Journal of Microelectromechanical Systems Volume 22 Issue 3 2013 [Doi 10.1109/JMEMS.2013.2243111] Konishi, Toshifumi; Machida, Katsuyuki; Maruyama, Satoshi; Mita, -- A Single-Platform

7/22/2019 Journal of Microelectromechanical Systems Volume 22 Issue 3 2013 [Doi 10.1109/JMEMS.2013.2243111] Konishi, T

http:///reader/full/journal-of-microelectromechanical-systems-volume-22-issue-3-2013-doi-101109jmems20132243 1/13

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 22, NO. 3, JUNE 2013 755

A Single-Platform Simulation and Design Techniquefor CMOS-MEMS Based on a Circuit Simulator

With Hardware Description LanguageToshifumi Konishi,Member, IEEE, Katsuyuki Machida,Member, IEEE, Satoshi Maruyama,

Makoto Mita, Kazuya Masu, Member, IEEE, and Hiroshi Toshiyoshi,Member, IEEE

AbstractThis paper presents a multiphysics simulationand layout design technique for complementary metaloxidesemiconductormicroelectromechanical systems (MEMS) (CMOS-MEMS) based on an electrical circuit simulator. An equivalentcircuit model for the mechanical equation of motion has beentranslated into a Verilog-A-compatible hardware descriptionlanguage (HDL) in the Cadence Virtuoso environment to attainnew designing capabilities such as automatic mask-layout synthe-

sis, design rule check, and layout-versus-schematic verification forMEMS structures. Microelectromechanical components such asparallel-plate actuator and bending suspension, whose analyticalequation models are already known, are also interpreted intoHDL-coded equivalent circuits. Behavior of a MEMS device, in-cluding the electrostatic displacement hysteresis and the negativespring constant effect, is numerically simulated as a lumped mass-and-spring system, which has been verified to quantitativelyagree with that of the corresponding analytical simulation results.A multiphysics model for the Colpitts oscillator circuit has beenbuilt in the developed simulation environment by replacing aquartz resonator with a compact model of an electrostatic siliconresonator, and its self-excited resonance has been confirmed bythe simulation after the coordination of the device and circuit pa-rameters. A prototype conversion tool for MEMS parameterized

cell has also been developed to demonstrate automatic generationof mask layouts for a silicon resonator, which has been cross-checked against the experimental measurements to verify thesimulation accuracy. [2012-0365]

Index TermsComplementary metaloxidesemiconductor(CMOS)microelectromechanical systems (MEMS) (CMOS-MEMS), equivalent circuit, hardware description language(HDL), mask layout, multiphysics simulation.

Manuscript received December 3, 2012; revised January 14, 2013; acceptedJanuary 15, 2013. Date of publication March 7, 2013; date of current versionMay 29, 2013. This work was supported in part by the Funding Program for

Next Generation World-Leading Researchers under Grant ID GR024 and inpart by a Grant-in-Aid for Scientific Research (B) of the Japan Society for thePromotion of Science under Grant 23360149. Subject Editor H. Zappe.

T. Konishi and K. Machida are with NTT Advanced Technology Cor-poration, Atsugi 243-0124, Japan (e-mail: [email protected];[email protected]).

S. Maruyama and H. Toshiyoshi are with the Institute of Industrial Science,The University of Tokyo, Meguro 153-8505, Japan (e-mail: [email protected]; [email protected]).

M. Mita is with the Institute of Space and Astronautical Science,Japan Aerospace Exploration Agency, Sagamihara 229-8510, Japan (e-mail:[email protected]).

K. Masu is with Tokyo Institute of Technology, Yokohama 226-8503, Japan(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2013.2243111

Fig. 1. MEMS design flowchart based on mechanoelectric cosolver.

I. INTRODUCTION

I NTEGRATION of complementary metaloxidesemiconductor (CMOS) and microelectromechanicalsystems (MEMS) technology is thought to be an enabling

power to deliver the More-than-Moore-type added values to the

large-scale integration (LSI) electronics [1]. Owing to the

technology development in the silicon micromachining in

the past decades, various types of CMOS-MEMS integration

process have been put into a practical use by employing the

existing production lines [2], [3]. Regardless of the importance

in comprehending the electromechanical behavior of a CMOS-

MEMS device, on the other hand, multiphysics simulation

tools have been still in the development phase compared with

the maturity of the computer-aided design tools for LSI.Methodology of MEMS development strongly depends on

the integration scale of functional elements. Fig. 1 shows a

typical flowchart to design an electrostatic microactuator, where

only mechanical deformation and electrostatic attraction force

are involved. In such a simple case, a trial design of MEMS is

created first by using a mask-layout tool, and a corresponding

3-D mesh structure is built by extruding the 2-D patterns

to the appropriate thicknesses. A data table of mechanical

stressstrain is then prepared by using a numerical simulation

tool based on the physical level finite-element method (FEM),

for instance. At the same time, the identical mesh model is

transferred to another simulation tool to prepare a lookup

1057-7157/$31.00 2013 IEEE



756 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 22, NO. 3, JUNE 2013

Fig. 2. MEMS design flowchart based on circuit simulator with HDL behav-ioral model.

table of electrostatic capacitance under given mechanical de-

formation. These two sets of tables are cross-referenced by

yet another tool (usually referred to as a cosolver) to iterate

mechanoelectric simulation to find mechanical deformation

at the equilibrium condition under applied voltage. ANSYS

Multiphysics [4], IntelliSuite [5], and the early version of

MEMCAD [6] fit into this cosolver approach. Transferringdata between the simulation kernels is automatically handled in

recent cosolver tools. Nonetheless, the protocol of such bottom-

up-type simulation is not straightforward because one needs to

rebuild the data set all over again every time the MEMS di-

mensions are changed for trial. Moreover, a nodal analysis data

set becomes very large particularly when simulation accuracy

is pursued, and it costs a considerable computation resource to

perform transient analysis.

