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A simple lumped electrical model for an RF MEMS switch considering lossy substrate effects
Sensors and Actuators A 123–124 (2005) 515–521
A simple lumped electrical model for an RF MEMS switch considering lossy substrate effects Giuseppe Cusmai a,∗ , Marco Mazzini a,1 , Paolo Rossi a,2 , Chantal Combi b , Benedetto Vigna b , Francesco Svelto a a
Dipartimento di Elettronica, Universit`a degli Studi di Pavia, via Ferrata 1, 27100 Pavia, Italy b STMicroelectronics, Milan, Italy Received 7 September 2004; received in revised form 4 April 2005; accepted 8 April 2005 Available online 31 May 2005
Abstract This work focuses on electrostatically actuated micro-electro-mechanical systems (MEMS) capacitive switches, intended for adaptive output stage of power amplifiers. These devices are particularly attractive because theoretically they are capable of very high quality factor values due to the air gap between plates and the low resistivity of lines and bridge. On the other hand, substrate parasitic effects, overlooked up to date, can seriously impair device performance. In this paper, we introduce a lumped element equivalent circuit taking into account substrate effects. Model validation is based on measurements carried out in the 50 MHz–40 GHz range. © 2005 Elsevier B.V. All rights reserved. Keywords: RF MEMS; Switches; Radio frequency; Micromachining; Substrate effects; Quality factor; Electrical model; Equivalent circuit
1. Introduction Over the last decades, micro-electro-mechanical system (MEMS) technologies have become very popular in the sensors area, where devices such as accelerometers and microactuators are attractive in integrated fashion for large scale production. By combining mechanical and electrical domains, MEMS for RF applications allow the realization of high performance filters and switches [1]. Fig. 1 shows the block diagram of a typical receiver for wireless applications. MEMS lend themselves to realize the circuits depicted in gray, leading to high performance, fully integrated solutions [2,3]. In particular, antenna switches would benefit due ∗
Corresponding author. Tel.: +39 0382 985 227; fax: +39 0382 422 583. E-mail addresses: [email protected] (G. Cusmai), [email protected] (M. Mazzini), [email protected] (P. Rossi), [email protected] (C. Combi), [email protected] (B. Vigna), [email protected] (F. Svelto). URL: http://microlab.unipv.it/. 1 Present address: CE Consulting, Milan, Italy. 2 Present address: Maxim Integrated Products, Rozzano (Milan), Italy. 0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.04.011
to the high RX-TX reverse isolation. LC voltage controlled oscillators with MEMS suspended inductors would lead to excellent power–noise ratio. Mixers can be obtained with MEMS switches operating at RF [4]. On the other hand, penetration in the market of such devices is still low due to several issues, e.g. packaging (hermetic solutions are required) and reliability [5–8]. The research activity is nonetheless very intensive and several prototypes with excellent performance were demonstrated. This work focuses on electrostatically actuated MEMS capacitive switches, intended for adaptive output stage of power amplifiers. The tuning capabilities of MEMS capacitors allow optimum matching in various frequency bands, leading to fully integrated, easily reconfigurable solutions. The quality factor required to matching components for efficient power amplifiers is much higher than available in fully integrated CMOS or BiCMOS solutions (MOS and P–N varactors). In fact, passive components represent one of the major bottlenecks in the development of efficient radio frequency circuits, especially at several GHz. MEMS tunable capacitors are theoretically capable of very high quality factors due to
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Fig. 1. Block diagram of a MEMS based RF receiver. The passive components suitable for MEMS implementation are depicted in gray blocks.
the air gap between plates and the low resistivity of lines and bridge. Moreover, the electrostatic actuation provides a large capacitance variation (up to 1:30) with virtually no power consumption [9]. Mechanical aspects usually draw designer attention [10], whereas accurate electrical description at radio frequency lacks. In particular, available models fail to predict the quality factor at frequencies of major interest for RF application (i.e. 1–10 GHz). This paper proposes a novel lumped electrical model, focusing the attention on substrate parasitic effects.
2. Device and process description The metallic variable capacitor, shown in Fig. 2, is realized in a dedicated RF micromachined process and consists of a membrane, the movable electrode of evapo-
rated nickel 1 m thick, suspended by springs of galvanic nickel 15 m thick, on top of a gold transmission line in coplanar waveguide (CPW) in 50 configuration (ground/waveguide/ground = 67/100/67 m). Ten micrometer diameter holes are mandatory to remove the copper sacrificial layer for membrane release. Silicon nitride is deposited as dielectric layer on top of the transmission line, the fixed electrode. The spring configuration was optimized to minimize the thermal drift while obtaining a spring constant of about 30 N/m, leading to an expected mechanical resonance frequency of about 30 kHz. Optimization has been carried out by means of mechanical simulator ANSYS. The overlapping area of the capacitor electrodes is about 100 m × 100 m, resulting in an estimated capacitance of 43 fF in the “off” or not-actuated state and in 3 pF in the “on” or actuated state. The device is fabricated on a 6 in. wafer using a 5 mask process. Fig. 3 shows technological steps. A thermal silicon dioxide is grown on a high resistivity silicon wafer in order to isolate the switches. The high resistive substrate (5 k/cm) is mandatory to reduce electromagnetic losses. The fabrication process starts with the Au metal definition to realize the thin transmission line in CPW configuration and the bonding pads (Fig. 3a). A 200-nm PECVD silicon nitride layer is deposited and patterned in the active area of the devices only (Fig. 3b). The sacrificial layer consists of evaporated Cu, 2 m thick (Fig. 3c). The subsequent planarization to smooth the underneath topography is not compulsory. The evaporation of 1 m of Ni realizes the thin moveable membrane, while the structuring of the Cu sacrificial layer by wet etching is necessary to realize the anchors of the suspended structures (Fig. 3d). The thick Ni springs are realized with an electroplating growth whereas a galvanic growth realizes the thick Au transmission
Fig. 2. Photomicrograph of the capacitive switch.
