Lumped Element MIM Capacitor Model for Si-RFICs
Daniel Gruner1#, Zihui Zhang1, Viswanathan Subramanian1, Falk Korndoerfer2, Georg Boeck1
1
Microwave Engineering Lab, Berlin University of Technology, 10587 Berlin, Germany
2
IHP GmbH, Im Technologiepark 25, 15236 Frankfurt (Oder), Germany
#
[email protected]
Abstract — This work describes a lumped element based MIM
capacitor model for the frequency range up to 110 GHz. Several
MIM capacitors with different areas have been fabricated in a
five metal layer 0.25 m SiGe HBT technology. All structures
have been analyzed in a 2.5 D EM simulation environment and
the simulated results are compared to measurements. A lumped
element model valid up to 110 GHz has been developed based on
curve fitting techniques. Good agreements with measurements
have been achieved up to 110 GHz. Finally, the extracted model
parameters suitable for the entire frequency range are tabulated.
Index Terms — MIM devices, integrated circuit modeling, EM
simulation, de-embedding, SiGe HBT.
I. INTRODUCTION
Metal-Insulator-Metal (MIM) capacitors are very important
passive components in radio frequency integrated circuits
(RFICs) and monolithic microwave integrated circuits
(MMICs), respectively. Because of their extensive use in DC
blocks, matching sections, on-chip filtering, etc. it is important
to predict the performance of such capacitors in terms of their
parasitic elements, particularly at very high frequencies. This
work is a part of the development of a complete passive
component library for the 180/220 GHz fT /fMAX SiGe HBT
technology from IHP, Frankfurt (Oder) Germany.
Many authors have worked on getting an approximate model
for such MIM capacitors [1]-[4]. They have included lumped
elements [1]-[2] and distributed elements [3] to their models
and applied curve fitting methods [4] to measurements. In an
earlier paper of the authors [5] an electromagnetic analysis and
experimental verification of integrated microstrip transmission
lines on silicon substrate have been performed up to 90 GHz.
Several microstrip lines with different widths and lengths have
been analyzed on a five metal layer silicon substrate together
with a commercial SiGe HBT process. In this work, a linecapacitor-line model has been developed based on
electromagnetic analysis and experimental characterization of
integrated capacitor test structures. The results of the EM
simulations and measurements have been compared and a
lumped model has been extracted from the measured results.
The organization of this paper is as follows. Section II
describes the designed structures. The comparison of EM
simulations with measurements is presented in section III
showing a good agreement up to 110 GHz. Section IV
introduces the applied de-embedding technique as shown in
[5] and presents the de-embedded MIM capacitor model.
II. TEST STRUCTURES
A 0.25 m SiGe BiCMOS technology with five levels of
Aluminium (Al) interconnects is used to implement various
MIM capacitors. The capacitors are realized between the
second (Metal 2) and the third metal level (Metal 3) using an
extra metallic layer (Metal C) in order to achieve high
capacitance values. The thickness of silicon nitride insulator
between the MIM capacitor plates is about 58 nm (Fig.1) with
εr = 7.3, whereas the thickness of the silicon bulk is about
370 μm. Fig. 2 shows a layout example of a 4.9 pF capacitor.
The other analyzed structures differ just in the size of the
capacitor. All layouts are made based on the same principle.
Starting on the left hand side, there are input pads
(80 μm × 80 μm) in GSG arrangement with 150 μm pitch,
16 μm microstrip line with 100 μm length, MIM capacitor,
once again 100 μm microstrip line and output pads with the
same configuration as input pads. The ground beneath the
capacitor (Metal 1) is suspended in order to minimize the
parasitic coupling capacitors.
Metal 5
Metal 4
Metal 3
Metal C
Nitride
Metal 2
Metal 1
149
c 2007 IEEE
1-4244-0661-7/07/$20.00 SiO
2
Epi layer
Si bulk
Fig. 1.
MIM capacitor within the stacked metallic layers.
Fig. 2.
Layout example of a 4.9 pF MIM capacitor.
In general, MIM capacitance values increase proportional to
their areas. For the given MIM layer permittivity of İr = 7.3,
the theoretical value of capacitance density is about 1 fF/μm2.
