Available online at www.sciencedirect.com
Procedia Engineering 25 (2011) 1521 – 1524
Proc. Eurosensors XXV, September 4-7, 2011, Athens, Greece
Modeling and design of higher order, multi-mode, multi-port MEMS resonators in 90nm CMOS J. E. Ramstad and O. Soeraasen Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, N-0316 Oslo, Norway Abstract This work presents various RF mixer-filter MEMS resonators implemented directly in CMOS. Three different composite resonator designs have been made in a 90nm CMOS process. These resonators move laterally in two different modes made possible by the flexible internal routing and stimulation of the multi-port creating these second mode mixer-filter capabilities. By utilizing post-processed self-assembly electrodes, narrow gaps between the electrodes and the resonator is achieved for increased electrostatic coupling. Based on three different resonator designs, 4th order filters are implemented by using a coupling beam connecting pairs of resonators. The higher order mechanical filters are driven differentially.
© 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license.
Keywords: Resonator, mixer-filter, CMOS-MEMS, flexural, multi-port, multi-mode, higher order
1. Introduction The need for integrated and compact Wireless Sensor Network (WSN) nodes have become an interesting research area [1,2]. The use of MEMS resonators as mixer-filters directly integrated with CMOS can potentially replace typical off-chip components. Integrated filters and mixer-filters in the transceiver part of a WSN node directly with CMOS can reduce the size, cost and power consumption. Integration with CMOS in this work follows a post-CMOS process which utilizes the top metal layer of the CMOS as a mask to define MEMS structures. The resonators vibrate laterally by using electrostatic actuation and consists of a 3 µm thick metal-dielectric stack. All of the designs in this process uses selfassembly electrodes which create narrow gaps for enhanced electromechanical coupling [3-5]. This paper shows how to use multiple modes of flexural moving resonators to perform mixing and filtering tasks. The direct integration with CMOS allows for voltage to voltage conversion using integrated amplifiers to compensate for loss through the resonator device. Intricate routing is possible through the multi metal layers offered by the CMOS process, allowing devices with for multiple ports on the same device. This will in turn allow summation of motional currents, mixing down signals from RF to IF and to clearly separate an input from an output node thus greatly reducing any system feedthrough. 2. Standalone and mechanically coupled composite resonators The square-shaped MEMS resonators are connected together through various beams. The electrical signals in these resonators are internally routed so that the resonator has four terminals and can be used as a mixer-filter to mix down a high-frequency (RF) signal down to an intermediate frequency (IF). * Corresponding author: Jan Erik Ramstad. Tel.: +47 41478925, Fax: +47 22 00 84 01 E-mail address
[email protected]
1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2011.12.376
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J.E. Ramstad and O. Soeraasen / Procedia Engineering 25 (2011) 1521 – 1524
Three different composite resonator types have been investigated: Free-Free Square-Frame Resonator (FFSFR), Clamped-Clamped Square-Frame Resonator (CCSFR) and Parallel-Plate Tuning Fork (PPTF). FRAME Coupl ng eam The FFSFR andWCCSFR are connected with specially designed tether beams as anchors. All of these three F different composite resonator designsCO and ENTO their associated anchoring beams vibrate at either a cantilever, Th coupling b am wil have f x r l mo nt and n repres mode nted s The a t ansformer T-netwo of k with clamped-clamped, or clampedbepinned FFSFR consists four winding beams F 1 T offree-free, PTF ( pepinned-pinned 1 rat a square-shaped escribe in eq 5 structure Equation seen desc in i sfig. th 1a. ca The citor connected together through their nodal points, creating a o t rs th P , the compositet structure When is Dbeams S are made of with os equal te so dimensions to s d th iand des t is symmetrical. s th h t the t resonator T t stimulated with as first of repr the free free replacedeigenmode by an indu of to one (eq 7) s nt ng th beams, mass of the the V i l a signal m d which f th is the same it t or second cou The ing masses eam Fo of th the PPTF th beams coupli does g beamnot dimens ns whole that frequency four add, so re showcomposite in fig 11 resonator These mo will es a eresonate based o atthe mod are r resen d h lf h pe. num ers given in able I The P F has tw dif erent l n t � the resonance frequency remains the same as if it was only one beam resonating This allows