A REPORT

ON

DESIGN AND ANALYSIS OF

MEMS FILTERS

BY

ANOOP.P.S

2004P3PS107

UNDER THE GUIDANCE OF

Mr. A. AMALIN PRINCE

IN PARTIAL FULFILLMENT OF COMPUTER ORIENTED

PROJECTS BITSGC331

May 24, 2007

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI

GOA CAMPUS

2

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE –

PILANI,

GOA CAMPUS

ZUARINAGAR - 403726

Certified that this is the record of the project work, entitled

‘Design and Analysis of MEMS Filters’, done by Mr.

Anoop P S, ID number 2004P3PS107 during semester II

(2006-2007) in partial fulfillment for the requirement of the

course BITSGC 331 - Computer Oriented Project.

Project Instructor Instructor-in-charge

3

ACKNOWLEDGEMENT

I would like to express my extreme gratitude to my project guide Mr. A. Amalin Prince

for his constant support through out the project. Without his knowledge and experience in

MEMS this project would not have been possible. His valuable advices played a major

role in shaping my project. I also express my heartfelt gratitude to Mr. M T Abilash for

all the encouragement support extended to me. Most of the licensing works of the

software would not have been possible with out him. I would like to make special thanks

to Mr. M.K. Deshmukh for permitting to use the institute facilities through out the

project. I express my gratitude to Dr Bharath Deshpande, instructor in charge of

computer oriented projects (BITSGC331) for giving me an opportunity to work in this

field.

I would also like to thank all my friends who helped me through all the difficulties during

the entire course of the project.

Finally I express my heartfelt gratitude to God almighty who kept my mind always

spirited up for the right knowledge and who took me through all the difficulties I faced

during the project.

4

TABLE OF CONTENTS

TABLE OF FIGURES AND TABLES …….07

INTRODUCTION TO MEMS …….07

BACKGROUND STUDIES …….07

CURRENT TRENDS IN MEMS …….08

FUTURE TRENDS OF MEMS …….08

PROJECT OBJECTIVES …….08

METHODOLOGY …….08

CHAPTER 1 MICRO FABRICATION …….09

1.1 BULK MICRO MACHINIG …….09

1.1.1 ISOTROPIC AND ANISOTROPIC …….09

WET ETCHING

1.1.2 DRY ETCHING …….10

1.2 SURFACE MICRO MACHINING …….10

1.3 MICRO MOULDING AND LIGA …….11

CHAPTER 2 FILTER DESIGN …….12

2.1 ELECTRICAL EQUIVALENT …….13

2.2 WORKING PRINCIPLE …….14

2.2.1 DRIVING CAPACITOR …….14

2.2.2 RESONATING UNIT …….15

2.2.3 COUPLING UNIT …….15

2.2.4 SENSING CAPACITOR …….16

CHAPTER 3 BONDGRAPH ANALYSIS …….17

3.1 POWER VARIABLES OF BONDGRAPH …….17

3.2 FILTER TOPOLOGY …….20

3.3 DESIGNED FILTER IN 20-SIM …….21

3.4 SIMULATED RESULTS …….21

3.4.1 BODE PLOT RESPONSE …….21

3.4.2 STEP RESPONSE …….22

3.4.3 NICHOLS PLOT …….22

3.4.4 NYQUIST PLOT …….23

3.4.5 POLE ZERO PLOT …….23

CHAPTER 4 MEMS PRO SIMULATIONS …….13

4.1 MEMS PRO PACKAGES …….24

4.1.1. LEDIT …….24

5

4.1.2 SEDIT …….24

4.1.3 TSPICE …….25

4.1.4 WEDIT …….25

4.2 FILTER DESIGN IN MEMSPRO …….26

4.2.1 LINEAR COMB DRIVE …….26

4.2.2 LINEAR FOLDED BEAM …….27

4.2.3 RECTANGULAR PLATE …….29

4.3 RESONATOR DESIGN …….31

4.3.1 SCHEMATIC ENTRY …….31

4.3.2 LAYOUT OF THE DESIGN …….32

4.3.3 FREQUENCY RESPONSE …….32

4.3.4 MONTE CARLO ANALYSIS …….33

4.4 FILTER DESIGN …….33

4.4.1 SCHEMATIC VIEW …….34

4.4.2 LAYOUT OF THE DESIGN …….35

4.4.3 FREQUENCY RESPONSE …….35

4.4.4 TSPICE CODE …….36

4.4.5 CHARACTERISTICS OF THE FILTER …….38

4.4.6 SCHEMATIC VIEW OF MODIFIED …….38

4.4.7 FREQUENCY RESPONSE …….39

4.4.8 VARIOUS ANGLE VIEW OF THE DESIGN …….40

CONCLUSION AND FUTURE SCOPE OF WORK …….41

GLOSSARY …….42

REFERENCES ….…43

6

TABLE OF FIGURES / TABLES

FIGURES

Figure:-1 Bulk micro machining ……….09

Figure:-2 Isotropic and Anisotropic wet etching ……….10

Figure:-3 Surface micro machining …….....10

Figure:-4 Surface micro machining …….....11

Figure:-5 Micro molding ……….11

Figure:-6 Filter design ……….12

Figure:-7 Electrical equivalent …….…13

Figure:-8 Driving capacitor ……….14

Figure:-9 Driving capacitor ……….14

Figure:-10 Resonating unit ……….15

Figure:-11 Coupling unit ……….15

Figure:-12 Sensing capacitor ……….16

Figure:-13 Filter topology ……….20

Figure:-14 Filter design ……… 21

Figure:-15 Bode plot ……….21

Figure:-16 Step response ……….22

Figure:-17 Nichols plot ……….22

Figure:-18 Nyquist plot ……….23

Figure:-19 Pole zero plot ……….23

Figure:-20 Comb drive ……….26

Figure:-21 Comb drive sub circuit ……….27

Figure:-22 Folded beam ……….28

Figure:-23 Electrical equivalent ……….29

Figure:-24 Rectangular plate ……….29

Figure:-25 Electrical equivalent ……….30

Figure:-26 Schematic view ……….31

Figure:-27 Layout ……….32

Figure:-28 Frequency response ……….32

Figure:-29 Monte Carlo analysis ……….33

Figure:-30 Schematic view ……….34

Figure:-31 Layout of the Design ……….35

Figure:-32 Frequency response ……….35

Figure:-33 Schematic view of the modified filter ……….38

Figure:-34 Frequency response of filter ……….39

Figure:-35 Various angle view ……….40

TABLES

Table:-1 Electro mechanical equivalent …………………………………………18

Table:-2 Bond graph representation …………………………………....….…….19

Table:-3 Pin out of linear comb drive………………………………………...….27

Table:-2 Pin out of linear Folded Spring ……………………………………….28

Table:-3 Pin out of Rigid Plate ………………………………………………….30

7

INTRODUCTION TO MEMS

The MEMS is the batch-fabricated integrated microscale that:

1. Converts physical stimuli, events, and parameters to electrical, mechanical, and optical

signals and vice versa;

2. Performs actuation, sensing and other functions;

3. Comprise control (intelligence, decision-making, evolutionary learning, adaptation,

self-organization, etc.), diagnostics, signal processing, and data acquisition features,”

Basically, MEMS is a system that consists of microstructures, microsensors,

microelectronics, and microactuators. Microstructure builds the framework of the system.

Microsensor detects signals. Microelectronics processes the signals and gives commands

to the microactuator to react to these signals.

The application of MEMS encompasses many fields beyond traditional electrical and

mechanical engineering. This presents exciting new opportunities for a student and

practitioner of MEMS to become involved in diverse application domains, such as

bioengineering, chemistry, nanotechnology, optical engineering, power and energy and

wireless communication to name a few.

BACKGROUND STUDIES

MEMS technology was evolved by borrowing the features of IC technology by

integrating mechanical parts in to it. So the history of MEMS goes along with IC

technology. After the invent of transistor in 1948 next major break point in the growth of

IC fabrication was the development of photo fabrication technology and that led to the

first integrated circuit in 1958. Later on many works were carried out in the actuating and

sensing properties of silicon. As a result of that first surface micro machined FET

accelerometer came up in 1965 itself. Although many fruitful works were going on that

time, K Peterson’s paper on “Silicon as a Mechanical Material” really revolutionized the

MEMS technology. Works which were going on in the research labs suddenly attained

new geometry and with in a short time they conquered the sensor and actuator markets all

around the globe. Digital Mirror Display from Texas Instruments in 1993 really set up a

land mark in digital light processing and image projection.

CURRENT TRENDS IN MEMS

Although some products like pressure sensors have been produced for 30 years, MEMS

industry in many aspects is still a young industry. The heavily segmented market is

probably the main reason why a consortium like SEMI is still to appear for MEMS.

However everybody agrees that better cooperation and planning has to happen if the cost

of the assembly, test and packaging is to come down. MEMS can currently only look

with envy as IC industry seriously considers producing RFID chips for cents - including

packaging. Again the path shown by the IC industry can serve as a model, and

8

standardization to insure packaging compatibility between different MEMS chip

manufacturers seems the way to go. Considering the smaller market size of most

MEMS component, standard is the only way to bring the numbers where unit packaging

price is reduced substantially. This implies of course automating assembly by defining

standard chip handling procedure, and probably standard testing procedure.

FUTURE TRENDS OF MEMS

MEMS create lots of possibilities in all areas of research and industry. Although MEMS

technology faces many challenges such as lacking advanced simulation and modeling

tools for MEMS design, non-standardized packaging of MEMS devices and systems, and

lack of MEMS Quality control standards, MEMS is still a huge market. So it is expected

that the labor force associated with and money invested in MEMS will keep growing. In

aerospace engineering, except the applications that provided above, future possible

MEMS applications include micro chemical actuators to monitor the emission of jet

engine, microsensors and microactuators for controlling of Euler angles and smart

reconfigurable geometry wings.

From the market side, MEMS will undoubtedly invade more and more consumer

products. The recent use of accelerometer in cameras, hand phone or in the Segway is a

clear demonstration of the larger applicability of the MEMS solutions - and as the prices

drop, this trend should increase in the future.

PROJECT OBJECTIVES

The objective of this work is to design a band pass Filter using MEMS technology. As a

background various manufacturing processes involved in MEMS technology are to be

done. Basic knowledge about the working and designing of a filter is required. A new

method for describing dynamic systems- Bond graph is used for the system study.

Acquaintance with EDA tools like 20-sim, MEMS PRO is required for the effective

design of the system. Finally a band pass filter is to be obtained by coupling various

resonating units. Entire layout and schematic of the design are to be done by MEMS

PRO.

METHODOLOGY

The three main pillars of knowledge for a MEMS engineer are design, fabrication and

materials. In this work various aspects of micro fabrication and design technology used in

the implementation of a MEMS filter are addressed. In the fabrication part, various steps

involved in the MEMS are dealt with limited elaboration. In the design part, analysis of

electrical equivalent of the system is done. Bond Graph analysis is used to study various

transient and frequency response of the system. A software tool 20-sim is used for the

same. Once the analysis of the electrical equivalent is done actual real system is

considered. An industry standard software MEMS PRO is used for this purpose.

Schematic as well as the layout of the design is done in the software. Various simulation

results are also noted.

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1. MICRO FABRICATION

Micro-fabrication is the set of technologies used to manufacture micro-sized structures.

Because of the micro scale operation of MEMS devices, MEMS fabrication technology

quickly took inspiration from microelectronics for fabrication purposes. Techniques like

photolithography, thin film deposition by chemical vapor deposition (CVD) or physical

vapor deposition (PVD), thin film growth by oxidation and epitaxy, doping by ion

implantation or di_usion, wet etching, dry etching, etc have all been adopted by the

MEMS technologists. Moreover, MEMS has spurred many unique fabrication techniques

that we will also describe in our panorama of MEMS fabrication introducing bulk

micromachining, surface micromachining, LIGA, etc.

1.1 BULK MICRO MACHINING

Bulk micromachining refers to the formation of micro

structures by removal of materials from bulk substrates.

The bulk substrate in wafer form can be silicon, glass,

quartz, crystalline Ge, SiC, GaAs, GaP or InP. The

methods commonly used to remove excess material are wet

and dry etching, allowing varying degree of control on the

profile of the final structure.