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Fig. 4. Classical electrical T-model for an RF MEMS switch. The horizontal branches take the lines into account, while the vertical branch represents the suspended membrane.
of the suspended membrane. The series resonance of this element is usually in the 10–100 GHz range and it depends on the actuation state. The horizontal branches represent the 50 impedance matched coplanar waveguide (Zline ). With good approximation, this impedance can be replaced by its series resistance (RS ) and inductance (LS ), leading to a simpler description [10]. Nevertheless, this model fails to predict the quality factor, especially in the 1–10 GHz range, where most commercial standards of radio communications are concentrated. Fig. 5 illustrates the qualitative behavior of Q versus frequency based on the classical T-model (QT-model ), according to the following definition: Q=−
Im(z11 ) Re(z11 )
(1)
where z11 = RS + jωL +
Fig. 3. Process steps: (a) definition of the thin T-line in CPW configuration (Au), (b) deposition of the dielectric layer (Six Ny ), (c) smoothed sacrificial layer (Cu), (d) evaporation of the moveable membrane (Ni) and structuring of the sacrificial layer and (e) definition of suspension springs (Ni) and thick T-line (Au), followed by membrane release.
1 +R jωC
(2)
Assuming fixed series parasitic resistors only results in a monotonic decrease of Q according to the frequency dependence of the capacitor reactance. In this case, the device losses are due to the resistance of lines and bridge only. Actually, experiments do not confirm this behavior [11,12]. On the contrary, Q as a function of frequency starts growing linearly, achieving a maximum value and then decreasing to 0 (curve
line (Fig. 3e). Finally, to release the suspended membrane, a wet etch of the Cu layer is performed.
3. Quality factor modelling Isolation and insertion loss are usually quoted to assess the performance of RF MEMS capacitive switches in the “on” and “off” states, respectively. The well-known lumped element electrical T-model [9], reported in Fig. 4, describes both parameters from dc up to tens of GHz. The vertical branch includes the effective variable capacitor and the series parasitics
Fig. 5. Experimental and classical T-model quality factors vs. frequency. The model does not explain experiments.
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Fig. 6. Switch cross-section highlighting substrate parasitics. COx-Si and COx-gnd are oxide capacitors, and CSi and RSi are capacitor and resistor through substrate.
QExper in the figure) [12]. The T-model of Fig. 4 is inadequate to describe the quality factor at RF because it does not take into account substrate effects, highlighted in Fig. 6, where a cross-section of the device is reported. Equivalent quantities taking into account substrate parasitics can now be expressed in terms of the parameters in Fig. 6, as follows: Cox =
2COx-gnd COx-sig 2COx-gnd + COx-sig
1 RSi 2 = 2CSi
(3)
Fig. 8. Qualitative behavior of Q vs. frequency. The combined effect of series and shunt losses determine the quality factor.
shunt losses, while at high frequency, the effect of the series parasitics Rseries = R + RS increases, finally becoming dominant. Based on this new, complete model, we can define Qseries and Qshunt , i.e. the quality factors due to series and shunt parasitics, respectively. Neglecting inductive parasitics and the capacitive effects of substrate, dominant for f fpole , these parameters are given by:
Rsub =
(4)
Qshunt (ω) = ωCRsub
Csub
(5)
Qseries (ω) =
Fig. 7 reports the complete lumped equivalent circuit, where a parallel branch, taking into account the substrate path from signal to ground, is added. The parallel branch impedance is characterized by a zero at frequency: fzero =
1 2π(Cox + Csub )Rsub 1 2πCsub Rsub
1 ωCRseries
(9)
The resulting switch quality factor (QSW ) is: QSW (ω) = Qshunt //Qseries =
ωCRsub 1 + ω2 C2 Rsub Rseries
(10)
(6)
A qualitative behavior for QSW is reported in Fig. 8. The frequency where QSW achieves the peak value (ωp ) is given by:
(7)
ωp =
and a pole located at: fpole =
(8)
In the frequency range between pole and zero, i.e. fzero < f < fpole , the substrate resistor shunts the MEMS capacitor. Overall losses of the device can now be looked at as the joint effect of series and shunt resistors. At low frequency (but greater than fzero ), the quality factor is determined by
1 C2 R
sub Rseries
with a corresponding quality factor: Rsub 1 Qp = QSW (ωp ) = 2 Rseries
(11)
(12)
This equation shows how a low value of the equivalent resistance Rsub impairs the achievable quality factor. Increasing the substrate resistivity and the distance between lines are both effective ways to increase the device Q. 4. Measurements
Fig. 7. Lumped electrical model of an RF MEMS switch taking into account substrate parasitics.
