Progress In Electromagnetics Research Symposium, Hangzhou, China, March 24-28, 2008
925
Design and Characterization of a Radio Frequency MEMS Inductor
Using Silicon MEMS Foundry Process
Deepak Uttamchandani and Lijie Li
Department of Electronic and Electrical Engineering
University of Strathclyde, Glasgow G1 1XW, UK
Abstract— A successful design of RF inductor based on a silicon MEMS foundry process is
presented. The suspended inductor has been realized in electroplated thick nickel with front side
bulk micromachining of the substrate. The overall size of the inductor is about 1 mm × 1 mm. The
inductors have been experimentally characterized and inductances around 2 nH in the frequency
range of 200 MHz–7 GHz have been measured with self resonant frequency of 9.8 GHz. The peak
measured value of the Q factor is 12 at a frequency of 4 GHz. After de-embedding, the Q factor
reaches 13 at a frequency of 4.8 GHz. Simulation based on a parameter extraction method has
been carried out for the inductor. There is a good agreement between simulated and experimental
results.
1. INTRODUCTION
High performance monolithic inductors are widely used in wireless communication systems. They
are key elements in RF integrated circuits, filters, amplifiers and baluns. Achievement of high
performance micromachined inductors on silicon substrates is one of the major challenges in the
move towards monolithic solutions [1]. The performance of silicon based inductors is limited by
substrate parasitics and the conductivity of the silicon substrate. The solution to overcome these
limitations involves separating the micromachined inductor from the proximity of the substrate.
Several approaches have been employed to lift or suspend the micromachined inductors as far as
possible from the silicon substrate. Mechanically orientated techniques such as surface tension based
self-assembly [2], plastic deformation magnetic assembly (PDMA) [3], bimorph based self-lifting
structures [4], and flip chip bonding [5] are amongst those that have been applied in microfabricating
3D vertical inductors or inductors which overhang the silicon substrate. Another approach has been
to use material orientated techniques such as the introduction of a thick, low-loss dielectric layer
(such as SiO2 ) between the inductor structure and the silicon substrate [6]. However, all of these
methods involve material processing or post-processing of the silicon substrates. Glass substrates
have also been used in the microfabrication of inductors [7], but this material does not lend itself
to monolithic integration of RF devices. In this Letter, we report a new implementation of low-loss
microfabricated RF inductors based on a commercial MEMS foundry process — MetalMUMPs [8].
Using this process, RF inductors have been achieved directly on a silicon substrate without further
post-processing, and their performance is shown to be comparable to MEMS inductors fabricated
by other more complex microfabrication processes. The foundry approach described here offers an
excellent platform for the integration of microactuators and RF components onto silicon substrates
that can be used to achieve monolithic systems, as the MetalMUMPs process is also capable of
yielding MEMS microactuators.
2. DESIGN AND FABRICATION
MetalMUMPs is a silicon based MEMS process provided by the commercial MEMS foundry MEMSCAP, Inc. Full details of the MetalMUMPs process, together with Design Rules can be obtained
from [8]. Figure 1 illustrates the cross section of the inductor fabricated using MetalMUMPs. The
process involves a high resistivity (∼ 5000 Ohm-cm) silicon wafer as substrate. First, a layer of
silicon oxide is deposited and pattemed. This oxide layer outlines the area that will he used to etch
a trench in the silicon substrate. The first nitride layer of 0.35 micron thickness is then deposited
and pattered. On top of the first nitride layer, a 0.7 micron layer of polysilicon is deposited and
patterned. A second nitride layer of 0.35 micron thickness is then deposited and patterned. A
second layer of oxide 1 micron thick is then deposited. The second oxide layer is patterned and
etched so that the metal layer, which is the last layer deposited in the process, is anchored to the
nitride. This metal layer consists of 20 microns of nickel with 0.5 micron of gold deposited on top
of the nickel layer. The last step in the process is to etch out the sacrificial layers as well as to etch
PIERS Proceedings, Hangzhou, China, March 24-28, 2008
926
planar view
ground
bond wire
inductor track
trench
nitride
cross section
view
substrate
Figure 1: Schematic diagram of the inductor, the top
picture is planar view and bottom picture is cross section view.
Figure 2: SEM photograph of fabricated inductor.
a 25 micron trench in the silicon substrate. The trench etch of the substrate is determined by the
first oxide layer.
