- Email: [email protected]
Pyroelectric thin-film detector performance
167
Sensors and Acluators A. 36 (1993) 167-171
Pyroelectnc thin-film detector performance B %gon and B B LavrenElE J Sfefan Inslrture Uwerstt~ of Lpb~ana, 61111 LJubl/ana (Slovenra) (Recewed March 3, 1992, m rewed
form November 13, 1992,accepted November 27, 1992)
Abstract Pyroelectnc film detectors exhlblt potential technological advantages due to the flexlblhty of sensor formation and mtegratlon We have consldered the temperature profiles as well as the sources of noise m a pyroelectnc detector m the form of a thm ferroelectrlc film which has been deposited on a substrate The voltage response (R,) and noise eqmvalent power (NEP) have been calculated as a function of modulation frequency for different film thicknesses We have compared the film detector with conventional pyroelectrlc detector designs Our calculations show that only membrane substrate film detectors should exceed the performance of conventional detectors
Introduction
The performance of pyroelectrlc detectors, which have been designed for high sensltlvlty at low modulation frequencies, can be derived from a simple model [l] Such a model usually assumes that the active material 1s uniformly lllummated and 1s basically thermally insulated by air, 1 e , the absorbed energy IS dlsslpated slowly through gas conduction The temperature profiles wlthm the pyroelectnc are not taken mto account Increased performance 1s achieved with thinner and fully insulated detectors [l] A more elaborate model has been worked out by Logan [2] He solved the thermal conductlvlty equations for the case of arbitrary slab thickness, yielding the temperature profiles wlthm the pyroelectrlc material The slab was still insulated by anRecent advances m material science have resulted m the pyroelectrlc materials being deposited m the form of thm ferroelectrlc films [3] The current research topics include substrate, material and possible dopant selection, film deposltlon techniques, and detector and readout electronics integration The choice of substrate 1s an lmportant step, for it promotes the epltaxlal growth At first sight this technology appears to be well suited for pyroelectrlc detectors At present the problems m achlevmg good epltaxlal growth must be overcome Nevertheless, successful detectors have been reported [ 31 Thus, m the case of film detectors we 0924-4247/93/%6 00
must assume that they are deposited on some substrate and not suspended m a holder, as 1s the case with the conventional design [4] Thin-film ( w 1 pm or less) detectors are therefore greatly influenced by the thermal conduction of absorbed heat mto the substrate It 1s well known that such heat loss reduces the detector performance On the other hand, greatly reduced thickness increases the performance through the dlmmlshed noise and therefore one looks for some kmd of trade-off Recently, Schopf et al [5] considered a similar model as explained below While they were lookmg for the voltage figure of merit, our calculations were directed towards the assessment of the thmfilm pyroelectrlc detector performance with respect to noise and signal-to-noise ratios
Temperature profiles
The detector configuration 1s depicted m Fig 1 We assume that smusoldally modulated radiation power (denoted as Q) 1s absorbed only m the absorber of neghgble thickness at x = 0 The heat is transferred to the detector (denoted as PYRO) and then to the substrate The detector 1s surrounded by air and placed mto the housing with temperature T, The housing prevents air convection so it 1s sufficient to consider only the conductive heat transfer We shall further assume bulk values for the matenal constants of the thm pyroelectric film @ 1993 -
Elsewer Sequoia
All nghts reserved
168
d
s
I
where the indices al, a2, p and s denote the first and second air regions, pyroelectrlc and substrate, respectively For each layer we are seeking a solution m the form
c
d
F(x) = Q(,4 cash lx + B smh 5x) -d
0
I
I+s+d
L+s
and find
Fig 1 Heat-transfer model for a pyroelectnc film detector (denoted as PYRO), deposlted on a substrate and exchangmg heat with the environment at temperature To vLa au Q 1s the absorbed power per umt volume We use mdlces al, p, sand a2 to denote the front air layer, the pyroelectnc layer, the substrate and the back au layer, respectively The coordmates of the layer boundanes and the layer thicknesses are deslgnated below and above the mam Figure, respectively
Let us start wth the thermal dlfluslon equation 1 dT
a*T -_--=
a2
K
_- Q
(1)
K
at
where T IS the temperature, K the thermal diffusion constant, K the thermal conductlvlty and Q the absorbed power per unit volume Inserting into eqn (1)
Qwexp(lN
Q=
(2)
and T(x, t) - T,, = F(x) exp(iwt)
F,, = Q(A, cash ax + B, smh MX),
temperature,
!p&+
(84 Fp = Q(& cash /lx + B2 smh /lx),
F, = Q(A3 cash yx + B3 smh yx),
F” - t*F = 0,
F,, = Q(A4 cash ax + B4 smh c(x), I+s
i.$,;
cL= (~w/K~)“*, j = (io/rc,)“*
F,=F,,
x=1
Fs =
x=l+s
Fa2
=
Fa2,
we get
The coefficients A, and B, are derived from the boundary conditions (6a) -( 6h) In particular, the coefficients A2 and B2 (descnbmg the temperature profile inside the pyroelectnc) are A2 = i smh ad[K,y smh j?l(K,a cash ad cash ys + KSy smh ad smh ys) + Kp/?