Comprehension of overall electromechanical system behav-

ior including the electrical circuit is needed for recent inte-

grated MEMS such as a silicon microphone with an amplifier

or RF-MEMS-tunable capacitors built in a voltage-controlledoscillator circuit. In the simulation methods using the FEM-

type cosolvers [7], an electronic-file-based behavioral model

is synthesized from the FEM simulation results and then ref-

erenced as a subcircuit macromodel in the electrical circuit

simulator, as shown in Fig. 2. The model order reduction

technique is also used to save computation time by extracting

net-list parameters to create an equivalent circuit model for

micromechanical components [8]. Several interface toolboxes

have been developed for commercially available simulation

software such as IntelliSuite with MATLAB Simulink [9].

However, the difficulty still remains as before, because the

simulations in different physical domains are performed on

separate simulation platforms, and that the raw data sets shouldbe prepared each time the photomasks are revised.

Fig. 3. MEMS design flowchart of this work.

One may need to use the FEM-based simulation tool when

parameters are not a priori known, such as the spring constant

of a complex suspension and the damping coefficient of air

around the vibrating body. FEM is also needed when one needs

to study the oscillation modes of a distributed mass system.

Once the appropriate analytical model has been found for such

system, however, we would create a compact model to save

the computational resource. A compact model is an equivalent

circuit originally used to describe the transfer function of anelectronic device by using an analytical equation, and it has

been extended to streamline the MEMS design protocols; it also

helps designers readily reason the consequence of changing

design parameters [6]. Several methodologies to deal with

multiphysics have been reported [10][12]. We also have devel-

oped simulation environments of MEMS based on the compact

model approach that operates on a single platform of electrical

simulator such as Qucs and LTspice to design a multiphysics

system in a top-down manner [13], [14]; a MEMS microactu-

ator or microsensor is represented by a lumped model using a

nonlinear dependent current source described in an analytical

equation model with a few design parameters and operationvoltages. Owing to the single-platform environment, the system

behavior of a MEMS device can be instantly calculated without

passing through any data conversion tools. This feature is quite

useful when one needs to repeat many cut-and-try cycles of

parameter adjustment in both the mechanical and the electrical

circuit designs.

As an extension of the previous work, we have recently

transplanted the multiphysics simulation kernel for MEMS into

a Verilog-A-compatible hardware description language (HDL).

The simulation operates in the single platform of the Cadence

Virtuoso environment [15], which is commonly used by the

analog/mixed-signal electronics engineers. As schematically

shown in Fig. 3, mechanoelectric simulation and circuit sim-ulation are processed simultaneously without transferring data



KONISHIet al.: SIMULATION AND DESIGN TECHNIQUE FOR CMOS-MEMS BASED ON A CIRCUIT SIMULATOR 757

Fig. 4. Analytical model for electrostatic parallel-plate actuator.

between solvers of different domains. The single-platform envi-ronment of Cadence Virtuoso allows us to have access to those

powerful tools for LSI designing such as automatic mask layout

using parameterized cell (PCell), design rule check (DRC), and

layout-versus-schematic (LVS) verification.

In this paper, we report the new scheme of the unified

multiphysics simulation technique developed on the Cadence

Virtuoso environment and present the Verilog-A version of

the equation-of-motion (EOM) solver. We also demonstrate

transient and ac harmonic analysis of electrostatic actuator/

resonator model using the developed simulation tools. As an

example of PCell, we demonstrate automatic synthesis of layout

patterns from the parametric simulation model of a siliconresonator.

II. ANALYTICALM ODEL FORMEMS

ELECTROSTATICM ICROACTUATOR

1) Equivalent Circuit Model: Fig. 4 shows an analytical

model for a parallel-plate electrostatic actuator. We use this

simplified model to explain the procedure to construct the

Verilog-A version of equivalent circuit. The bottom plate is a

mechanically fixed electrode, where a bias voltageV is appliedthrough an electrical resistance R, while the upper electrodeis suspended onto a mechanical anchor with a suspension of a

spring constantk. The motion of the upper plate experiences aviscous damping represented by a dash pod of a coefficient c.The electrostatic attractive force acting on the plates is

F1 = 1

20

S

(gini x)2V2 (1)

where 0 = 8.85 1012 F/m is the dielectric constant of

vacuum,Sis the plate area, giniis the initial gap between theplates, and x is the displacement of the upper plate [16]. Inthis model, we ignored the electrical field concentration on the

edges of the plates but assumed the plate as a part of an infinite

plane.

