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Improved simulation for strongly coupled micro-electro-mechanical systems: resonant vacuum sensor optimization
Sensors and Actuators 74 Ž1999. 190–192
Improved simulation for strongly coupled micro-electro-mechanical systems: resonant vacuum sensor optimization B. Folkmer a
a,)
, A. Siber b, W. Großse Bley c , H. Sandmaier a , W. Lang
a
Hahn-Schickard-Institute of Micro- and Information Technology, Wilhelm-Schickard-Str. 10, D-78052 Villingen, Schwenningen, Germany b Gesellschaft f. Sensoren, Wilhelm-Schickard-Str. 10, D-78052 Villingen, Schwenningen, Germany c Leybold Vakuum, Wilhelm-Schickard-Str. 10, D-78052 Villingen, Schwenningen, Germany
Abstract This paper describes a new approach for simulation and optimization of micro-electro-mechanical systems ŽMEMS. with strongly physical coupled behaviour. By the use of commercial analysis tools only, without any specific add-ons, MEMS simulation can be carried out to the end of system optimization. The combination of general purpose finite-elements analysis with multi-physics system simulation is successfully demonstrated, here by the example of a resonant total pressure sensor system. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Simulation; Micro-electro-mechanical systems; Vacuum sensor
1. Theory Behavioural models for description of a wide range of physical effects were developed and implemented in a standard system simulator, which provides coupled cosimulation of thermal, mechanical and electric networks. Information, dependent on the structures geometry, e.g., the thermal and mechanical characteristics, is obtained by one-time finite element simulations, extracted and then fed to the network models. Thus, for system design the sensor model with its complex physical couplings can be combined easily with the netlist description of conventional microelectronic and control system design environments.
nical systems ŽMEMS. on different system levels as well as inclusion of physical cross coupling w1–3x. Electrical, thermal and mechanical networks calculated in parallel ŽFig. 1. are used to ensure the equilibrium of power within the system. Standard models were enhanced to allow the input of technology and geometry data. New models, to determine the eigen-values and buckling of pre-stress beams, based on well-known physics, are included in addition together with nonlinear models for heat transfer description. 3D finite element analysis was performed Že.g., with ANSYS. to obtain the appropriate values for thermal resistancesrcapacitances, residual forces, . . . acting on the mounting Žbulk and chip header. and certain parts of the chip structure w4x.
2. Simulation concept The presence of new enhanced numerical simulators Že.g., SABER. together with a mixed-signal-hardware-description-language Že.g., MAST. allows efficient modelling of the architecture and behaviour of micro-electro-mecha-
) Corresponding author. Tel.: q49-7721-943-146; Fax: q49-7721943-210; E-mail: [email protected]
3. Total pressure sensor A total pressure sensor, based on a thermal resonant principle, was realized in silicon technology. The over temperature of a resonator beam ŽFig. 2., heated by resistors, is altered by changes in the heat transfer rate as a function of the surrounding total pressure. Therefore internal stress occurs and the resonant frequency of the beam is shifted ŽFig. 3..
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 3 6 - 7
B. Folkmer et al.r Sensors and Actuators 74 (1999) 190–192
191
Fig. 1. Sensor model Žexcerpt.: physical network with couplings.
Fig. 3. Total pressure sensor system simulations: frequency shift, force on resonator, beam over temperature, local temperature at drive resistor as function of pressure change Žmolecularq viscous model..
192
B. Folkmer et al.r Sensors and Actuators 74 (1999) 190–192
Fig. 5. Total pressure sensor Žair, gas temperature 208C, Udrive 11 V; environment temperature 208C.: calculated frequency shift and measured data versus pressure. Fig. 2. Total pressure sensor: thermal finite element model Žsymetric cut..
The thermal as well as the pre-stress state of the entire structure have to be considered in equilibrium with the electrical power losses. Thus, within the sensor system, electro-thermal heaters, thermo-mechanical pre-stress, nonlinear heat transfer Žacoustic, molecular., meccano-electrical read-out, with conventional conduction and storing effects are apparent. In order to develop appropriate electronic control systems for different application specific setups a detailed
model of sensorsuitable for integration in circuit simulation ŽFig. 4. was essential to ensure system simulation and design verification.
4. Conclusion A new method for MEMS simulation was established and demonstrated on a sensor example with strongly coupled electro-thermal–mechanical behaviour. The complete model of the device was established in good agreement with the measured data ŽFig. 5.. Since all the essential physical effects have been included in the model direct access on the design parameters allowed fast adaption and system optimization.
References
Fig. 4. Sensor model external connectors: electrical pins: driÕe, sense, ground, thermal pins: gas temperature, enÕironment temperature, and fluidic pins: gas pressure.
w1x S. Senturia, CAD for microelectromechanical systems, Transducers ’95 and Eurosensors IX Ž1995. . w2x B. Folkmer, N. Hey, H. Sandmaier, W. Lang, Multi level coupled simulations for MEMS design, Eurosensors X Ž1996. . w3x ANSYS Ref. Manual, Rel. 5.2, Swanson, 1996. w4x SABER Manual, Rel. 4.0, Analogy, 1995.
