Pyroelectric Infrared Detectors - DIAS Infrared Systems

Pyroelectric Infrared Detectors 1. Principal set-up Figure 1 shows the principle set-up of a pyroelectric infrared detector. Components are the responsive element and the preamplifier whose essential elements are integrated in the detector. The sensitive element consists of a pyroelectric chip which is thin and covered with electrodes. In some cases an absorption layer is applied to the front of the responsive element to improve its absorption behavior.

ΦS (t) pyroelectric material top electrode

sensitive element

AS dp u´S (t) u´R (t)

bottom electrode amplifier Figure 1: Principle set-up of a pyroelectric infrared detector

The incident radiation flux ΦS(t) hits the radiation-sensitive element with the area AS and absorption coefficient α. The absorption of radiation flux results in a temperature change ∆T(t) within the pyroelectric material. The pyroelectric effect generates charges ∆Q(t) on the electrodes. These charges are transformed into a signal voltage uS´(t). Various noise sources in the pyroelectric chip and the preamplifier generate a noise voltage uR´(t) at the detector output. This voltage limits the radiation flux, which can be detected in the minimum. 2. Detector characteristics The essential characteristics of pyroelectric detectors are the responsivity SV, the noise equivalent power NEP and the specific detectivity D*. They are defined in the steady-state condition for sinusoidal processes. They generally depend on modulation frequency f, wavelength λ and detector temperature T. a) Responsivity The responsivity SV is defined as:  DIAS Infrared GmbH, 2006

u~S′ SV = ~ ΦS where:

~ ΦS u~S′

[V/W]

(1)

rms value of the sinusoidally modulated radiation flux rms value of the sinusoidal signal voltage at the detector output.

b) Noise equivalent power The noise equivalent power NEP characterises the signal-to-noise ratio of the detector: NEP =

where:

u~R′

u~R′ SV

[W]

(2)

rms value of the noise voltage at the detector output.

The combination of the equations (1) and (2) shows that the noise equivalent power represents the minimum detectable power of the detector, and is given by a ratio of 1 between signal voltage and noise voltage ( u~S′ / u~R′ = 1 ). c) Specific detectivity The specific detectivity characterises also the signal-to-noise ratio: D∗ =

where:

AS B NEP

=

AS SV u~ ′

(3)

[V/Hz1/2]

(4)

Rn

′ = u~R′ / B u~Rn

′ u~Rn

[cmHz1/2/W]

effective value of the noise voltage at the preamplifier output normalized on a bandwidth B = 1 Hz.

The definition of the specific detectivity allows a simple comparison between the D* value of the real sensor and the theoretical D* limit. This limit depends only on nature constants (Boltzmann constant k, Stefan-Boltzmann constant σ) and the temperature T: ∗ Dmax = 1 / 16kσT 5

(5)

For a temperature of 300 K this value amounts to: ∗ Dmax = 1,8 . 1010 cmHz1/2/W .

 DIAS Infrared GmbH, 2006

3. Pyroelectric material The pyroelectric material takes a fundamentally position as the real transducer element in the pyroelectric radiation detector. Of 32 existing crystal classes crystals with the point group balance 1, m, 2, mm2, 3, 3 m, 4, 4 mm, 6 and 6 mm have a so-called spontaneous polarization which makes the appearance of the pyroelectric effect possible. Crystals of these crystal classes are called pyroelectric materials. Pyroelctric materials at which the spontaneous polarization can appear only in one single direction in the crystal (uniaxial pyroelectric materials) are technically meaningful. The crystal classes 2, mm2, 3, 3 m, 4, 4 mm, 6 and 6 mm, are included. The direction of the spontaneous polarization and the polar axis of the crystal are the same. For use in pyroelectric radiation detectors the following material characteristics of the pyroelectric material are of importance: p εr tanδ c P´

pyroelectric coefficient dielectric constant dielectric loss volume-specific heat capacity