The plates position under the equilibrium condition at thedifferential voltageV is calculated by (1) with the mechanical

viscoelastic force

F2 = c x k x (2)

where the restoring force F2 has been set in the oppositedirection from the electrostatic attractive forceF1.

The relationship between F1 and F2 is calculated by theEOM as follows:

mx+c x+k x= 1

20

S

(gini x)2V2 (3)

wherem is the lumped mass of the movable upper plate. Thedistributed mass of the spring has been ignored.

The analytical model has been translated into an equivalent

circuit model in the Cadence Virtuoso environment as shown

in Fig. 5 to find a displacement value as a function of the

applied voltage. Module I in Fig. 5 is a subcircuit model for the

parallel-plate electrostatic actuator, and it has been designed to

calculate the electrostatic force F1as electrical current output asa function of drive voltage(s). Module II is for the viscoelasticsuspension to calculate the restoring forceF2as current output.Module III, which has been inserted between the viscoelastic

suspension and the electrostatic actuator, is the EOM cosolver

to calculate the velocity and the displacement x as a functionof the impinging electrostatic and restoring forces. Module IV

is the mechanical anchor. Those subcircuit symbols IIV have

been designed to visually represent the elements.

2) Verilog-A Expressions: We used Verilog-A, which is an

HDL that can handle various mathematical operations, includ-

ing derivation and integration as well as logical expressions

such as an ifthenelse clause. It also has versatility of defining

the input and output ports in either the electrical current andvoltage modes. Apart from our previous publications, in which

we used cascaded electrical capacitors to analog compute the

second-order integral equation [13], Verilog-A description can

be placed in a more straightforward manner by using mathe-

matical expressions. For instance, electrical currentIis writtenas a derivation equation of charge qas

I=ddt(q) (4)

whereddtis a mathematical function of Verilog-A for temporaldifferentiation, which is useful to describe a current flowing

in and out from an electrical capacitance. Also, integration isused to calculate mechanical displacement (as voltageV) fromvelocity (as currenti) as

V =idt(i,ic,y) (5)

whereidt is another Verilog-A function for temporal integra-tion. Parametery is a programmable logical condition to forcethe output value reset toicwhen the conditionaly is fulfilled.

In this paper, we define mechanical force and velocity

as electrical current and voltage, respectively, following the

analogy between mechanical and electrical systems [17]. The

constant parameters such as the plate areaSand the initial gap

g are set in the SI units by using the Edit Object Propertiesdialog of Cadence Virtuoso, as can be seen in Fig. 5 inset.




Fig. 5. Screenshot image of equivalent circuit simulator. Mechanical elements are shown by subcircuits.

Fig. 6. HDL equivalent circuit description for electrostatic parallel-plateactuator.

3) Electrostatic Actuator Module: Fig. 6 shows the elec-

trostatic parallel-plate actuator model coded in the Verilog-A

language, where the massm of the plate is calculated by usingthe plate area S, thickness tp, and material density dp. Thecalculated value ofmis displayed in theEdit Object Properties

dialog as a read-only parameter and is automatically sharedwith the EOM module III by simply connecting the subcircuits.

The electrical behavior of the actuator is described by variable

capacitance, which is written in a plain text format as

cv = ep S/ (gini V(x)) . (6)

This expression is interpreted to an algebraic form of Cp =0S/(g x); note that the displacement x is read as voltage.Those parameters such as ep, S, and gini are passed to themodule as an argument parameter; typical values used in this

work are listed in Table I, including the material constantssuch as the dielectric constant of vacuum ep, Youngs modulusof single crystalline silicon Yg, and movable plate densityof silicon dp. The damping coefficient c has been used as afitting parameter, which is tuned to deliver plausible values of

oscillation amplitude at resonance. In the line next following

the definition of the capacitance, we write

V(Cp)




TABLE IMECHANICAL ANDE LECTRICALPARAMETERS

OF THEDEVICEU NDERTES T

has its own unit in farads, for we are only interested in the

values of variables.

In the same manner, the electrostatic force F1defined by (1)is exported as electrical current as

I(gnd, F)




Fig. 8. HDL equivalent circuit description for viscoelastic suspension.

The velocity v is calculated by integrating the accelerationa in the third block (iii) by using the Verilog-A function idtand then read out from the output portsv1 and v2 as voltage.Block (iii) also has preceding lines with ifthen clauses, where

a logical flagvi0integ is set to be one when the displacementx1comes into contact with the mechanical stoppers at limitor

limit_m on the positive and negative directions, respectively.Whenvi0integ is fulfilled to be one, the velocity is forced tobe null by the conditional description in the idt function, andaccordingly, displacementx1remains at the stopper position.

In a similar manner, the displacement is obtained by integrat-

ing the velocity; the value ofv1is read as voltage, as describedin block (iv). To avoid accumulative error in calculating the

displacement, we force x1 at the stopper position either onthe positive or negative side whenever it comes to the limit,

as described in block (v). Finally, in block (vi), the resultant

displacementx1 is exported to the output ports; the identicalvoltage value ofx1is provided to the output ports on both sides

of the EOM module.5) Viscoelastic Suspension Module: Fig. 8 is a program

code for the viscoelastic suspension module (II). The sum of the

elastic restoring force and the viscosity friction sampled on the

left-hand side (connected to the anchor in Fig. 5) is interpreted

into electrical current as

I(gnd, F m1)




Fig. 10. Transient analysis result of electrostatic parallel-plate actuator; dis-placement as a function of applied voltage.

