- Email: [email protected]
Characterization and modeling of a CMOS-compatible MEMS technology
Sensors and Actuators 74 Ž1999. 143–147
Characterization and modeling of a CMOS-compatible MEMS technology Laurent Latorre a , Pascal Nouet a
a,)
, Yves Bertrand a , Philippe Hazard b, Francis Pressecq
c
LIRMM— UniÕersite´ Montpellier II (UMR CNRS No. 5506), 161 Rue Ada, 34392 Montpellier Cedex, France b Schneider Electric, Nanterre, France c CNES, Quality Assurance Delegation, Toulouse, France
Abstract In this paper we present a new methodology for efficient electromechanical characterization of a CMOS-compatible micro-electro mechanical sensors ŽMEMS. technology. Using an original test structure, the so-called ‘U-shape cantilever beam’, we are able to determine all mechanical characteristics of force sensors constituted with elementary beams in a given technology. A complete set of electromechanical relations that can be used for the design of Microsystems have been also developed. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Mechanical properties; Micro-electromechanical sensors; Front-side bulk micromachining ŽFSBM.; Modeling; Test structures; Simulation
1. Introduction Recent trends in the technology of VLSI CMOS circuits lead both integrated circuit ŽIC. designers and system providers to add more and more functionalities to a single application specific integrated circuit ŽASIC.. In that way, it seems interesting to implement a sensing element directly on the die where electronic parts have been processed w1,2x. Using a CMOS wafer with electronic parts on it, several techniques can be used to implement sensors. Front-side bulk micromachining ŽFSBM. can be associated or not with back-side bulk micromachining ŽBSBM. and sacrificial or extra layer techniques. As the cost of the post-process is strongly affected by the need for alignment, FSBM seems to be a very promising technique due to its selfalignment capability. This technique is largely available in France through CMP service, 1 post-process operates as an anisotropic
)
Corresponding author: Tel.: q33-467-41-85-27; Fax: q33-467-4185-00; E-mail: [email protected] 1 Information is available on the World Wide Web at the following address: http:rrtima-cmp.imag.frrtimarmcsrmcs.html.
silicon etching that uses the various oxide layers as natural mask. ²100: substrate planes can then be etched leaving the ²111: planes of the silicon substrate. Suspended structures such as cantilever beams, bridges or membranes are then obtained. Fabless designers can easily address this technology and low development costs are expected due to the reuse of the same technology for various physical phenomena. However, a CMOS VLSI technology is neither characterized nor optimized for its electromechanical properties. In this paper we present a complete methodology that allows to fully characterize mechanical and electromechanical properties of beams realized in a CMOS process.
2. U-shape cantilever device To characterize both mechanical and electromechanical properties of sensor parts, we have designed an original test structure. The so-called U-shape cantilever device ŽFig. 1. is formed with two parallel cantilever beams that are connected at their free extremity by a ‘linking arm’. Piezoresistive polysilicon strain gauges are located at the clamped end of each cantilever to obtain the best sensitivity to bending stresses. A metal line is also located in the
0924-4247r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 4 5 - 8
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
144
placement z Ž s . is linked to the applied external force F Ž s . by the following transfer function: z Ž s. s
F Ž s . rk M 2 D s q sq1 k k
Ž 1.
This system is characterized by a natural resonance with a quality factor Q at a radian frequency v 0 s krM . This Q-factor is written as: Q s Ž k .rŽ v 0 D .
'
3.1. Static characterization
Fig. 1. SEM photograph of two ‘U-shape’ cantilever beams.
Static characterization is realized by assigning a vertical displacement to the center part of the ‘linking arm’ using a micrometric screw. The vertical force Ž F . is then unknown but can be directly deduced from Eq. Ž1. as: F s kz. Using strain gauges located in both beams, it is also possible to experimentally link the relative gauge resistance variation Žin %. with the vertical displacement ŽFig. 3. as: D RrR s Az.
device in order to implement a current loop flowing through the device.
