ElectrostaticTransducers

Outline

• Introduction• Basic Capacitor Configurationsp g

– Parallel Plate– Interdigitated Drive

• Applications examplespp p– sensors– actuators

• Analysis of electrostatic actuatory– second order effect - “pull in” effect

Introduction

A capacitor is made of two conductors that can hold opposite charges.

It can be used as a sensor or an actuator.

If the distance and relative position between two conductors is changed, the capacitance value will change capacitive sensing

If l i li d d l i f ld d lIf a voltage is applied across two conductors, an electrostatic force would developbetween two objects electrostatic actuation

Microactuation: micro-devices have large surface area to volume ratio, and having small massesg , gmakes electrostatic forces attractive for actuation…

Electrostatically driven micromotor

Earliest MEMS actuator….A rotor is attached to a substrate with a hub, and a set of fixed electrodes, called stators are on the periphery…The stators are grouped with each of 4 electrodes (biased simult ) this develops and in-planeThe stators are grouped with each of 4 electrodes (biased simult.) this develops and in-plane electric field between any stator electrode in the biased group and the closest rotor tooth next to it generates an electrostatic force that alignes (rotates) the tooth with the stator electrode…torque values are on the order of pico Nm for 100 V biasing overcomes friction…The bias is shifted to the next group of stator electrodes another small rotation As you shiftThe bias is shifted to the next group of stator electrodes another small rotation… As you shift the biasing to the groups, you achieve rotation…

Some drawbacks:-High voltage necessary for actuation DMD mirrors need 25 V for 7.5 degree rotationOther applications may need higher voltage…

Fundamental configuration of electrostatic transducers…

A parallel plate capacitor consists of two parallel conducting plates…

Example: TIs DMD chip: large arraiy micro-mirrors that serve as binary light switches…Each mirror is a reflective plate and can rotate about a torsional hinge applying a bias voltageto electrodes under the mirror can rotate via electrostatic forces…

Charge stored in media

Capacitance between two plates

Electrostatic potentialtwo plates

Electric energy stored in the capacitor

For a parallel plate capacitor, electric field linesp p p ,are parallel to each other and perpendicular to platesurfaces.

Fringe electric fields reside outside the boundaryof the plates fringe lines are 3D…

Magnitude of electric field

ε permittivity of media between plates (relative value timesthe permittivity in vacuum)

E.d gives the voltage…

In reality, the parallel plates can move by normal displaccement or by sliding displacement…

Idea: by measuring the capacitance value, we can senseThe changes in in permittivity, d or A…

The magnitude of electrostatic attraction force generated equals thegradient of the stored electrical energy with respect to a dimension…

g p y,

Permittivity can be modulated by temperature and Humidity widely used for sensing liquid, gases or biologicalmaterials…

Th i b d f di l if

If one plate is suspended and can be moved along the normal axis, the gapbetween electrodes changes short range force that can be used for movements of a few micrometers upper limit give by breakdown of

The capacitor can be used to generate force or displacement if at Least one of the plates is suspended or deformable…

dielectric media…

Basic Principles for transducers…

• Sensing– capacitance between moving and fixed plates change as

• distance and position is changed• media is replaced

• Actuation– electrostatic force (attraction) between moving and fixed

l tplates as• a voltage is applied between them.

• Two major configurations• Two major configurations– parallel plate capacitor (out of plane)– interdigitated fingers - IDT (in plane)

Interdigitated finger configuration

dA

Parallel plate configuration

Examples

• Parallel Plate Capacitor• Comb Drive Capacitorp

Parallel Plate Capacitor (summary)

dA

Fringe electric field

V

QC =

AQE ε/=

g(ignored in first orderanalysis)

d

A

dA

QQ

Cε

ε

==

– Equations without considering fringe electric field.– A note on fringe electric field: The fringe field is frequently ignored

in first-order analysis. It is nonetheless important. Its effect can be captured accurately in finite element simulation tools.p y

Fabrication Methods

• Surface micromachining• Wafer bonding• 3D assembly3D assembly

Flip andbondbond

Movablevertical platevertical plate

Forces of Capacitor Actuators (summary)

• Stored energyC

QCVE

22

2

1

2

1==

• Force is derivative of energy with respect to pertinent dimensional variable

• Plug in the expression for capacitor

2

2

1V

d

C

d

EF

∂∂

=∂∂

=

AQC

ε• Plug in the expression for capacitor

• We arrive at the expression for

d

A

dA

QQ

Cε

ε

==

CVV

AEF

22 11

−=−=∂

=ε

• We arrive at the expression for force d

Vdd

F2 22

−=−=∂

=

For transducing purposes, one plate is deformable supported by springs.We need to know how to calculate the displacement under static (DC) and quasi-static (AC)biasing conditions.

Top plate is supported by spring (Km) and is movable.

At rest, applied voltage, displacement and mechanical restoring force are all zero.