Fig. 11. AC harmonic analysis result of electrostatic parallel-plate actuator;input reactance spectrum.

of 48.2 V, also known as the pull-in effect. Also, the complete

hysteresis loop has been reproduced by simulation, including

the release from the pull-in status and the subsequent damped

oscillation. Simulation error has been quantitatively verified to

match with the analytical static model (48.2 V).

2) Harmonic Analysis: Harmonic analysis of electrome-chanical behavior is also possible within the Cadence Virtuoso

environment by using the identical simulation model (Fig. 5)

and design parameters (Table I). The actuator model was

considered as an electrical two-port resonator, and the input

impedance was calculated by monitoring the electrical current

through the device and the voltage across the ports.

Fig. 11 shows the simulation results of electrical reactance,

which is the imaginary part of the input impedance plot as a

function of excitation frequency. A peak can be seen at the

mechanical resonance of the modeled actuator, 347.5 kHz (bias

voltage of 15 V), where the reactance component drastically

changes from inductive to reactive around the resonance due to

the phase shift of the mechanical oscillation with respect to theexcitation voltage.

3) Transient and Harmonic Analysis of MEMS in Electrical

Circuit: The developed compact model for a MEMS resonator

has been inserted to replace a quartz resonator used in the

Colpitts oscillator circuit to demonstrate the multiphysics simu-

lation capability of MEMS with integrated circuits, as shown in

Fig. 12, using those parameters listed in Table I. After the cut-

and-try cycles of parameter tuning, including the bias voltagesto the transistor and MEMS, the circuit was found to start

a stable oscillation at the resonant frequency of the MEMS,

as shown in the transient simulation results in Fig. 13(a);

the upper curve shows the output voltage tapped at a node

between the load resistor and the transistor, and the lower the

MEMS resonators mechanical amplitude (perpendicular to the

substrate plane) in tens of nanometric range. A low-pass filter

has been used at the bias voltage port of the actuator to round

off the rising edge of the applied voltages at the beginning of

the simulation, by which the sudden pull-in trip of the movable

plate is avoided. The auxiliary ports on the suspension and the

anchor modules are electrically connected to the bias port of the

actuator to tell the LVS tool of Cadence that all the suspended

structures are of equipotential.

Using the built-in fast Fourier transform (FFT) function of

the Cadence Virtuoso, we obtained the frequency spectrum of

the oscillation, as shown in Fig. 13(b); the oscillation peak

under a bias voltage of 15 V was calculated to be 319.2 kHz,

which was 8% lower than the resonance under a bias voltage of

30 V, i.e., 347.5 kHz, due to the negative spring constant effect

caused by the electrostatic attractive force of the bias voltage. In

fact, silicon resonator can also be represented by a lumped lin-

earLCRmodel by appropriately assigning the mass m, springconstantk , and damping factor c to electrical L, R, and1/C,

respectively [18]. However, an LCR model cannot deal withthe nonlinear phenomenon such as the negative spring constant

effect associated to the electrostatic mechanical coupling.

At this moment, we did not seek for low-voltage operation

of MEMS but demonstrated the simulation capability to find

appropriate design parameters for stable oscillation of an in-

tegrated MEMS circuit, which would have been difficult by

the conventional numerical cosolver based on the 3-D mesh

model because the numerical computation would have taken a

considerably long time to perform.

IV. AUTOMATICM AS K-L AYOUTS YNTHESIS

Automatic synthesis of photomask patterns is an advantage

of using the Cadence Virtuoso environment as a multiphysics

simulation platform for MEMS. In our simulation scheme, the

detail mask layout is generated after the multiphysics simula-

tion. However, it is important to predict the device footprint

beforehand by using the PCell technique to foresee the cost per

device and the electromechanical characteristics associated to

the stray capacitance. We used the script language to correlate

the schematic model of MEMS to a PCell to automatically

generate corresponding mask-layout patterns of appropriate

dimensions and layers for the oscillating mass, suspensions, and

anchors.

Detail descriptions of the converting program are to be re-ported elsewhere, but an example of pattern synthesis has been




Fig. 12. Screenshot image of transient analysis of electrostatic silicon resonator inserted in a Colpitts oscillation circuit.

Fig. 13. Transient analysis results of electrostatic silicon resonator inserted in Colpitts oscillation circuit. (a) Waveforms of plate displacementxand output

voltage V d. (b) FFT analysis of the output voltage.

developed as shown in Fig. 14; only a part of the script code is

shown, as it contains a total of more than 700 lines of codes, in-

cluding parameter declaration, graphic drawing, and automatic

correlation of schematics to cell. The master structure for the

PCell has been prescribed in the program to be a plate with

2 2 release holes, supported with four sets of cantilever-

type suspensions extending out in the horizontal directions, and

anchored onto the substrate surface, as illustrated in Fig. 5 inset.