Improved simulation for strongly coupled micro-electro-mechanical systems: resonant vacuum sensor optimization B. Folkmer a
a,)
, A. Siber b, W. Großse Bley c , H. Sandmaier a , W. Lang
a
Hahn-Schickard-Institute of Micro- and Information Technology, Wilhelm-Schickard-Str. 10, D-78052 Villingen, Schwenningen, Germany b Gesellschaft f. Sensoren, Wilhelm-Schickard-Str. 10, D-78052 Villingen, Schwenningen, Germany c Leybold Vakuum, Wilhelm-Schickard-Str. 10, D-78052 Villingen, Schwenningen, Germany
Abstract This paper describes a new approach for simulation and optimization of micro-electro-mechanical systems ŽMEMS. with strongly physical coupled behaviour. By the use of commercial analysis tools only, without any specific add-ons, MEMS simulation can be carried out to the end of system optimization. The combination of general purpose finite-elements analysis with multi-physics system simulation is successfully demonstrated, here by the example of a resonant total pressure sensor system. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Simulation; Micro-electro-mechanical systems; Vacuum sensor
1. Theory Behavioural models for description of a wide range of physical effects were developed and implemented in a standard system simulator, which provides coupled cosimulation of thermal, mechanical and electric networks. Information, dependent on the structures geometry, e.g., the thermal and mechanical characteristics, is obtained by one-time finite element simulations, extracted and then fed to the network models. Thus, for system design the sensor model with its complex physical couplings can be combined easily with the netlist description of conventional microelectronic and control system design environments.
nical systems ŽMEMS. on different system levels as well as inclusion of physical cross coupling w1–3x. Electrical, thermal and mechanical networks calculated in parallel ŽFig. 1. are used to ensure the equilibrium of power within the system. Standard models were enhanced to allow the input of technology and geometry data. New models, to determine the eigen-values and buckling of pre-stress beams, based on well-known physics, are included in addition together with nonlinear models for heat transfer description. 3D finite element analysis was performed Že.g., with ANSYS. to obtain the appropriate values for thermal resistancesrcapacitances, residual forces, . . . acting on the mounting Žbulk and chip header. and certain parts of the chip structure w4x.
2. Simulation concept The presence of new enhanced numerical simulators Že.g., SABER. together with a mixed-signal-hardware-description-language Že.g., MAST. allows efficient modelling of the architecture and behaviour of micro-electro-mecha-
) Corresponding author. Tel.: q49-7721-943-146; Fax: q49-7721943-210; E-mail: [email protected]
3. Total pressure sensor A total pressure sensor, based on a thermal resonant principle, was realized in silicon technology. The over temperature of a resonator beam ŽFig. 2., heated by resistors, is altered by changes in the heat transfer rate as a function of the surrounding total pressure. Therefore internal stress occurs and the resonant frequency of the beam is shifted ŽFig. 3..
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 3 6 - 7
B. Folkmer et al.r Sensors and Actuators 74 (1999) 190–192
191
Fig. 1. Sensor model Žexcerpt.: physical network with couplings.
Fig. 3. Total pressure sensor system simulations: frequency shift, force on resonator, beam over temperature, local temperature at drive resistor as function of pressure change Žmolecularq viscous model..
192
B. Folkmer et al.r Sensors and Actuators 74 (1999) 190–192
Fig. 5. Total pressure sensor Žair, gas temperature 208C, Udrive 11 V; environment temperature 208C.: calculated frequency shift and measured data versus pressure. Fig. 2. Total pressure sensor: thermal finite element model Žsymetric cut..
The thermal as well as the pre-stress state of the entire structure have to be considered in equilibrium with the electrical power losses. Thus, within the sensor system, electro-thermal heaters, thermo-mechanical pre-stress, nonlinear heat transfer Žacoustic, molecular., meccano-electrical read-out, with conventional conduction and storing effects are apparent. In order to develop appropriate electronic control systems for different application specific setups a detailed
model of sensorsuitable for integration in circuit simulation ŽFig. 4. was essential to ensure system simulation and design verification.
4. Conclusion A new method for MEMS simulation was established and demonstrated on a sensor example with strongly coupled electro-thermal–mechanical behaviour. The complete model of the device was established in good agreement with the measured data ŽFig. 5.. Since all the essential physical effects have been included in the model direct access on the design parameters allowed fast adaption and system optimization.
References
Fig. 4. Sensor model external connectors: electrical pins: driÕe, sense, ground, thermal pins: gas temperature, enÕironment temperature, and fluidic pins: gas pressure.
w1x S. Senturia, CAD for microelectromechanical systems, Transducers ’95 and Eurosensors IX Ž1995. . w2x B. Folkmer, N. Hey, H. Sandmaier, W. Lang, Multi level coupled simulations for MEMS design, Eurosensors X Ž1996. . w3x ANSYS Ref. Manual, Rel. 5.2, Swanson, 1996. w4x SABER Manual, Rel. 4.0, Analogy, 1995.