1.1.1. ISOTROPIC AND ANISOTROPIC WET ETCHING

Wet etching is obtained by immersing the material in a chemical bath that dissolves the

surfaces not covered by a protective layer. The main advantages of the technique are that

it can be quick, uniform, very selective and cheap. The etching rate and the resulting

profile depend on the material, the chemical, the temperature of the bath, the presence of

agitation, and the etch stop technique used if any. Wet etching is usually divided between

isotropic and anisotropic etching. Isotropic etching happens when the chemical etches the

bulk material at the same rate in all directions, while anisotropic etching happens when

different etching rate exists along different directions. However the etching rate never

reaches 0 and it is actually impossible to obtain etching in only one direction. This is

commonly quantified by estimating the over etch (w/d), that is the lateral etch with

respect to the vertical etch, as shown in the figure. This parameter may range between 1

for isotropic etching to about 0.01 for very anisotropic etch, obtained for example by

etching Silicon in a KOH bath. For substrates made of homogeneous and amorphous

material, like glass, wet etching must be isotropic, although faster surface etching is

sometimes observed. However, for crystalline materials, e.g. silicon, the etching is either

isotropic or anisotropic, depending on the type of chemical used. In general, isotropic

etchants are acidic, while anisotropic etchants are alkaline.

10

1.1.2 DRY ETCHING

Dry etching is a series of methods where the solid substrate surface is etched by gaseous

species. Plasma is usually involved in the process to increase etching rate and supply

reacting ions and radicals. The etching can be conducted physically by ion bombardment

(ion etching or sputtering and ion-beam milling), chemically through a chemical reaction

occurring at the solid surface (plasma etching or radical etching), or by mechanisms

combining both physical and chemical effects (reactive ion etching or RIE). These

methods have various etching selectivity and achieve different etching profiles and

usually the etching is more anisotropic and vertical when the etching is more physical,

while it is more selective and isotropic when it is more chemical. Most of these methods

are discussed in standard microelectronics process books, but they take a different twist

when they are applied to MEMS fabrication as in general MEMS necessitates deep (> 5

µm) etching.

1.2. SURFACE MICROMACHINING

Unlike bulk micromachining in

which microstructures are formed

by etching Into the bulk substrate,

surface micromachining builds

up structures by adding materials,

layer by layer, on the surface of

the substrate. The thin film layers

deposited are typically 15 µm

thick, some acting as structural

layer and others as sacrificial

layer. Dry etching is usually used

11

to define the shape of the structure layers, and a final wet etching step releases them from

the substrate by removing the supporting sacrificial layer.

The choice of the deposited layers is dictated by many

different considerations, as the deposition temperature

(dictated by the temperature resistance of the material

on the substrate and the allowable thermal stress), the

magnitude of the residual stress in the layer (too much

stress cause layer cracking), the con-formality of the

deposition (how the deposited layer follows the profile

of the substrate as shown in Fig. 3.5), the roughness of the deposited layer, the existence

of pinholes and the uniformity of the deposition, the speed of deposition (to obtain

thicker layers).

1.3. MICRO MOULDING AND LIGA

Other methods exist where no material is removed but this time molded to achieve the

desired pattern. LIGA, a German acronym for lithography, electroforming and molding is

the mother of these methods. LIGA makes very high aspect ratio 3-D microstructures

with non-silicon materials such as metal, plastic or ceramics using replication or molding.

LIGA process begins with X-ray lithography using a synchrotron source (e.g. energy of

2.4 GeV and wavelength of 2 °A) to expose a thick layer of X-ray photo resist (e.g.

PMMA). Because of the incredibly small wavelength, diffraction effects are minimized

and thick layer of photo resist can be patterned with sub-

micron accuracy. The resist mold is subsequently used for

electroforming and metal (e.g. nickel using NiCl2 solution) is

electroplated in the resist mold. After the resist is dissolved,

the metal structure remains. This structure may be the final

product but to lower down the costs, it usually serves as a

mold insert for injection molding or hot embossing. The

possibility to replicate hundreds of part with the same insert

opens the door to cheap mass production. When the sub-

micrometer resolution is not much of a concern, pseudo-

LIGA processes can be advantageously used. These

techniques avoid using the high cost X-ray source for the mold fabrication by replacing it

by the thick photo resist SU8 and a standard UV exposure or even by fabricating a silicon

mold using DRIE.

12

2. FILTER DESIGN

This work presents a new filter synthesis approach based on the electrical coupling of

individual MEMS resonators. In this method, inductors are used to couple MEMS

resonators to each other and provide a high order transfer function. The main advantage

of electrical coupling approach in filter synthesis is its greater potential for extension into

the UHF frequency range. In the UHF frequency range (0.3-3GHz) and above, which is

the band of interest for many wireless applications, due to the very small size of the

resonator element (<10µm), mechanical coupling will require sub-micron in size

coupling elements (i.e., wires) that are difficult to fabricate using optical lithography. In

addition, filter characteristics are sharply dependant on the positioning and dimensions of

the coupling elements and optimized design of a filter will require mechanical design

expertise and specialized simulation tools. Filter synthesis using electrical coupling does

not require mechanical design expertise and provides more design flexibility for electrical

engineers.

Filter design

13

Over the past few years, extensive efforts have been devoted to replace off-chip

frequency-selective components (i.e., frequency references and filters) in

telecommunication systems with on-chip silicon-micro machined MEMS resonators. In

order to achieve the desired selectivity, high order band pass filters consisting of a

number of coupled resonators are required. Mechanical coupling technique, traditionally

used for implementation of high order filters from individual mechanical resonators, has

been applied to micromechanical resonators for filter synthesis. Electrically sensed and

actuated MEMS filters up to the third order with center frequencies up to 68MHz as

well as electrically actuated and optically sensed filters up to the 20th order at center

frequencies of a few MHz have been reported using the mechanical coupling technique.

In this approach of filter designing, dividing the filter into functional blocks i.e.,

resonators and coupling units is being used. A resonator is a series or parallel

combination or passive elements resistor, capacitor and inductor. Resonance of a circuit

occurs when the reactive component of the impedance cancels out. At this frequency

capacitive reactance will be equal to inductive counterpart. So system turns out to be

purely resistive i.e., minimum impedance level. Circuit will carry maximum current at

this frequency. The above given description is for series resonant circuits. Operating

conditions changes entirely for parallel resonant circuits. Here at resonant frequencies

circuits suffers maximum impedance and so minimum current. Here we are making use

of series resonant circuits. Output of a series resonating circuit will be an overshoot at the

resonant frequency and attenuated output at all other frequencies.