Capacitance versus actuation voltage measurements were carried out by means of a HP 4284A LCR meter. A dc voltage is imposed to the signal line to vary the height of the top electrode: the capacitance versus actuation voltage, reported in Fig. 9, changes from 70 fF to 1.85 pF. Deviation from predicted values are due to buckling (“off” state) and
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Table 1 The lumped circuit component values (see Fig. 7) used to generate the fitting curves in Fig. 10
Fig. 9. Measured capacitance of the RF MEMS switch vs. actuation voltage. Arrows indicate different voltage sweep directions. Device mechanical properties lead to an hysteretic behavior.
surface roughness (“on” state). The analog characteristic at low voltages and the hysteretic behavior confirm theoretical analyses. The pull-in voltage is 20 V. The radio frequency characteristics are measured by means of a Cascade probe station and a HP 8722D network analyzer (50 MHz–40 GHz). The quality factor is evaluated in both states according to Eq. (1). Actually, scattering parameters only are directly provided by the analyzer, requiring a numerical conversion from S to Z, according to: [Z] =
1 1 − s11 − s22 − (S) 1 + s11 − s22 − (S) 2s12 × 2s21 1 − s11 + s22 − (S) (13)
where (S) is the determinant of the S matrix. Eq. (13) is normalized with respect to the characteristic impedance of the network. The resulting quality factors are reported in Fig. 10 from dc to self-resonance frequency. According to the new model, curves show non-monotonic behaviors. Note that the quality factor reaches zero at the self-resonance frequency, where
Parameter
Value
C L (pH) R (m) RS (m) LS (pH) COx (pF) Rsub (k) Csub (fF)
70 fF “off”–1.8 pF “on” 170 275 275 80 1.8 1.4 150
the bridge impedance reduces to a pure resistance. At higher frequency, the quality factor is negative due to the change in the imaginary part of z11 .
5. Model validation Several measurements have been performed in order to evaluate the components of the model depicted in Fig. 7. Given the capacitance C, measured by an LCR meter, the membrane inductance L has been derived from the electrical resonance frequency (around 9 GHz in the “on” state and 28 GHz in the “off” state), evaluated directly from |S21 | [9]. The line resistance RS has been obtained through low frequency measurements and modified to take into account the high frequency increase due to skin effect (an average value at 10 GHz has been adopted for the model). Substrate parasitic components have not been measured directly. COx-gnd and COx-sig have been calculated as plane plates capacitors. Note their values do not impact the quality factor at RF for Rsub in the k range. Based on process parameters and geometrical values, 150 fF for Csub is estimated. Rsub , playing a key role to determine Q, is derived as 1.4 k through fitting. This value is in good agreement with estimation. Note that the fitting curves, derived from simulations on the above measured parameters and based on the equivalent circuit of Fig. 7, differ only for the value of the capacitance (70 fF or 1.8 pF). No other parameter is expected to change in the two configurations. In the “on” state, the measured curve is fitted very accurately. In the “off” state, the discrepancy is attributed to the measuring setup and to other capacitive and inductive parasitic elements, not considered in the model and affecting the quality factor especially at high frequency Table 1. Finally, Table 2 gives further insights derived from measurements: the slope of Q at low frequency changes Table 2 Comparisons between measured and predicted values for Qp , fp and State
∂Q ∂f Low-freq(1GHz)
“On” Fig. 10. Measured quality factors for both states and model validation. The value of the air gap capacitance only is changed to fit the quality factor in both states.
Measurements 16 Model 17
(GHz)
Qp
∂Q ∂f
fp (GHz)
“Off” “On” “Off” “On” “Off” 1.4 2.3
26 27
25 24
3.1 2.5
18 17.5
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with capacitance, according to Eq. (8). The peak value of Q is almost independent of C, as predicted by Eq. (12). The frequency at which the peak occurs changes according to Eq. (11). Inaccuracies for the “off” (high frequency) state is attributed to inductive elements, present in the fitting model, but ignored in the theoretical equations of Section 3.
[11] Th.G.S.M. Rijks, J.T.M. van Beek, P.G. Steeneken, M.J.E. Ulenaers, J. De Coster, R. Puers, RF MEMS tunable capacitors with large tuning ratio, in: International Conference on MEMS, January 2004, pp. 777–780. [12] A.B.M. Jansman, J.T.M. van Beek, M.H.W.M. van Delden, A.L.A.M. Kemmeren, A. den Dekker, F.P. Widdershoven, Elimination of accumulation charge effects for high-resistive silicon substrates, Digest European Solid-State Device Research (ESSDERC), Estoril, Portugal, September 2003, pp. 16–18.
6. Conclusions Biographies This paper proposes a lumped element electrical model for MEMS switches able to describe the quality factor in a wide frequency range. The detrimental effect of the substrate of MEMS switches is discussed in this paper for the first time. A lumped equivalent model, validated in the 50 MHz–40 GHz range, has been introduced. We believe this will constitute a valuable tool for designers of RF integrated receivers based on MEMS technology.
Acknowledgments The authors would like to thank T. Lisec and the ISITFraunhofer Institute team for fruitful discussions and technology access.