3. Mechanical modeling Assuming that both beams are identical, the U-shape cantilever is mechanically equivalent to a simple cantilever with a beam width equal to twice the real one. When applying a force or a displacement to the center of the ‘linking arm’, each beam acts as a leaf-spring. If vertical displacement remains low, a mechanical model for this device is a linear second-order mechanical system ŽFig. 2. where k, M and D are the spring constant, the mass and the damping factor respectively. Then, the vertical dis-
Fig. 2. Second-order mechanical model of a ‘U-shape’ cantilever beam.
Ž 2.
The slope A is then an important feature for the electromechanical characterization of the test structure. This parameter includes all relations of strength of materials such as bending torque, moment of inertia, Young’s modulus and also gauge factor of the sensitive layer Ži.e., polysilicon.. 3.2. Dynamic characterization In order to apply a dynamic force in a contactless manner to the U-shape cantilever we use the Lorentz’s force. The device is located in a calibrated static magnetic field Ž Bdc . with the same orientation as both cantilever beams. If an alternative current Ž Iac . is flowing through the device, a force is vertically generated in the ‘linking arm’. The force magnitude can be easily calculated as: Fac s Iac Bdc Larm where Larm is the length of the ‘linking arm’.
Fig. 3. Resistance variations of the polysilicon gauge vs. vertical displacement.
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
145
4.1. CantileÕer beam modeling The behavior of an homogeneous cantilever may be modeled by the vertical deflection of a beam Žlength, L. with an external force F applied at its free end. Using basic mechanical relationships w3x the following equation can be established: z s FL3r3 En In where En and In are respectively the Young’s modulus and the moment of inertia of the beam. Consequently, F and z are linearly dependent as in Eq. Ž1.. The spring constant equivalent coefficient is given as: ks Fig. 4. Dynamic characteristic of a U-shape cantilever beam. Experimental results Žcrosses. are compared with simulated results Žcontinuous line..
A frequency sweep can then be applied to Iac to generate the dynamic characteristic of the mechanical system ŽFig. 4.. Both resonant frequency Ž f 0 . and quality Žor resonant. factor Ž Q . are then experimentally determined. 3.3. Parameter extraction After both characterization steps, it is then possible to determine all the mechanical parameters of the system. First, if s s j v 0 is substituted in Eq. Ž1., we first obtain the peak to peak deflection of the beam as: z pp s Ž Fpprk . Q. This deflection can then be linked to the peak to peak resistance variation of the strain gauge Ži.e., Ž D RrR . pp, at f 0 using Eq. Ž2.. Finally the stiffness k is written as: k s Fpp QArŽ D RrR . pp, at f 0 Mass Ž M . and damping Ž D . are then calculated easily in the following way: Ms
Ds
k
Ž 2 P f0 .
3 En In L3
A mass model has also been developed by calculating the reduced mass of the device at the center of the ‘linking arm’. Damping is modeled as the displacement of a plane Žsurface S and thickness T . in the air as: D s mair Ž SrT . with mair s 1.85 = 10y5 kg my1 sy1 being the air dissipation factor. 4.2. Heterogeneous section modeling Previous results are only applicable in the case of a homogeneous beam. As seen above, FSBM structures consist in a heterogeneous stacking of layers. To avoid the use of numerical simulations, the heterogeneous section must be converted into a new shape with an equivalent homogeneous Young’s modulus Ž En .. This is done by normalizing each layer width Ž b i . to the Si 3 N4 Young’s modulus En w3x. The normalized cross-section corresponds to a homogeneous passivation nitride beam with the same mechanical properties as the initial cross-section. The neutral axis of the new section Ž h n . is then a horizontal line crossing the inertial center of the normalized cross-section and the moment of inertia Ž In . writes:
2
k 2 P f0 Q
4. Electromechanical modeling Each structure consists in a heterogeneous stack of various process layers, namely silicon oxides, metals, polysilicon and passivation nitride. The sensing capability of such a device comes from the piezoresistivity of the polysilicon layer. To provide simulation models for designers we have first developed analytical expressions for mechanical parameters Ž k, M and D .. Then, we have defined a homogeneous section, mechanically equivalent to the original one, in order to determine the gauge factor of the polysilicon layer.
