Presentation 2 - Ferroelectric Capacitors · Radiant Technologies, Inc. 1 Ferroelectric Capacitors Joe T. Evans, Jr. Radiant Technologies, Inc. October 2, 2005 Updated November 11,

Radiant Technologies, Inc. 1

Ferroelectric Capacitors

Joe T. Evans, Jr.Radiant Technologies, Inc.

October 2, 2005Updated November 11, 2008


Overview of Presentation• Introduction to ferroelectric capacitors today

• The materials science of non-linear capacitors

• The capacitor science of non-linear capacitors

• Example Applications

• The future: Intelligent Aware Decisive ??? Sensors


Current Applications• PZT is the most common ferroelectric material in use today.• It is made as a boule of glass which is then sawed up, polished, and

electroded.• It has the following properties:

– Indirect Piezoelectricity - changes size with electric field• Sonar (tons are used in US Navy submarines and ships)• Medical ultrasound• Adventure rides at Disney Land

– Direct Piezoelectricity - applied force generates an electric field• Solid state accelerometers• Piezoelectric microphones

– Pyroelectricity - changes in temperature generates an electric field• high definition infrared cameras• fire detectors

– High Dielectric Constant - the ubiquitous “ceramic” disk capacitor isPZT.


Materials Science of Ferroelectrics

• The effect of lattice structure on electrical properties.– Covalent like diamond– Ionic like PZT

• The lattice and temperature– spring/ball model– Coefficient of Thermal Expansion

• Asymmetrical Lattice and the built-in electric dipole– Curie Temperature– Remanent Polarization

• Definition of a Ferroelectric Material


The Lattice and its BondsDiamond has a trihedral structure withsymmetrical covalent bonds betweenall carbon atoms:

PZT has a tetragonalstructure with asymmetrical,partially ionic bondsbetween the oxygensand the metals.

Symmetrical lattice + covalent bondingmeans no net electric fields.

DIAMOND

Carbon

Lead

Titanium (or Zirconium)

Oxygen


The electrons surround each atom equallyin time and space. Hence, there are noseparated charges for an electric field toact on. Diamond has a low, very lineardielectric constant, ~5.6.

The carbon atoms in diamond are about1.5Å apart along an edge. Each carbon atomoccupies about 1Å. So, as temperature goesdown, there is plenty of room for the carbon atomsto move closer without bumping into each other.Diamonds electrical properties are uniformover a wide temperature range!

Diamond


Perovskite LatticeIn the perovskite structure most ferroelectric materials have,no metals are bonded to metals. Every metal is bonded onlyto nearby oxygens. The real bonding diagram looks like this:

The electrons stay near the red oxygens,giving every metal/oxygen pair a netelectric dipole. An external electricfield will repel the metals and attractthe oxygens, severely distortingthe lattice as it expands.

Since dielectric constant depends on“Displacement”, perovskites can haveHUGE dielectric constants, as high as 30,000!

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The Titanium/Oxygen Cage!An easy way to visualize the distortion is to lookat the effect of a field on the Titanium/Oxygen sub-lattice.

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The Lead/Oxygenlattice also distorts.

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Coefficient of Thermal ExpansionAll solids can be treated as a network of balls and springs:

Temperature is simply the motion energy of each atom. The higher thetemperature, the faster they move, theharder they bounce off each other, and

the further apart they force each other to stay on average. Hence,the physical size of solids changes with temperature. The change indimensions vs the change in temperature is the Coefficient ofThermal Expansion!

The CTE of PZT is ~15 times that of Diamond.


Remanent PolarizationPZT has a 4Å lattice constant, but many moreatoms are squeezed into that volume than with diamond! Asthe temperature drops and the lattice shrinks, eventually thereis not enough room for all the atoms in the symmetricalformat. The lattice begins distorts to squeeze the atomscloser together. A simple model is that thethe body-centered atom slides up about 0.05Å soit is no longer co-planar with the oxygen atoms.

Since the electrons stay mostlyaround the oxygen atoms, a net vertical dipole is created.

Remember: P = Q x d ~ 100µC/cm2 for PZT unit cell.

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Direct PiezoelectricityThe remanentdipole existswithout anexternal forceapplied.

An externalforce stretchingthe latticestretches thedipole.

F

An externalforcecompressingthe latticeshrinks thedipole.