for 3 1 H b w d o o cc = ηstimulation separated input and output electrodes and a differential of the device. cij = (5) MO MEM l d i The CCSFR in fig. 1a is very similar to the FFSFR, except that it is based on having nodal points that TABLE I and end of the beam rather than at 1/4 andlc3/4 (7) =m Hc Wc Lof are “motionless” at the start ofc = the2 length c the beam. The Mo e ons o p es CCSFR follows the same equations of operation as the FFSFR, except that the mode constants β n are P TF F R (+) different. The PPTF is a one terminal, two-port resonator that consists of two long beams with a square73 0 07 ( d $ (L 200 m) shape in the middle as shown in fig. 1a. In the first mode the PPTF acts as a large clamped-clamped + #N mo with e 2) (L= 7 85 204 2 73004074 while in the second mode the PPTF acts as a proper Vtuning resonator an extra in the middle 00"m) mass fork behavior. Mode numbers and standalone composite resonator dimensions are given in table 1. V + 28
E 006 Hz
P
P
P
FFSFR
CCSFR
PPTF
Mode 1
Mode 2 (a) (b) Fig 1. Two mode constants for three composite resonators (left) and mechanical coupling of these resonator types (right)
Pub ishing 2011 The three Eurosenso different scomposite resonators have been also been implemented as higher-order filters by connecting two resonators together with aT coupling beam (fig. 1b), creating two distinct resonance y 5 1 frequencies (eq. 1) where k is the spring stiffness, meff is the effective mass and kc is the stiffness of the coupling beam. These higher order mixer-filters are driven and sensed differentially. The FFSFR and CCSFR follow the same λ/4 operational mode as the tether beam so that the coupling beam between two resonators will resonate at a frequency four times of the resonator. The PPTF is not designed with a λ/4 coupling beam, but rather a set of two soft beams in a 45° angle that will add both mass and spring stiffness. For all three resonator types, the coupling beam will have a flexural movement and can be represented as a transformer T-network with winding ratio described in eq. 2. An electromechanical schematic of a 4th order mixer-filter is shown in fig 2a. For the PPTF, the λ/4 criteria is not used, so the series capacitor in the T-network is replaced by an inductor representing the mass of the coupling beam. Note that even though λ/4 is implemented for the FFSFR and CCSFR, they may have additional masses which will lower f1, f2 and fc(filter) due to geometry variations. Table 2 shows the dimensions for the tether and coupling beams for the � three different composite resonators. � �
f1 =
1 2π
1 k , f2 = mef f 2π
k + kc mef f
(1)
ηcij =
kc k
Table 1. Mode constants for the three resonator composites (left) and their respective dimensions (right) Mode constants PPTF FFSFR CCSFR Resonator dimensions PPTF FFSFR LFRAME=100 Resonator length [µm] 47 4.73004074 LCANTILEVER=50 βN (mode 1) 4.73004074 π (L=200µm) WFRAME=6 Resonator width [µm] 4 WCANTILEVER=4 4.73004074 βN (mode 2) 7.85320462 4.73004074 Electrode length [µm] 100 16.5 (L=100µm) Resonator-to-electrode gap [nm] 200 300
(2)
CCSFR 47 4 45 300
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J.E. Ramstad and O. Soeraasen / Procedia Engineering 25 (2011) 1521 – 1524 Table 2. Filter coupling and tether beam dimensions (left) and Transimpedance Amplifier results (right) Coupling dimensions PPTF FFSFR CCSFR Amplifier results TT FF FS SF SS MC,µ MC,σ Tether length [µm] Tether width [µm] Coupling length [µm] Coupling width [µm]
14 1
9.1 0.6 16.2 2
9.1 0.6 16.2 2
Phase Margin [ ] Bandwidth [MHz] ZTIA @ 10MHz [MΩ] SNR 10-11MHz [dB]
92.50 38.11 11.84 16.56
95.27 34.62 12.26 16.51
92.78 38.03 12.19 16.55
VLO
VP
92.10 88.56 92.34 38.21 40.59 38.08 11.39 9.21 12.02 16.58 16.62 16.52
0.79 0.75 0.22 0.01
Rf
1 : !a1
lza
cza
rza
1 : !ac -cc
-cc !bc : 1
lzb
czb
rzb
!b1 : 1
IOUT
VRF
VRF
cc
CP
-
VOUT
!"#
VOUT
+ Rf VLO-
VRF-
CP
VPIOUT-
VOUT- VRF-
-
VOUT-
!"#
1 : !a2
+
!b2 : 1
(a) (b) Fig 2. Two mode constants for three composite resonators (left) and mechanical coupling of these resonator types (right)
3. Mixer-Filter implementations and results All resonator designs have been implemented in a TSMC 90nm CMOS process using a post-CMOS process [5]. All of these designs have Transimpedance Amplifiers (TIA) to convert the motional resonator current to an output voltage, Vout=ioZTIA, where ZTIA is the transimpedance of the TIA circuit. The total ur day May 2011 system performance, conversion loss, is therefore how much output voltage obtained for a given input voltage (Vout/VRF) as shown in eq. 3. Fig. 2b shows how a differential 4th order mechanically coupled mixer-filter is connected with two TIAs for a differential drive. The TIA consists of three CMOS inverters creating a 12MΩ transimpedance gain. The standalone 2nd order mixer-filters are not differential and contains only one TIA. The parasitic capacitance from a resonator to an amplifier is roughly 25fF. CL = 20log10