.
In s Ý
b i t i3 12
q Si Ž h n y h i .
2
with b i s b = Ž EirEn . and where Si Žs b i t i . represents the area of a given rectangular section in the normalized shape w4x. The moment of inertia is then a function of a single design parameter Žthe width of the beam, b . and few technological parameters Ži.e., thickness and Young’s modulus of each layer.. It is then possible to convert Žin a fully reciprocal way. a strength applied at the extremity of the beam into a vertical displacement. Another useful relation links the bending torque ŽT b ., the moment of inertia and the longitudinal stress Ž s . in a given point Ž x . of the beam as: s Ž x,Õ . s ŽT b xrIn . Õ, where Õ is the vertical distance between the investigated point and the neutral axis of the beam. The corresponding relative elongation of the gauge is then given by: ´ s smeanrEn , where smean is the average stress in the polysilicon layer.
146
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
Normalization process has been performed according to typical Young’s modulus found in the literature w5x. 4.3. Gauge-factor determination Assuming a piezoresistive behavior of polysilicon, the relative change in resistance of gauges is linearly linked to the mechanical stress by a matrix relation. However, in most applications it is not necessary to fully define the piezoresistive tensor. The geometry of the mechanical parts often allows to isolate a given stress direction. In our case w3x, the gauge factor Ž G . is simply defined as the ratio between the strain ´ and the corresponding resistance variation: G s D RrR ´ . From the experimental value of D RrR and the strain magnitude ´ , we can easily calculate the gauge factor for the polysilicon layer w4x. A piezoresistive factor GF of about y15 has been found for the polysilicon layer of the FSBM process under study. This value is in the same range as those published by Seto w6x for boron-doped CVD polysilicon films. Indeed, the latter ranges between 10 and 20 depending on the boron-to-silicon ratio.
5. Analog HDL modeling and simulation To take advantage of the monolithic approach, designers need to simulate the sensing device in a VLSI designer framework. In that way, analog HDL language and subsequent electrical simulators such as Eldo appear as very promising. It is then possible to describe the mechanical behavior of the sensing device and to simulate the sensor as a resistance in an electronic design. We have described the behavior of our test structure as seen above. Model inputs are geometrical dimensions of the device and mechanical parameters such as k, M and D which are easily calculated together with the slope of the electromechanical characteristic vertical deflection vs. resistance variation ŽEq. Ž2... It is then possible to simulate both the dynamic and the static behavior of force sensors. As an example, the polysilicon gauge is placed in a Wheastone bridge and a 5-mN dynamic force is applied. It is then possible for a designer to compare the resonant modes of cantilever beams with various geometries and to use the best device for a given application ŽFig. 5.. The benefit of such an approach is obviously demonstrated by the sensitivity improvement obtained between device S1 that has been designed without model-based optimization and other ones ŽS2 to S4. that have been designed with similar silicon cost Žless than 1 mm2 ., thanks to our simulation model. In Fig. 4, experimental results are also compared with analog HDL simulations for the large cantilever of Fig. 1. Observed mismatches are then the following: –less than 4% for the natural frequency Ž9.54 vs. 9.9 kHz., –about 50% Ž64 vs. 132. for the Q-factor.
Fig. 5. Simulation of natural resonances for several cantilever beams of various dimensions.
The latter demonstrates the main limitation of our analytical model that concerns the damping factor of the device. On one hand, the calculated one is lower than the real one. On the other hand, the experimental behavior demonstrates a strong nonlinearity as the Q-factor increases continuously up to 100 when displacement is reduced. Studies are still under progress concerning that point.