+ KSy smh ad cash ys)]
(64 (6b) (64 (64 (64
dFa, -Kpz=Q, Ka,-
x=0
dx
B2 = -i
KdFs “dx
(60
K
dF,,=O a2 dx
’ ’
x=1
(6g)
x=l+s
(6h)
(9a)
smh ad[K,y cash pi(K,a cash ad cash ys
+ K,y smh ad smh ys) + Kpfi x smh /Il(K=a cash ad smh ys
+ K,y smh ad cash ys)]
(9b)
where A = K,y(K,a cash ad smh pi + KJ3 smh ad cash 81) x (K,a cash ad cash ys + K,y smh ad smh ys) + K$(K,a
K dFP_KdF,=O “dx ’ dx
and y = (lo/
x cash fiI(K,a cash ad smh ys
(5)
x=l+s+d
0,
(8d)
s
for each of the four layers with the boundary condltlons x=0
l
Thus we shall solve the equation
Fe-,,= Fp,
O
(4)
u
x=-d
-d
(3)
where T,, IS the environmental
F,, = 0,
(7)
cash ad cash Bl
+ K,/I smh ad smh /?I) x (K,a cash ad smh ys + K,y smh ad cash ys) (9c)
169
Voltage response Figure 2 depicts the conventlonal detector configuration attached to the preamphfier Our aim IS to calculate the voltage response We start with the pyroelectrlc current source, which IS gven as
The loss tangent tan 6 1s the ratio between the imaginary and the real part of the dlelectnc constant R, and RA are the reslstlvltles and C,, and C, are the capacltles of the pyroelectnc layer and amplifier, respectively Usmg the Ansatz U = U, exp(iwt) we get
I
I(t)
=‘$
s
T(x, t) dx =pA
dF((t)
(10)
dt
0
where p IS the pyroelectrlc coefficient, A the surface area of the PYRO layer and T the average temperature within the PYRO layer From eqn (3) we find
(14) where ZE= CTRT With these values we arnve at the voltage response +~p,&?&
Rv+/= PlU
smh /31+ B2( cash /iii - 1) I pq 1 + w*zE*)I’* (15)
- = I& exp( lot) dt
(11)
where P =f s
F(x) dx = $ [A2 smh /3l+B,(cosh
/_IE - l)]
”
(12) Looking at Fig 2 we find the circuit equation
where the pyroelectnc (10) We put
current I IS gven m eqn
$=‘,i T
R, RA
1 -=0S,tan6 R, and
with Q = qPw P, IS the total radlatlve power falling on the PYRO layer and q IS the fraction of this power absorbed m the layer
Noise sources
The sources of noise m a pyroelectrlc detector have been considered by Lang [I] and roughly consist of contnbutlons from the Johnson noise of the detector and load resistor, noise due to the leakage current of the FET and the amplifier voltage noise as well as thermal noise The case of a thm-film detector does not produce new sources of noise and we calculated the noise voltage following Lang [l] The expression for the Johnson noise due to the detector and the load resistor 1s as follows v2= J
We have to add the noise due to the amplifier leakage current I,,, v2
=
I
Rg 2 Eqmvalent electrical model for the pyroelectnc detector attached to an FET preamphfier Indxes p denote the pyroelectnc and A the preamphfier, respechvely
4kTRT 1 +o*~E*
2e&Jb* 1 + cl&*
(17)
and the amplifier voltage noise VA The temperature fluctuation noise results from exchanging the energy between the detector and the environment at temperature To (see. Fig 1) The power spectrum density PT* for this noise can be wntten [l] as PT* = 4kT*G
(18)
170
where G 1s the real part of the thermal admittance The admittance & 1s defined as
TABLE 2 Mdterldl and preamplifier pdrdmeters used m cdlculdtmg the NEP For the descnptlon of the parameters see text
d(T,
A=lmm’ [ =]O-‘ZA e>>
q=O85 &=3x10-“F
,o_2cn
Voltage nare[nV/fii
- r,,) = heat loss from PYRO
(19)
R A = 1O”R
T,, = 300 K
Thus using eqn (3) we write delta
,ooo
Using the boundary condltlons (6f) and (6g), this can be written as 100
(21) Inserting eqn (Sb) mto eqn complex admittance
’
“‘1111’
10
100
’ ’
11111’ 1000
1
10
FREQUENCY[Hz] Fig 3 Measured values for the loss tangent of bulk LlTaO, and the voltdge [email protected] of the low-leakage FET transistor, respectwely, as d function of modulation frequency These values were used In our cdlculdtlons of now sources