F

The lattice distorts under force according to the Young’s Modulus. The ratio ofshrinkage in one dimension to the expansion in the others is the Poisson’s Ratio.


Indirect PiezoelectricityThe remanentdipole existswithout anexternal appliedfield.

An externalelectric fieldopposite thedipole stretchesthe dipole.

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An externalelectric fieldparallel withthe dipoleshrinks thedipole.

E

If the external fieldis strong enough,the titanium willpush the oxygenatoms aside to moveto the other end!

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Electrically opposite. Dimensionally symmetrical!


PyroelectricityThe remanentdipole existswithout anexternal appliedfield.

A decrease in thetemperature makesthe lattice shrink

moreasymmetrically andthe dipole strength

grows.

An increase in thetemperature makesthe lattice expand,

allowing moresymmetry, and the

dipole strengthreduces.


Memory

Leaving the remanent dipole in oppositestates allows the storage of information inthe lattice!


Material ParametersThere are six parameters that define the response of a material lattice toexternal environmental factors:

(S) Stress (force) N/m => J/m3

(T) Strain (change in dimension) m/m => 1

(E) Electric Field (electrical force) Newtons/Coulomb

(D) Polarization (dielectric constant) C/m2 => µC/cm2

(θ ) Temperature °K

(σ) Entropy J/ (°K-m3)(Magnetism is not included in this discussion. It adds two more factors.)


Material ParametersEach of the six parameters are linked to the other five parameters byconstants:

See Rosen, et al., Key Papers in Physics, “Piezoelectricity”, American Institute in Physics,1992.

δT δS δE δD δθ δσ

δT 1 s -g d -αθ/ς α

δS C 1 -h e -cαθ /ς cα

δE -e d 1 ε -pθ/ς p

δD -h g β 1 -βpθ/ς βp

δθ -cα α - βp p 1 ς/θ

δσ -cαθ/ς αθ/ς -βpθ/ς pθ/ς θ/ς 1

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Note: These parameters can have different values in the X, Y, and Z direction so they are tensors!









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Coefficient of Thermal Expansion

Dielectric ConstantYoung’s Modulus

Specific Heat

Material ParametersMany of these constants you already know!


Material ParametersNow, new constants for you!

Piezoelectric Constants








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Pyroelectric Constants


All Parameters are CoupledUse Silicon Dioxide (glass, sand, insulator on ICs) as an example.

• What happens when you apply a force to a volume of silicon dioxide?– Simple model: Use Young’s modulus to calculate the new dimensions.

• But, the change in dimensions invokes the specific heat constant,increasing the temperature of the silicon dioxide in the smallervolume. (Assuming a “fast” compression.)

• The increase in temperature invokes the Coefficient of ThermalExpansion, which tries to increase the volume of the silicon dioxide,creating a force that fights the compressive force.

• As the temperature of the volume decreases to ambient, the force ofthe CTE goes away, leaving only the Young’s modulus effect atsteady state!


The internal electric field of ferroelectric materials causes all six of theparameters to be coupled simultaneously!

Force -> Strain -> Field -> Polarization -> Temperature -> Entropy ->Force, etc. etc. etc.

Ferroelectric Coupling

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Summary of Materials Properties• All of the materials parameters used in different fields of study

– Electrical Engineering– Mechanical Engineering– Civil Engineering– Thermodynamics

are actually coupled together.

• The advantage of ferroelectric materials is that all of the otherparameters couple into polarization (D), allowing us to see thecoupling as it happens!


Capacitors!

Capacitance is the storage of energyin separated charges. It can take

many forms.


Linear Capacitors!• The “trajectory” of a linear capacitor can be described with two

parameters:

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1nF Polystyrene Capacitor[ 0.1% Precision, 1E-4 Loss ]

Pola

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µC

/cm

2)

Volts


Paraelectric Capacitors!

Q = C(V,θ,F)V

δQ = C(V,θ,F) δV

I = δQ / δt = C(V,θ,F) δV/ δt

The capacitance of the paraelectric device is affected by thevoltage, the temperature, and the force acting on thecapacitor.


Paraelectric Capacitors!

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Radiant 9/65/35 PLZT[ 1700A ]

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Paraelectric:Above theCurie Point!


Ferroelectric Capacitors!

Q = C(V,θ,F,H)V

δQ = C(V,θ,F,H) δV

I = δQ / δt = C(V,θ,F,H) δV/ δt

A ferroelectric capacitor has memory so its history H plays a part in themeasurement. With ferroelectric, or memory capacitors, you absolutelyDO NOT KNOW what δQ you will get for the next δV!