References [1] L. Dussopt, G.M. Rebeiz, Intermodulation distortion and power handling in RF MEMS switches, varactors, and tunable filters, IEEE Trans. Microw. Theory Tech. 51 (April (4)) (2003) 1247–1256. [2] C.T.-C. Nguyen, Micromechanical circuits for communication transceivers, in: Proceedings of the Bipolar/BiCMOS Circuits and Technology Meeting (BCTM), 24–26 September, 2000, pp. 142–149. [3] C.T.-C. Nguyen, RF MEMS for wireless applications, in: Device Research Conference, 2002 60th DRC Conference Digest, 24–26 June, 2002, pp. 9–12. [4] C.T.-C. Nguyen, Transceiver front-end architectures using vibrating micromechanical signal processors silicon monolithic integrated circuits in RF systems, in: Digest of Papers. 2001 Topical Meeting on, 12–14 September, 2001, pp. 23–32. [5] A. Margomenos, L.P.B. Katehi, Fabrication and accelerated hermeticity testing of an on-wafer package for RF MEMS, IEEE Trans. Microw. Theory Tech. 52 (June (6)) (2004) 1626–1636. [6] J. DeNatale, R. Mihailovich, RF MEMS reliability, in: 12th International Conference on TRANSDUCERS, Solid-State Sensors, Actuators and Microsystems, vol. 2, 8–12 June, 2003, pp. 943–946. [7] D. Peroulis, S.P. Pacheco, L.P.B. Katehi, RF MEMS switches with enhanced power-handling capabilities, IEEE Trans. Microw. Theory Tech. 52 (January (1)) (2004) 59–68. [8] G.M. Rebeiz, RF MEMS switches: status of the technology, 12th International Conference on TRANSDUCERS, Solid-State Sensors, Actuators and Microsystems, vol. 2, 8–12 June 2003, pp. 1726–1729. [9] J.B. Muldavin, G.M. Rebeiz, High isolation CPW MEMS shunt switches—Part 1: modeling, IEEE Trans. Microw. Theory Tech. 48 (June (6)) (2000) 1045–1052. [10] J.B. Muldavin, G.M. Rebeiz, Nonlinear electro-mechanical modeling of MEMS switches, Microwave Symposium Digest, IEEE MTTInternational, vol. 3, 20–25 May 2001, pp. 2119–2122.
Giuseppe Cusmai was born in Pavia, Italy in 1978. He graduated in electrical engineering from the University of Pavia, Italy in 2003, with a final project activity concerning the design of CMOS oscillators for optical communications receivers. He is currently a PhD student in electronics at the University of Pavia. Main interests include wireless receivers for RF applications and high quality factor RF MEMS devices. The research activity is focused on the design of a CMOS front-end for Ultra-WideBand applications. Marco Mazzini graduated from the University of Pavia, Italy, in electronic engineering in 2004, with a degree thesis concerning the applications of RF MEMS devices. Currently, he is working as a consultant for CEC, an italian society dealing with innovation technology. Paolo Rossi was born in Milan, Italy, in 1975. He received the Laurea degree (summa cum laude) and the Ph.D. degree in electrical engineering and computer science from the University of Pavia, Pavia, Italy, in 2000 and 2004, respectively. During his studies, he worked on CMOS and BiCMOS RF front-end circuits for wireless transceivers, with particular focus on the analysis and design of LNAs and mixers for multistandard applications. He is currently with Maxim Integrated Products (Standard Products Business Unit), Rozzano, Italy. Chantal Combi received her degree in subnuclear physics from University of Milan in 1998. Meanwhile, she worked at CERN (Geneve-CH) on the electrical and noise characterization of the silicon vertex-detectors, in 1998, she joined STMicroelectronics R&D Laboratories, Italy. She started to work on test structures to characterize the structural and sacrificial layers for MEMS. In the last five years, she contributed to develop the design of RF MEMS for telecommunication systems: switch, varcap, resonator and filters, high Q inductors and RF package at wafer level. She was involved in the MELODICT project on the integration of RF MEMS passives in the mobile phone and nowadays in other European project on RF MEMS. She has made some patents on RF MEMS devices. Benedetto Vigna was born in Potenza, Italy, in 1969. He received his degree in subnuclear physics from University of Pisa in 1993. After two years of cooperation with European Synchrotron Radiation Facility in Grenoble and Max Planck Institute on X-ray laser, in 1995, he joined STMicroelectronics Research and Development Laboratory in Castelletto, Italy. He was the pioneer of micromachining activity in STMicroelectronics and now he is the general manager of MEMS Development Unit in ST. His research program has concentrated on micro-electro-mechanical systems and include merged circuit/micromechanical technologies and integrated accelerometers, gyroscopes and microactuators for Consumer and Automotive markets. His current interests are in the field of biochips and micromachined devices for radio-frequency applications. He has filed a lot of patents on micromachining field and he has some publications on this field. He belongs also to the Scientific Committee of IMST Workshop and DTIP Conference. Francesco Svelto received the Laurea and PhD degrees in electrical engineering from the University of Pavia, Pavia, Italy, in 1991 and 1995, respectively. From 1996 to 1997, he held a grant from STMicroelectronics to design CMOS RF circuits. In 1997, he was appointed assistant
G. Cusmai et al. / Sensors and Actuators A 123–124 (2005) 515–521 professor at the University of Bergamo, Italy, and in 2000, he joined the University of Pavia, where he is an associate professor. His current research interests are in the field of RF design and high frequency integrated circuits for telecommunications. Dr. Svelto has been a member of the technical program committee of the IEEE Custom Integrated Circuits
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Conference since 2000 and the Bipolar/BiCMOS Circuits and Technology Meeting (BCTM) since 2003, and the European Solid State Circuits Conference in 2002. He served as guest editor of the March 2003 special issue of the IEEE Journal of Solid-State Circuits, of which he is currently an associate editor.