2
(
1
(21), we get the
d=++AK,~ B, -’ AZ
10-L’’ ’ ““1”
A2 smh fll + B2 cash PI A2 cash PI+ B, smh fil >
(22)
are taken from Slhcomcs Co low-leakage FET transistor
Data Sheet for a
and finally G = Re(&)
(23)
The noise equivalent power (NEP) 1s defined as NEp _
[(P,R,y + vJ2+ v,2+ v*2]“2 RV
(24)
We have considered the case of LITaOj film detectors on Sl substrates The matenal constants are presented m Table 1 and detector and amplifier data m Table 2 Figure 3 shows the values of loss tangent and amphfier noise, respectively, as a function of frequency The loss tangent values were measured on the General Radio Co 1621 Preclslon Capacitance Measurement System, usmg the bulk LlTaO, crystal The amplifier noise values TABLE I Materlal constants used m calculatmg temperature profiles and voltage response K 1s the thermal conductwlty, h the thermal dliTususlonconstant, p the pyroelectnc coeffinent and E the dlelectrlc constant Constant
Air
LfaO,
SI
K[W cm-’ K-‘1 h [cm2 s-‘1 p [PA s me2 K-‘1 E
0 00024 0 188
0 035 0011 200 53
1 49 0 90
Figure 4 shows the calculated values for Rv as a function of the modulation frequency The parameter 1s the film thickness It should be noted that m the case of detectors suspended m air (1 e ,
10-21 1
10 Frequency
102
103
[Hz]
Fig 4 Voltage response R, m thin-film pyroelectnc detectors as a function of modulation frequency Parameters 1-4 denote the followmg pyroelectnc layer thxknesscs I, 0 1 pm, 2, 1 pm, 3, 10 pm, 4, 100 pm These detectors are constdered as bemg deposlted on a 1 mm thick SI substrate The parameter 5 denotes a 10 pm detector suspended m air (I e , conventional detector design) The surface area of the pyroelectrlc layer IS 1 mm* for each detector The actwe material consldered here IS LITaO, Other parameters are gwen m Tables 1 and 2 as well as m Fig 3
171
parameter 5) the voltage response RV does not depend on thickness [l] The present calculation shows conslderable lowermg of RV for the films on an & substrate with decreasmg film thickness This dlmmlshed value 1s a consequence of the rapid transfer of heat from the PYRO film into the substrate, thus preventing a temperature rise m the active layer This transfer increases with decreasmg film thickness The lowering of the signal 1s somewhat smaller with increasing frequency and reflects the fact that the thinner film does not have a higher temperature nse (denoted as F m eqn ( 12)) due to the absorption of power Q compared with a thicker one Figure 5 depicts the NEP as a function of frequency for detectors with the same thickness parameters as considered m Fig 4 All detectors attached to the substrate, regardless of thickness, show a higher NEP than an--insulated ones By lowering the thickness of the detector, the Johnson noise decreases due to increased capacitance, whereas the amplifier noise (independent of thlckness) becomes dominant below 10 pm The thermal or conduction noise has been found to be smaller than the amplifier voltage noise at all the modulation frequencies considered Thus, by employing thin-film technology we expect a conslderable reduction of total noise However, this smaller overall noise cannot offset the much greater reduction of voltage response, thus leading to an increase of the NEP with reduced thickness, unlike the case of insulated detectors We have also considered the technologically lmportant case of an LlTa03 film detector deposited on an LlTaO, substrate As 1s seen from Table 1, the thermal conductlvlty coefficient K for tantalate 1s l/40 of the slhcon value Nevertheless, we found