Each resonator can be coupled with other to form a band pass filter. This coupling can be

done in two ways, either capacitive coupling or inductive coupling. Here we are using

inductive coupling for our purpose. With each resonator unit added, pass band ripples

also increase. For the optimized design we need to consider the area and power constraint

before deciding upon the number of resonating units.

Design of any MEMS system starts from the electrical equivalent of the same. This

conversion is done basically to reduce the complexity of working in two energy domains

(electrical and mechanical).

2.1 ELECTRICAL EQUIVALENT

14

2.2 WORKING PRINCIPLE

The MEMS filter designed consist of the following functional blocks.

1. Driving Capacitor C01

2. Resonating Unit

3. Coupling Unit

4. Sensing Capacitor

2.2.1 DRIVING CAPACITOR

Driving capacitor comes in the input section of the filter. Input signal is fed to this

driving capacitor. Driving capacitor is selected to be a comb drive type with one fixed

and other variable plate.

Supply voltage is given to the fixed end. Free end is connected to the resonating unit.

When a supply voltage is applied to the fixed plate electric filed is set up between the

plates of the comb drive. It creates an electrostatic force on both plates. This causes

movable plate to move according to the input voltage applied. When a sine wave is

applied movable plate starts vibrating. These vibrations are coupled to the resonating unit

by the movable plate.

15

When the actuating voltage is applied at one terminal due to the electrostatic force

movable plate moves in. This introduces more capacitance in the path. Capacitance of

dual plate capacitor is directly proportional to the common area. So when movable plate

moves in it increases the area covered and thereby increases the capacitance.

2.2.2 RESONATING UNIT

Vibrations from the driving capacitor are carried over to the resonating unit. It is simply a

flexible mass attached to the movable end of comb drive. This flexible mass has got the

electrical equivalent of a resonator

Resonating mass can be converted to electrical equivalent given above. It receives the

vibrations from the driving capacitor and start vibrating according to the input frequency.

Vibrations will reach maximum for a particular frequency called resonant frequency

given by the R L C combination. These vibrations it will pass on to the sensing capacitor

or next resonating unit.

2.2.3 COUPLING UNIT

Coupling unit connects two resonating units. It receives vibrations from one resonator

and passes it on to the other. Here we are using inductive springs for coupling.

16

Coupling of two resonators results in introducing one more peak in the response of the

resonator. By adjusting the parameters of the coupling unit, we can attain the required

band for the filter designed. Various types of coupling are in use. Some of them are

inductive coupling, capacitive coupling and both inductive and capacitive coupling. In

the current design inductive coupling is made into use.

2.2.4 SENSING CAPACITOR

This part of the design is assigned with the job of receiving the vibrations from the

resonating unit. Sensing unit is also a comb drive with one end fixed and other end

movable. Movable end is connected to the resonating unit while output of the system is

taken from the fixed end of the comb drive. Unlike the driving capacitor, this acts more

like a sensor. It responds to the mechanical input and produces electrical output. Output

produced is directly proportional to the frequency of vibration of the resonating unit.

Resonating mass will be having maximum vibration at its resonant frequency. Eventually

sensing capacitor senses this shoot up in the vibration and produces an output shoot in

terms of voltage.

This completes the full working of the system. Next step in the designing is the

simulation part. In this work a two step approach is being used for simulation. First the

electrical equivalent of the filter is considered and simulated using software called 20-

SIM. This software is using Bondgraph analysis to convert the mechanical filter to

electrical domain. After studying the electrical characteristics of the circuit,

corresponding mechanical equivalent was considered. This part of the work was done in

another tool MEMSPRO. Both the simulation works are provided.

17

3. BOND GRAPH ANALYSIS

The bond graph is a modeling tool that provides a unified approach to the modeling and

analysis of dynamic systems, especially hybrid multi-domain systems including

mechanical, electrical, pneumatic, hydraulic components, etc. It is the explicit

representation of model topology that makes the bond graphs a good candidate for use in

open-ended design search.

Bond graphs have four embedded strengths for design applications, namely, the wide

scope of systems that can be created because of the multi- and inter-domain nature of

bond graphs, the efficiency of evaluation of design alternatives, the natural combinatorial

features of bond and node components for generation of design alternatives, and the ease

of mapping to the engineering design process. Those attributes make bond graphs an

excellent choice for modeling and design of a multi-domain system.

By this approach, a physical system can be represented by symbols and lines, identifying

the power flow paths. The lumped parameter elements of resistance, capacitance and

inductance are interconnected in an energy conserving way by bonds and junctions

resulting in a network structure. From the pictorial representation of the bond graph, the

derivation of system equations is so systematic that it every thing can be put in an

algorithm. The whole procedure of modeling and simulation of the system may be

performed by some of the existing software, ENPORT, Camp-G, SYMBOLS,

COSMO, 20-SIM and LorSim.

3.1 POWER VARIABLES OF BOND GRAPH

The language of bond graphs aspires to express general class physical systems through

power interactions. The factors of power i.e., Effort and Flow have different

interpretations in different physical domains. Yet, power can always be used as a

generalized co-ordinate to model coupled systems residing in several energy domains.

One such system may be an electrical motor driving a hydraulic pump or an thermal

engine connected with a muffler; where the form of energy varies within the system.

Power variables of bond graph may not be always realizable (viz. in bond graphs for

economic systems); such factual power is encountered mostly in non-physical domains

and pseudo bond graphs.

18

Generally for the analysis of any system, its response in terms of differential equations is

written and those equations are solved simultaneously to get the time domain analysis of

the system. Bond graph analysis provides an easier way of representing system in terms

of the power flow in the system. If we consider electrical systems in bond graph, there are

only two kinds of junction “1” junction and “0” junction

“0” junction corresponds to a parallel junction in electrical circuits. So current flow

marked by ‘f’ will be the summation of rest. Where as the voltage marked by ‘e’ or effort

will remain same at the junction

“1” junction corresponds to series junctions in electrical circuits. So current ’f’ will

remain same while voltage ‘e’ will be the algebraic sum.