6. Conclusions The use of MEMS is conditioned by several aspects. Among them, the global cost Žboth for technology and products. and reliability Žshort- and long-term. play a major role. Our approach focuses on low-cost MEMS obtained by processing chips issued from an industrial CMOS process. Such a technique allows the implementation of both sensing and electronic parts on the same chip. Integrating the whole conditioningrprocessing chain gives the opportunity of precociously digitizing the analog signal issued from the sensor, thus enhancing the noise immunity of the system. Finally, this technique easily allows the addition of built-in self-test andror on-chip self-calibration facilities. However, the use of a CMOS process implies that the process is neither characterized nor optimized for its sensing capabilities. In this paper, we have presented a complete methodology for the characterization of mechanical sensors obtained by FSBM of a CMOS VLSI wafer. Our approach consists in using an original test structure to determine all mechanical parameters and to verify analytical models. Moreover, the use of analytical formulations allows VLSI designers to implement directly those relations in an electrical simulator such as Eldo. The way is then opened to use electromechanical devices in a standard analog IC design flow.
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
References w1x H. Baltes, IC MEMS Microtransducers, Tech. Digest, IEEE Int. Electron Devices Meet., 1996, pp. 521–524. w2x H. Baltes et al., Thermomechanical microtransducers by CMOS technology combined with micromachining, Micro System Technologies 91 Ž1991. 98–103. w3x S.P. Timoshenko, Strength of Materials, D. Van Nostrand, Princeton, New Jersey. w4x L. Latorre, On the use of test structures for the EM characterization of a CMOS compatible MEMS technology, Proc. ICMTS’98, Vol. 11, March 1998, pp. 177–182. w5x K.E. Petersen, Silicon as mechanical material, Proc. IEEE 70 Ž1982. 420–457. w6x J.Y.W. Seto, Piezoresistive properties of polycrystalline silicon, J. Appl. Phys. 47 Ž11. Ž1976. 4780–4783. Laurent Latorre received the Diplome from l’Ecole Nationale ˆ d’ingenieur ´ d’Ingenieurs de Belfort, France in 1994. He received the Diplome ˆ d’Etudes Approfondies in microelectronics from Montpellier II University, France in 1995. He is preparing for his PhD on microsystems at the LIRMM Microelectronic laboratory. Pascal Nouet received the ‘Maıtrise’ of Electrical Engineering, the ˆ ‘Diplome ˆ d’Etudes Approfondies’ and the PhD in Microelectronics from the University of Montpellier, France, in 1987, 1988 and 1991, respectively. Since 1992, he has been a researcher at LIRMM and an associate professor at the University of Montpellier. His current research interests concern process characterization, interconnection effects in VLSI circuits, analog IC design and monolithic microsystems.
147
Yves Bertrand is a researcher at LIRMM and a professor at the University of Montpellier. He previously worked in the field of solid-state physics and published several papers, especially on the photoemission of semiconductors under synchrotron radiation. He joined the LIRMM in 1988. His research interests are principally Ži. fault modeling, Žii. designfor-test and built-in self-test for digital and mixed-signal analogrdigital integrated circuits and Žiii. design and test of microsystems. He is author or coauthor of more than 100 papers in the field of solid-state physics and microelectronics. He is presently responsible for the CRTC ŽCentre de Ressources en Test du CNFM.. Philippe Hazard received the engineering degree in Microelectronics Technology from the Conservatoire National des Arts et Metier ´ de Paris in 1988. He joined TelemecaniquerSchneider Electric Research Center in ´´ ´ Nanterre in 1985. Currently, he manages R&D projects on microsystems in the field of magnetic field sensors and miscellaneous applications to process control. From 1993 to 1994, he worked on power factor correction circuits dedicated to speed drive for asynchronous motor. From 1985 to 1993 he managed R&D projects on power semiconductor devices. Previously, he worked at Fairchild Research Center in Montrouge on power semiconductors. Francis Pressecq received the engineering degree in Microelectronics from Institut National des Sciences Appliquees ´ in 1987 and graduated from Ecole Nationale Superieure des Telecommunications in Space Sys´ ´´ tem Technology in 1988. From 1989 to 1995 he worked on ASIC test and design at CNES, the French Space Agency. Since 1995, he has managed R&T projects on microsystem technology, mainly concerning reliability and design.