A simple lumped electrical model for an RF MEMS switch considering lossy substrate effects Giuseppe Cusmai a,∗ , Marco Mazzini a,1 , Paolo Rossi a,2 , Chantal Combi b , Benedetto Vigna b , Francesco Svelto a a
Dipartimento di Elettronica, Universit`a degli Studi di Pavia, via Ferrata 1, 27100 Pavia, Italy b STMicroelectronics, Milan, Italy Received 7 September 2004; received in revised form 4 April 2005; accepted 8 April 2005 Available online 31 May 2005
Abstract This work focuses on electrostatically actuated micro-electro-mechanical systems (MEMS) capacitive switches, intended for adaptive output stage of power amplifiers. These devices are particularly attractive because theoretically they are capable of very high quality factor values due to the air gap between plates and the low resistivity of lines and bridge. On the other hand, substrate parasitic effects, overlooked up to date, can seriously impair device performance. In this paper, we introduce a lumped element equivalent circuit taking into account substrate effects. Model validation is based on measurements carried out in the 50 MHz–40 GHz range. © 2005 Elsevier B.V. All rights reserved. Keywords: RF MEMS; Switches; Radio frequency; Micromachining; Substrate effects; Quality factor; Electrical model; Equivalent circuit
1. Introduction Over the last decades, micro-electro-mechanical system (MEMS) technologies have become very popular in the sensors area, where devices such as accelerometers and microactuators are attractive in integrated fashion for large scale production. By combining mechanical and electrical domains, MEMS for RF applications allow the realization of high performance filters and switches [1]. Fig. 1 shows the block diagram of a typical receiver for wireless applications. MEMS lend themselves to realize the circuits depicted in gray, leading to high performance, fully integrated solutions [2,3]. In particular, antenna switches would benefit due ∗
Corresponding author. Tel.: +39 0382 985 227; fax: +39 0382 422 583. E-mail addresses: [email protected] (G. Cusmai), [email protected] (M. Mazzini), [email protected] (P. Rossi), [email protected] (C. Combi), [email protected] (B. Vigna), [email protected] (F. Svelto). URL: http://microlab.unipv.it/. 1 Present address: CE Consulting, Milan, Italy. 2 Present address: Maxim Integrated Products, Rozzano (Milan), Italy. 0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.04.011
to the high RX-TX reverse isolation. LC voltage controlled oscillators with MEMS suspended inductors would lead to excellent power–noise ratio. Mixers can be obtained with MEMS switches operating at RF [4]. On the other hand, penetration in the market of such devices is still low due to several issues, e.g. packaging (hermetic solutions are required) and reliability [5–8]. The research activity is nonetheless very intensive and several prototypes with excellent performance were demonstrated. This work focuses on electrostatically actuated MEMS capacitive switches, intended for adaptive output stage of power amplifiers. The tuning capabilities of MEMS capacitors allow optimum matching in various frequency bands, leading to fully integrated, easily reconfigurable solutions. The quality factor required to matching components for efficient power amplifiers is much higher than available in fully integrated CMOS or BiCMOS solutions (MOS and P–N varactors). In fact, passive components represent one of the major bottlenecks in the development of efficient radio frequency circuits, especially at several GHz. MEMS tunable capacitors are theoretically capable of very high quality factors due to
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Fig. 1. Block diagram of a MEMS based RF receiver. The passive components suitable for MEMS implementation are depicted in gray blocks.
the air gap between plates and the low resistivity of lines and bridge. Moreover, the electrostatic actuation provides a large capacitance variation (up to 1:30) with virtually no power consumption [9]. Mechanical aspects usually draw designer attention [10], whereas accurate electrical description at radio frequency lacks. In particular, available models fail to predict the quality factor at frequencies of major interest for RF application (i.e. 1–10 GHz). This paper proposes a novel lumped electrical model, focusing the attention on substrate parasitic effects.
2. Device and process description The metallic variable capacitor, shown in Fig. 2, is realized in a dedicated RF micromachined process and consists of a membrane, the movable electrode of evapo-
rated nickel 1 m thick, suspended by springs of galvanic nickel 15 m thick, on top of a gold transmission line in coplanar waveguide (CPW) in 50 configuration (ground/waveguide/ground = 67/100/67 m). Ten micrometer diameter holes are mandatory to remove the copper sacrificial layer for membrane release. Silicon nitride is deposited as dielectric layer on top of the transmission line, the fixed electrode. The spring configuration was optimized to minimize the thermal drift while obtaining a spring constant of about 30 N/m, leading to an expected mechanical resonance frequency of about 30 kHz. Optimization has been carried out by means of mechanical simulator ANSYS. The overlapping area of the capacitor electrodes is about 100 m × 100 m, resulting in an estimated capacitance of 43 fF in the “off” or not-actuated state and in 3 pF in the “on” or actuated state. The device is fabricated on a 6 in. wafer using a 5 mask process. Fig. 3 shows technological steps. A thermal silicon dioxide is grown on a high resistivity silicon wafer in order to isolate the switches. The high resistive substrate (5 k/cm) is mandatory to reduce electromagnetic losses. The fabrication process starts with the Au metal definition to realize the thin transmission line in CPW configuration and the bonding pads (Fig. 3a). A 200-nm PECVD silicon nitride layer is deposited and patterned in the active area of the devices only (Fig. 3b). The sacrificial layer consists of evaporated Cu, 2 m thick (Fig. 3c). The subsequent planarization to smooth the underneath topography is not compulsory. The evaporation of 1 m of Ni realizes the thin moveable membrane, while the structuring of the Cu sacrificial layer by wet etching is necessary to realize the anchors of the suspended structures (Fig. 3d). The thick Ni springs are realized with an electroplating growth whereas a galvanic growth realizes the thick Au transmission
Fig. 2. Photomicrograph of the capacitive switch.