for parameters 1 and 2 of Fig 5 a reduction of NEP at 10 Hz by only a factor of three Conclusions We have calculated the thermal equation for the case of a thm pyroelectrlc film detector The film 1s considered to be deposited on a crystalline substrate In addition, we have taken mto account the noise present m a detector coupled to an amplifier and have determmed the NEP It has been shown that the film pyroelectrlc performance 1s well below that of the conventional design due to rapid heat loss, which cannot be compensated by a reduction of noise Our result underscores the need for active layer insulation if one aims for maximum sensitivity in thin-film pyroelectnc detectors Takayama et al [ 31 m fact etched a hole mto the substrate and exposed the active layer and thus got excellent NEP figures References 1 S B Lang, Sourcebook of Pyroelectrrcrty, Gordon and Breach, New York, 1974, p 40 2 R M Logan and K Moore, Calculation of temperature dlstnbutlon and temperature noise m a pyroelectnc detector 1 Gas-filled Tube, Infrared Phys, 13 (1973) 37 3
R
Takayama, Y Tomlta, K Iqma and I Ueda, Pyroelectrz propertles and apphcatlon to Infrared sensors of PbT103 and PbLaTIO, ferroelectnc thm films, Ferroelecercs, 118 (1991) 325 4 B B LavrenhE, J Polanec, P Cevc and A KanduSer, Technology of double parallel pyroelectnc detector, Ferroelecfrrcs, 91(1989) 323 5 H Schopf, W Ruppel and P Wuerfel, Voltage responslwty of pyroelectnc detectors on a heat-smk substrate, Ferroelecrrw, 118 (1991) 297
Biographies Borut .&gon graduated from the Physics Department, University of LJublJana, in 1987 and started to work for the Iskra Company, where he was involved m photometlc mstrumentatlon design Since 1900 he has been enrolled at the Graduate School of the University of LJUblJitna His main interests are optical design and infrared sensors
I 1
10
Frequency
I
102
I
I
103
[Hz]
F1.g 5 NEP m thm-film pyroelectrx the same as m Fig 4
detectors
The parameters
are
Borut B LavrenEzE received his Ph D m physics from the University of LJublJana in 1973 Ha mam interests are melastlc scattering of laser light, ferroelectnc phase transitions, pyroelectnc detectors, and recently thm ferroelectrlc films
Sensors and Acluators A. 36 (1993) 167-171
Pyroelectnc thin-film detector performance B %gon and B B LavrenElE J Sfefan Inslrture Uwerstt~ of Lpb~ana, 61111 LJubl/ana (Slovenra) (Recewed March 3, 1992, m rewed
form November 13, 1992,accepted November 27, 1992)
Abstract Pyroelectnc film detectors exhlblt potential technological advantages due to the flexlblhty of sensor formation and mtegratlon We have consldered the temperature profiles as well as the sources of noise m a pyroelectnc detector m the form of a thm ferroelectrlc film which has been deposited on a substrate The voltage response (R,) and noise eqmvalent power (NEP) have been calculated as a function of modulation frequency for different film thicknesses We have compared the film detector with conventional pyroelectrlc detector designs Our calculations show that only membrane substrate film detectors should exceed the performance of conventional detectors
Introduction
The performance of pyroelectrlc detectors, which have been designed for high sensltlvlty at low modulation frequencies, can be derived from a simple model [l] Such a model usually assumes that the active material 1s uniformly lllummated and 1s basically thermally insulated by air, 1 e , the absorbed energy IS dlsslpated slowly through gas conduction The temperature profiles wlthm the pyroelectnc are not taken mto account Increased performance 1s achieved with thinner and fully insulated detectors [l] A more elaborate model has been worked out by Logan [2] He solved the thermal conductlvlty