Characterization and modeling of a CMOS-compatible MEMS technology Laurent Latorre a , Pascal Nouet a
a,)
, Yves Bertrand a , Philippe Hazard b, Francis Pressecq
c
LIRMM— UniÕersite´ Montpellier II (UMR CNRS No. 5506), 161 Rue Ada, 34392 Montpellier Cedex, France b Schneider Electric, Nanterre, France c CNES, Quality Assurance Delegation, Toulouse, France
Abstract In this paper we present a new methodology for efficient electromechanical characterization of a CMOS-compatible micro-electro mechanical sensors ŽMEMS. technology. Using an original test structure, the so-called ‘U-shape cantilever beam’, we are able to determine all mechanical characteristics of force sensors constituted with elementary beams in a given technology. A complete set of electromechanical relations that can be used for the design of Microsystems have been also developed. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Mechanical properties; Micro-electromechanical sensors; Front-side bulk micromachining ŽFSBM.; Modeling; Test structures; Simulation
1. Introduction Recent trends in the technology of VLSI CMOS circuits lead both integrated circuit ŽIC. designers and system providers to add more and more functionalities to a single application specific integrated circuit ŽASIC.. In that way, it seems interesting to implement a sensing element directly on the die where electronic parts have been processed w1,2x. Using a CMOS wafer with electronic parts on it, several techniques can be used to implement sensors. Front-side bulk micromachining ŽFSBM. can be associated or not with back-side bulk micromachining ŽBSBM. and sacrificial or extra layer techniques. As the cost of the post-process is strongly affected by the need for alignment, FSBM seems to be a very promising technique due to its selfalignment capability. This technique is largely available in France through CMP service, 1 post-process operates as an anisotropic
)
Corresponding author: Tel.: q33-467-41-85-27; Fax: q33-467-4185-00; E-mail: [email protected] 1 Information is available on the World Wide Web at the following address: http:rrtima-cmp.imag.frrtimarmcsrmcs.html.
silicon etching that uses the various oxide layers as natural mask. ²100: substrate planes can then be etched leaving the ²111: planes of the silicon substrate. Suspended structures such as cantilever beams, bridges or membranes are then obtained. Fabless designers can easily address this technology and low development costs are expected due to the reuse of the same technology for various physical phenomena. However, a CMOS VLSI technology is neither characterized nor optimized for its electromechanical properties. In this paper we present a complete methodology that allows to fully characterize mechanical and electromechanical properties of beams realized in a CMOS process.
2. U-shape cantilever device To characterize both mechanical and electromechanical properties of sensor parts, we have designed an original test structure. The so-called U-shape cantilever device ŽFig. 1. is formed with two parallel cantilever beams that are connected at their free extremity by a ‘linking arm’. Piezoresistive polysilicon strain gauges are located at the clamped end of each cantilever to obtain the best sensitivity to bending stresses. A metal line is also located in the
0924-4247r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 4 5 - 8
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
144
placement z Ž s . is linked to the applied external force F Ž s . by the following transfer function: z Ž s. s
F Ž s . rk M 2 D s q sq1 k k
Ž 1.
This system is characterized by a natural resonance with a quality factor Q at a radian frequency v 0 s krM . This Q-factor is written as: Q s Ž k .rŽ v 0 D .
'
3.1. Static characterization
Fig. 1. SEM photograph of two ‘U-shape’ cantilever beams.
Static characterization is realized by assigning a vertical displacement to the center part of the ‘linking arm’ using a micrometric screw. The vertical force Ž F . is then unknown but can be directly deduced from Eq. Ž1. as: F s kz. Using strain gauges located in both beams, it is also possible to experimentally link the relative gauge resistance variation Žin %. with the vertical displacement ŽFig. 3. as: D RrR s Az.
device in order to implement a current loop flowing through the device.