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Fig. 4. Classical electrical T-model for an RF MEMS switch. The horizontal branches take the lines into account, while the vertical branch represents the suspended membrane.
of the suspended membrane. The series resonance of this element is usually in the 10–100 GHz range and it depends on the actuation state. The horizontal branches represent the 50 impedance matched coplanar waveguide (Zline ). With good approximation, this impedance can be replaced by its series resistance (RS ) and inductance (LS ), leading to a simpler description [10]. Nevertheless, this model fails to predict the quality factor, especially in the 1–10 GHz range, where most commercial standards of radio communications are concentrated. Fig. 5 illustrates the qualitative behavior of Q versus frequency based on the classical T-model (QT-model ), according to the following definition: Q=−
Im(z11 ) Re(z11 )
(1)
where z11 = RS + jωL +
Fig. 3. Process steps: (a) definition of the thin T-line in CPW configuration (Au), (b) deposition of the dielectric layer (Six Ny ), (c) smoothed sacrificial layer (Cu), (d) evaporation of the moveable membrane (Ni) and structuring of the sacrificial layer and (e) definition of suspension springs (Ni) and thick T-line (Au), followed by membrane release.
1 +R jωC
(2)
Assuming fixed series parasitic resistors only results in a monotonic decrease of Q according to the frequency dependence of the capacitor reactance. In this case, the device losses are due to the resistance of lines and bridge only. Actually, experiments do not confirm this behavior [11,12]. On the contrary, Q as a function of frequency starts growing linearly, achieving a maximum value and then decreasing to 0 (curve
line (Fig. 3e). Finally, to release the suspended membrane, a wet etch of the Cu layer is performed.
3. Quality factor modelling Isolation and insertion loss are usually quoted to assess the performance of RF MEMS capacitive switches in the “on” and “off” states, respectively. The well-known lumped element electrical T-model [9], reported in Fig. 4, describes both parameters from dc up to tens of GHz. The vertical branch includes the effective variable capacitor and the series parasitics
Fig. 5. Experimental and classical T-model quality factors vs. frequency. The model does not explain experiments.
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Fig. 6. Switch cross-section highlighting substrate parasitics. COx-Si and COx-gnd are oxide capacitors, and CSi and RSi are capacitor and resistor through substrate.
QExper in the figure) [12]. The T-model of Fig. 4 is inadequate to describe the quality factor at RF because it does not take into account substrate effects, highlighted in Fig. 6, where a cross-section of the device is reported. Equivalent quantities taking into account substrate parasitics can now be expressed in terms of the parameters in Fig. 6, as follows: Cox =
2COx-gnd COx-sig 2COx-gnd + COx-sig
1 RSi 2 = 2CSi
(3)
Fig. 8. Qualitative behavior of Q vs. frequency. The combined effect of series and shunt losses determine the quality factor.
shunt losses, while at high frequency, the effect of the series parasitics Rseries = R + RS increases, finally becoming dominant. Based on this new, complete model, we can define Qseries and Qshunt , i.e. the quality factors due to series and shunt parasitics, respectively. Neglecting inductive parasitics and the capacitive effects of substrate, dominant for f fpole , these parameters are given by:
Rsub =
(4)
Qshunt (ω) = ωCRsub
Csub
(5)
Qseries (ω) =
Fig. 7 reports the complete lumped equivalent circuit, where a parallel branch, taking into account the substrate path from signal to ground, is added. The parallel branch impedance is characterized by a zero at frequency: fzero =
1 2π(Cox + Csub )Rsub 1 2πCsub Rsub
1 ωCRseries
(9)
The resulting switch quality factor (QSW ) is: QSW (ω) = Qshunt //Qseries =
ωCRsub 1 + ω2 C2 Rsub Rseries
(10)
(6)
A qualitative behavior for QSW is reported in Fig. 8. The frequency where QSW achieves the peak value (ωp ) is given by:
(7)
ωp =
and a pole located at: fpole =
(8)
In the frequency range between pole and zero, i.e. fzero < f < fpole , the substrate resistor shunts the MEMS capacitor. Overall losses of the device can now be looked at as the joint effect of series and shunt resistors. At low frequency (but greater than fzero ), the quality factor is determined by
1 C2 R
sub Rseries
with a corresponding quality factor: Rsub 1 Qp = QSW (ωp ) = 2 Rseries
(11)
(12)
This equation shows how a low value of the equivalent resistance Rsub impairs the achievable quality factor. Increasing the substrate resistivity and the distance between lines are both effective ways to increase the device Q. 4. Measurements
Fig. 7. Lumped electrical model of an RF MEMS switch taking into account substrate parasitics.
