are shown for an electrostatic field between two capacitor plates with neglected spreading on the boundaries. The number of nodes varies between 1000 and 9000. Obviously, the simulation of models with up to 10 000 nodes should be viable within acceptable time limits, assuming that an average transient simulation requires between 500 and 10 000 time steps.
5. Conclusion The method for developing complex models for system-level simulation using a hardware description language is presented. The modeling process cannot be significantly different among different analogue simulators. Our methodology can be widely employed in various commercial systems based on standardized HDLs ŽVHDL-AMS, Verilog-A.. Such an approach permits simulation of spatially distributed fields with other physical effects Ždiscrete or
space-continuous. and accompanying electronics within a single simulator environment. The final model is a blend of FE, analytical, semi-analytical or parametric behavioral models and circuit networks. This must be distinguished from other methods for coupled simulation found in FE simulators Žiterative coupling and mixed finite elements. w1x, because they are heavily device-oriented and specialized for a few physical effects. They are unable to simulate complex discrete electronics or switched capacitor networks, which are fundamental in the design of smart microsystems. Today’s analogue simulation employs different kinds of behavioral modeling in order to represent the behavior of the systems of higher complexity. However, they are rarely sufficient for determining the transient system-level behavior of more complex closely coupled space-continuous system. It is not expected that this methodology will replace device simulation in the microsystem design, since device simulators can solve specialized PDE tasks faster Ž2–3 orders of magnitude., due to application-specific solver technology. The sole intention is to fill a gap in a systemlevel design by making complex models in the MEMS simulation more accurate and easier to design. As a result, previously inconceivable systems-level models can be simulated. The simulation of the flow sensor system is employed to prove the feasibility of the method. The analysis of the computational speed with the finite element electrostatic field model has been evaluated with conclusion that transient models with up to 10 000 nodes can be simulated within a working day. The transfer of finite element models into the analogue simulator environment is a fully automated and fast process.
Acknowledgements This work was supported by the Austrian foundation ‘‘Fonds zur Forderung der wissenschaftlichen Forschung’’, ¨ project P11251 ŽYear 1996–1998. — ‘‘MEMSSIM — development of tools for the simulation of micro-electromechanical systems’’ and project P13121 ŽYear 1999– 2001. — ‘‘MEMSSIM2 — simulation of complex microelectromechanical systems’’.
References w1x SAS, ANSYS V5.3 Manual, Houston, TX, USA, 1996. w2x J.M. Funk, J.G. Korvink, J. Buhler, M. Bachtold, H. Baltes, SO¨ ¨ LIDIS: a tool for microactuator simulation in 3-D, J. Microelectromech. Sys. 6 Ž1. Ž1997. 70–81. w3x Numerical Modelling, NM-SESES User Manual, Winterthur, Switzerland, 1998. w4x A. Schroth, T. Blochwitz, G. Gerlach, Simulation of a complex sensor system using coupled simulation programs, Sens. Actuators, A 54 Ž1996. 632–635. w5x S.D. Senturia, N. Aluru, J. White, Simulating the behavior of
M. JakoÕljeÕic et al.r Sensors and Actuators 82 (2000) 30–39
w6x
w7x w8x
w9x
w10x w11x
w12x
w13x
w14x w15x
w16x w17x w18x
w19x
w20x