3. Mechanical modeling Assuming that both beams are identical, the U-shape cantilever is mechanically equivalent to a simple cantilever with a beam width equal to twice the real one. When applying a force or a displacement to the center of the ‘linking arm’, each beam acts as a leaf-spring. If vertical displacement remains low, a mechanical model for this device is a linear second-order mechanical system ŽFig. 2. where k, M and D are the spring constant, the mass and the damping factor respectively. Then, the vertical dis-
Fig. 2. Second-order mechanical model of a ‘U-shape’ cantilever beam.
Ž 2.
The slope A is then an important feature for the electromechanical characterization of the test structure. This parameter includes all relations of strength of materials such as bending torque, moment of inertia, Young’s modulus and also gauge factor of the sensitive layer Ži.e., polysilicon.. 3.2. Dynamic characterization In order to apply a dynamic force in a contactless manner to the U-shape cantilever we use the Lorentz’s force. The device is located in a calibrated static magnetic field Ž Bdc . with the same orientation as both cantilever beams. If an alternative current Ž Iac . is flowing through the device, a force is vertically generated in the ‘linking arm’. The force magnitude can be easily calculated as: Fac s Iac Bdc Larm where Larm is the length of the ‘linking arm’.
Fig. 3. Resistance variations of the polysilicon gauge vs. vertical displacement.
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
145
4.1. CantileÕer beam modeling The behavior of an homogeneous cantilever may be modeled by the vertical deflection of a beam Žlength, L. with an external force F applied at its free end. Using basic mechanical relationships w3x the following equation can be established: z s FL3r3 En In where En and In are respectively the Young’s modulus and the moment of inertia of the beam. Consequently, F and z are linearly dependent as in Eq. Ž1.. The spring constant equivalent coefficient is given as: ks Fig. 4. Dynamic characteristic of a U-shape cantilever beam. Experimental results Žcrosses. are compared with simulated results Žcontinuous line..
A frequency sweep can then be applied to Iac to generate the dynamic characteristic of the mechanical system ŽFig. 4.. Both resonant frequency Ž f 0 . and quality Žor resonant. factor Ž Q . are then experimentally determined. 3.3. Parameter extraction After both characterization steps, it is then possible to determine all the mechanical parameters of the system. First, if s s j v 0 is substituted in Eq. Ž1., we first obtain the peak to peak deflection of the beam as: z pp s Ž Fpprk . Q. This deflection can then be linked to the peak to peak resistance variation of the strain gauge Ži.e., Ž D RrR . pp, at f 0 using Eq. Ž2.. Finally the stiffness k is written as: k s Fpp QArŽ D RrR . pp, at f 0 Mass Ž M . and damping Ž D . are then calculated easily in the following way: Ms
Ds
k
Ž 2 P f0 .
3 En In L3
A mass model has also been developed by calculating the reduced mass of the device at the center of the ‘linking arm’. Damping is modeled as the displacement of a plane Žsurface S and thickness T . in the air as: D s mair Ž SrT . with mair s 1.85 = 10y5 kg my1 sy1 being the air dissipation factor. 4.2. Heterogeneous section modeling Previous results are only applicable in the case of a homogeneous beam. As seen above, FSBM structures consist in a heterogeneous stacking of layers. To avoid the use of numerical simulations, the heterogeneous section must be converted into a new shape with an equivalent homogeneous Young’s modulus Ž En .. This is done by normalizing each layer width Ž b i . to the Si 3 N4 Young’s modulus En w3x. The normalized cross-section corresponds to a homogeneous passivation nitride beam with the same mechanical properties as the initial cross-section. The neutral axis of the new section Ž h n . is then a horizontal line crossing the inertial center of the normalized cross-section and the moment of inertia Ž In . writes:
2
k 2 P f0 Q
4. Electromechanical modeling Each structure consists in a heterogeneous stack of various process layers, namely silicon oxides, metals, polysilicon and passivation nitride. The sensing capability of such a device comes from the piezoresistivity of the polysilicon layer. To provide simulation models for designers we have first developed analytical expressions for mechanical parameters Ž k, M and D .. Then, we have defined a homogeneous section, mechanically equivalent to the original one, in order to determine the gauge factor of the polysilicon layer.