0 e1

e2

e3 f1

f2

f3

e1 = e2 e2 = e3

f1 – f2 – f3 = 0

⇔⇔⇔⇔

19

Similar representations are there for the sources as well as passive elements. Its Bond

graph representation is given in the following table.

Inductance

Capacitance

Resistance

Transformer

Gyrator

Effort source

Flow source

1 e1

e2

e3 f1

f2

f3

⇔⇔⇔⇔

f1 = f2 f2 = f3 e1 – e2 – e3 = 0

20

3.2 FILTER TOPOLOGY

The required filter topology can be attained in two ways- series connection of resonating

unit and bridge unit or cascaded connection of resonator unit. Both the topologies are

illustrated below.

21

3.3 DESIGNED FILTER IN 20-SIM.

3.4SIMULATED RESULTS

3.4.1 BODE PLOT RESPONSE

22

3.4.2 STEP RESPONSE

3.4.3 NICHOLS PLOT

23

3.4.4 NYQUIST PLOT

3.4.5 POLE ZERO PLOT

All the electrical properties of filter are studied from various plots. But the effect of

dimension of each component in frequency response is still unknown. In order to solve

that problem, yet software called MEMSPRO is used. Complete analysis of the filter in

terms of physical dimensions can be done.

24

4. MEMS PRO SIMULATIONS

In MEMS PRO we will be utilizing the actual MEMS actuators and sensors. A wide

variety of transducers are available in MEMS library.

The MEMS Pro behavioral library (MemsLib.sdb) contains building blocks for system-

level simulations. The library contains schematic symbols and behavioral models for

common MEMS components. All of the components in this library are parameterized,

and most of them have corresponding layout generators in L-Edit.

MEMSPRO comes with 4 basic units LEDIT, SEDIT, WEDIT and TSPICE.

4.1 MEMSPRO PACKAGES

4.1.1 LEDIT

LEDIT is used to create the layout of the design. It is equipped with all the drawing

toolbars and MEMSPRO tool bar. This MEMSPRO tool bar is used to create MEMS

designs. All the MEMS components can be accessed from the library of this tool bar. It

works in a drag and drop format. Library includes elements for active elements, passive

elements, test elements, thermal elements, optical elements, fluidic elements and

resonator elements. While selecting each component itself, all of its parameters are listed.

Desired values for the dimensional parameters can be entered there itself.

Interconnections between the components can be done by overlapping of one over the

other. One the design is done, 3D model can be generated from it. Views from all the

angles are possible using it. Cross sections can be generated from the 3D models. 3D

animations are also added features of MEMSPRO.

4.1.2 SEDIT

SEDIT is used to create the schematic entry of the design. All components are assigned

some schematic equivalent and put in a library. Required components are taken from this

library. S-Edit design files consist of modules. A module is a functional unit of design,

such as a transistor, a gate, an amplifier, or an entire design. Modules contain two types

of components.

PRIMITIVES: Geometrical objects created with drawing tools

INSTANCES: References to other modules in the file.

An instancing module is a module that contains an instance; the instanced module is the

original. In an efficient design, primitives, instances, and modules form a pyramid-like

hierarchical structure. The most elementary, often-instanced modules reside near the

bottom of the hierarchy; modules composed largely of instances, near the top. Actions on

a particular module affect all of its instances in modules above it in the hierarchy.

25

SEDIT has two viewing modes, schematic mode and symbol mode. Symbol consists of

drawn shapes, ports and properties. All the drawing tools like box, polygon, circle etc are

available in this mode to create the schematic entry. Schematics define the connectivity

of primitives and lower-level modules within higher-level modules. Schematics show

how smaller functional units or basic devices (such as transistors) are connected to form

higher-level units (such as inverters). TSPICE code for the designed system can be

extracted from the same file.

4.1.3 TSPICE

At the heart of T-Spice’s operation is the input file (also known as the circuit description,

the netlist, or the input deck). This is a plain text file that contains the device statements

and simulation commands, drawn from the SPICE circuit description language, with

which T-Spice constructs a model of the circuit to be simulated. Input files can be created

and modified with any text editor, though the text editor integrated with T-Spice is ideal

as it includes default and fully-customized syntax highlighting. Input files can be very

long and complex, but they do not have to be written from scratch; they can be efficiently

created using the export facility of a schematic editor (such as S-Edit™), or the extraction

facility of a layout editor (such as L-Edit™). In addition, T-Spice includes a Command

Tool that automates error-free SPICE language entry.

Any number of text files can be open at once, each in its own window in the display area.

However, only one window can be “active” at any given time, and only an input file

displayed in an active window can be edited and simulated.

4.1.4 WEDIT

Visualizing the complex numerical data resulting from VLSI circuit simulation is critical

to testing, understanding, and improving those circuits. W-Edit is a waveform viewer that

provides ease of use, power, and speed in a flexible environment designed for graphical

data presentation. Some of the advantages of W-Edit are as follows.

o It has got tight integration with T-Spice, Tanner EDA’s circuit-level simulator. W-

Edit can chart data generated by T-Spice directly, without modification of the

output data files. W-Edit charts data dynamically as it is produced during the

simulation.

o Charts are automatically configured for the type of data being presented.

o A data set is treated by W-Edit as a unit called a trace. Multiple traces from different

output files can be viewed simultaneously, in single or multiple windows. You can

copy and move traces between charts and windows. You can perform trace

arithmetic or spectral analysis on existing traces to create new ones.

o You can pan back and forth and zoom in and out of chart views, including

specifying the exact x-y coordinate range W-Edit displays. You can measure

positions and distances between points easily and precisely with the mouse.

26

Numerical data is input to W-Edit in the form of plain or binary text files. Header and

comment information supplied by T-Spice is used for automatic chart configuration.

Runtime update of results is made possible by linking W-Edit to a running simulation in

T-Spice.

4.2 FILTER DESIGN IN MEMSPRO

For the required filter, two resonators coupled with an inductive element are required.

Linear electrostatic comb drive is used as the driving and sensing capacitor. Linear folded

beam is used as the inductive unit. Rectangular plate is used as the resonating mass.

These components are taken from the library and connections are made. A short

description of those components is given below.