Capacitance versus actuation voltage measurements were carried out by means of a HP 4284A LCR meter. A dc voltage is imposed to the signal line to vary the height of the top electrode: the capacitance versus actuation voltage, reported in Fig. 9, changes from 70 fF to 1.85 pF. Deviation from predicted values are due to buckling (“off” state) and
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Table 1 The lumped circuit component values (see Fig. 7) used to generate the fitting curves in Fig. 10
Fig. 9. Measured capacitance of the RF MEMS switch vs. actuation voltage. Arrows indicate different voltage sweep directions. Device mechanical properties lead to an hysteretic behavior.
surface roughness (“on” state). The analog characteristic at low voltages and the hysteretic behavior confirm theoretical analyses. The pull-in voltage is 20 V. The radio frequency characteristics are measured by means of a Cascade probe station and a HP 8722D network analyzer (50 MHz–40 GHz). The quality factor is evaluated in both states according to Eq. (1). Actually, scattering parameters only are directly provided by the analyzer, requiring a numerical conversion from S to Z, according to: [Z] =
1 1 − s11 − s22 − (S) 1 + s11 − s22 − (S) 2s12 × 2s21 1 − s11 + s22 − (S) (13)
where (S) is the determinant of the S matrix. Eq. (13) is normalized with respect to the characteristic impedance of the network. The resulting quality factors are reported in Fig. 10 from dc to self-resonance frequency. According to the new model, curves show non-monotonic behaviors. Note that the quality factor reaches zero at the self-resonance frequency, where
Parameter
Value
C L (pH) R (m) RS (m) LS (pH) COx (pF) Rsub (k) Csub (fF)
70 fF “off”–1.8 pF “on” 170 275 275 80 1.8 1.4 150
the bridge impedance reduces to a pure resistance. At higher frequency, the quality factor is negative due to the change in the imaginary part of z11 .
5. Model validation Several measurements have been performed in order to evaluate the components of the model depicted in Fig. 7. Given the capacitance C, measured by an LCR meter, the membrane inductance L has been derived from the electrical resonance frequency (around 9 GHz in the “on” state and 28 GHz in the “off” state), evaluated directly from |S21 | [9]. The line resistance RS has been obtained through low frequency measurements and modified to take into account the high frequency increase due to skin effect (an average value at 10 GHz has been adopted for the model). Substrate parasitic components have not been measured directly. COx-gnd and COx-sig have been calculated as plane plates capacitors. Note their values do not impact the quality factor at RF for Rsub in the k range. Based on process parameters and geometrical values, 150 fF for Csub is estimated. Rsub , playing a key role to determine Q, is derived as 1.4 k through fitting. This value is in good agreement with estimation. Note that the fitting curves, derived from simulations on the above measured parameters and based on the equivalent circuit of Fig. 7, differ only for the value of the capacitance (70 fF or 1.8 pF). No other parameter is expected to change in the two configurations. In the “on” state, the measured curve is fitted very accurately. In the “off” state, the discrepancy is attributed to the measuring setup and to other capacitive and inductive parasitic elements, not considered in the model and affecting the quality factor especially at high frequency Table 1. Finally, Table 2 gives further insights derived from measurements: the slope of Q at low frequency changes Table 2 Comparisons between measured and predicted values for Qp , fp and State
∂Q ∂f Low-freq(1GHz)
“On” Fig. 10. Measured quality factors for both states and model validation. The value of the air gap capacitance only is changed to fit the quality factor in both states.
Measurements 16 Model 17
(GHz)
Qp
∂Q ∂f
fp (GHz)
“Off” “On” “Off” “On” “Off” 1.4 2.3
26 27
25 24
3.1 2.5
18 17.5
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with capacitance, according to Eq. (8). The peak value of Q is almost independent of C, as predicted by Eq. (12). The frequency at which the peak occurs changes according to Eq. (11). Inaccuracies for the “off” (high frequency) state is attributed to inductive elements, present in the fitting model, but ignored in the theoretical equations of Section 3.
[11] Th.G.S.M. Rijks, J.T.M. van Beek, P.G. Steeneken, M.J.E. Ulenaers, J. De Coster, R. Puers, RF MEMS tunable capacitors with large tuning ratio, in: International Conference on MEMS, January 2004, pp. 777–780. [12] A.B.M. Jansman, J.T.M. van Beek, M.H.W.M. van Delden, A.L.A.M. Kemmeren, A. den Dekker, F.P. Widdershoven, Elimination of accumulation charge effects for high-resistive silicon substrates, Digest European Solid-State Device Research (ESSDERC), Estoril, Portugal, September 2003, pp. 16–18.
6. Conclusions Biographies This paper proposes a lumped element electrical model for MEMS switches able to describe the quality factor in a wide frequency range. The detrimental effect of the substrate of MEMS switches is discussed in this paper for the first time. A lumped equivalent model, validated in the 50 MHz–40 GHz range, has been introduced. We believe this will constitute a valuable tool for designers of RF integrated receivers based on MEMS technology.
Acknowledgments The authors would like to thank T. Lisec and the ISITFraunhofer Institute team for fruitful discussions and technology access.