In our current work, the analyzed structures include quadratic
plate areas between 250 μm2 and 4900 μm2 for capacitance
values from 250 fF to 4.9 pF. To maintain a uniform parasitic
ground capacitance, Metal 1 is cut at 12 μm from the edges of
the rectangular capacitor plates. For the microstrip feeding line,
a length of 100 μm has been chosen, since this line has been
already measured, modelled and de-embedded in [5].
S11 Simulation
S11 Measurement
Frequency Range: 10 to 110 GHz
III. EM SIMULATION AND MEASUREMENTS
Fig. 4 (a). Reflection coefficients for measurement (triangle)
and 2.5D simulation (rectangle) of a 250 fF capacitor.
A. EM Analysis
Due to the planar arrangement, the planar EM solver
SONNET [6] based on method of moments (MoM) has been
used. In [5] the importance of thick metal characterization for
the metallic layers and their influence on the simulation
accuracy is presented. Considering these aspects the MIM
capacitor EM simulation of this work is based on a similar
approach. Fig. 3 shows the SONNET 3D visualization of a
MIM capacitor with thick metal option for all the metallic
layers.
S21 Simulation
S21 Measurement
Frequency Range: 10 to 110 GHz
Fig. 4 (b). Transmission coefficients for measurement (triangle)
and 2.5D simulation (rectangle) of a 250 fF capacitor.
Fig. 3. 3D visualization of a MIM capacitor from SONNET
EM simulation.
B. Measurements
Several MIM capacitor structures have been characterized
with an Agilent 8510XF 110 GHz vector network analyzer
through on-wafer probing in GSG configuration. A shortopen-load-through calibration technique (SOLT) has been
applied to calibrate the measurement setup over the complete
frequency range. Representative for all MIM capacitors results
we will only present the results of a 250 fF MIM capacitor.
Fig. 4 shows the comparison of the reflection (a) and
transmission (b) coefficients of EM simulations (rectangle)
and measurements (triangle) up to 110 GHz. To evaluate the
accuracy of the simulations, the frequency dependent deviation
between measured and simulated magnitude values in
percentage has been calculated. The results are shown in
Fig. 4 (c).
150
Error Magnitude [%]
20
C
15
10
Error Magnitude of S21
5
Error Magnitude of S11
0
0
20
40
60
80
100
120
Frequency [GHz]
Fig. 4 (c). Magnitude of the error vector of S11 (rectangle) and
S21 (triangle) for a 250 fF capacitor.
It can be seen that the EM simulated data is close to the
measured values at lower frequencies. The agreement of
simulations and measurements degrades at higher frequencies
due to the increasing parasitic effects, which cannot be
represented correctly with EM simulation. The maximum error
magnitude is 20 % at 100 GHz. Hence a proper modeling of
passive structures in the RFIC design is absolutely necessary at
such high frequencies.
2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2007)
IV. DE-EMBEDDED MODEL
The applied de-embedding technique already has been
introduced in [5]. Using this procedure the S-parameters of the
MIM capacitor can be determined from measurement results.
The calculated S-parameters of the MIM capacitor are the base
for the development of a lumped element MIM capacitor
model.
As a first step, a microstrip line of 200 μm length with GSG
pad arrangements on each side has been measured. Due to the
symmetry of this structure (pad-200 μm microstrip line-pad),
the A-parameter matrix of each of both pad-100 μm microstrip
line structures can be de-embedded from the cascaded Aparameter matrix as shown in the Fig. 5 (a) and equation (1).
[P] [P]=[T200]
(1)
Pads + Line
MIM Capacitor
Line + Pads
G
G
C
Lvia,t Rvia,t
Rvia,b Lvia,b
S
S
Ct
Cb
G
G
Fig. 6. De-embedding plane and equivalent electrical circuit of
MIM capacitors.
Figure 7 (a)-(c) show the S-parameter comparison between
measurements and the developed lumped element model for a
250 fF capacitor.