MEMS devices: computational needs and trends, IEEE Comput. Sci. Eng. Ž1997. 30–43, January–March. Z. Mrcarica, G. Randjelovic, M. Jakovljevic, V.B. Litovski, H. Detter, Methods for description of microelectromechanical device models for system level simulation, in: Proc. MICROSIM 97, Lausanne, Switzerland, 1997, p. 79. G. Pelz, J. Bielefeld, F.J. Zappe, G. Zimmer, Simulating micro-electromechanical systems, IEEE Circuits Devices Ž1995. 10–13, March. G. Gerlaach, A. Klein, Strategies of modelling and simulation of microsystems with electromechanical energy conversion, Microelectron. J. 29 Ž1998. 773–783. J. Bielefeld, G. Pelz, G. Zimmer, Electrical network formulations of mechanical finite-element models, in: Proc. MICROSIM 97, Lausanne, Switzerland, 1997, pp. 239–247, Sept. G. Wachutka, Tailored modeling: a way to the ‘ virtual microtransducer fab’?, Sens. Actuators, A 46–47 Ž1995. 603–612. B. Romanowicz, Methodology for the Modeling and Simulation of Microsystems, Doctoral Thesis, IMS, Swiss Federal Institute of Technology of Lausanne ŽEPFL., Switzerland, 1997. K. Hoffman, J.M. Karam, B. Courtois, M. Glesner, Generation of HDL-A-Code for nonlinear behavioral models, in: Proceedings of IEEE International Workshop on Behavioral Modeling and Simulation ŽBMAS ’97., Washington DC, USA, 1997, Oct. M. Jakovljevic, Z. Mrcarica, P. Fotiu, H. Detter, V.B. Litovski, Implementation of finite elements using an A-HDL environment, Numer. Simul. Feinwerktech.-rMikrotechnik und Elektronik, Munchen 4–5 Ž1998. B6, March. ¨ J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1982. Z. Mrcarica, T. Ilic, D. Glozic, V. Litovski, H. Detter, Mechatronic simulation using Alecsis — Anatomy of the simulator, in: Proc. EUROSIM ’95, Vienna, 1995, pp. 651–656. www.analogy.com. www.mentorg.comreldor. V. Jimenez, V. Masana, M. Dominguez, L. Castanyer, Simulation of flow sensor for home appliances, Microelectron. J. 29 Ž1998. 283– 289, Elsevier. L. Castanyer, V. Jimenez, M. Dominguez, F. Masana, A. Rodigruez, Design and Fabrication of a low cost water flow meter, in: Transducers 97, Chicago, 1997, pp. 159–162, June. R. Muller, Grundlagen der Halbleiter Elektronik, Springer, Heidel¨ berg, 1971.
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w21x K. Fukahori, P.R. Gray, Computer simulation of integrated circuits in the presence of electrothermal interaction, IEEE J. Solid State Circuits Ž1976. 835–846, December. w22x Z. Mrcarica, V. Risojevic, M. Lenzner, M. Jakovljevic, V. Litovski, Integrated simulator for MEMS using FEM implementation in AHDL and frontal solver for large sparse systems of equations, in: Proc. Design and Test of Microsystems 99, Paris, 1999, pp. 271–278, March.
Biographies Mirko JakoÕljeÕic was born in Zagreb, Croatia, in 1970. He received the Dipl.Ing. degree in EE engineering from the Vienna University of Technology in 1997. He continued his education at the Institute for Precision Engineering as research assistant and doctoral student. His research interest covers the modeling of microsystems using analogue simulators, ASIC design and numerical methods. Peter A. Fotiu received his Ph.D. degree in civil engineering from the Vienna University of Technology, Austria, in 1990. Since 1995, he is Professor of Applied Mechanics at the University of Applied Sciences at Wiener Neustadt, Austria. His current research is dedicated to numerical methods in mechanical and electromechanical engineering with emphasis on coupled systems. Zeljko Mrcarica was born in Nis, Yugoslavia, in 1965. He received the Dipl.Ing. and M.Sc. degrees from the University of Nis, Yugoslavia, in 1989 and 1993, respectively, and the Dr.techn. degree from the Vienna University of Technology, Austria, in 1996. Currently, he is an Assistant Professor for design of integrated circuits at the Faculty of Electronic Engineering, University of Nis. His research interests are in integrated circuits and microelectromechanical systems design automation, analogue hardware description languages, analysis and design of adaptronic systems, and design of integrated systems. Helmut Detter was born in Wiener Neustadt, Austria, in 1939. He received the Dipl.Ing. and Dr.tech. degrees in precision engineering from the Vienna University of Technology, Austria, in 1965 and 1969, respectively. He is a full professor at the Vienna University of Technology, Institute for Precision Engineering. His research interests are in precision engineering, mechatronic simulation and application of microsystems in the medicine and automotive industry.