The inductor consists of a square coil of 1.5 turns, as shown in Figure 2. The width of the
track forming the inductor is 80 microns while the spacing between the tracks is 40 microns. The
inductor is based on a coplanar waveguide (CPW) design for the convenience of RF characterization
which makes use of waveguide probes of ground-signal-ground (G-S-G) configuration. In the CPW
design, the width of the signal line and the spacing between the signal line and ground plane are
80 microns and 22 microns respectively in order to produce a waveguide of 50 Ohm characteristic
impedance. A K&S 4526 wire bonding machine has been used to bond 25 micron diameter gold
wire between the centre of the inductor and the ground plane. There is a further 25 micron air gap
between the bottom of the inductor structure and the high resistivity silicon substrate. This gap is
formed by front side bulk micromachining which, as stated earlier, is a feature of the MetalMUMPs
fabrication process. This air-gap significantly helps reduce the substrate induced loss in the device.
Figure 2 shows a scanning electron microscope image of the inductor.
3. MEASUREMENTS
The performances of the RF inductor was measured using a vector network analyzer, Agilent
N5230A and a Cascade Microtech 9000 probe station with on-wafer G-S-G probes. Before measuring the RF MEMS inductor, a Line-Reflect-Reflect-Match (LRRM) impedence standard substrate
(ISS) was used to calibrate the probe station and VNA. The calibrated 1-port measurement result
of the inductor was then imported from the VNA to WinCal software. The inductance L and the
Q factor derived from the measured S parameters are given by
L=
imag(1/Y11 )
,
ω
Q=−
imag(Y11 )
real(Y11 )
(1)
where ω is angular frequency. Both inductance and Q factor were obtained over a frequency range of
200 MHz to 10 GHz. A set of simple open coplanar pads was also designed and fabricated adjacent
to the inductor in order to de-embed the effect of the inductor pads. The de-embedding process
followed the methodology described in detail in [5]. The measured results are shown in Figure 3.
4. ANALYSIS OF THE INDUCTOR
Analysis of the MEMS inductor is based on a parameter extraction method. The on-chip inductor
can be represented by a nine-element equivalent circuit as shown in Figure 4 [9]. Ls represents
the series inductance of the structure, Rs represents the series resistance of the metallization and
includes the frequency dependent term to model skin effect and other high frequency effects, Cs
represents the fringing capacitance between the metal lines, Csub1 represents the capacitance from
the metal layer to the substrate, Rsub represents the substrate resistance, and Csub2 represent the
capacitance into the substrate. The values of the equivalent circuit elements of Figure 4 can be
obtained from the measured S parameter of the inductor following the method described in [10].
Progress In Electromagnetics Research Symposium, Hangzhou, China, March 24-28, 2008
927
Figure 3: RF Measurement results of the inductor.
The series components can be obtained using Equations (2) and (3):
1
L2
= Rs + ω 2 s
real(Ys )
Rs
imag(Ys )
Ls
= Cs −
real(Ys )
ω
Rs
(2)
(3)
Here Ys = −Y12 , where Y12 can be derived from measured S parameters. In order to include the
substrate loss, the shunt branch (Csub1 , Csub2 , Rsub ) should be considered and can be extracted
using Equations (4) and (5):
2 (C
2
Rsub
ω2
1
sub1 + Csub2 )
=
+
ω2
2
2
real(Ysub )
Rsub Csub1
Rsub Csub1
2 C
Rsub
imag(Ysub )ω
Csub1
sub1 Csub2 (Csub1 + Csub2 ) 2
=
+
ω
2
2
real(Ysub )
Rsub Csub1
Rsub Csub1
(4)
(5)
Here Ysub = Y11 +Y12 . Using Equations (2)–(5), the equivalent circuit values have been calculated as
follows: Ls = 1.8 nH, Rs = 2.1 Ohm, Cs = 85 fF, Csub1 = 95 fF, Csub2 = 0.16 pF, Rsub = 350 Ohm.
Cs
Ls
Rs
Csub1
Csub1
Csub2
Rsub
Csub2
Rsub
Figure 4: Equivalent circuit of the inducor.
