a holistic approach to automated synthesis of mixed-technology digital mems sensors

8/12/2019 A Holistic Approach to Automated Synthesis of Mixed-Technology Digital MEMS Sensors

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Sensors & Transducers Journal, Vol. 117, Issue 6, June 2010,pp. 1-15

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SSSeeennnsssooorrrsss&&&TTTrrraaannnsssddduuuccceeerrrsssISSN 1726-5479

2010 by IFSA

http://www.sensorsportal.com

A Holistic Approach to Automated Synthesis

of Mixed-technology Digital MEMS Sensors

Part 1: Layout Synthesis of MEMS Component with DistributedMechanical Dynamics

Chenxu ZHAO and Tom J. KAZMIERSKISchool of Electronics and Computer Science

University of Southampton, UK

E-mail: [email protected], [email protected]

Received: 13 May 2010 /Accepted: 21 June 2010 /Published: 25 June 2010

Abstract: This contribution presents a novel, holistic methodology for automated optimal layout

synthesis of MEMS systems embedded in electronic control circuitry from user-defined high-level

performance specifications and design constraints. The proposed approach is based on simulation-based

optimization where the genetic-based synthesis of both mechanical layouts and associated electronic

control loops is coupled with calculations of optimal design parameters. The underlying MEMS models

include distributed mechanical dynamics described by partial differential equations to enable accurate

performance prediction of critical mechanical components. The proposed genetic-based synthesis

technique has been implemented in SystemC-A and named SystemC-AGNES. A practical case study of

an automated design of a capacitive MEMS accelerometer with Sigma-Delta control demonstrates theoperation of the SystemC-AGNES platform. This Part 1 of the paper focuses on the layout synthesis of

mechanical components, while the full synthesis methodology including automated and optimal

electronic control loop synthesis is outlined in Part 2.Copyright 2010 IFSA.

Keywords:MEMS accelerometer, Synthesis, Sigma-Delta control, SystemC-A

1. Introduction

This two-part paper presents an effective holistic genetic-based synthesis flow (SystemC-AGNES)applied to automated layout synthesis of mechanical components of Micro-Electro Mechanical Systems

(MEMS) and configuration synthesis of associated electronic control system. Part 1 of this paper focuses


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on the layout synthesis of mechanical sensing component and automated configuration synthesis of the

control system is demonstrated in Part 2 [1].

MEMS are currently used in a wide range of applications due to their significant advantages such as low

cost, small form factor and low power consumption. MEMS sensors, for example accelerometers and

gyroscopes, are widely used in consumer applications, mainly by the automotive industry, in

mixed-technology control designs such as safety air cushion, active suspension or anti-lock brakesystem. Modern high precision inertial navigation and guidance systems are also based upon MEMS

sensors embedded in mixed-technology control loops [2].

The design of a typical MEMS system requires an integration of elements from two or more disparate

physical domains: mechanical (translational, rotational, hydraulic), electrical, magnetic, thermal etc.

Different parts of a MEMS system are traditionally designed separately using different methodologies

and different tools applied to different energy domains. Two engineering teams traditionally collaborate

to create a MEMS-based IC: one using 3-D CAD such as CoventorWare to create the MEMS

mechanical model, and the other team, meanwhile, using an EDA tool from such companies such as

Cadence to create the associated ICs. Although this approach provides accurate behaviour simulation of

MEMS devices with their associated electronics, it requires multiple tools and it is difficult to provide ICdesigners with an automated synthesis and performance optimization system. This difficulty is primarily

caused by disparities between the different tools and the inconvenience of generating new MEMS

macromodels, when the MEMS layout changes, for incorporation into the IC simulations performed at

the IC design stage.

Analogue and Mixed-Signal(AMS) Hardware Description Languages(HDLs) such as VHDL-AMS

which was standardized by the IEEE in 1999 [3] and later equipped with another IEEE standard for

multiple energy domain packages [4] or Verilog-AMS [5] are able to integrate components from

different energy domains into a single model. However, automated design methodologies for the whole

integrated system supporting mixed physical domains are still lagging. This is mainly due to the fact that

state-of-the-art tools supporting AMS HDLs. such as the commonly used SystemVision from MentorGraphics [6] are not designed to support simulation-based synthesis and optimization where users would

be able to develop and implement complex numerical algorithms. Wang proposed a methodology to

realize a genetic optimization algorithm (GA) in a VHDL-AMS testbench [7], but the software tools

used took about 16 hours to fulfill a simple task.