The plate is assumed to vibrate in the out-of-plane direction as

a rigid body, and the bumps located underneath the suspensions

are the mechanical stoppers. Different from the nodal models

[10], no air-damping model has been included yet, but a damp-

ing coefficient is used as a fitting parameter in this work.

The mechanical correspondence between the connected mass

and suspension modules is known by the electrical connections

set on the auxiliary ports of the developed simulation modules.

The script language has been programmed such that the PCell

dimensions for the structures could be picked up from the

corresponding schematic modules designed with the parameters

shown in Table I, and mask-layout patterns are generated as

shown in Fig. 15. Simple DRC is also performed within the

PCell to check, for instance, whether the plate dimensions

would be large enough to accommodate the release holes.

Owing to the PCell feature of Cadence Virtuoso, any changein parametric dimensions in the schematic model is instantly

reflected to the PCell layout patterns without using extra con-

verting tools.

The generated mask patterns and design parameters have

been transferred to the COMSOL Multiphysics simulator to

cross-check the results. The electrostatic pull-in voltage was

numerically solved to be 48.5 V by COMSOL, which had

a good agreement with the result of this work, i.e., 48.2 V.

Modal analysis of COMSOL, on the other hand, had found

the resonant frequency of the out-of-plane oscillation at

288.8 kHz (with no bias voltage), as shown in Fig. 16; the

resonant frequency predicted by the equivalent circuit model,

i.e., 347.5 kHz, was 17% higher than the COMSOL result, most

probably because no distributed mass of the suspensions was

taken into account in our model but only the lumped mass of

the movable upper plate is considered. The equivalent circuit

model is to be improved to deliver more accurate result by

using corrective coefficients in a similar way that a compact

model for transistor uses many adjustment parameters to fit the

corresponding 3-D device model.

V. DISCUSSION

1) Comparison of Simulation Platforms: In our previous

report, we presented multiphysics simulation methods by usingother circuit simulator platforms of Qucs and LTspice [13],




Fig. 14. Part of PCell script codes to automatically generate layout patternsfor the viscoelastic suspension module.

Fig. 15. Automatically synthesized mask layout for the electrostatic siliconresonator. Dimensional parameters are used in the corresponding PCell scriptcode.

[14]. As compared in Table II, they commonly use a solver for

the EOM programmed as an analog computing circuit. The first

prototype simulator developed on Qucs describes the equiva-

lent circuit models by using the programmable current source

called equation-defined device (EDD) element that could be

written in an algebraic or Boolean form as a function of input

voltage(s); however, Qucs EDD can accept only voltage as

input and generate current as output, which urges us to use

extra circuit modules of current-controlled voltage source for

variable conversion to cascade an EDD output to another. Thesecond prototype implemented on the LTspice environment, on

Fig. 16. COMSOL simulation results of modal analysis.

the other hand, accepts either voltage or current as input to the

LTspice version of EDD, also known as arbitrary behavioral

voltage source (BV) and current source (BI). From a mathemat-ical point of view, no temporaldifferential or integral operation

is supported in Qucs, while such operation can be called by a

dedicated function in the LTspice and Verilog-A environments,

which allows us to program the code in a more readable style.

As an overall evaluation, Verilog A is the most versatile to

develop compact models using equations.

Table III compares the different approaches for MEMS mul-

tiphysics simulation. In the conventional method (correspond-

ing to the flowcharts shown in Figs. 1 and 2), a macromodel for

the micromechanical element is created by the FEM analysis

such as ANSYS or COMSOL, and it is transferred as an

electronic-file-based behavioral model to the circuit or systemsimulator such as Spice, SABER, and MATLAB to perform

cosolving; this method is a very powerful tool to handle the

multiphysics behavior of a distributed mass system of complex

structures, but it requires computation labor because macro-

models usually contain a large number of data points for nodal

analysis.

For a compact model method, on the other hand, one needs to

define the behavior of a MEMS element appropriately by using

an equation before proceeding to the multiphysics simulation

with electrical circuitry. Simulation results are not as accurate

as that of the nodal analysis, due to a limited number of parame-

ters used for simplified lumped analytical models. The compactanalytical model presented in this paper is not intended to

replace the FEM-based simulation methods or nodal analysis,

but it should be used as a shortcut to reach the most proba-

ble simulation results once an appropriate analytical model is

known, in a similar manner that LSI circuit is not usually put

into a simulation tool based on the first principle 3-D tran-

sistor model but designed with a higher level logic simulator.