5. DISCUSSION
The measured Q factor, de-embedded Q factor, and the measured inductance plotted against
frequency are shown in Figure 3. The inductance and the self-resonance frequency of the device
are 2 nH and 9.8 GHz respectively. The Q factor is measured to have a value of 12 at the peak
frequency of 4 GHz frequency, while the Q factor after de-embedding is 13 at a peak frequency
of 4.8 GHz. The inductance and Q factor of the device are comparable to the values of devices
reported previously [2–6] which were fabricated by more elaborate processes or on materials of
inherently low RF loss. Analysis of the equivalent circuit of the inductor has been accomplished by
PIERS Proceedings, Hangzhou, China, March 24-28, 2008
928
a parameter extraction method. The comparison between measured and modelled results is shown
in Figure 5. The fit between measurement and modelled inductance is within 5% root-meansquare (RMS) deviation over the frequency range of 0.2–10 GHz. The fit between measurement
and modelled Q factor is within 10% RMS deviation over the same frequency range. It can be seen
that the modelled results are closely matched to the measurements.
20
1.60E-08
1.40E-08
Q Measured
Q Model
1.20E-08
Inductance(H)
QualityFactor
16
12
8
L Measured
L Model
1.00E-08
8.00E-09
6.00E-09
4.00E-09
4
0
0.00E+00
2.00E-09
0.00E+00
0.00E+00
2.00E+09
4.00E+09
6.00E+09
Frequency(Hz)
(a)
8.00E+09
1.00E+10
2.00E+0 9
4.00E+09
6.00E+09
8.00E+09
1.00E+10
Frequency(Hz)
(b)
Figure 5: Comparison of measured and simulated L and Q.
6. CONCLUSION
Modelling and characterization of a high performance RF MEMS inductor fabricated using a commercial MEMS foundry process (MetalMUMPs) is reported. The overall size of the inductor is
about 1 mm × 1 mm, and the inductor is formed in electroplated nickel of 20 microns thickness. To
reduce parasitic effects of the substrate, bulk micromachining has been used to etch a 25 microns
deep trench directly below the inductor, leaving behind a suspended inductor. The inductance is
around 2 nH over the frequency range of 200 MHz–7 GHz. The self resonance frequency is 9.8 GHz.
The de-embedded Q factor reaches 13 at a frequency of 4.8 GHz. Modelling based on parameter
extraction was performed, and the results fit very well with the measurements.
REFERENCES
1. Burghartz, J. N., “Progress in RF inductors on silicon-understanding substrate losses,” IEDM
Teck. Dig., 523–526, 1998.
2. Dahlmann, G. W. and E. M. Yeatman, “High Q microwave inductors on silicon by surface
tension self-assembly,” Electron. Lett., Vol. 36, 1707–1708, 2000.
3. Zou, J., C. Liu, D. R. Trainor, J. Chen, J. E. Schutt-Aine, and P. L. Chapman, “Development
of three-dimensional inductors using plastic deformation magnetic assembly (PDMA),” IEEE
Trans. Microw. Theory Tech., Vol. 51, 1067–1075, 2003.
4. Lubecke, V. M., B. Barber, E. Chan, D. Lopez, M. E. Gross, and P. Gammel, “Self-assembling
MEMS variable and fixed RF inductors,” IEEE Trans. Microw. Theory Tech., Vol. 49, 2093–
2098, 2001.
5. Zeng, J., A. J. Pang, C. H. Wang, and A. J. Sangster, “Flip chip assembled MEMS inductors,”
Electron. Lett., Vol. 41, 480–481, 2005.
6. Sun, J. and J. Miao, “High performance MEMS inductors fabricated on localized and planar
thick SiO2 layer,” Electron. Lett., Vol. 41, 446–447, 2005.
7. Wu, W., F. Huang, Y. Li, S. Zhang, X. Han, Z. Li, Y. Hao, and Y. Wang, “RF inductors
with suspended and copper coated thick crystalline silicon spirals for monolithic MEMS LC
circuits,” IEEE Microw. Wireless Compon. Lett., Vol. 15, 853–855, 2005.
8. Cowen, A., B. Dudley, E. Hill, M. Walters, R. Wood, S. Johnson, H. Wynands, and B. Hardy,
MetalMUMPs Design Handbook, MEMSCAP Inc.
http://memsrus.com/documents/MetalMUMPs.dr.v1.pdf.
9. Ashby, K. B., I. A. Koullias, W. C. Finley, J. J. Bastek, and S. Moinian, “High Q inductors for
wireless applications in a complementary silicon bipolar process,” IEEE J. Solid-State Circuits,
Vol. 31, No. 1, 4–9, 1996.
10. Huang, F. Y., N. Jiang, and E. L. Bian, “Modeling of single-pi equivalent circuit for on-chip
spiral inductors,” Solid-State Electron., Vol. 49, 473–478, 2005.