Ferroelectric Capacitors

Transcription

1 Ferroelectric Capacitors Joe T. Evans, Jr. Radiant Technologies, Inc. October 2, 2005 Updated November 11, 2008 Radiant Technologies, Inc. 1

2 Overview of Presentation Introduction to ferroelectric capacitors today The materials science of nonlinear capacitors The capacitor science of nonlinear capacitors Example Applications The future: Intelligent Aware Decisive??? Sensors Radiant Technologies, Inc. 2

3 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 is PZT. Radiant Technologies, Inc. 3

4 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 builtin electric dipole Curie Temperature Remanent Polarization Definition of a Ferroelectric Material Radiant Technologies, Inc. 4

5 The Lattice and its Bonds Diamond has a trihedral structure with symmetrical covalent bonds between all carbon atoms: Carbon DIAMOND Symmetrical lattice covalent bonding means no net electric fields. PZT has a tetragonal structure with asymmetrical, partially ionic bonds between the oxygens and the metals. Lead Titanium (or Zirconium) Oxygen Radiant Technologies, Inc. 5

6 Diamond The electrons surround each atom equally in time and space. Hence, there are no separated charges for an electric field to act on. Diamond has a low, very linear dielectric constant, ~5.6. The carbon atoms in diamond are about 1.5Å apart along an edge. Each carbon atom occupies about 1Å. So, as temperature goes down, there is plenty of room for the carbon atoms to move closer without bumping into each other. Diamonds electrical properties are uniform over a wide temperature range! Radiant Technologies, Inc. 6

7 Perovskite Lattice In the perovskite structure most ferroelectric materials have, no metals are bonded to metals. Every metal is bonded only to nearby oxygens. The real bonding diagram looks like this: The electrons stay near the red oxygens, giving every metal/oxygen pair a net electric dipole. An external electric field will repel the metals and attract the oxygens, severely distorting the lattice as it expands. Since dielectric constant depends on Displacement, perovskites can have HUGE dielectric constants, as high as 30,000! Radiant Technologies, Inc. 7

8 The Titanium/Oxygen Cage! An easy way to visualize the distortion is to look at the effect of a field on the Titanium/Oxygen sublattice. E The Lead/Oxygen lattice also distorts. Radiant Technologies, Inc. 8

9 Coefficient of Thermal Expansion All solids can be treated as a network of balls and springs: Temperature is simply the motion energy of each atom. The higher the temperature, the faster they move, the harder 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 in dimensions vs the change in temperature is the Coefficient of Thermal Expansion! The CTE of PZT is ~15 times that of Diamond. Radiant Technologies, Inc. 9

10 Remanent Polarization PZT has a 4Å lattice constant, but many more atoms are squeezed into that volume than with diamond! As the temperature drops and the lattice shrinks, eventually there is not enough room for all the atoms in the symmetrical format. The lattice begins distorts to squeeze the atoms closer together. A simple model is that the the bodycentered atom slides up about 0.05Å so it is no longer coplanar with the oxygen atoms. Since the electrons stay mostly around the oxygen atoms, a net vertical dipole is created. Remember: P = Q x d ~ 100µC/cm 2 for PZT unit cell. Radiant Technologies, Inc. 10

11 Direct Piezoelectricity The remanent dipole exists without an external force applied. An external force stretching the lattice stretches the dipole. F An external force compressing the lattice shrinks the dipole. F The lattice distorts under force according to the Young s Modulus. The ratio of shrinkage in one dimension to the expansion in the others is the Poisson s Ratio. Radiant Technologies, Inc. 11

12 Indirect Piezoelectricity The remanent dipole exists without an external applied field. An external electric field opposite the dipole stretches the dipole. An external electric field parallel with the dipole shrinks the dipole. If the external field is strong enough, the titanium will push the oxygen atoms aside to move to the other end! E E E Electrically opposite. Dimensionally symmetrical! Radiant Technologies, Inc. 12

13 The remanent dipole exists without an external applied field. Pyroelectricity A decrease in the temperature makes the lattice shrink more asymmetrically and the dipole strength grows. An increase in the temperature makes the lattice expand, allowing more symmetry, and the dipole strength reduces. Radiant Technologies, Inc. 13

14 Memory Leaving the remanent dipole in opposite states allows the storage of information in the lattice! Radiant Technologies, Inc. 14

15 Material Parameters There are six parameters that define the response of a material lattice to external environmental factors: (S) Stress (force) N/m => J/m 3 (T) Strain (change in dimension) m/m => 1 (E) Electric Field (electrical force) Newtons/Coulomb (D) Polarization (dielectric constant) C/m 2 => µc/cm 2 (θ ) Temperature K (σ) Entropy J/ ( Km 3 ) (Magnetism is not included in this discussion. It adds two more factors.) Radiant Technologies, Inc. 15

16 Material Parameters Each of the six parameters are linked to the other five parameters by constants: I D Note: These parameters can have different values in the X, Y, and Z direction so they are tensors! 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 See Rosen, et al., Key Papers in Physics, Piezoelectricity, American Institute in Physics, Radiant Technologies, Inc. 16

17 Material Parameters Many of these constants you already know! Young s Modulus Dielectric Constant D I 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 Coefficient of Thermal Expansion Specific Heat Radiant Technologies, Inc. 17