equations for the case of arbitrary slab thickness, yielding the temperature profiles wlthm the pyroelectrlc material The slab was still insulated by anRecent advances m material science have resulted m the pyroelectrlc materials being deposited m the form of thm ferroelectrlc films [3] The current research topics include substrate, material and possible dopant selection, film deposltlon techniques, and detector and readout electronics integration The choice of substrate 1s an lmportant step, for it promotes the epltaxlal growth At first sight this technology appears to be well suited for pyroelectrlc detectors At present the problems m achlevmg good epltaxlal growth must be overcome Nevertheless, successful detectors have been reported [ 31 Thus, m the case of film detectors we 0924-4247/93/%6 00
must assume that they are deposited on some substrate and not suspended m a holder, as 1s the case with the conventional design [4] Thin-film ( w 1 pm or less) detectors are therefore greatly influenced by the thermal conduction of absorbed heat mto the substrate It 1s well known that such heat loss reduces the detector performance On the other hand, greatly reduced thickness increases the performance through the dlmmlshed noise and therefore one looks for some kmd of trade-off Recently, Schopf et al [5] considered a similar model as explained below While they were lookmg for the voltage figure of merit, our calculations were directed towards the assessment of the thmfilm pyroelectrlc detector performance with respect to noise and signal-to-noise ratios
Temperature profiles
The detector configuration 1s depicted m Fig 1 We assume that smusoldally modulated radiation power (denoted as Q) 1s absorbed only m the absorber of neghgble thickness at x = 0 The heat is transferred to the detector (denoted as PYRO) and then to the substrate The detector 1s surrounded by air and placed mto the housing with temperature T, The housing prevents air convection so it 1s sufficient to consider only the conductive heat transfer We shall further assume bulk values for the matenal constants of the thm pyroelectric film @ 1993 -
Elsewer Sequoia
All nghts reserved
168
d
s
I
where the indices al, a2, p and s denote the first and second air regions, pyroelectrlc and substrate, respectively For each layer we are seeking a solution m the form
c
d
F(x) = Q(,4 cash lx + B smh 5x) -d
0
I
I+s+d
L+s
and find
Fig 1 Heat-transfer model for a pyroelectnc film detector (denoted as PYRO), deposlted on a substrate and exchangmg heat with the environment at temperature To vLa au Q 1s the absorbed power per umt volume We use mdlces al, p, sand a2 to denote the front air layer, the pyroelectnc layer, the substrate and the back au layer, respectively The coordmates of the layer boundanes and the layer thicknesses are deslgnated below and above the mam Figure, respectively
Let us start wth the thermal dlfluslon equation 1 dT
a*T -_--=
a2
K
_- Q
(1)
K
at
where T IS the temperature, K the thermal diffusion constant, K the thermal conductlvlty and Q the absorbed power per unit volume Inserting into eqn (1)
Qwexp(lN
Q=
(2)
and T(x, t) - T,, = F(x) exp(iwt)
F,, = Q(A, cash ax + B, smh MX),
temperature,
!p&+
(84 Fp = Q(& cash /lx + B2 smh /lx),
F, = Q(A3 cash yx + B3 smh yx),
F” - t*F = 0,
F,, = Q(A4 cash ax + B4 smh c(x), I+s
i.$,;
cL= (~w/K~)“*, j = (io/rc,)“*
F,=F,,
x=1
Fs =
x=l+s
Fa2
=
Fa2,
we get
The coefficients A, and B, are derived from the boundary conditions (6a) -( 6h) In particular, the coefficients A2 and B2 (descnbmg the temperature profile inside the pyroelectnc) are A2 = i smh ad[K,y smh j?l(K,a cash ad cash ys + KSy smh ad smh ys) + Kp/?