Usually, the design of a MEMS system requires a significant amount of specialist human resources and

time in the iterative trial-and-error design process to determine the crucial trade-offs in meeting the

performance specifications. Therefore there is an increasing need for automated synthesis techniques

that would shorten the development cycle and facilitate the generation of optimal configurations for a

given set of performance and constraint guidelines. Some methodologies have already been proposed for

automated synthesis of mechanical parts in MEMS systems [8-13]. For example, Tamal presented a

method for rapid layout synthesis of a lateral surface-micromachined accelerometer from high-level

functional specifications and design constraints [9]. The design problem is regarded as a nonlinear

optimization problem. Standard off-the-shelf solvers (NPSOL) and a grid-based numerical optimization

algorithm are used to maximize the system's performance. In another approach, Zhun and Wang

presented a hierarchical evolutionary synthesis of MEMS device layout [12]. They divided the design

into two levels: system-level which uses behavioral macromodels and detailed physical-level based on

geometric layout models. At the system level, a combination of genetic programming and bond graphs

are used to generate and search for design candidates satisfying design specifications. At the physical

layout level, optimizations are carried out to meet more detailed design objectives.

In the above approaches the automated design of MEMS is accomplished either by simulation-based

optimization or formulating the design requirements as a numerical nonlinear constrained optimization


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problem, and solved with powerful optimization techniques. However, these methodologies are

constrained to the layout synthesis of a mechanical MEMS device. The salient feature of our approach

proposed here is that it realizes an automated design of a whole MEMS system which contains not only

layout synthesis of the sensing elements but also optimal configuration synthesis for associated

electronics. Synthesis of the electronic control loop is demonstrated in Part 2 of this paper [1]. The

proposed approach integrates a MEMS component library, an electronic control loop library, an efficient

fast MEMS simulation engine implemented in SystemC-A [14] and an evolutionary computationmethod (GA).

SystemC-A is a superset of SystemC developed to extend modeling capabilities of SystemC to the

analogue and mixed physical domain [14]. In addition to standard digital modelling capabilities of

SystemC, SystemC-A provides constructs to support user-defined ordinary differential and algebraic

equations (ODAEs), analogue system variables, and analogue components to enable modeling of

analogue and mixed-signal systems from very high levels of abstraction down to the circuit level.

Support for digital-analogue interfaces is also provided for smooth integration of digital and analogue

parts. The analogue simulator uses efficient linear and nonlinear solvers to assure accurate and fast

simulations of the analogue model. Most of the powerful features of VHDL-AMS and Verilog-AMS are

provided in SystemC-A in addition to a number of extra advantages such as high simulation speed,support for hardware-software co-design and for high levels of modeling. However, the current

SystemC-A can only describe analogue systems by using ODAEs. In modern mixed-domain

applications this limits accurate modelling of system blocks, especially in the mechanical domain, which

exhibit distributed physical effects described by Partial Differential Equations (PDEs). To ensure

accurate modeling of distributed components, Finite Difference Approximation (FDA) approach is

applied to convert PDEs to a series of ODAEs which can be solved by SystemC-A. Distributed

mechanical modelling is important in MEMS designs with digital control because dynamics of

mechanical components may severely affect the system's performance. For example, it has been well

documented that sense fingers in lateral capacitive accelerometers may vibrate due to their own

dynamics, thus rendering the feedback excitation ineffective, causing an incorrect output and a failure of

the system [15, 16]. This scenario cannot be reflected by the conventional mass-damper-spring modelbased on a 2nd order ordinary differential equation. In our dedicated SystemC-A model, distributed

mechanical dynamics models are implemented through FDA to enable accurate performance prediction

of critical mechanical components embedded in the mixed-technology control loop.

The synthesis technique presented here is applicable to a wide class of digital MEMS sensors with

electronic control. We demonstrate its operation using a capacitive MEMS accelerometer in a

Sigma-Delta control loop [17, 18] as a case study. The capacitive digital MEMS accelerometers are

notoriously difficult to design using traditional methods because here the mechanical element forms an

integral part of the control loop. This feature makes a separation of the two technology domains in

the design process very effortful.