.
In s Ý
b i t i3 12
q Si Ž h n y h i .
2
with b i s b = Ž EirEn . and where Si Žs b i t i . represents the area of a given rectangular section in the normalized shape w4x. The moment of inertia is then a function of a single design parameter Žthe width of the beam, b . and few technological parameters Ži.e., thickness and Young’s modulus of each layer.. It is then possible to convert Žin a fully reciprocal way. a strength applied at the extremity of the beam into a vertical displacement. Another useful relation links the bending torque ŽT b ., the moment of inertia and the longitudinal stress Ž s . in a given point Ž x . of the beam as: s Ž x,Õ . s ŽT b xrIn . Õ, where Õ is the vertical distance between the investigated point and the neutral axis of the beam. The corresponding relative elongation of the gauge is then given by: ´ s smeanrEn , where smean is the average stress in the polysilicon layer.
146
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
Normalization process has been performed according to typical Young’s modulus found in the literature w5x. 4.3. Gauge-factor determination Assuming a piezoresistive behavior of polysilicon, the relative change in resistance of gauges is linearly linked to the mechanical stress by a matrix relation. However, in most applications it is not necessary to fully define the piezoresistive tensor. The geometry of the mechanical parts often allows to isolate a given stress direction. In our case w3x, the gauge factor Ž G . is simply defined as the ratio between the strain ´ and the corresponding resistance variation: G s D RrR ´ . From the experimental value of D RrR and the strain magnitude ´ , we can easily calculate the gauge factor for the polysilicon layer w4x. A piezoresistive factor GF of about y15 has been found for the polysilicon layer of the FSBM process under study. This value is in the same range as those published by Seto w6x for boron-doped CVD polysilicon films. Indeed, the latter ranges between 10 and 20 depending on the boron-to-silicon ratio.
5. Analog HDL modeling and simulation To take advantage of the monolithic approach, designers need to simulate the sensing device in a VLSI designer framework. In that way, analog HDL language and subsequent electrical simulators such as Eldo appear as very promising. It is then possible to describe the mechanical behavior of the sensing device and to simulate the sensor as a resistance in an electronic design. We have described the behavior of our test structure as seen above. Model inputs are geometrical dimensions of the device and mechanical parameters such as k, M and D which are easily calculated together with the slope of the electromechanical characteristic vertical deflection vs. resistance variation ŽEq. Ž2... It is then possible to simulate both the dynamic and the static behavior of force sensors. As an example, the polysilicon gauge is placed in a Wheastone bridge and a 5-mN dynamic force is applied. It is then possible for a designer to compare the resonant modes of cantilever beams with various geometries and to use the best device for a given application ŽFig. 5.. The benefit of such an approach is obviously demonstrated by the sensitivity improvement obtained between device S1 that has been designed without model-based optimization and other ones ŽS2 to S4. that have been designed with similar silicon cost Žless than 1 mm2 ., thanks to our simulation model. In Fig. 4, experimental results are also compared with analog HDL simulations for the large cantilever of Fig. 1. Observed mismatches are then the following: –less than 4% for the natural frequency Ž9.54 vs. 9.9 kHz., –about 50% Ž64 vs. 132. for the Q-factor.
Fig. 5. Simulation of natural resonances for several cantilever beams of various dimensions.
The latter demonstrates the main limitation of our analytical model that concerns the damping factor of the device. On one hand, the calculated one is lower than the real one. On the other hand, the experimental behavior demonstrates a strong nonlinearity as the Q-factor increases continuously up to 100 when displacement is reduced. Studies are still under progress concerning that point.