For high values of responsivity SV and specific detectivity D* a big pyroelectric coefficient p and small values of dielectric constant εr, dielectric loss tan δ and volume-specific heat capacity cP´ are required. For many years the pyroelectric material lithium tantalate (LiTaO3 ) has proved itself at use in pyroelectric detectors. It fulfils not only the demands on material characteristic quantities just mentioned but also stands out due to an excellent temperature stability and very good reproducibility of the detector performance. Typical material properties of LiTaO3 at room temperature are: p = 1,8 . 10-8 Ccm-2K-1 εr = 43 tanδ = 0,001 cP´ = 3,2 Jcm-3K-1 4. Equivalent electric circuits of the responsive element and preamplifier The absorption of the radiant flux ΦS causes a temperature change ∆T in the pyroelectric material. This temperature change ∆T generally depends on the place in the pyroelectric material. This local dependence can be often neglected in good approximation. The thermal behavior of the responsive element can be represented in these cases by a simple analogous electrical substitute circuit diagram (figure 2) with heat capacity H P = c ′P d P AS where:

dP

(6)

thickness of the responsive element

and thermal conductance G between the sensitive element and his surroundings.


Because of the statistical behaviour of the heat exchange between responsive element and surrounding a so-called temperature noise is produced. Therefore in figure 2 an additional noise source is included, with:

~ p RnT = 4kT 2 G

α ΦS

pRT

(7)

1

j. ω. HP

1 G

Figure 2: Analogous electric circuit of the responsive element at simplified thermal conditions The temperature variation ∆T leads to a pyroelectric current which flows at short circuit of the electrodes of the sensitive element. This pyroelectric current arises under consideration of the definition of the pyroelectric coefficient and the thermal conditions according to figure 2:

with

ˆS αpΦ iˆP∠ = TR c ′P d P

(8)

jωτ T 1 + jωτ T

(9)

TR =

τT = H /G

(10)

ω = 2πf

(11)

The dimensionless function TR is called complex normalized current responsivity. For a sensitive element isolated ideally thermally (G = 0) the complex normalized current responsivity reaches the value 1. For most sensor constructions and for practically interesting modulation frequencies f = 1…1000 Hz this value 1 is a good approximation, if the thermal time constant τT has corresponding values. If the incident radiation is not modulated (f = 0), no pyroelectric current is produced. A pyroelectric detector is not responsible for a constant radiation. He always needs a temporal modulation of the incident radiant flux e.g. by chopping. Figure 3 shows the electrical circuit of the responsive element. Input quantity is the pyroelectric current after equation (8). Substitute elements are the electrical capacity CP =

ε o ε r AS dP

,


(12)

the frequency dependent resistance rP = 1 / (ωC P tan δ )

(13)

and the so-called tanδ noise source ~ iRnD = 4kTωC P tan δ

.

(14)

It describes thermal noise of the element resistance rP.

α. p . Φ i P = c . d S TR P P

i RD

1

j. ω. C

P

rP

Figure 3: Electrical circuit of the responsive element In figures 4 and 5 the electrical circuits of two fundamental preamplifier variants (preamplifier in voltage mode or current mode) are represented. Substitute elements are in both cases the input resistance reV and input capacitance CeV as well as current noise and ~ voltage noise iRnV or u~RnV of the preamplifier. The thermal noise of the input resistance is desciped by noise source: ~ iRnR =

4kT reV

.

(15)

If the preamplifier is operated in voltage mode, gain vV must be taken into account. The preamplifier in current mode contains a negative feedback op-amp (gain → ∞) with resistor RGK, his capacity CGK and his thermal noise: ~ iRnGK =

4kT RGK

.

(16)

u RV

in

1

j. ω . C

eV

r eV

i RR

i RV

u

Figure 4: Electrical circuit of a preamplifier in voltage mode  DIAS Infrared GmbH, 2006

vV . u

out

i RGK R GK 1

j. ω. C

GK

u RV

in

1

j. ω. C

r eV

eV

i RR

i RV

out

Figure 5: Electrical circuit of a preamplifier in current mode 5. Responsivity According to the defining equation (1) the responsivity SV in voltage mode is given by: SV = α

with

p TR c ′P d P

R 1 + (ωCR )

2

(17)

vV

R = rP // reV C = CP + CeV

(18) (19)

The electrical time constant is given by:

τ E = CR

.