S11 Measurement
S11 Model
[P]
[P]
(a)
[P] [C] [P]=[Tcap]
[P]
[C]
(2)
[P]
Frequency Range: 10 to 110 GHz
Fig. 7 (a). Reflection coefficients for measurement (rectangle)
and the model (triangle) of a 250 fF capacitor.
(b)
Fig. 5. De-embedding principle (a) shorted through line with
200 μm length (b) 100 μm line + MIM capacitor + 100 μm Line.
The A-parameter matrices of the MIM capacitors are
calculated by extracting the pads and feeding lines as
displayed in Fig. 5 (b) and equation (2). Finally, the Sparameters of the MIM capacitors can be obtained from the
evaluated A-parameter matrices.
A MIM capacitor can be modeled by characterizing all its
discontinuities and coupling mechanisms using lumped
elements. Fig. 6 shows a simple equivalent circuit based on
lumped elements, whose values are determined from
measurements by curve fitting using ADS from Agilent. C is
the main element of the MIM capacitor. Lvia,t and Lvia,b are
the parasitic inductances existing in electrodes and via
connections. Rvia,t and Rvia,b model the parasitic losses of
the vias and capacitor plates. Cb and Ct represent the
capacitance of the top and bottom MIM capacitor plate to
ground. All elements are extracted by minimizing the squared
error vector magnitude of all S-parameter between measured
and modeled data.
S21 Measurement
S21 Model
Frequency Range:10 to 110 GHz
Fig. 7 (b). Transmission
coefficients
for
measurement
(rectangle) and the model (triangle) of a 250 fF capacitor.
The evaluation of modeling accuracy is based on the error
calculation between measured and modeled S-parameter. From
10 to 90 GHz the maximum error magnitudes of S11 and S21
are nearly zero, for higher frequencies the error magnitudes
are less than 8 %. These facts justify the development of a
lumped element MIM capacitor model as suggested above.
2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2007)
151
Table I shows the extracted values of the lumped elements
for the proposed equivalent circuit of the MIM capacitor.
TABLE I
DE-EMBEDDED ELEMENT VALUES OF THE EQUIVALENT CIRCUIT
Structure
C
250 fF
500 fF
1000 fF
1500 fF
2000 fF
2500 fF
4900 fF
Rvia,t
1.8 ȍ
1.4 ȍ
1.2 ȍ
1.4 ȍ
1.9 ȍ
1.6 ȍ
1.4 ȍ
Element values from Measurement
Rvia,b Lvia,t Lvia,b
Ct
Cb
1.5 ȍ 12 pH
7 pH
7 fF
15 fF
1.7 ȍ 10 pH
8 pH
8 fF
17 fF
2.5 ȍ 11 pH
9 pH
9 fF
18 fF
1.8 ȍ 15 pH 10 pH
9 fF
25 fF
1.3 ȍ 18 pH 15 pH
9 fF
28 fF
2.0 ȍ 19 pH 16 pH 10 fF
33 fF
1.7 ȍ 31 pH 33 pH 11 fF
31 fF
From the table above we can draw some important
conclusions regarding the developed lumped element model:
The increasing value of inductances (Lvia,t and Lvia,b) and
metal to ground capacitors (Cb and Ct) are due to the
increasing metallic areas of the MIM capacitor plates. These
elements are in turn proportional to the nominal value of the
MIM capacitor. Because of the fact, that the two capacitor
plates do not use the same metal layer, the feeding elements
and ground capacitors connected to the top and bottom plate
differ slightly. This can be clearly seen from Table I.
V. CONCLUSION
Several MIM capacitors have been fabricated in a 0.25 μm
BiCMOS standard technology. The characterization and
modeling of these integrated capacitor structures is presented.
Good agreements of measured data, EM simulation and
models have been achieved from 10 GHz to 110 GHz for
capacitance values between 250 fF and 4.9 pF.
This work can be seen as part of passive component library
containing all types of lumped elements, interconnects and
parasitic structures on silicon substrate with multi layer stack.
Together with the active models it should be the design
starting point for SiGe HBT based circuits up to and beyond
110 GHz [5].
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ACKNOWLEDGEMENT
The authors would like to thank their IHP colleagues for the
fruitful collaboration.
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2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2007)