6. Conclusions The use of MEMS is conditioned by several aspects. Among them, the global cost Žboth for technology and products. and reliability Žshort- and long-term. play a major role. Our approach focuses on low-cost MEMS obtained by processing chips issued from an industrial CMOS process. Such a technique allows the implementation of both sensing and electronic parts on the same chip. Integrating the whole conditioningrprocessing chain gives the opportunity of precociously digitizing the analog signal issued from the sensor, thus enhancing the noise immunity of the system. Finally, this technique easily allows the addition of built-in self-test andror on-chip self-calibration facilities. However, the use of a CMOS process implies that the process is neither characterized nor optimized for its sensing capabilities. In this paper, we have presented a complete methodology for the characterization of mechanical sensors obtained by FSBM of a CMOS VLSI wafer. Our approach consists in using an original test structure to determine all mechanical parameters and to verify analytical models. Moreover, the use of analytical formulations allows VLSI designers to implement directly those relations in an electrical simulator such as Eldo. The way is then opened to use electromechanical devices in a standard analog IC design flow.
L. Latorre et al.r Sensors and Actuators 74 (1999) 143–147
References w1x H. Baltes, IC MEMS Microtransducers, Tech. Digest, IEEE Int. Electron Devices Meet., 1996, pp. 521–524. w2x H. Baltes et al., Thermomechanical microtransducers by CMOS technology combined with micromachining, Micro System Technologies 91 Ž1991. 98–103. w3x S.P. Timoshenko, Strength of Materials, D. Van Nostrand, Princeton, New Jersey. w4x L. Latorre, On the use of test structures for the EM characterization of a CMOS compatible MEMS technology, Proc. ICMTS’98, Vol. 11, March 1998, pp. 177–182. w5x K.E. Petersen, Silicon as mechanical material, Proc. IEEE 70 Ž1982. 420–457. w6x J.Y.W. Seto, Piezoresistive properties of polycrystalline silicon, J. Appl. Phys. 47 Ž11. Ž1976. 4780–4783. Laurent Latorre received the Diplome from l’Ecole Nationale ˆ d’ingenieur ´ d’Ingenieurs de Belfort, France in 1994. He received the Diplome ˆ d’Etudes Approfondies in microelectronics from Montpellier II University, France in 1995. He is preparing for his PhD on microsystems at the LIRMM Microelectronic laboratory. Pascal Nouet received the ‘Maıtrise’ of Electrical Engineering, the ˆ ‘Diplome ˆ d’Etudes Approfondies’ and the PhD in Microelectronics from the University of Montpellier, France, in 1987, 1988 and 1991, respectively. Since 1992, he has been a researcher at LIRMM and an associate professor at the University of Montpellier. His current research interests concern process characterization, interconnection effects in VLSI circuits, analog IC design and monolithic microsystems.
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Yves Bertrand is a researcher at LIRMM and a professor at the University of Montpellier. He previously worked in the field of solid-state physics and published several papers, especially on the photoemission of semiconductors under synchrotron radiation. He joined the LIRMM in 1988. His research interests are principally Ži. fault modeling, Žii. designfor-test and built-in self-test for digital and mixed-signal analogrdigital integrated circuits and Žiii. design and test of microsystems. He is author or coauthor of more than 100 papers in the field of solid-state physics and microelectronics. He is presently responsible for the CRTC ŽCentre de Ressources en Test du CNFM.. Philippe Hazard received the engineering degree in Microelectronics Technology from the Conservatoire National des Arts et Metier ´ de Paris in 1988. He joined TelemecaniquerSchneider Electric Research Center in ´´ ´ Nanterre in 1985. Currently, he manages R&D projects on microsystems in the field of magnetic field sensors and miscellaneous applications to process control. From 1993 to 1994, he worked on power factor correction circuits dedicated to speed drive for asynchronous motor. From 1985 to 1993 he managed R&D projects on power semiconductor devices. Previously, he worked at Fairchild Research Center in Montrouge on power semiconductors. Francis Pressecq received the engineering degree in Microelectronics from Institut National des Sciences Appliquees ´ in 1987 and graduated from Ecole Nationale Superieure des Telecommunications in Space Sys´ ´´ tem Technology in 1988. From 1989 to 1995 he worked on ASIC test and design at CNES, the French Space Agency. Since 1995, he has managed R&T projects on microsystem technology, mainly concerning reliability and design.