(20)

For many detectors TR ≈ 1 , (ωCR)2 >> 1 and CP >> CeV are valid. Then equation (17) simplifies considerably: SV = α

vV c ′P ε r ε oωAS p

(21)

In this case, responsivity is indirectly proportional to the modulation frequency. The responsivity in current mode is given by: SV = α

p TR c ′P d P

RGK 1 + (ωC GK RGK )

(22) 2


If TR ≈ 1 and (ωCGKRGK)2 > 1, then

SV = α

p 1 c ′P d P ωC GK

.

(24)

6. Normalized noise voltage Different noise sources exist in the pyroelectric detector. They produce a noise voltage at the output. The normalised noise voltage shares are: ′ u~RnT ′ u~RnD ′ u~RnR ′ u~RnI ′ u~RnU ′ u~RnGK

noise voltage share, caused by the temperature noise source ~ p RnT of the responsive element noise voltage share, caused by the tanδ noise source ~ iRnD of the responsive element noise voltage share, caused by the thermal noise ~ iRnR of the input resistor reV of the preamplifier noise voltage share, caused by the current noise ~ iRnV of the preamplifier noise voltage share, caused by the voltage noise u~RnV of the preamplifier noise voltage share, caused by the thermal noise ~ iRnGK of the resistor RGK of the preamplifier (only in the current mode of the preamplifier)

The whole normalized noise voltage at the preamplifier output arises from square addition of the noise voltage shares: Preamplifier in voltage mode: ′ 2 = u~RnT ′ 2 + u~RnD ′ 2 + u~RnR ′ 2 + u~RnI ′ 2 + u~RnU ′2 u~Rn

(25)

Preamplifier in current mode: ′ 2 = u~RnT ′ 2 + u~RnD ′ 2 + u~RnR ′ 2 + u~RnI ′ 2 + u~RnU ′ 2 + u~RnGK ′2 u~Rn The equations for the normalised noise voltage shares are arranged in table 1.


(26)

Table 1: Effective values of the normalised noise voltage shares at the preamplifier output ′ u~RnX

X voltage mode: R = rP // reV, C = CP + CeV

current mode: R`= rP // reV // RGK, C´= CP + CeV + CGK SV

T

α

D

4kTωC P tan δ

R

4kT reV

R 1 + (ωCR )

R 1 + (ωCR ) R

I

~ iRnV

U

u~RnV vV

1 + (ωCR )

GK

2

2

vV

-

vV

2

vV

4kT 2 G

(27)

(28)

4kTωC P tan δ

(30)

4kT reV


2


(31)

2

RGK

(32)

~ iRnV

(34)

R u~RnV GK R′

1 + (ωC GK RGK )

4kT RGK

(33)

2

1 + (ωC ′R ′)

2

2 1 + (ωC GK RGK )


(29)

2

(35)

(36)

7. Specific detectivity The shares of the specific detectivity caused by the noise voltage shares result from the defining equation (3) of the specific detectivity as well as the basic equations of the responsivity (section 5) and normalized noise voltage (section 6): DT∗

share of the specific detectivity, caused by the temperature noise source ~ p RnT of the responsive element

DD∗

share of the specific detectivity, caused by the tan δ noise source ~ iRnD of the responsive element

DR∗

share of the specific detectivity, caused by thermal noise ~ iRnR of the input resistor reV of the preamplifier

DI∗

share of the specific detectivity, caused by the current noise ~ iRnV of the preamplifier

DU∗

share of the specific detectivity, caused by the voltage noise  DIAS Infrared GmbH, 2006

u~RnV of the preamplifier ∗ DGK

share of the specific detectivity, caused by the thermal noise ~ iRnGK of the resistor RGK of the preamplifier (only in the current mode of the preamplifier)

The whole specific detectivity is given by: Preamplifier in voltage mode: 2

 1  1   ∗  =  ∗ D   DT

2

  1  +  ∗   DD

2

  1  +  ∗   DR

2

2

  1   1  +  ∗  +  ∗   DI   DU

   

2

(37)

Preamplifier in current mode: 2

2

2

2

2

2

 1   1   1   1   1   1  1   ∗  =  ∗  +  ∗  +  ∗  +  ∗  +  ∗  +  ∗ D   DT   D D   DR   DI   DU   DGK

   

2

Table 2 contains the equations for the individual shares of the specific detectivity.