18 Material Parameters Now, new constants for you! D I Piezoelectric Constants 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 Pyroelectric Constants Radiant Technologies, Inc. 18

19 All Parameters are Coupled Use 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 smaller volume. (Assuming a fast compression.) The increase in temperature invokes the Coefficient of Thermal Expansion, 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 of the CTE goes away, leaving only the Young s modulus effect at steady state! Radiant Technologies, Inc. 19

20 The internal electric field of ferroelectric materials causes all six of the parameters to be coupled simultaneously! Force > Strain > Field > Polarization > Temperature > Entropy > Force, etc. etc. etc. I D Ferroelectric Coupling 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 Radiant Technologies, Inc. 20

21 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 other parameters couple into polarization (D), allowing us to see the coupling as it happens! Radiant Technologies, Inc. 21

22 Capacitors! Capacitance is the storage of energy in separated charges. It can take many forms. Radiant Technologies, Inc. 22

23 Linear Capacitors! The trajectory of a linear capacitor can be described with two parameters: nF Polystyrene Capacitor [ 0.1% Precision, 1E4 Loss ] 300 Polarization (µc/cm2) Volts Radiant Technologies, Inc. 23

24 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 the voltage, the temperature, and the force acting on the capacitor. Radiant Technologies, Inc. 24

25 Paraelectric Capacitors! 60 Radiant 9/65/35 PLZT [ 1700A ] Polarization Paraelectric: Above the Curie Point! Volts Radiant Technologies, Inc. 25

26 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 the measurement. With ferroelectric, or memory capacitors, you absolutely DO NOT KNOW what δq you will get for the next δv! Radiant Technologies, Inc. 26

27 Ferroelectric Capacitors! 30 Nested Loops for 0.2u 20/80 [ VCU 1st 20/80 ] 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: Polarization Ferroelectric: Below the Curie Point! Volts Radiant Technologies, Inc. 27

28 Ferroelectric Capacitors! With ferroelectric, or memory capacitors, you absolutely DO NOT 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 the simulation must include the critical history factors. C = Q/V V = 0! C? = Q R /0 =???? SPICE crashes at this point! Radiant Technologies, Inc. 28

29 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 with as of yet unexplored capabilities! Memory means intelligence. Intelligent Sensors? Radiant Technologies, Inc. 29

30 Radiant Technologies, Inc. 30 Capacitors as Sensors V 0 I Infinite Impedance Zero Impedance Change in Temperature or Force

31 Capacitors as Sensors Change in Temperature or Force Csense V s = Q s / C s Vsense Vsense Infinite Impedance Zero Impedance Radiant Technologies, Inc. 31

32 Capacitors as Sensors Q s = V s * C s F * d 33 = V s * C s F = V s * C s / d 33 Radiant Technologies, Inc. 32

33 Capacitors as Sensors Assume the sensor rests on a surface with a vertical motion described by A sin ωt. Sensor Radiant Technologies, Inc. 33

34 Capacitors as Accelerometers M Capacitor Assume the sensor rests on a surface with a vertical motion described by A sin ωt. Place a mass M on the capacitor. Motion is perpendicular to the plane of the capacitor. δ 2 Y/δt 2 = a = Aω 2 sin ωt F = Ma = AMω 2 sin ωt AMω 2 sin ωt = V s * C s / d 33 AMω 2 sin ωt * d 33 /C s = V s Signal decreases with the square of the frequency as the frequency decreases. Increasing the mass increases the signal. Radiant Technologies, Inc. 34

35 Capacitors as Sensors Build a network of vibration or accelerometer sensors and place them throughout the body, wings, and engines of an aircraft or the structure of a car. Csense µp w/adc I 2 C or CAN or FAN Actual Size Radiant Technologies, Inc. 35

36 Sensors in the Future? The design efficiencies of biological systems will filter into sensor design: decreased cost increased sensitivity decision making decentralized to the sensor Radiant Technologies, Inc. 36

37 Logarithmic Analog Force Sensor The design efficiencies of biological systems will filter into sensors. The ratios of the resistors set the relative levels so the system can be tuned for linear or logarithmic or a custom sensing function. Radiant Technologies, Inc. 37

38 Parasitics on Static Sensors New circuits will be needed to effectively use the capacitor sensors. The reverse bias diode leakage will charge up the sensor! Radiant Technologies, Inc. 38

39 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 the signal indicating that your hand is on the way. How can it always get away? Stochastic Noise Detection Radiant Technologies, Inc. 39

40 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 a statistical 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. The neurons have a range of thresholds so each one will itself fire when a certain number of hair cells fire simultaneously. There is a weighted average of hair cells firing simultaneously according to the local noise level. A slight increase in a signal well below the weighted average noise level adds to the average noise level, so more detection neurons will fire, warning the fly of potential impending danger! There will be false alarms but so what! Radiant Technologies, Inc. 40

41 Flies, Cell Phones, and GPS Patch of skin with hairs! N = 452 N = 378 N = 344 N = 273 N = 177 We can build simple versions of this system today! Radiant Technologies, Inc. 41

42 Conclusion Ferroelectric capacitors are always listening! Are you sure you want them to hear what you are saying? Radiant Technologies, Inc. 42