Gravitational forces are ignored…

When a voltage is applied, an electrostatic force develops.. This forcetends to decrease the gap gives rise to displacement and restoring force

For an electrostatic actuator, the magnitude of the force itselfis a function of displacement, and this also modifies the springconstant The spatial gradient of the electric force is defined asth l t i l i t t it d h ith d d Vthe electrical spring constant magnitude changes with d and V

The effective spring constant of a structure equals the mechanicalspring constant minus the electrical spring constant…

Electrostatic force at equilibrium

Equilibrium displacement of a spring supported plate under biasvoltage V is x, where x-axis is pointing to increasing gap distance…

With displacement gap becomes d + x = x0 + x

at equilibrium

Magnitude of the restoring force

Equating both forces

Quadratic equation representing distance between two capacitor platesp p

Interception pointsare solutions to equation4.11 in previous slide eqm4.11 in previous slide eqmpositions of the movable plate

But the solution closest to the rest point is the realistic one

Horizontal axis is space between two plates and vertical axis is amplitude of mechanical or electrostatic forces.p p p

The mechanical restoring force changes linearly with distance, and the electrical force changes quadratically…

Eqm position as a function of bias voltage voltages V1 V2 V3Eqm position as a function of bias voltage voltages V1, V2, V3..As the voltage increases, electric forces shift upwards and the interceptionpoints are moved farther away from the rest position

Pull-in voltage (Vp): at some voltage value, the two balancing force curvesWill intercept only at one point beyond this voltage, the eqm solution disappears

The electrostatic force continues to increase and the restoring force cannot compensate,so the plates will move until they make contact snap in

Equating two forces at VEquating two forces at Vp

Gradients of both curves at the intersection are identical

(plug in 4.12)

O l l i h h h l i di lOnly solution occurs such that the relative displacementof the parallel plate is exactly one third of the original spacingat the pull-in voltage

Plug in 4.16 into 4.12

However, there are deviations from this idea model: fringe capactianceWill change the expression of the electrostatic force. Also, the restoringForce may become non-linear for large displacements..

Relative Merits of Capacitor Actuators

Pros• Nearly universal sensing and

t ti d f

Cons• Force and distance inversely

l d t bt i lactuation; no need for special materials.

• Low power. Actuation driven by voltage, not current.

scaled - to obtain larger force, the distance must be small.

• In some applications,by voltage, not current.• High speed. Use charging

and discharging, therefore realizing full mechanical

d

In some applications, vulnerable to particles as the spacing is small - needs packaging.V l bl t ti kiresponse speed. • Vulnerable to sticking phenomenon due to molecular forces.

• Occasionally, sacrificial Occas o a y, sac c arelease. Efficient and clean removal of sacrificial materials.

A fully integrated capacitive acceleration sensor micromachined on Si with integerated CMOS (Peterson et al., 1982)A metal coated oxide cantilever with a 0.35 μg electroplated gold patch as proof mass. Length: 108 microns, width: 25 microns, th: 0.46 micronsCounter electrode: heavily doped p-type SiCapacitor gap is defined during processing via an epitaxially deposited Si layer

The total capacitance is given by

Wh L d b l th d idth d i th itti it f th i diWhere L and b are length and width, and ε0 is the permittivity of the air medium.

Capacitance change is experimentally read using a simple impedance converter. The sensor aboveIs capable of 2.2 mV/g of acceleration sensitivity, corresponding to a beam displacement of of68 nm/g. and the mechanical resonance frequency of the cantilever is 22 kHz.

Surface micromachining processThermal oxide forms the cantilever structure and and epi-Si is the sacrificial layer

Start with n-type Si (100) substrate

Form drain, source and electrical conduction paths on the slopes of via hole

Use ion implantation

A heavily Boron doped region (p+, 1020 /cm3) isfabricated using an oxide as a mask for doping

Use ion implantation Remove oxide barrier, and deposite a fresh oxide (below) which serves as dielectric insulator, cantilever, and etching barrier)

An epi Si layer with 0 5 ohm cm resistivity is deposited

and etching barrier)

A layer of metal is deposited next and patterned providing electrical connectsto p+ region, the electrode on top ofAn epi-Si layer with 0.5 ohm.cm resistivity is deposited to p region, the electrode on top of cantilever and contact to gate

A second oxide layer is deposited and patterned servingas etch mask for a via hole and as a barrier for doping The metal layer consists of 20 nm Cr,

40 nm gold (Cr is adhesion layer)

A wet Si etch is performed to undercut epi-Si beneath the oxide cantilever

Monolithic integration includes an interwoven process flowg pcombining micromechanical elements with IC circuitry.

Such integrated processes could sometimes lead to reliabilitySuch integrated processes could sometimes lead to reliabilityproblems due to material incompatibility.

I t di t hi h t t t f id d iti ldIntermediate high temperature steps of oxide deposition coulddamage the dopant profiles (dopant diffusion)

(Cole et al., 1991)

A flat Ni top plate is supported by torsion bars

Wafer has devices built in

Conducting electrode patches in wafer serve as bottom electrodes. First, a conductive later (metal-1) is depositedwhich is a seed layer

P f 1 0 6 2 d 5 thi k

(metal-2) is deposited and patterned forming bottom electrode Patterns combined metal thickness is 5 microns. Patterningis done next to reach the metal-1 later.

