Reaney- Pyroelectricity and Infrared Detection

Question 1

Which point groups exhibit pyroelectricity?

Answer 1

Of 32, 21 are non-centrosymmetric, 20 of these exhibit piezoelectricity. Of these the ones that have a unique polar axis exhibit pyroelectricity.

Question 2

What is pyroelectricity?

Answer 2

The ability of a material to generate charge when uniformly heated

Question 3

How can piezoelectric material generate a charge under heating?

Answer 3

When they are non-uniformly heated because of piezoelectric stress generated by thermal expansion

Question 4

How do ferroelectric fit in with pyroelectrics?

Answer 4

All ferroelectric materials are pyroelectric since they have a unique polar axis. But for ferroelectrics the dipole must be reversible under applied field

Question 5

Formula for total dielectric displacement when an electric field is applied to a polar material

Answer 5

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

Question 6

Formula for permittivity of a material

Answer 6

ε=ε0(1+χsubε)

Where χsubε is dielectric susceptibility for a linear dielectric (how easily it can be polarised)

Question 7

Formula for induced polarisation

Answer 7

Pind=χsubε ε0E

Question 8

Formula for relative permittivity

Answer 8

εr=1+χsubε=ε/ε0

Question 9

Formula for total dielectric displacement after substitution and rearranging

Answer 9

D=εE+Ps

Question 10

Deriving the formula for pyroelectric coefficients

Answer 10

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

Question 11

Terms of the equation for pyroelectric coefficients

Answer 11

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

Question 12

Pyroelectric coefficient in different directions

Answer 12

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

Question 13

Where are the highest values of p obtained?

Answer 13

In the region as a phase transition is approached sinc there is a rapid change in Ps

Question 14

Why are second order phase transitions preferred?

Answer 14

Since no hysteresis is observed on heating and cooling (see dielectric notes)

Question 15

How does a pyroelectric detector generally work?

Answer 15

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

Question 16

Formula for voltage responsivity in a pyroelectric detector

Answer 16

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

Question 17

Why must radiation appear pulsed for a pyroelectric detector?

Answer 17

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

Question 18

Figures of merit for pyroelectric detectors

Answer 18

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

Question 19

PZFNTU

Answer 19

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

Question 20

Why were PbTiO3 and U added to make PZFNTU?

Answer 20

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

Question 21

Why are intruder alarms common and cheap but thermal imagers are expensive?

Answer 21

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.

Question 22

How are reticulated arrays formed?

Answer 22

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

Question 23

Why must the ceramic in thermal imaging very thin?

Answer 23

About 10 microns otherwise it wouldn’t conduct the heat

Question 24

How to make a reticulated arrays by ion beam etching

Answer 24

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.

Question 25

Why bits for thermal imaging?

Answer 25

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.

Question 26

Flipped chip design for thermal imaging array

Answer 26

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

Question 27

Why is the flipped chip design good?

Answer 27

It is an uncooked detector so does not require cooling (which could need liquid nitrogen)

Question 28

Figures of merit for thin film pyroelectric devices

Answer 28

Low compared to the bulk materials but they can be successfully integrated into Si.

Question 29

Why is FsubD much lower in thin films than bulk ceramics?

Answer 29

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.

Question 30

Why might porous rather than dense films be superior for pyroelectric devices?

Answer 30

Because the controlled introduction of porosity decreases the permittivity but has a lesser effect on the pyroelectric coefficient. Therefore FD (p/ε) is optimised

Question 31

Example of controlled porosity

Answer 31

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