+ KSy smh ad cash ys)]
(64 (6b) (64 (64 (64
dFa, -Kpz=Q, Ka,-
x=0
dx
B2 = -i
KdFs “dx
(60
K
dF,,=O a2 dx
’ ’
x=1
(6g)
x=l+s
(6h)
(9a)
smh ad[K,y cash pi(K,a cash ad cash ys
+ K,y smh ad smh ys) + Kpfi x smh /Il(K=a cash ad smh ys
+ K,y smh ad cash ys)]
(9b)
where A = K,y(K,a cash ad smh pi + KJ3 smh ad cash 81) x (K,a cash ad cash ys + K,y smh ad smh ys) + K$(K,a
K dFP_KdF,=O “dx ’ dx
and y = (lo/
x cash fiI(K,a cash ad smh ys
(5)
x=l+s+d
0,
(8d)
s
for each of the four layers with the boundary condltlons x=0
l
Thus we shall solve the equation
Fe-,,= Fp,
O
(4)
u
x=-d
-d
(3)
where T,, IS the environmental
F,, = 0,
(7)
cash ad cash Bl
+ K,/I smh ad smh /?I) x (K,a cash ad smh ys + K,y smh ad cash ys) (9c)
169
Voltage response Figure 2 depicts the conventlonal detector configuration attached to the preamphfier Our aim IS to calculate the voltage response We start with the pyroelectrlc current source, which IS gven as
The loss tangent tan 6 1s the ratio between the imaginary and the real part of the dlelectnc constant R, and RA are the reslstlvltles and C,, and C, are the capacltles of the pyroelectnc layer and amplifier, respectively Usmg the Ansatz U = U, exp(iwt) we get
I
I(t)
=‘$
s
T(x, t) dx =pA
dF((t)
(10)
dt
0
where p IS the pyroelectrlc coefficient, A the surface area of the PYRO layer and T the average temperature within the PYRO layer From eqn (3) we find
(14) where ZE= CTRT With these values we arnve at the voltage response +~p,&?&
Rv+/= PlU
smh /31+ B2( cash /iii - 1) I pq 1 + w*zE*)I’* (15)
- = I& exp( lot) dt
(11)
where P =f s
F(x) dx = $ [A2 smh /3l+B,(cosh
/_IE - l)]
”
(12) Looking at Fig 2 we find the circuit equation
where the pyroelectnc (10) We put
current I IS gven m eqn
$=‘,i T
R, RA
1 -=0S,tan6 R, and
with Q = qPw P, IS the total radlatlve power falling on the PYRO layer and q IS the fraction of this power absorbed m the layer
Noise sources
The sources of noise m a pyroelectrlc detector have been considered by Lang [I] and roughly consist of contnbutlons from the Johnson noise of the detector and load resistor, noise due to the leakage current of the FET and the amplifier voltage noise as well as thermal noise The case of a thm-film detector does not produce new sources of noise and we calculated the noise voltage following Lang [l] The expression for the Johnson noise due to the detector and the load resistor 1s as follows v2= J
We have to add the noise due to the amplifier leakage current I,,, v2
=
I
Rg 2 Eqmvalent electrical model for the pyroelectnc detector attached to an FET preamphfier Indxes p denote the pyroelectnc and A the preamphfier, respechvely
4kTRT 1 +o*~E*
2e&Jb* 1 + cl&*
(17)
and the amplifier voltage noise VA The temperature fluctuation noise results from exchanging the energy between the detector and the environment at temperature To (see. Fig 1) The power spectrum density PT* for this noise can be wntten [l] as PT* = 4kT*G
(18)
170
where G 1s the real part of the thermal admittance The admittance & 1s defined as
TABLE 2 Mdterldl and preamplifier pdrdmeters used m cdlculdtmg the NEP For the descnptlon of the parameters see text
d(T,
A=lmm’ [ =]O-‘ZA e>>
q=O85 &=3x10-“F
,o_2cn
Voltage nare[nV/fii
- r,,) = heat loss from PYRO
(19)
R A = 1O”R
T,, = 300 K
Thus using eqn (3) we write delta
,ooo
Using the boundary condltlons (6f) and (6g), this can be written as 100
(21) Inserting eqn (Sb) mto eqn complex admittance
’
“‘1111’
10
100
’ ’
11111’ 1000
1
10
FREQUENCY[Hz] Fig 3 Measured values for the loss tangent of bulk LlTaO, and the voltdge [email protected] of the low-leakage FET transistor, respectwely, as d function of modulation frequency These values were used In our cdlculdtlons of now sources
2
(
1
(21), we get the
d=++AK,~ B, -’ AZ
10-L’’ ’ ““1”
A2 smh fll + B2 cash PI A2 cash PI+ B, smh fil >
(22)
are taken from Slhcomcs Co low-leakage FET transistor
Data Sheet for a
and finally G = Re(&)
(23)
The noise equivalent power (NEP) 1s defined as NEp _
[(P,R,y + vJ2+ v,2+ v*2]“2 RV
(24)
We have considered the case of LITaOj film detectors on Sl substrates The matenal constants are presented m Table 1 and detector and amplifier data m Table 2 Figure 3 shows the values of loss tangent and amphfier noise, respectively, as a function of frequency The loss tangent values were measured on the General Radio Co 1621 Preclslon Capacitance Measurement System, usmg the bulk LlTaO, crystal The amplifier noise values TABLE I Materlal constants used m calculatmg temperature profiles and voltage response K 1s the thermal conductwlty, h the thermal dliTususlonconstant, p the pyroelectnc coeffinent and E the dlelectrlc constant Constant