• Proof mass area 1x0.6 mm2, and 5 μm thick.

• Net capacitance 150fF

• External IC signal processing circuits

• Mass of plate is 6.9x10-7 gMass of plate is 6.9x10 g

Ni is electroplated which determines the thickness of movable layer. Metal-1 and metal-2 (sacrifical) are etched next

Counter electrodes are located on the substrate surface. Since the plate weight is asymmetricallydistributed, acceleration normal to substrate planewill cause the top plate to rock in one direction

Etching is timed so thatMetal-1 layer under the anchor stays

Sealed Cavity Pressure Sensor

Capacitive Tactile Sensors

• Sensitivity 0.13 pF/gram to normal force, 0.32 pF/gram to shear forceto shear force.

• Spatial resolution 2.2 mm

Deformable Mirrors for Adaptive Optics

• 2 μm surface normal stroke • for a 300 μm square mirror, the displacement is 1.5

micron at approximately 120 V applied voltage• T. Bifano, R. Mali, Boston University

(http://www.bu.edu/mfg/faculty/homepages/bifano.html)

Optical Micro Switches

• Texas Instrument DLP • Torsional parallel plate capacitor supportT t bl iti• Two stable positions (+/- 10 degrees with respect to rest)

• All aluminum structureAll aluminum structure• No process steps

entails temperature above 300-350 oC.

“Digital Light” Mirror Pixels

Mirrors are on 17 μmMirrors are on 17 μm center-to-center spacing

Gaps are 1.0 μm nominalp μ

Mirror transit time is <20 μs from state to state

Tilt Angles are minute at ±10 degrees

Four mirrors equal the width of a human hair

Digital Micromirror Device (DMD)

Mirror-10 deg

Mirror+10 deg

Hinge

CMOSYoke

CMOS Substrate

3 Pixel Image on Screen

Light Source Projection Lens

Light Absorber

3 DMD Micromirrors

(Actual Top View)

3 Pixel Image on Screen

Light Source Projection Lens

Light Absorber

3 DMD Micromirrors

(Actual Top View)

3 Pixel Image on Screen

Light Source Projection Lens

Light Absorber

3 DMD Micromirrors

(Actual Top View)

DMD™ Pixel Exploded ViewDMD™ Pixel Exploded View

MirrorMirror

Landing Tip Torsion HingeMirror Layer

Mirror AddressElectrode

Yoke

Yoke andYoke Address

ElectrodeVia 2 Contact

to CMOS

Yoke and Hinge Layer

Bias/Reset Bus Landing Site

Metal-3Layer

Memory Cell(CMOS SRAM)

DMD™ Process FlowDMD™ Process Flow

Details of DMD™ Superstructure ProcessDetails of DMD™ Superstructure Process

Condenser microphone: pressure sensor for measuring acoustic pressure fronts created when sound waves travel throughair or liquid. Definition of strength of sound pressure is SPL (decibels or dbm or db).

(Pederson et al, J. MEMS, 1998)

P1 is the sound pressure and P0 is the reference value (a value of 0.0002 microbars is commonly used for air).

A condenser microphone consists of a parallel plate capacitor with two layers: one solid plate (diaphragm) that moves under incoming acoustic waves; and a perforated plate that reduces amount of plate deformation value of capacitance will change due to incoming sounds waves

High resolution, high fidelity and miniature design depends on monolithoc integration reduced noise

Fabrication consists of bulk and surface micromachining…

Active device regions are made in epitaxial p-type layers…Both n and p channel FETs are made on the same substrate…Each kind are shown at both ends of the device

The polyimide layer is patternable over the metal layer. (Cr)increases adhesion on both sides of the (Pt) interconnects.

Al is deposited and its thickness defines the gap of the capacitor.On top of Al, Cr/Pt/Cr is deposited and patterned to form a capacitor with perforation holes (see figure d).

Another layer of polyimide is deposited and patterned

A layer of Cr is deposited on the backside and patterned. DRIEis used to etch through the backside of the wafer until the firstCr/Pt/Cr multilayer is reached. Cr provides good etch selectivity.

The sacrifical Al layer is etched away, resulting in the final device.

The diaphragm exhibits a tensile intrinsic stress of 20MPa, which keeps it flat. Its thickness is ~1.1 microns, and the backplate thickness is 15 microns. The gap is about 3.6 microns. Membranearea is 2.2 x 2.2 mm2, and the acoustic holes and their spacing

30 30 i 2 d 80 i ti lare 30x30 microns2 and 80 microns respectively.

The circuit features a Dickson type DC-DC voltage converter and a MOS buffer amplifier. The voltage converteryields an output voltage of 14.3 V for an input voltage of 1.9 V. Sensitivity: 29 mV/Pa.

R di i t C 4 5 d 4 6Reading assignment: Cases 4.5 and 4.6.