2) Experimental Cross-Check: Simulation accuracy has

been cross-checked with an experimental device, which is

an electrostatic parallel-plate actuator (oscillator) shown in

Fig. 17; this device was developed by the surface microma-

chining technology using electroplated gold as a structural

layer. Fig. 18 shows the experimental and its fitting simulationcharacteristics of the pull-in hysteresis as a function of applied




TABLE IICOMPARISON OFMEMS EQUIVALENTC IRCUITM ODELING

TABLE IIIMEMS SIMULATION PLATFORMS

voltage and the electrostatic capacitance as a function of exci-

tation frequency. The experimentally obtained pull-in voltage

of 30.3 V was in good agreement with the theoretical value

of 30.8 V, as shown in Fig. 18(b), which was calculated by

the presented simulation method based on the following di-

mensions extracted from the photomask design parameters and

material properties:lp = 300m,wp = 300m,ehl= 20m,ehs= 20 m, ehc= 7 7 = 49, S= 7.04 108 m2, tp =3m,dp = 19300 kg/m

3,m = 4.08 109 kg,gini = 3m,lk = 131.5m,wk = 20m,wp = 20m,tk = 3m,Yg =73GPa,k = 74.1N/m,c= 1.5 105 Pa s,limit = 1.8m,limit_m= 1.8m,ls = 20m, andws = 20m. The vis-cosity coefficient c was used as a fitting parameter to bringthe theoretical results to fit with the experimental behavior

of the electromechanical transient response. The experimental

resonant frequency of 21.2 kHz also exhibited a good agree-ment with the simulation value of 20.7 kHz. The equivalent

Fig. 17. SEM micrograph and design parameters of the measured electrostaticparallel-plate actuator.




Fig. 18. Simulation and experimental results of the actual electro-static parallel-plate actuator. (a) Capacitance-versus-drive-voltage curve.(b) Capacitance-versus-frequency characteristics.

circuit model was tuned to fit the frequency response of the

capacitance, as shown in Fig. 18(b), by inserting a parasitic

capacitor in parallel with the MEMS actuator and by using a

value of 265 fF as a fitting parameter. With this proportion ofsuspension length with respect to the meshed mass, the device

can be well represented by a lumped mass model.

The validity of compact model has also been cross-checked

with other MEMS devices of mechanical rotational systems.

A resonant-type optical MEMS scanner with the electrostatic

vertical comb-drive actuator has been analytically studied to

produce an equation-defined compact model, and its resonant

amplitude behavior to the pulsewidth-modulated voltage has

been reproduced by simulation [19]; this study has been per-

formed to produce a driver circuit for the fiber optic endoscope

with a MEMS spatial modulator. A semiparallel-plate electro-

static torsion mirror for a variable optical attenuator application

has also been studied by this simulation method to predict thevoltage waveform appropriate to minimize the settling time

after the damped oscillation of the scanner [20]. The developed

simulation platform is also good to comprehend the system-

level behavior when MEMS elements are integrated in quantity

such as an electrostatically addressable and latchable multislit

shutter array [21]. MEMS designers would appreciate the short

computation time particularly when repeating the simulation

to seek for a speculative draft version of parameters in thefeasibility study phase. For this reason, we propose the use of

compact-model-based multiphysics simulation to do a rough

sketch of a CMOS-MEMS before giving a final touch on the

mask layout by using the FEM simulation models.

VI. CONCLUSION

We have developed a novel multiphysics simulation and

design technique for CMOS-MEMS based on an electrical

circuit simulator with a Verilog-A-compatible HDL in the

Cadence Virtuoso environment. The EOM for mechanical be-

havior has been implemented as an equivalent circuit in an

analog-computation style such that electromechanical motion

can be cosolved with electrical circuitry on a single platform

without transferring FEM-generated data set between different

simulation tools. An electrostatic MEMS resonator has been

modeled within the developed simulation platform to show the

multiphysics handling capability for the microelectromechan-

ical behavior and the electrical transistor circuit. A prototype

PCell has also been developed to demonstrate automatic mask-

layout synthesis of a simple MEMS resonator. Extension mod-

ules are under development for DRC and LVS functions within

the Virtuoso environment.

ACKNOWLEDGMENT

The authors would like to thank Dr. T. Maruno, Dr. Y. Akatsu,

M. Yano, K. Kudo, and T. Matsushima of NTT Advanced

Technology Corporation for the technical discussions. They

would also like to thank Prof. H. Ito and Prof. N. Ishihara of

the Tokyo Institute of Technology and Prof. H. Fujita of the

Institute of Industrial Science, The University of Tokyo, for the

useful discussion and suggestions regarding the verification of

simulation accuracy.

REFERENCES

[1] Technol. Working Group Rep., International Technology Roadmapfor Semiconductors, Jan. 2011. [Online]. Available: http://www.itrs.net/Links/2011ITRS/Home2011.htm

[2] E. Ogawa, T. Ikehashi, T. Saito, H. Yamazaki, K. Masunishi, Y. Tomizawa,T. Ohguro, Y. Sugizaki, Y. Toyoshima, and H. Shibata, A creep-immuneelectrostatic actuator for RF-MEMS tunable capacitor, Sens. Actuators

A, Phys., vol. 169, no. 2, pp. 373377, Oct. 2011.[3] J. L. Steyn, T. Brosnihan, J. Fijol, J. Gandhi, N. Hagood, IV, M. Halfman,

S. Lewis, R. Payne, and J. Wu, A MEMS digital microshutter (DMS) forlow-power high brightness displays, inProc. IEEE Int. Conf. Opt. MEMS

Nanophoton., Sapporo, Japan, Aug. 912, 2010, pp. 7374.[4] M. Gyimesi, I. Avdeev, and D. Ostergaard, Finite-element simulation

of micro-electromechanical systems (MEMS) by strongly coupled elec-tromechanical transducers, IEEE Trans. Magn., vol. 40, no. 2, pp. 557560, Mar. 2004.