4.2.1 LINEAR ELECTROSTATIC COMB DRIVE.

It is designated as LinearCombDrive_DirX. It is mainly a capacitor with specific

features. Each of the two plates of the capacitor are comb-like. One of the plates is

anchored to the substrate while the other, by a specific mechanism, is allowed to move in

one direction only (direction of the comb teeth).

The electrostatic force due to the electrical field between the plates can make the movable

plate actuate on another mechanism. Hence, LinearCombDrive_DirX can be used as an

actuator. The capacitance between the plates depends on the position of the movable plate

with respect to the anchored one. In other words, the capacitance of the comb is sensitive

to the displacement of the movable plate. Hence, LinearCombDrive_DirX can be used as

a sensor.

DEVICE SYMBOL

27

Pins

LinearCombDrive_DirX is a capacitor with specific features. It is a four-pin device with

VAnchor and VActuate as the capacitor terminals. Disp and Anchor provide

information about the electrostatic force between the capacitor plates in the form of the

current flowing through them and they receive information about the displacement

of the movable plate in the form of the voltage across them.

4.2.2 LINEAR FOLDED BEAM SUSPENSION

The LinearFoldedSpring_DirX component models the spring constant of a linear folded

beam suspension element. It is a passive device. The mechanical part of the model

describes the spring constant K where it is modeled as a support beam fixed at one side

28

with guided movement on the other end. The electrical part of the model consists of a

resistance that accounts for the electric resistance of different parts. This part is usually

used as a part of a resonator.

DEVICE SYMBOL

PINS

29

The linear folded beam suspension is a passive element: It responds to movement rather

than generating movement.

4.2.3 RECTANGULAR PLATE WITH ONE DEGREE OF FREEDOM

The RigidPlate_DirX component models the mechanical and the electrical behavior of a

rectangular micro-machined plate joining different MEMS components. The plate is

mostly used in comb resonators where it joins the mechanical springs, the

Actuating comb and the sensing comb. This module has one mechanical degree of

freedom in the Y axis direction.

DEVICE SYMBOL

30

The plate function is to connect several MEMS components together. The mass of the

plate and the damping induced on it when it is in motion contribute significantly to the

overall performance of the system of connected components.

EQUIVALENT CIRCUIT

31

4.3 RESONATOR DESIGN:

For the filter design first the design of a resonator is considered. It consists of a single

resonating unit with a driving capacitor and one sensing capacitor. Resonating frequency

will be decided by the device dimensions. Schematic entry of a resonating unit is as given

below.

4.3.1 SCHEMATIC ENTRY

right_eright_m

V=50

V=0mag=1.0

phase=0.0

Vdc=0.0

Disp_b

Disp_l Disp_r

Disp_t

RigidPlate_DirX

Vactuate_l Vactuate_r

Vpassive_b

Vpassive_t

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

DirX

Disp

LinearCombDrive

VActuate VAnchor

Anchor

DirX

Disp

LinearCombDrive

VActuateVAnchor

32

4.3.2 LAOUT OF THE DESIGN

4.3.3 FREQUENCY RESPONSE

0 10 20 30 40 50 60 70 80 90 100

Frequency (kHz)

0

5

10

15

20

25

30

35

40

45

Vo

lta

ge

Ma

gn

itu

de

(n

V)

v m(right_m)

x1= x2= dx=-980.00 -980.00 0.00 myreson

0 10 20 30 40 50 60 70 80 90 100

Frequency (kHz)

-150

-100

-50

0

Vo

lta

ge

Ph

as

e (

de

g)

v p(right_m)

0.00

x1= x2= dx=-980.00 -980.00 0.00 myreson

33

4.3.4 MONTE CARLO ANALYSIS

Flexural width of linear folded beam is continuously varied with values by a Gaussian

approximation. For each value of width each resonating frequency is obtained. 30 such

runs were performed and the resulting graph is plotted.

1k 3k 10k 32k 100k

Frequency (Hz)

-200

-190

-180

-170

-160

-150

-140

-130

-120

Vo

lta

ge

Ma

gn

itu

de

(d

B)

vdb(right_m)

myreson

From the graph it can be seen that output of the filter is going high at its resonant

frequency decided by the device dimensions. Corresponding phase response is also given.

Inter relation between the layout and schematic can also be understood. In the layout,

actual view of the device on chip is obtained with exact dimensions. In schematic, only

electrical connections are visible. By MONTE CARLO analysis, the dependency of

resonant frequency on device dimensions is made clear. When the flexural width of linear

folded beam is varied, resonant frequency also varies with it.

4.4 FILTER DESIGN

From the resonator design above, filter can be designed by coupling it with another

resonator. Various types are coupling are used for this purpose. Here inductive coupling

is made into use. Two resonating masses are connected together using a linear folded

beam. Second resonating unit introduces one more peak in the response curve. All the

frequencies between these two peaks are passed by the filter. Length and width of the

folded beam decides the location of the second peak and thereby the bandwidth.

34

right_eright_m

V=50

V=0

mag=1.0

phase=0.0

Vdc=0.0Disp_b

Disp_l Disp_r

Disp_t

RigidPlate_DirX

Vactuate_l Vactuate_r

Vpassive_b

Vpassive_t

Disp_b

Disp_l Disp_r

Disp_t

RigidPlate_DirX

Vactuate_l Vactuate_r

Vpassive_b

Vpassive_t

Anch

orBeam

_Dir

X

Disp

Line

ar F

olde

d VAnc

hor

VPas

sive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

DirX

Disp

LinearCombDrive

VActuate VAnchor

Anchor

DirX

Disp

LinearCombDrive

VActuateVAnchor

4.4.1 SCHEMATIC VIEW OF A FILTER

35

4.4.2 LAYOUT OF THE DESIGN

4.4.3 FREQUENCY RESPONSE

36

Here the second peak can be seen because of the coupled resonator. All frequencies in

between the two peaks will be passed by the filter.