2. Genetic-based Synthesis of MEMS Sensors with Electronic Control Loop

The proposed automated synthesis approach explores the design according to user defined specifications

and optimizes the structural parameters of the mechanical MEMS elements and the associated electronic

control loop parameters. The automated optimal synthesis flow is shown in Fig. 1. After specifying the

design objectives and constraints, such as the die area of the sensing element and feedback voltage in the

electronic control loop, available components in the MEMS primitive library and the electronic control

loop primitive library are combined automatically to form a valid initial design set. This set of initial

designs is loaded into the synthesis module after parameter initialization and encoding phase. Thesynthesis module uses a genetic algorithm to create new MEMS structures and optimizes their

parameters for best performance. Our approach integrates mixed-technology models into a single


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simulation engine which could be easily invoked from various optimization loops. Unlike traditional

MEMS design tool sets, this approach avoids a generation of macromodels in order to realize co-design

and co-simulation.

Fig. 1.Automated synthesis flow in SystemC-AGNES.

2.1. Synthesis Initialization

The two libraries, MEMS primitive library and electronic control loop primitive library, contain typical

components that are widely used in practical MEMS designs. Every member in the libraries is a data

structure record which includes its type code, geometrical parameters for MEMS primitives,

system-level design parameters for electronic primitives and constraints. This Part 1 of the paper focuseson layout synthesis of the mechanical component while the configuration of the associated electronic

control loop is fixed.

2.1.1. MEMS Primitive Library

The mechanical part of a lateral capacitive MEMS accelerometer is composed of a proof mass, springs

and comb fingers. In the lateral capacitive structure, the proof mass is suspended by springs and it is

equipped with sense and force comb fingers which are placed between fixed fingers to form a capacitive

bridge. The sense fingers moves with the proof mass resulting in a differential imbalance in capacitance

which is measured. The electrostatic force acting on the force fingers is used as the feedback signal to

pull the proof mass in the desired direction. The available mechanical components in the MEMS

primitive library (Fig. 2) are discussed below.

1. Springs:4 typical springs are available in the MEMS components library for this case study: classic

serpentine spring, rotated serpentine spring, folded spring and spring beam. The layout and geometrical

parameters with constraints are shown in Fig. 2.

2. Proof mass:The proof mass contains unit squires with etch holes for release. The number of these

holes is determined by the size of proof mass and size of holes. There are 4 connecting nodes and

2 connecting sides on the proof mass, 4 connecting nodes is used to connect springs and 2 connectingsides are used for comb sense and force fingers connection.


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3. Comb fingers:The sensing element dynamics in the sense-direction is normally modeled to reflect

only one resonant mode by a lumped mass, spring, and damper, which is represented by a simple 2nd

order ordinary differential equation:

2

2

( ) ( )( ) ( )

in

d z t dz t M D Kz t Ma t

dt dt , (1)

whereMis the total mass of the structure,D and Kare damping and spring coefficients correspondingly.

( )z t is the deflecttrion of the proof mass and ( )ina t is the input acceleration.

m m

m m

m m

m m

m

m

m

m

m

m

m m

m m

m

m m

m m

m m

m m

m m

m

m

m

m m

m

m m

mm

m m

m m

m

m m

m m

m m

m m

m m

m m

m m

m

Fig. 2. MEMS primitive component library.


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In reality, the sensing fingers in a lateral structure are distributed elements with many resonant modes.

As their dynamics affect the performance of a control system, the motion of the sense beam should

be distributed, for example using the following partial differential equation [16]:

2 5 4

2 4 4

( , ) ( , ) ( , )( , ) ( )

D in

y x t y x t y x tA C I EI Fe x t Aa t

t x t x

, (2)

wherey(x, t), a function of time and position, represents the beam deflection,E,I, DC , ,A are physical

properties of the beam: is the material density,A is the cross sectional area (Wf * T), where Wf and T

are width and thickness of the beam,E is Young's modulus andI is the second moment of area and DC is

the internal damping modulus. The product EI is usually regarded as the stiffness. Fe(x, t) is the

distributed electrostatic force along the finger.