[5] G. B. Chong, K. S. Hoon, I. H. Jafri, and D. J. Keating, Simulations

based design for a large displacement electrostatically actuated microre-lay, Analog Integr. Circuits Signal Process., vol. 32, no. 1, pp. 3746,Jul. 2002.




[6] S. D. Senturia, Simulation and design of microsystems: A 10-year per-spective, Sens. Actuators A, Phys., vol. 67, no. 13, pp. 17, May 1998.

[7] M. Niessner, G. Schrag, J. Iannacci, and G. Wachutka, Experimen-tally validated and automatically generated multi-energy domain coupledmodel of a RF-MEMS switch, in Proc. 10th Int. Conf. EuroSimE, Delft,The Netherlands, Apr. 2629, 2009, pp. 16.

[8] L. D. Tin, J. Iannacci, R. Gaddi, A. Gnudi, E. B. Rudnyi, A. Greiner, andJ. G. Korvink, Non linear compact modeling of RF-MEMS switches by

means of model order reduction, in Proc. 14th Int. Conf. TRANSDUC-ERS, Lyon, France, Jun. 1014, 2007, pp. 635638.[9] IntelliSense Corp., [Online]. Available: http://www.intellisense.com/

MEMS-SoC/MEMS-SoC.html[10] J. E. Vandemeer, M. S. Kranz, and G. K. Fedder, Hierarchical representa-

tion and simulation of micromachined inertial sensors, inProc. Int. Conf.MSM, Santa Clara, CA, Apr. 68, 1998, pp. 540545.

[11] J. V. Clark and K. S. J. Pister, Modeling, simulation, and verificationof an advanced micromirror using SUGAR, J. Microelectromech. Syst.,vol. 16, no. 6, pp. 15241536, Dec. 2007.

[12] G. Schropfer, G. Lorenz, S. Rouvillois, and S. Breit, Novel 3-D modelingmethods for virtual fabrication and EDA compatible design of MEMSvia parametric libraries, J. Micromech. Microeng., vol. 20, no. 6,pp. 064003-1064003-15, Jun. 2010.

[13] M. Mita, S. Maruyama, Y. Yi, K. Takahashi, H. Fujita, and H. Toshiyoshi,Multi-physics analysis for micro electromechanical systems based onelectrical circuit simulator, IEEJ Trans. Elect. Electron. Eng., vol. 6,

no. 2, pp. 180189, Mar. 2011.[14] T. Konishi, S. Maruyama, T. Matsushima, M. Mita, K. Machida,

N. Ishihara, K. Masu, H. Fujita, and H. Toshiyoshi, A SPICE-basedmulti-physics seamless simulation platform for CMOS-MEMS, in Proc.

Int. Conf. SSDM, Tokyo, Japan, Sep. 2224, 2010, G-6-5.[15] Cadence Design Systems, Inc., [Online]. Available: http://www.cadence.

com/products/cic/pages/default.aspx[16] Y. B. Gianchandani, O. Tabata, and H. Zappe,Comprehensive Microsys-

tems, vol. 2. Amsterdam, The Netherlands: Elsevier, 2008, pp. 138.[17] R. A. Johnson,Mechanical Filters in Electronics. Hoboken, NJ, USA:

Wiley, 1983.[18] Y. Nishimori, H. Ooiso, S. Mochizuki, N. Fujiwara, T. Tsuchiya, and

G. Hashiguchi, A multiple degrees of freedom equivalent circuit for acomb-drive actuator,Jpn. J. Appl. Phys., vol. 48, no. 12, pp. 124504-1124504-7, Dec. 2009.

[19] S. Maruyama, M. Nakada, M. Mita, T. Takahashi, H. Fujita, and

H. Toshiyoshi, An equivalent circuit model for vertical comb driveMEMS optical scanner controlled by pulse width modulation, IEEJTrans. Sensors Micromach., vol. 132, no. 1, pp. 19, Jan. 2012.

[20] S. Maruyama, M. Mita, K. Isamoto, C. Chong, H. Fujita, andH. Toshiyoshi, An equivalent circuit model for semi-parallel plate elec-trostatic torsion mirror,IEEJ Trans. Sensors Micromach., vol. 132, no. 4,pp. 7785, Apr. 2012.

[21] T. Takahashi, M. Mita, K. Motohara, N. Kobayashi, H. Fujita, andH. Toshiyoshi, Electrostatically addressable visored shutter array byelectroplating for astronomical spectrography, in Proc. IEEE Int. Conf.Opt. MEMS Nanophoton., Istanbul, Turkey, Aug. 811, 2011, pp. 7980.

Toshifumi Konishi (M12) was born in Kagawa,Japan, in 1976. He received the B.S. and M.S. de-grees in nuclear engineering from Osaka University,Osaka, Japan, in 1999 and 2001, respectively.

