Reaney- Pyroelectricity and Infrared Detection Flashcards
Which point groups exhibit pyroelectricity?
Of 32, 21 are non-centrosymmetric, 20 of these exhibit piezoelectricity. Of these the ones that have a unique polar axis exhibit pyroelectricity.
What is pyroelectricity?
The ability of a material to generate charge when uniformly heated
How can piezoelectric material generate a charge under heating?
When they are non-uniformly heated because of piezoelectric stress generated by thermal expansion
How do ferroelectric fit in with pyroelectrics?
All ferroelectric materials are pyroelectric since they have a unique polar axis. But for ferroelectrics the dipole must be reversible under applied field
Formula for total dielectric displacement when an electric field is applied to a polar material
D=ε0E+Ptot=ε0E+(Ps+Pind) Where ε0 is permittivity of free space E is applied field Ps is spontaneous polarisation Pind is induced polarisation
Formula for permittivity of a material
ε=ε0(1+χsubε)
Where χsubε is dielectric susceptibility for a linear dielectric (how easily it can be polarised)
Formula for induced polarisation
Pind=χsubε ε0E
Formula for relative permittivity
εr=1+χsubε=ε/ε0
Formula for total dielectric displacement after substitution and rearranging
D=εE+Ps
Deriving the formula for pyroelectric coefficients
Differentiate total dielectric displacement formula with respect to temperature
dD/dT=dPs/dT+Edε/dT
Assume E is constant with in form of
pg=p+Edε/dT
Where p is true dielectric coefficient and psubg is general pyroelectric coefficient
Terms of the equation for pyroelectric coefficients
p is true pyroelectric coefficient as it reflects the change in spontaneous polarisation as a function of temperature.
pg is general coefficient and assumes that there is an applied field.
Edε/dT refers to all dielectrics whether polar or not.
The temperature coefficient of permittivity for ferroelectrics is always high particularly with a phase transition close by. Therefore dε/dT is large anyway
Pyroelectric coefficient in different directions
Since polarisation is a vector value the pyroelectric coefficient is different depending on the direction in which it is measured so:
ΔPi=piΔT
P is spontaneous, p is true
i is 1, 2, or 3 depending on direction of measurement using same principles as define for directions with piezoelectrics
Where are the highest values of p obtained?
In the region as a phase transition is approached sinc there is a rapid change in Ps
Why are second order phase transitions preferred?
Since no hysteresis is observed on heating and cooling (see dielectric notes)
How does a pyroelectric detector generally work?
By absorbing radiation on the surface of a detecting element. The element constitutes a thin slice of material coated with conducting electrodes one of which is a good absorber of radiation
Formula for voltage responsivity in a pyroelectric detector
rv=pη/c’Aεω Where r sub v is voltage responsivity η is measure of the fraction of incident energy absorbed c’ is the volume specific heat A is area ω is frequency of pulsed radiation
Why must radiation appear pulsed for a pyroelectric detector?
Continuous radiation won’t illicit a response as only ΔT is measured. Therefore a chopper fan is used to ensure the radiation always appears pulsed
Figures of merit for pyroelectric detectors
Fv=p/c’ε is what rv formula suggests
To optimise SNR then
FsubD=p/c’(εtanδ)^1/2
Devices however operate under low bias fields and value of loss should not be taken as that associated with domain wall motion often used in piezoelectrics
PZFNTU
Pb1.02(Zr0.58 Fe0.2 Nb0.2 Ti0.02)0.994 U0.006 O3
Has simple perovskite structure based on lead zirconate.
Add 10mol% Pb(Fe0.5 Nb0.5)O3 to convert the antiferroelectric structure of PbZrO3 to a low permittivity ferroelectric.
See next card
Why were PbTiO3 and U added to make PZFNTU?
After addition of Pb(Fe0.5 Nb0.5)O3 there was a phase transition at 40C between two rhombohedral forms. This affected Ps meaning p wasn’t stable. Add 5mol% PbTiO3 to increase this phase transition temperature to 100C (oit of range of detector). U was used to control the resistance of the material at the same time reducing permittivity and loss. Overall PZFNTU can be manufactured reproducibly and cheaply
Why are intruder alarms common and cheap but thermal imagers are expensive?
Charge from a pyroelectric material is relatively easy to transform into a usable signal for detection but imaging is more difficult. For an image, reticulated arrays of thermally isolated elements are needed.
How are reticulated arrays formed?
By ion beam etching a thin ground slice of ceramic. Thermal isolation is possible using polymer insulation but this is only done by high tech electronics companies who specialise in micromachining.
Recirculated means cut up into squares
Why must the ceramic in thermal imaging very thin?
About 10 microns otherwise it wouldn’t conduct the heat
How to make a reticulated arrays by ion beam etching
Have a layer of pyroelectric with ion-beam resistant layers on its top and bottom surfaces. Put photoresist on top surface in pattern that protects the areas you want to keep and leaves other areas in between exposed. The exposed regions get etched away leaving an array of pyroelectric bits.
Why bits for thermal imaging?
The IR in one place must be recognised as being different to that in another place to make an imaging array. Each bit cannot be too thermally or electrically connected to the next bit.
Flipped chip design for thermal imaging array
Invert the array of bits so they hang down from the electrode. This has a support and an absorber (black paint) on the outside. Each bit has some polymer isolation on its bottom surface and a thin connecting metallisation from the bit going around and under the polymer. This is connected by a solder bump to the silicon chip carrying the microcircuitry
Why is the flipped chip design good?
It is an uncooked detector so does not require cooling (which could need liquid nitrogen)
Figures of merit for thin film pyroelectric devices
Low compared to the bulk materials but they can be successfully integrated into Si.
Why is FsubD much lower in thin films than bulk ceramics?
Thin films are mechanically clamped by the substrate. Therefore changes in polarisation as a function of temperature are also clamped as they rely on small changes in dimensions of the cells.
Also the films may not grow in an orientation that optimises the pyroelectric coefficient.
Why might porous rather than dense films be superior for pyroelectric devices?
Because the controlled introduction of porosity decreases the permittivity but has a lesser effect on the pyroelectric coefficient. Therefore FD (p/ε) is optimised
Example of controlled porosity
In PbTiO3 sol-gel thin films by incorporating Ca ions on the A-site. Graph of FD vs % A-site dopant increases with decreasing gradient
