Lecture 7 - Pyroelectric Materials Flashcards
What is the pyroelectric effect?
The release of electric charge that occurs as the temperature changes inside the material.
p = ΔPs/ΔT = dPs/dT
p: pyroelectric coefficient
Ps: polarisation
The direction of polarisation is constrained by the symmetry of the polar lattice, however only the magnitude of p is relevant.
What is the current produced by pyroelectric materials?
It’s the detection current
i=ApdT/dt
Where: A, the area, p, the polarization parallel to the thickness of the material
What are the desired properties of pyroelectric materials?
1) to absorb and retain as much heat as possible
2) to have a low thermal capacity (H)
3) to retain charge long enough for it to be amplified
What are the parameters required to describe a schematic of a pyroelectric element connected to an amplifier?
Thermal Capacity - H [J/°C]
(of material)
Thermal Conductance - G_T [W/°C]
(of surroundings)
Thermal Time Constant τ_Τ = Η / G_T
Gate Resistor R_G
Material Capacitance C_E
Amplifier Capacitance C_A
Electrical Time Constant τ_Ε = R_G*(CE+CA)
Detector Frequency Response
τ_T + τ_E
Define the Current Responsivity of a pyroelectric detection system
The pyroelectric current generated per watt of input power
I/Wo =Ri =
ηpAω/[G_Τ*√(1+ω²τ_Τ²)]
Current Responsivity = Ri
How does Current Responsivity vary with frequency?
At frequencies less than the thermal time constant, the Responsivity is proportional to frequency
ω< Ri ∝ ω
At frequencies larger than the thermal time constant, the Responsivity is constant
Let H =cdA
where d thickness, A area, and c specific heat capacity J/°Cm³
Then for ω»_space;τ_T
Ri = ηpA/H = ηp/cd
Define Voltage Responsivity for pyroelectric materials
First we need to be working in electrical admittance instead of impedance.
I =VY
where
Y = 1/Rg +iωC,
C =CA+CE
From this we can estimate the voltage generated on the FET gate where the FET is acting as an amplifier:
Vg= i_p/Y
Therefore the voltage Responsivity is the gate voltage per input watt power
i_p/YWo = Rv =
RgηpAω/[Gt√(1+ω²τT²)√(1+ω²τE²)]
How do we maximise voltage Responsivity?
dRv/dω = 0 gives the maximum, which occurs when ω = 1/√(τΕ*τΤ)
This gives a value of
Rv,max = (ηpARg/GT)(1/(τΕ+τΤ))
There are also 3dB points that result to the max value scaled by 1/√2 at ω=τΕ and at ω=τΤ
How does the voltage Responsivity change with frequency?
Rises up to Rv,max then dips at high frequencies
It is limited at high frequencies by the electric time constant τΕ and it takes the value
Rv =ηp/cd(CE+CA)ω
Where c: volume specific heat capacity
What is the overall responsivity of a pyroelectric detection system?
At low frequencies, the charge produced leads to generation of current and thus the system is under current mode operation.
At high frequencies, the charge produced leads to generation of voltage and thus the system is under voltage mode operation.
What are the figures of merit used to determine the quality of pyroelectric materials?
Fv = p/(cεrεo)
FD = p/(c√εοεrtanδ)
Where tanδ the loss tangent obtained from the ratio of real to imaginary impedance of the system.
Where does the figure of merit Fv arise from?
Consider if CE»CA then
At high frequencies RV= ηp/CεrεοΑω
Then we can use Fv as defined to be p/Cεoεr as a figure of merit for materials
If we match CE and CA closely to improve SNR, we need materials with higher εr
Fv is the figure of merit maximised for high voltage responsivity
What are the main sources of noise in a pyroelectric system?
We consider the noise disturbing a pyroelectric detection system.
From 3 main sources, Thermal Noise, Amplifier Noise and Johnson noise, the last one dominates in its effects.
Johnson noise is given by
ΔVj=sqrt(4kTtanδ/CE)*sqrt(1/ω)
Define detectivity in a pyroelectric system and its relation to FD
Detectivity is the ratio of Voltage Responsivity to Johnson Noise in a system
Rv/ΔVj = FD * sqrt(4kTtanδ/CE)*sqrt(1/ω)
FD is the figure of merit used to maximise signal to noise ratio in a system