References [1] L. Dussopt, G.M. Rebeiz, Intermodulation distortion and power handling in RF MEMS switches, varactors, and tunable filters, IEEE Trans. Microw. Theory Tech. 51 (April (4)) (2003) 1247–1256. [2] C.T.-C. Nguyen, Micromechanical circuits for communication transceivers, in: Proceedings of the Bipolar/BiCMOS Circuits and Technology Meeting (BCTM), 24–26 September, 2000, pp. 142–149. [3] C.T.-C. Nguyen, RF MEMS for wireless applications, in: Device Research Conference, 2002 60th DRC Conference Digest, 24–26 June, 2002, pp. 9–12. [4] C.T.-C. Nguyen, Transceiver front-end architectures using vibrating micromechanical signal processors silicon monolithic integrated circuits in RF systems, in: Digest of Papers. 2001 Topical Meeting on, 12–14 September, 2001, pp. 23–32. [5] A. Margomenos, L.P.B. Katehi, Fabrication and accelerated hermeticity testing of an on-wafer package for RF MEMS, IEEE Trans. Microw. Theory Tech. 52 (June (6)) (2004) 1626–1636. [6] J. DeNatale, R. Mihailovich, RF MEMS reliability, in: 12th International Conference on TRANSDUCERS, Solid-State Sensors, Actuators and Microsystems, vol. 2, 8–12 June, 2003, pp. 943–946. [7] D. Peroulis, S.P. Pacheco, L.P.B. Katehi, RF MEMS switches with enhanced power-handling capabilities, IEEE Trans. Microw. Theory Tech. 52 (January (1)) (2004) 59–68. [8] G.M. Rebeiz, RF MEMS switches: status of the technology, 12th International Conference on TRANSDUCERS, Solid-State Sensors, Actuators and Microsystems, vol. 2, 8–12 June 2003, pp. 1726–1729. [9] J.B. Muldavin, G.M. Rebeiz, High isolation CPW MEMS shunt switches—Part 1: modeling, IEEE Trans. Microw. Theory Tech. 48 (June (6)) (2000) 1045–1052. [10] J.B. Muldavin, G.M. Rebeiz, Nonlinear electro-mechanical modeling of MEMS switches, Microwave Symposium Digest, IEEE MTTInternational, vol. 3, 20–25 May 2001, pp. 2119–2122.
Giuseppe Cusmai was born in Pavia, Italy in 1978. He graduated in electrical engineering from the University of Pavia, Italy in 2003, with a final project activity concerning the design of CMOS oscillators for optical communications receivers. He is currently a PhD student in electronics at the University of Pavia. Main interests include wireless receivers for RF applications and high quality factor RF MEMS devices. The research activity is focused on the design of a CMOS front-end for Ultra-WideBand applications. Marco Mazzini graduated from the University of Pavia, Italy, in electronic engineering in 2004, with a degree thesis concerning the applications of RF MEMS devices. Currently, he is working as a consultant for CEC, an italian society dealing with innovation technology. Paolo Rossi was born in Milan, Italy, in 1975. He received the Laurea degree (summa cum laude) and the Ph.D. degree in electrical engineering and computer science from the University of Pavia, Pavia, Italy, in 2000 and 2004, respectively. During his studies, he worked on CMOS and BiCMOS RF front-end circuits for wireless transceivers, with particular focus on the analysis and design of LNAs and mixers for multistandard applications. He is currently with Maxim Integrated Products (Standard Products Business Unit), Rozzano, Italy. Chantal Combi received her degree in subnuclear physics from University of Milan in 1998. Meanwhile, she worked at CERN (Geneve-CH) on the electrical and noise characterization of the silicon vertex-detectors, in 1998, she joined STMicroelectronics R&D Laboratories, Italy. She started to work on test structures to characterize the structural and sacrificial layers for MEMS. In the last five years, she contributed to develop the design of RF MEMS for telecommunication systems: switch, varcap, resonator and filters, high Q inductors and RF package at wafer level. She was involved in the MELODICT project on the integration of RF MEMS passives in the mobile phone and nowadays in other European project on RF MEMS. She has made some patents on RF MEMS devices. Benedetto Vigna was born in Potenza, Italy, in 1969. He received his degree in subnuclear physics from University of Pisa in 1993. After two years of cooperation with European Synchrotron Radiation Facility in Grenoble and Max Planck Institute on X-ray laser, in 1995, he joined STMicroelectronics Research and Development Laboratory in Castelletto, Italy. He was the pioneer of micromachining activity in STMicroelectronics and now he is the general manager of MEMS Development Unit in ST. His research program has concentrated on micro-electro-mechanical systems and include merged circuit/micromechanical technologies and integrated accelerometers, gyroscopes and microactuators for Consumer and Automotive markets. His current interests are in the field of biochips and micromachined devices for radio-frequency applications. He has filed a lot of patents on micromachining field and he has some publications on this field. He belongs also to the Scientific Committee of IMST Workshop and DTIP Conference. Francesco Svelto received the Laurea and PhD degrees in electrical engineering from the University of Pavia, Pavia, Italy, in 1991 and 1995, respectively. From 1996 to 1997, he held a grant from STMicroelectronics to design CMOS RF circuits. In 1997, he was appointed assistant
G. Cusmai et al. / Sensors and Actuators A 123–124 (2005) 515–521 professor at the University of Bergamo, Italy, and in 2000, he joined the University of Pavia, where he is an associate professor. His current research interests are in the field of RF design and high frequency integrated circuits for telecommunications. Dr. Svelto has been a member of the technical program committee of the IEEE Custom Integrated Circuits
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Conference since 2000 and the Bipolar/BiCMOS Circuits and Technology Meeting (BCTM) since 2003, and the European Solid State Circuits Conference in 2002. He served as guest editor of the March 2003 special issue of the IEEE Journal of Solid-State Circuits, of which he is currently an associate editor.