The boundary conditions at the clamped end and the free end are shown in the following equations. At

the clamped end (x=0):

(0, ) ( )y t z t (3)

(0, )0

y t

x

(4)

and at the free end (x=l):

2

2

( , )0

y l tM

x

(5)

3

3

( , )0

y l tQ

x

, (6)

where ,M and Q denote the slope angle, the bending moment and the shear force respectively and l is

the finger length.

The total distributed sense capacitances between the sense fingers and electrodes are:

10

0

1( )

( , )

l

sC t N T dxd y x t

(7)

20

0

1( )

( , )

l

sC t N T dx

d y x t

, (8)

whereNs is the number of sense fingers. The output voltage can be calculated as:

1 2

1 2

( ) ( )out m

C CV t V t

C C

, (9)

where Vm(t) is high frequency carrier voltage applied on the fixed electrode in comb fingers unit.

Here the Finite Difference Approximation (FDA) is applied to convert PDEs to a series of ODAEs. If the


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beam is divided into N segments and the deflection of the beam is discretized as:

( ) ( , )n

y t y n x t n=1,2,3... N (10)

The first order spatial derivatives can be approximated by finite differences:

1( ) ( ) ( )n n ny t y t y t

x x

(11)

Similar approximation can be applied to higher order spatial derivatives. Eq. (2) is hence transformed to

a system of the following ODAEs:

2

2 1 1 2

2 4

( ) ( ) ( ) ( ) ( ) ( )( 4 6 4 )

( )

n n n n n nDd y t dy t dy t dy t dy t dy t C I

At x t t t t t

2 1 1 24

( )

( ( ) 4 ( ) 6 ( ) 4 ( ) ( )) ( )( )

n

n n n n n in

Fe tEI

y t y t y t y t y t Aa tx x ; n=3,4,5...N-2 (12)

1( ) ( )y t z t ; n=1 (13)

2

32 4 2 1

2 4

( )( ) ( ) ( ) ( )( 4 6 3 )

( )

D dy td y t C I dy t dy t dy t At x t t t t

24 3 2 14

( )( ( ) 4 ( ) 6 ( ) 3 ( )) ( )

( )in

Fe tEIy t y t y t y t Aa t

x x

; n=2 (14)

2

1 1 2 3

2 4

( ) ( ) ( ) ( ) ( )( 2 5 4 )

( )

N N N N NDd y t dy t dy t dy t dy t C IAt x t t t t

11 2 34

( )( 2 ( ) 5 ( ) 4 ( ) ( )) ( )

( )

NN N N N in

Fe tEIy t y t y t y t Aa t

x x

; n=N-1 (15)

2

1 2

2 4

( ) ( ) ( ) ( )( 2 )

( )

N N N NDd y t dy t dy t dy t C IA

t x t t t

1 24

( )( ( ) 2 ( ) ( )) ( )

( )

NN N N in

Fe tEIy t y t y t Aa t

x x

; n=N (16)

Boundary conditions provide additional equations. The slope angle at the fixed end is approximated as:

1 01( ) ( )( )

0y t y ty t

x x

(17)

and the bending momentMand shear force Qat the free end as:


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21 1

2 2

( ) ( ) 2 ( ) ( )0N N N N

y t y t y t y tM

x x

(18)

3

2 1 1

3 3

( ) ( ) 3 ( ) 3 ( ) ( )0N N N N N

y t y t y t y t y tQ

x x

(19)

Eq. (13) represents the motion of the clamped end of the sense fingers (1( )y t ) which moves with the

lumped proof mass whose deflection z(t) is obtained from the solution of Eq.(1).