(38)

Table 2: Shares of the specific detectivity X

DX*

T

α

D

α

R

α

p c ′P

I

α

AS p TR ~ c ′P iRnV d P

U

α

p c ′P

α

p c ′P

GK

Remarks

AS 4kT 2 G

(39)

p

1

c ′P ε r tan δ

4kTε oωd P

TR

AS reV TR 4kT d P

(40)

(41)

(42)

AS

R

2 ~ 1 + (ωCR ) u RnV d P

R′

AS

TR

2 ~ 1 + (ωC ′R ′) u RnV d P

p

TR

(43)

(44)

α

1 TR ~ c ′P ε r ε o u RnV ω AS

(45)

α

p c ′P

RGK AS TR 4kT d P

(46)


voltage mode: R = rP // reV C = CP + CeV current mode: R`= rP // reV // RGK C´= CP + CeV + CGK voltage mode: (ωCR)2 >> 1, CP >> CeV current mode: (ωC´R´)2 >> 1, CP >> CeV + CGK only in current mode

8. Examples For the following detector layouts, frequency dependence of responsivity, normalized noise voltage and specific detectivity are represented in the figures 6 to 11. Detector layout

current mode

LiTaO3 2 x 2 mm2 5 µm 0,7 1

LiTaO3 2 x 2 mm2 5 µm 0,7 1

1011 Ω 2 pF 1 5.10-16 A/Hz1/2 6 nV/Hz1/2

1011 Ω 2 pF 1010 Ω 0,2 pF 5.10-16 A/Hz1/2 6 nV/Hz1/2

1E+4

1E+6

1E+3

1E+5

SV in V/W

SV in V/W

Responsive element: Pyroelectric material Responsive area AS Thickness of the element dP Absorption coefficient α Normalised current responsivity TR Preamplifier: Input resistance reV Input capacity CeV Gain vV Resistor RGK Capacity CGK ~ Current noise iRnV (10 Hz) Voltage noise u~RnV (1 kHz)

voltage mode

1E+2

1E+1

1E+0

1E+4

1E+3

1

100

10

1E+2

1000

1

100

10

f in Hz

1000

f in Hz

Figure 6: Frequency dependence of the responsivity at voltage mode

Figure 7: Frequency dependence of the responsivity at current mode

1E+3

1E+5

1E+2

~ u'Rn ~' u RnR

~' u RnI

1E+1

1E+0

~ ' in nV/Hz1/2 uRn

~ ' in nV/Hz1/2 uRn

~ u'Rn

1

~ ' uRnD

~ ' uRnR

~' u RnI

~' u RnU

~ ' uRnD

1E+3

~ ' uRnU

100

10

~' u RnGK

1E+4

1000

1E+2

1

f in Hz

100

10

f in Hz

Figure 8: Frequency dependence of the normalized noise voltage at voltage mode

Figure 9: Frequency dependence of the normalized noise voltage at current mode


1000

1E+11

1E+10

D*R D*I

1E+9

D*D

D*

D*U

1E+8

1E+7

1

100

10

1000

D* in cm.Hz1/2/W

D* in cm.Hz1/2/W

1E+11

1E+10

D*R D*I

1E+9

D*GK D*

D*D D*U

1E+8

1E+7

1

f in Hz

100

10

1000

f in Hz

Figure 10: Frequency dependence of the specific detectivity at voltage mode

Figure 11: Frequency dependence of the specific detectivity at current mode