In 2001, he joined NTT Advanced Technology,Mitaka, Japan. Since then, he has been engaged indeveloping optical-fiber-type devices and measure-ment systems. He is currently an Engineer with NTTAdvanced Technology Corporation, Atsugi, Japan,and he is currently engaged in research and devel-opment of multiphysics simulation in conventional

circuit simulators for integrated complementary metaloxidesemiconductormicroelectromechanical systems (MEMS); various MEMS devices, includingoptical MEMS and RF-MEMS devices; electrical circuit design such as sensor

large-scale integrations; and measurement systems for MEMS devices.Mr. Konishi is a member of the Japan Society of Applied Physics and theInstitute of Electrical Engineers of Japan.

Katsuyuki Machida(M99) was born in Nagasaki,Japan, in 1954. He received the B.E., M.E., andPh.D. Engineering degrees from Kyushu Institute ofTechnology, Kitakyushu, Japan, in 1979, 1981, and1995, respectively.

In 1981, he joined the Musashino Electrical Com-munications Laboratory, NTT Advanced Technol-ogy, Musashino, Japan, where he was engaged

in research on electron-cyclotron-resonance plasmachemical vapor deposition and the development oflarge-scale integration (LSI) processes and manufac-

turing technologies. Since 1995, he has been engaged in fingerprint sensor LSIand microelectromechanical systems (MEMS) devices and fabrication processas the integrated complementary metaloxidesemiconductor (CMOS)-MEMStechnology. Also, he proposed the spin coating film transfer and hot pressingtechnology as the advanced film formation technology with LSI and MEMSfabrication. He is currently an Executive Engineer with the Nano-TechnologyBusiness Unit, Advanced Products Business Headquarters, NTT AdvancedTechnology Corporation, Atsugi, Japan. He is currently managing the businessand development of material and manufacturing technologies for the integratedCMOS-MEMS devices. Since 2010, he has been a Visiting Professor in theDepartment of Electronics and Applied Physics, Interdisciplinary GraduateSchool of Science and Engineering, Tokyo Institute of Technology, Yokohama,Japan.

Dr. Machida was the recipient of the 2004 Computer Security Symposium

Best Paper Award, the Micro Nano Conference 2006 Most Impressive Presenta-tion Award, the 2006 Institute of Electronics, Information, and CommunicationEngineers Best Paper Award, and the 2009 Integrated MEMS Symposium BestPaper Award.

Satoshi Maruyama received the B.S. degree inelectronic engineering from Gunma University,Maebashi, Japan, in 2008 and the M.E. degree inelectrical and electronic engineering from The Uni-versity of Tokyo, Meguro, Japan, in 2010, wherehe is currently working toward the Ph.D. degree inmultiphysics simulation for microelectromechanicalsystems.

Makoto Mita received the B.E. degree fromTohoku University, Sendai, Japan, and the M.S.and Ph.D. degrees from The University of Tokyo,Meguro, Japan, in 1999 and 2002, respectively.

Since 2003, he has been an Assistant Profes-sor with the Institute of Space and AstronauticalScience, Japan Aerospace Exploration Agency,Sagamihara, Japan. His research interests include

microelectromechanical systems for space applica-tions and nanomechatronics.




Kazuya Masu (M91) received the B.S., M.S., andPh.D. degrees in electronics engineering from TokyoInstitute of Technology, Yokohama, Japan, in 1977,1979, and 1982, respectively.

In 1982, he joined the Research Institute of Elec-trical Communication, Tohoku University, Sendai,Japan. Since 2000, he has been with the Precisionand Intelligence Laboratory, Tokyo Institute of Tech-

nology, where he is currently a Professor in theSolutions Research Laboratory and also serves as theDirector of the ICE Cube Center. He was a Visiting

Professor at Georgia Institute of Technology, Atlanta, GA, USA, in 2002 and2005. His current interests are scalable and reconfigurable RF complementarymetaloxidesemiconductor circuit technology, design environment of integra-tion with diverse functionalities, and circuit and system implementation forswarm electronics.

Dr. Masu is a Fellow of the Japan Society of Applied Physics and theInstitute of Electrical Engineers of Japan. He is a member of the Instituteof Electronics, Information, and Communication Engineers, Japan Institute ofElectronics Packaging, and Japan Management of Technology Society.

Hiroshi Toshiyoshi(M97) received the M.S. andPh.D. degrees in electrical engineering from TheUniversity of Tokyo, Meguro, Japan, in 1993 and1996, respectively.

From 1999 to 2001, he was a Visiting As-sistant Professor at the University of California,Los Angeles, CA, USA. In 2002, he became anAssistant Professor with the Institute of Industrial

Science, The University of Tokyo. From 2002 to2007, he was a Codirector of LIMMS/CNRS-IISUMI-2820, an international joint laboratory of the

Centre National de la Recherche Scientifique, Paris, France. From 2005 to2008, he was the Project Leader of the Optomechatronics Project at KanagawaAcademy of Science and Technology, Kawasaki, Japan. Since May 2009, hehas been a Professor with the Research Center for Advanced Science andTechnology, The University of Tokyo. His research interests include opticaland RF microelectromechanical systems.

Documents

Journal of Microelectromechanical Systems Volume 22 Issue 3 2013 [Doi 10.1109/JMEMS.2013.2243111] Konishi, Toshifumi; Machida, Katsuyuki; Maruyama, Satoshi; Mita, -- A Single-Platform