2.1.2. Electronic Control Loop

High-performance MEMS sensors exploit the advantages of closed-loop control strategy to increase the

dynamic range, linearity, and bandwidth of sensor. In particular, digital modulators for closed-loop

feedback control schemes, whose output is digital in the form of pulse-density-modulated bitstream,

have become very attractive in a number of MEMS applications [17-19]. A conventional 2 nd order

electromechanical control systems is shown in Fig. 3. In this configuration, mechanical sensingelement is used as a loop filter to form the 2ndorder electromechanical modulator. Vf1 and Vf2 are the

feedback voltages obtained from the DAC and Vm(t) is a high frequency modulation carrier voltage. The

gain Kcv represents the signal pick-off from differential change in capacitance to voltage and K is the

gain of the voltage booster amplifier following the pick-off stage. The lead compensator is used to

ensure the stability of the control loop. It is an optional component in electronic control primitive library

depending on whether the sensing element is over damped or under damped. A clocked 1-bit quantizer is

used for oversampling and generating a pulse-density modulated digital output signal. However, the

equivalent DC gain of the mechanical integrator in the 2nd-order electromechanical modulator is

relatively low and this leads to a poor signal-to-noise ratio (SNR). To improve the SNR, the mechanical

element can be cascaded with additional electronic integrators to form high order topologies [17 ].The

example of automated synthesis discussed in this section focuses on the synthesis of MEMS layout and

the electromechanical accelerometer is fixed and of 2ndorder. Full synthesis which includes both

MEMS layout and electronic control loop is presented in Part 2 [1].

Fig. 3. 2nd

order electromechanical modulator.

2.1.3. Parameter Initialization and Encoding

The automated design process starts with a specification of the design objectives and constraints.Drawing from the MEMS primitive component library and electronic control loop library, a set of

configurations is automatically selected (parents of first generation in GA) and loaded into the synthesis


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module. These feasible configurations not only contain MEMS mechanical layouts but also associated

electronic control system topologies. Fig. 4 and Table 1 show an example of a feasible configuration to

illustrate the parameter initialization and encoding phase. This MEMS accelerometer here contains 4

spring beams, 14 force fingers, 20 sense fingers and a proof mass with associated 2ndorder control

loop. The component code of each component is shown in the Fig. 2. Then the geometrical layout

parameters of mechanical part and the associated system-level design parameters of electrical control

systems are generated to describe the feasible layouts combining with the component code (Fig. 4).

Fig. 4. Example of Parameter Initialization and Encoding.

Table 1. Representation of a population member in GA for the MEMS accelerometer example.

MEMS component library Code Description

Spring 2 Beam spring

Proof mass 5 Proof mass with etching holes

Comb drive 6 Sense and force fingers

Electronic Control loop library Code DescriptionSigma-Delta Control system 1(fixed) 2

ndorder Sigma-Delta Control

2.2. Genetic Approach to Synthesis

Genetic Algorithm (GA) has been selected for our case studies as it is a very popular and well tested

optimization algorithm which has demonstrated good performance in a wide variety of complex global

optimization problems where modelling difficulties arise and there is no obvious way to find optimal

solutions [20]. It has already been used for mechanical layout optimization [21].

The optimization problem is considered as a constrained optimization as both of the design and

performance parameters are bound by inequality constraints that must be met:

Maximize: ( )F x (20)

Subject to:

_ _[ , ]n n low n highx V V , n=1,2,3, (21)

where F(x)is the fitness function to be optimized with design parameter vector x, nx represents the nth

design parameter, Vn_low and Vn_high are the lower and upper constraints of the nth design parameter.


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Performance figures of the candidate designs are evaluated by a fitness function that rates the solutions

according to their performance parameters. Fitness function is usually constructed in a weighted scalarerror form:

( )R

F x wR

, (22)

where w is the weight coefficient,R is the system performance measure obtained from each simulation

while R is the designer specified objective value. In this case study, w is equal to 1 if all user definedperformance constraints are met, otherwise w is set to 0.0001. If minimization of a fitness parameter is

required, e.g. the sensing element area, w is set to -1 if performance constraints are met or -10 otherwise.

In the case study discussed below, a performance evaluation engine is added to the simulator to enable

measurements of the power spectrum density (PSD) and signal-to-noise ratio (SNR), as the designobjectives, through FFT of the output bitstream. The die area of and static sensitivity of the mechanical

sensing element are also used as system performance objectives or constraints.