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Nested Loops for 0.2u 20/80[ VCU 1st 20/80 ]

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1ms 8V hyst: 1 1ms 8V hyst: 2 1ms 8V hyst: 3 1ms 8V hyst: 4 1ms 8V hyst: 5

1ms 8V hyst: 6 1ms 8V hyst: 7 1ms 8V hyst: 8 1ms 8V hyst: 9

Ferroelectric:Below theCurie Point!



With ferroelectric, or memory capacitors, you absolutely DONOT KNOW what δQ you will get for the next δV! Linear,differentiable, continuous equations are not possible.Simulation or modeling can only be done numerically and thesimulation must include the critical history factors.

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V = 0!C = Q/V

C? = QR/0 = ????SPICE crashes at this point!


Ferroelectric Capacitors!These capacitors remember everything that was done to them,even during fabrication. Every one is different.Manufacturing them to meet a quality goal is like

Herding Sheep!

But, this very deficiency makes them wonderful sensors withas of yet unexplored capabilities!

Memory means intelligence. Intelligent Sensors?


Capacitors as Sensors

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Infinite Impedance Zero Impedance

Change in Temperature or Force



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Infinite Impedance Zero Impedance

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Csense Vs = Qs / Cs


Capacitors as SensorsQs = Vs * Cs

F * d33 = Vs * Cs

F = Vs * Cs / d33


Capacitors as SensorsAssume the sensor rests on a surface with a vertical motion described byA sin ωt.

Sensor


Capacitors as Accelerometers

Assume the sensor rests on a surface with a vertical motion described byA sin ωt. Place a mass M on the capacitor. Motion is perpendicular to theplane of the capacitor.

δ2Y/δt2 = a = - Aω2sin ωtF = Ma = -AMω2sin ωt

-AMω2sin ωt = Vs * Cs / d33

-AMω2sin ωt * d33/Cs = Vs

Signal decreases with the square of the frequency as the frequencydecreases. Increasing the mass increases the signal.

M Capacitor



Build a network of vibration or accelerometer sensors and place themthroughout the body, wings, and engines of an aircraft or the structure of acar.

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µPw/ADC

I2C or CAN or FAN

Actual Size


Sensors in the Future?

• The design efficiencies of biological systems will filterinto sensor design:– decreased cost– increased sensitivity– decision making decentralized to the sensor


Logarithmic Analog Force Sensor• The design efficiencies of biological systems will filter

into sensors.The ratios ofthe resistors setthe relativelevels so thesystem can betuned for linearor logarithmicor a customsensingfunction.

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Parasitics on Static Sensors• New circuits will be needed to effectively use the capacitor

sensors.

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The reverse bias diode leakagewill charge up the sensor!


Flies, Cell Phones, and GPS• Cell phones and GPS receivers pull information from

signals far below the local noise level:– They know ahead of time the function they are looking for.– Sophisticated math techniques like correlation functions can

recover incredibly small signals from the noise.

• A fly does not have the benefit of knowing the shape of thesignal indicating that your hand is on the way.– How can it always get away?

– Stochastic Noise Detection


Flies, Cell Phones, and GPS• Imagine an area of the fly’s skin that has a thousand hair cells. They

self tune to a threshold just above the noise level so each one has astatistical chance of firing at least once within a fixed time frame.

• The fly has neurons that sum all of the outputs of the hair cells. Theneurons have a range of thresholds so each one will itself fire when acertain number of hair cells fire simultaneously.

• There is a weighted average of hair cells firing simultaneouslyaccording to the local noise level.

• A slight increase in a signal well below the weighted average noiselevel adds to the average noise level, so more detection neurons willfire, warning the fly of potential impending danger!

• There will be false alarms but so what!


Flies, Cell Phones, and GPS

Patch of skin with hairs!

N = 177

N = 273

N = 344

N = 378

N = 452

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We can build simple versions of this system today!


Conclusion

Ferroelectric capacitors are always listening!

Are you sure you want them to hear what youare saying?

Documents

Presentation 2 - Ferroelectric Capacitors · Radiant Technologies, Inc. 1 Ferroelectric Capacitors Joe T. Evans, Jr. Radiant Technologies, Inc. October 2, 2005 Updated November 11,