4.4.4 TSPICE CODE

* SPICE netlist written by S-Edit Win32 11.20

* Written on Apr 22, 2007 at 11:08:54

* Waveform probing commands

.probe

.options probefilename="final.dat"

+ probesdbfile="C:\Program Files\SoftMEMS\MEMS Pro

v6.0\Tutorial\Resonator\final.sdb"

+ probetopmodule="myresonator"

.SUBCKT Derivative in out Cin=1e-6 Rfb=1 GAIN=1 A0=1k

Eamp out1 0 ampneg 0 '-1*A0'

Eampin ampin 0 in 0 1

Eampout out 0 out1 0 '-1*GAIN*(A0+1)/(A0*Rfb*Cin)'

Cin ampin ampneg 'Cin'

Rfb out1 ampneg 'Rfb'

.ENDS

.SUBCKT LinearCombDrive_DirX Anchor Disp VActuate VAnchor TPOLY=TPOLY1

+ finger_overlap=3e-005 rotor_active_width=9.8e-005 stator_yoke_width=1.4e-005

+ rotor_yoke_width=1.2e-005 finger_length=6e-005 finger_gap=3e-006

+ finger_width=4e-006 floore='Rotor_Active_Width/(Finger_Width+Finger_Gap)'

+ number_of_gaps='2*FLOOR(FLOORE/2)+2'

+ C0='NUMBER_OF_GAPS*EPS0*EPSREL*TPOLY/FINGER_GAP'

XDERIV_V3_1 Disp vel_free Derivative

XDERIV_V3_2 Anchor vel_fix Derivative

Gcomb Disp Anchor POLY(1) VAnchor VActuate 0 0 '0.5*C0'

Gcomb2 VAnchor VActuate POLY(2) vel_free vel_fix VAnchor VActuate 0 0 0 0 'C0' 0

G1 VAnchor VActuate

chg='(FINGER_OVERLAP+V(DISP,ANCHOR))*C0*V(VAnchor,VActuate)'

.ENDS

.SUBCKT LinearFoldedSpring_DirX Anchor Disp VAnchor VPassive

+ flexure_length=0.0002 flexure_width=3e-006

Relec VAnchor VPassive R='rsPoly1*(flexure_length/flexure_width+2)'

Rspr Anchor Disp

R='1/(ymodPoly1*tPoly1)*(flexure_length/flexure_width)*(flexure_length/flexure_widt

h)*(flexure_length/flexure_width)'

.ENDS

37

.SUBCKT DERIV_V3 in out Cin=1e-6 Rfb=1 GAIN=1 A0=1k

Eamp out1 0 ampneg 0 '-1*A0'

Eampin ampin 0 in 0 1

Eampout out 0 out1 0 '-1*GAIN*(A0+1)/(A0*Rfb*Cin)'

Cin ampin ampneg 'Cin'

Rfb out1 ampneg 'Rfb'

.ENDS

.SUBCKT RigidPlate_DirX Disp_b Disp_l Disp_r Disp_t Vactuate_l Vactuate_r

+ Vpassive_b Vpassive_t plate_width=0.0002 plate_length=0.0002

Velec Vpassive_t Vactuate_l 0.0

Velec2 Vactuate_r Vpassive_t 0.0

Velec3 Vpassive_b Vactuate_r 0.0

Cdamp Disp_l 0 '(9*plate_width*plate_length*mu)/tOx1'

Xderiv_acc vel acc DERIV_V3

Xderiv_vel Disp_l vel DERIV_V3

Gmass Disp_l 0 POLY(1) acc 0 0 'plate_width*plate_length*tPoly1*rhoPoly1' 0

Vmass1 Disp_t Disp_l 0.0

Vmass2 Disp_r Disp_t 0.0

Vmass Disp_b Disp_r 0.0

.ENDS

* Main circuit: myresonator

XLinearCombDrive_DirX_1 0 N4 N2 N10 LinearCombDrive_DirX finger_gap=3e-006

+ finger_length=6e-005

XLinearCombDrive_DirX_2 0 right_m right_e N1 LinearCombDrive_DirX

+ finger_gap=3e-006 finger_length=6e-005

XLinearFoldedSpring_DirX_1 0 N9 N17 N7 LinearFoldedSpring_DirX

+ flexure_length=0.0002 flexure_width=3e-006

XLinearFoldedSpring_DirX_2 0 N6 N17 N3 LinearFoldedSpring_DirX

XLinearFoldedSpring_DirX_3 0 N14 N17 N13 LinearFoldedSpring_DirX

XLinearFoldedSpring_DirX_4 0 N18 N17 N19 LinearFoldedSpring_DirX

+ flexure_length=0.0002 flexure_width=3e-006

XLinearFoldedSpring_DirX_5 N20 N23 N21 N12 LinearFoldedSpring_DirX

+ flexure_length=0.0002 flexure_width=3e-006

XRigidPlate_DirX_1 N6 N4 N23 N9 N2 N12 N3 N7 RigidPlate_DirX

XRigidPlate_DirX_2 N14 N20 right_m N18 N21 right_e N13 N19 RigidPlate_DirX

v1 N10 Gnd 0.0 AC 1.0 0.0

v2 N1 Gnd 0

v3 N17 Gnd 50

.ac dec 100 1k 40k

.include "C:\Program Files\SoftMEMS\MEMS Pro v6.0\Tutorial\Resonator\process.sp"

* End of main circuit: myresonator

.END

38

wqwqq w

out

V=350

V=-5

mag=1.0

phase=0.0

Vdc=0.0

Disp_b

Disp_l Disp_r

Disp_t

RigidPlate_DirX

Vactuate_l Vactuate_r

Vpassive_b

Vpassive_t

Disp_b

Disp_l Disp_r

Disp_t

RigidPlate_DirX

Vactuate_l Vactuate_r

Vpassive_b

Vpassive_t

Disp_b

Disp_l Disp_r

Disp_t

RigidPlate_DirX

Vactuate_l Vactuate_r

Vpassive_b

Vpassive_t

Disp_b

Disp_l Disp_r

Disp_t

RigidPlate_DirX

Vactuate_l Vactuate_r

Vpassive_b

Vpassive_t

+ -+ -

Anch

orBeam

_Dir

X

Disp

Line

ar F

olde

d VAnc

hor

VPas

sive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear Folded

VAnchor

VPassive

Anch

orBeam

_Dir

X

Disp

Line

ar F

olde

d VAnc

hor

VPas

sive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear Folded

VAnchor

VPassive

Anch

orBeam

_Dir

X

Disp

Line

ar F

olde

d VAnc

hor

VPas

sive

Anchor

Beam_DirX

Disp

Linear FoldedVAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear Folded

VAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear Folded

VAnchor

VPassive

Anchor

Beam_DirX

Disp

Linear Folded

VAnchor

VPassive

Anchor

DirX

Disp

LinearCombDrive

VActuate VAnchor

Anchor

DirX

Disp

LinearCombDrive

VActuateVAnchor

4.4.5 CHARACTERISTICS OF THE FILTER

Lower cut off frequency : 16.66 kHz

Upper cut off frequency : 23.62 kHz

Mid band frequency : 19.83 kHz

Quality factor : 2.849 :

The designed filter is having a mid band frequency of 19.83 kHz. Quality factor of the

filter is relatively low. Performance of filter can be improved by coupling more

resonators in series. Modified designs and their frequency responses are given below.