After the synthesis initialization, the classical genetic operations of selection, crossover and mutation areapplied to the current generation parents in order to create a new generation. In the selection operation,

designs with better performance (higher fitness) are retained. After the selection, if the crossoveroperation is triggered, i.e. crossover probability is higher than a fixed threshold, new MEMS layouts are

composed from primitives and associated control systems by exchanging elements of randomly selectedparents, such as mechanical springs and electronic control blocks. Details of an example of crossoveroperation in mechanical sensing element synthesis are illustrated in Fig. 5. As shown in the figure, in this

example only the crossover probability of the spring component is higher than the trigger probability of

70%, so the spring components of parents A and B exchange leaving the other components unchanged inthe creation of new offspring.

Fig. 5. An example of crossover operation in mechanical layout synthesis.

For each individual in the new generation, the genes in their chromosomes have a fixed probability tomutate at random positions. The mutation operation for the mechanical sensing element is illustrated by

the example shown in Fig. 6 and Table 2. The mutation operation contains two phases: componentmutation and components parameter mutation. In the first phase, if the mutation probability for thecomponents is higher than the fixed trigger (50 % in this example) such as the beam spring and comb

fingers, new components are automatically composed using the MEMS primitive library and each

parameter of the mutated components gets a random value within its specified range. If there is nomutation in the first phase, the mutation probability of each component parameter will be compared withthe trigger (60 % in the example) to decide whether this parameter should mutate. As shown in Fig. 6,


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after the mutation the beam spring mutated to a folded spring and comb fingers mutated to themselves

but with different parameters such as a shorter length and a higher number of force fingers. For the proofmass, only the number of holes and width were changed at the second mutation phase.

This evolution process finishes when the generation number exceeds the specified maximum number.

The optimal solution within a given generation is that with the highest fitness.

Fig. 6. An example of mutation operation in mechanical layout synthesis.

Table 2. An example of mutation operation in mechanical layout synthesis.

MEMS

component

MEMS component

Mutationprobability

(trigger 50 %)

Component

parameters

Component parameters

Mutation probability

(trigger 60 %)

Beam Spring 56 % Spring mutationEach parameter of themutated spring get random

value within range

Lm: length of proof mass 55 % No mutation for length

Wm: Width of proof

mass70 % Mutation

Wh: Size of holes 23 % No Mutation

Ns: Number of holes 92 % Mutation

Proof mass withetching holes

30 % No mutation forproof mass

T: Thickness of proofmass

10% No mutation

Comb fingers73 % Comb fingers

mutation

Each parameter of themutated comb sense and forcefingers such as Lf, d0 and Nsget random value withinrange

3. Synthesis Verification to Provide Appropriate Performance Metrics for the

Synthesized MEMS Geometries

The practical operation of the proposed synthesis flow for the accelerometer embedded in a conventionalcontrol loop is demonstrated below by three experiments listed in Table 3. In the first experiment, the

system is optimized for maximum SNR with performance constraints, and in the second and third

experiments - for maximum static sensitivity and minimum area respectively.

As can be seen from the results presented in Table 3 and Fig. 8 for each experiment, the genetic synthesis


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algorithm composed different layout structures and produced different performance parameters. Kx, Kz

are the stiffnesses in the axes X and Z correspondingly, and Ky is the stiffness in the sensing axis Y inthis case study. The larger the stiffness ratios Kx/Ky, and Kz/Ky the larger the relative movement of the

accelerometer along the sensing axis.

The synthesis process was carried out using the following design parameters:

1) Oversampling ratio: OSR=1282) Bandwidth: 512 Hz

3) Oversampling frequency:fs= 172 Hz4) Input force: 100 Hz acceleration with 1g amplitude

Table 3. Summary of synthesis experiments.

Design

objective

Performance constrants Synthesized

layout

SNR

(dB)

Static

sensitivity

Kzy Kzy Area

(2

m )1 Maximum

SNR

SNR>30dB

Area1fF/G

Fig. 8. (a) 39.8 1.8fF/G 202 1.875 1.82e-7

2 MaximumStatic

sensitivity

SNR>30dBStatic sensitivity>2fF/G

Fig. 8. (b) 32.9 4.77fF/G 4.91 10.72 3.78e-7

3 Minimumarea ofmechanical

sensingelement

SNR>30dB

Area


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0 20 40 60 80 1000

0.5

1

1.5

2

2.5

Generation

Fitness

(b) Experiment 2: Maximum static sensitivity

Optimized result:SNR=32.9dBStatic Sensitivity=4.77fF/G

Area=3.78e-7m2

0 20 40 60 80 100-14

-12

-10

-8

-6

-4

-2

0

Generation

Fitness

(c) Experiment 3: Minimum area


Area=1.07e-7m2

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

Generation

Fitness

(a) Experiment 1: Maximum SNR


Area=1.82e-7m2

Fig. 7. Fitness improvement between generations.