io ZT IA VRF
�
Simulation Analytic
35
20
Conversion Loss [dB20]
5 50 55 60
5
55 3.98
7.75 Frequency [MHz]
7.8
7.85
.02
08
.1
25 30
5 1.22
.12
1.2
1.26
36 38 0 2 Simulation Analytic
6 23.1 23.11 23.12 23.13 23.1 Frequency [MHz]
23.15 23.16
1.3
1.32
1.3
Simulation Analytic
15
30
35
0
20
25
30
5
50 9.2
1.28 Frequency [MHz]
(c) 10
Conversion Loss [dB20]
Conversion Loss [dB20]
3 Conversion Loss [dB20]
.0 .06 Frequency [MHz]
25
(d)
20
0
20
32
(4)
Simulation Analytic
(b)
30
8 23.06 23.07 23.08 23.09
�
Q −1 qi Qf ilter
35
(a)
�
15
0
70
7.7
5
35
50
Rz 2n 10
30
65
7 65
Rqij = Simulation Analytic
25
0 Conversion Loss [dB20]
(3)
Conversion Loss [dB20]
30
�
Simulation Analytic 9.21
9.22
9.23 9.2 9.25 Frequency [MHz]
9.26
9.27
9.28
35 6. 6
6. 8
(e) Fig. 3a,b,c is M1, fig. 17d,e,f is M2 for the FFSFR, CCSFR and PPTF
6.5
6.52 6.5 Frequency [MHz]
(f)
6 56
6.58
6.6
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J.E. Ramstad and O. Soeraasen / Procedia Engineering 25 (2011) 1521 – 1524 Table 3. Simulation and analytical results for 1st and 2nd mode of the resonators PPTF PPTF FFSFR FFSFR CCSFR CCSFR Resonator results (M1) (M2) (M1) (M2) (M1) (M2) Resonance frequency [MHz] 1.267 6.578 7.662 23.02 3.982 9.238 Effective mass [pkg] 16.6 4.89 2.88 4.471 5.83 4.417 Eff. stiffness [N/m] 993 8 357 6 684 93 540 3 654 14 884 ηIN [nN/V] 42.2 50.63 2.45 2.45 6.68 6.68 ηOUT [nN/V] 422 506.3 49.1 49.1 133.7 133.7 Motional impedance [MΩ] 7 7.88 290 194.1 11 14.09 Conversion Loss [dB] +3.09 +2.06 -29.33 -25.76 -0.89 -2.97 Filter center freq. [MHz] 1.277 6.522 7.754 23.12 4.052 9.243 Filter BW [kHz] 29.07 58.70 222.3 52.84 95.92 19.35 Filter Q-factor 43.93 111.1 34.89 437.5 42.25 477.5 Termination resistors [MΩ] 185.1 130.5 3 001 109.8 804.9 27.4
The right part of table 2 shows the results of the TIA corner and Monte Carlo (MC) simulations where the TIA is designed to amplify at least 10MΩ with a bandwidth of 38MHz and at least larger than a 75° phase margin. Eq. 4 describes the required input termination resistance for the filter in order to reduce ripple which occurs due to the sharp resonator response. Rz is the resonator motional impedance, n is the number of terminals, Q is the loaded Q-factor of a single resonator and qi is a filter shape coefficient. The large Rqij values can be reduced by reducing the electrostatic gap, thus reducing the motional impedance of the resonator. Fig. 3a) to fig. 3f) shows ac analysis results from all of these systems. Table 3 shows the mixer-filter resonator characteristics. Conclusion Multi-port, multi-terminal composite resonators have been made and described by combining beams connected in various ways. These three composite resonator types have also been implemented as full differential mixer-filters by using coupling beams. All six mixer-filter designs have self-assembly beams and have been implemented with transimpedance amplifiers to convert the resonator motional current to an output voltage. These mixer-filters are also operated at two different modes encompassed in the amplifier bandwidth. Equations describing tether beams, coupling beams and resonator and mixer-filter performance has been shown. The system implementations and results of these mixer-filters have been shown, including process and mismatch variation simulations for the CMOS circuitry. The PPTF mixerfilters shows good Conversion Loss (CL) results and demonstrates the feasibility of achieving adequate performance for CMOS-MEMS based WSN front-end components. Acknowledgements The authors would like to thank Suresh Santhanam from Carnegie Mellon University for postprocessing the dies. References [1] G. K. Fedder, R. T. Howe, T.-J. K. Liu and E. P. Quévy, Technologies for cofabricating MEMS and electronics. In Proceedings of the IEEE 2008, vol. 96, no. 2, pp. 306–322, IEEE 2008. [2] W.-L. Huang, Z. Ren, Y. Lin, J. Lahann and C. T.-C. Nguyen. Fully monolithic CMOS Nickel Micromechanical resonator oscillator. In the 21st Int. Conf. on Micro Electro Mechanical Systems (MEMS’08), pp. 10-13, IEEE 2008. [3] J. E. Ramstad, K. G. Kjelgaard, B. E. Nordboe and O. Soeraasen. RF MEMS front-end resonator, filters, varactors and a switch using a CMOS- MEMS process. In Proceedings of DTIP 2009, Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS, pp. 170–175, IEEE 2009. [4] J. E. Ramstad and O. Soeraasen. Higher order FFSFR coupled micromechanical mixer-filters integrated in CMOS. In the 28th Proceedings of Norchip, IEEE 2010. [5] J. E. Ramstad, J. A. Michaelsen, O. Soeraasen and D. T. Wisland. Implementing MEMS resonators in 90 nm CMOS. In Proceedings of DTIP 2009, Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS, pp. 151–156, IEEE 2011.