4.4.6 SCHEMATIC VIEW OF MODIFIED FILTER

39

4.4.7 FREQUENCY RESPONSE

In the modified design the pass band ripples which were present in the earlier design are

removed. This design provides better quality factor too. We can see that there is always a

trade off between filter performances and area occupied by it on the chip. Power

consumed by the system is also a major concern. Normally MEMS devices consume a

large amount of power for the actuation of micro structures. Here an optimum design

with 4 resonating units is presented. This design strikes exact balance between area

occupied and the performance indices. Once the design in done, layout file is converted

to GDS II format and sent to furnace for manufacturing.

40

4.4.8 VARIOUS ANGLE VIEWS OF THE DESIGN

41

CONCLUSION AND FUTURE SCOPE OF WORK

Various aspects in designing of a MEMS device were dealt with ample illustrations. I

selected filter design because it illustrates the excellent relationship between electrical

and mechanical domains. Energy given in the electrical form is converted to mechanical

form by the driving capacitor and then converted into electrical domain by the sensing

capacitor. MEMS filter synthesis approach based on the electrical coupling of electro

mechanical resonators was used. All the electro mechanical conversions were done using

Bond graph analysis. A trial and error method was used in designing the final design in

MEMSPRO. Resonator designed gave an output peak at 16.63 kHz. Two such resonators

were coupled inductively to give a bandpass filter with cut off frequencies at 16.63 kHz

and 23.62 kHz. Later on more than 2 resonators were coupled to get a novel filter design

with optimum chip area and perfect working parameters.

In MEMSPRO we have the freedom of using only components available in MEMS

library. All designs already exist in library. User can just drag and drop components and

make connections accordingly. The freedom which user lacks here is being provided by

yet another EDA tool COVENTORWARE. Using that one can design any MEMS

structure by placing the layer one over the other and removing materials from it, which is

more systematic in approach. So the current work can be extended by doing the complete

design of each component, which we were just using from library now. Such a design

flow provides much more insight into the manufacturing process involved in the design

too.

42

GLOSSARY

DLP : Digital Light Processing

LQR : Linear Quadratic Regulator

PWM : Pulse Width Modulation

CVD : Chemical Vapor Deposition

PVD : Physical Vapor Deposition

LPCVD : Low Pressure Chemical Vapor Deposition

PECVD : Plasma Enhanced Chemical Vapor Deposition

RIE : Reactive Ion Etching

IBM : Ion beam Milling

SOI : Silicon on Insulator

GDS : Graphic Data System

43

REFERENCES

[1]. Fan Z., Hu J., Seo K., Goodman E., Rosenberg R., and Zhang B.: Bond Graph

representation and GP for Automated Analog Filter Design. Genetic and Evolutionary

Computation Conference Late-Breaking Papers, San Francisco. (2001) 81-86

[2]. Fan Z., Seo K., Rosenberg R. C., Hu J., Goodman E. D.: Exploring Multiple Design

Topologies using Genetic Programming and Bond Graphs. Proceedings of the Genetic

and Evolutionary Computation Conference, GECCO-2002, New York. (2002)

1073-1080.

[3]. Zhou Y.: Layout Synthesis of Accelerometers. Thesis for Master of Science.

Department of Electrical and Computer Engineering, Carnegie Mellon University.

(1998)

[4]. Kailath, T., Linear Systems. 1980, New Jersey: Prentice Hall, Inc.

[5]. Karnopp, D. C., “Power-Conserving Transformation: Physical Interpretations

And Applications using Bond Graphs,” Journal of the Franklin Institute, 1969,

288(3), pp. 175-201.

[6] Louca, L. S., Stein, J. L., “Energy-Based Model Reduction of Linear

Systems,” Proceedings International Conference on Bond Graph Modeling,

San Francisco, California, 1999.

[7]. T. Mattila, J. Kiihamaki, T. Lamminmaki, O. Jaakkola, P. Rantakari, A. Oja, H.

Seppa, H. Kattelus, and I. Tittonen, “A 12 MHz micromechanical bulk acoustic mode

oscillator,” Sensors & Actuators A-Physical, vol. A101, pp. 1-9, 2002.

[8]. M. L. Roukes, “Nanoelectromechanical systems,” Technical Digest, Solid-State

Sensor and Actuator Workshop, Hilton Head Island, SC, USA, 2000.

[9] K. Wang and C. T.-C. Nguyen, High-Order Medium Frequency Micromechanical

Electronic Filters, Journal of Microelectromechanical Systems, Vol. 8 No. 4, December

1999.

[10] L. Lin, C. T.-C. Nguyen, R. T. Howe, and A. P. Pisano, Micro Electromechanical

Filters for Signal Processing, Micro Electro Mechanical Systems 1992.

[11] B. Piekarski, D. DeVoe, M. Dubey, R. Kaul, J. Conrad, R. Zeto, Surface

Micromachined Piezoelectric Resonant Beam Filters,

http://www.enme.umd.edu/SSSC/pdf_3/HH00.pdf.

[12] Tai-Ran and Hsu, MEMS & MICROSYSTEMS Design and Manufacture, 2002

44

[13] Chang Liu, Foundations of MEMS, 2006

[14] http://www.ee.duke.edu/~jungsang/ECE299_02

[15] http://www.dlp.com/dlp_technology/dlp_technology_overview.asp

[16] http://www.memsrus.com/documents/MUMPs.Papers.htm

[17] http://web.mit.edu/jcperry/6.777/Project/MEMS.pdf