Table 4. Summary of synthesized results for Experiments 1, 2 and 3.

MEMS components Experiment 1 Experiment 2 Experiment 3

Proof mass Ml = 341 m

Mw = 73 m T = 2.9 m

Wh = 4.9 m

Nh = 28

Ml = 695 m

Mw = 136 m T = 2.85 m

Wh = 4.2 m

Nh = 496

Ml = 205 m

Mw = 125 m T = 2.5 m

Wh = 5.7 m

Nh = 40

Comb fingers Lf = 122 m

Tf = 2.2 m

d0 = 1.0 m

Ns = 42Nf = 4

Wanchor=4 m

Lf = 183 m

Tf = 2.1 m

d0 = 1.5 m

Ns = 50Nf = 10

Wanchor=4 m

Lf = 84.6 m

Tf = 2 m

d0 = 1.36 m

Ns = 24Nf = 8

Wanchor=4 m

Spring (Folded spring)

Lo1 = 218 m Lo2=255 m

Wo = 2 m

Lp = 11.5 m

Wp = 2.1 m

(Classic serpentine spring)

N = 2Lo = 182 m Wo = 2.0 m

Lp =4.5 m Wp = 2.6 m

Lroot=45 m

W=5 m

(Beam spring)

Lo =200 m Wo = 2.0 m

Control system

(2ndorder Sigma-Delta)

Vf = 0.6VVm = 1.2VK=23.8Zero=0.1Pole=12

Vf = 0.94VVm = 1.0VK=4.8Zero = 0.2Pole= 13

Vf = 0.72VVm = 1.5VK=9ZERO = 0.1POLE= 10

4. Conclusions

Part 1 of this two-part paper presents an effective simulation-based synthesis flow (SystemC-AGNES)

for automated layout synthesis of a MEMS component in a mixed-domain electrical-mechanical design.Due to the complex nature of the synthesis process, the synthesis algorithm has been implemented inSystemC-A. This platform is extremely well suited for complex modeling, implementation of

post-processing of simulation results and optimization algorithms [14]. A distributed model of the

mechanical sensing element is developed to ensure accurate behaviour of the MEMS accelerometermodel when embedded in a force feedback control loop. The proposed approach is fully automatedand it effectively deals with the trade-offs in complex digital MEMS sensor design to generate the layout

of the mechanical sensing element according to user defined performance constraints. Synthesis of a fullmixed-technology system which combines the layout synthesis methodology outlined above with the

synthesis of the associated electronic control is discussed in Part 2 [1].


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100 m

a)

101

102

103

104

-140

-120

-100

-80

-60

-40

-20

0PSD of output bitstream

Frequency [Hz]

PSD[

dB

]

System PerformanceSNR=39.8dB Sensitivity= 1.8e-015F/g area=1.82e-007 Kyx=202 Kzx=1.875 Resonant frequency= 8.2KHz

2m

100 m

2m

System PerformanceSNR=32.9dB Sensitivity= 4.77e-015F/g area=3.78e-007 Kyx=4.91 Kzx=10.72 Resonant frequency= 4.6KHz

b)

10

1

10

2

10

3

10

4-140

-120

-100

-80

-60

-40

-20

0

PSD of output bitstream

Frequency [Hz]

PSD[

dB]

2m

System PerformanceSNR=31.5dB Sensitivity= 2.7e-016F/g area=1.07e-7 Kyx=10346 Kzx=1.95 Resonant frequency= 7.9KHz

c)

100 m 101

102

103

104

-140

-120

-100

-80

-60

-40

-20

0PSD of output bitstream

Frequency [Hz]

P

SD[

dB]

Fig. 8. Synthesized results a) and (b: Experiment 1 and 2 (Maximum SNR); c): Experiment 3 (Maximum Static

Sensitivity); d): Experiment 4 (Minimum area of mechanical sensing element).


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