Air
LfaO,
SI
K[W cm-’ K-‘1 h [cm2 s-‘1 p [PA s me2 K-‘1 E
0 00024 0 188
0 035 0011 200 53
1 49 0 90
Figure 4 shows the calculated values for Rv as a function of the modulation frequency The parameter 1s the film thickness It should be noted that m the case of detectors suspended m air (1 e ,
10-21 1
10 Frequency
102
103
[Hz]
Fig 4 Voltage response R, m thin-film pyroelectnc detectors as a function of modulation frequency Parameters 1-4 denote the followmg pyroelectnc layer thxknesscs I, 0 1 pm, 2, 1 pm, 3, 10 pm, 4, 100 pm These detectors are constdered as bemg deposlted on a 1 mm thick SI substrate The parameter 5 denotes a 10 pm detector suspended m air (I e , conventional detector design) The surface area of the pyroelectrlc layer IS 1 mm* for each detector The actwe material consldered here IS LITaO, Other parameters are gwen m Tables 1 and 2 as well as m Fig 3
171
parameter 5) the voltage response RV does not depend on thickness [l] The present calculation shows conslderable lowermg of RV for the films on an & substrate with decreasmg film thickness This dlmmlshed value 1s a consequence of the rapid transfer of heat from the PYRO film into the substrate, thus preventing a temperature rise m the active layer This transfer increases with decreasmg film thickness The lowering of the signal 1s somewhat smaller with increasing frequency and reflects the fact that the thinner film does not have a higher temperature nse (denoted as F m eqn ( 12)) due to the absorption of power Q compared with a thicker one Figure 5 depicts the NEP as a function of frequency for detectors with the same thickness parameters as considered m Fig 4 All detectors attached to the substrate, regardless of thickness, show a higher NEP than an--insulated ones By lowering the thickness of the detector, the Johnson noise decreases due to increased capacitance, whereas the amplifier noise (independent of thlckness) becomes dominant below 10 pm The thermal or conduction noise has been found to be smaller than the amplifier voltage noise at all the modulation frequencies considered Thus, by employing thin-film technology we expect a conslderable reduction of total noise However, this smaller overall noise cannot offset the much greater reduction of voltage response, thus leading to an increase of the NEP with reduced thickness, unlike the case of insulated detectors We have also considered the technologically lmportant case of an LlTa03 film detector deposited on an LlTaO, substrate As 1s seen from Table 1, the thermal conductlvlty coefficient K for tantalate 1s l/40 of the slhcon value Nevertheless, we found
for parameters 1 and 2 of Fig 5 a reduction of NEP at 10 Hz by only a factor of three Conclusions We have calculated the thermal equation for the case of a thm pyroelectrlc film detector The film 1s considered to be deposited on a crystalline substrate In addition, we have taken mto account the noise present m a detector coupled to an amplifier and have determmed the NEP It has been shown that the film pyroelectrlc performance 1s well below that of the conventional design due to rapid heat loss, which cannot be compensated by a reduction of noise Our result underscores the need for active layer insulation if one aims for maximum sensitivity in thin-film pyroelectnc detectors Takayama et al [ 31 m fact etched a hole mto the substrate and exposed the active layer and thus got excellent NEP figures References 1 S B Lang, Sourcebook of Pyroelectrrcrty, Gordon and Breach, New York, 1974, p 40 2 R M Logan and K Moore, Calculation of temperature dlstnbutlon and temperature noise m a pyroelectnc detector 1 Gas-filled Tube, Infrared Phys, 13 (1973) 37 3
R
Takayama, Y Tomlta, K Iqma and I Ueda, Pyroelectrz propertles and apphcatlon to Infrared sensors of PbT103 and PbLaTIO, ferroelectnc thm films, Ferroelecercs, 118 (1991) 325 4 B B LavrenhE, J Polanec, P Cevc and A KanduSer, Technology of double parallel pyroelectnc detector, Ferroelecfrrcs, 91(1989) 323 5 H Schopf, W Ruppel and P Wuerfel, Voltage responslwty of pyroelectnc detectors on a heat-smk substrate, Ferroelecrrw, 118 (1991) 297
Biographies Borut .&gon graduated from the Physics Department, University of LJublJana, in 1987 and started to work for the Iskra Company, where he was involved m photometlc mstrumentatlon design Since 1900 he has been enrolled at the Graduate School of the University of LJUblJitna His main interests are optical design and infrared sensors
I 1
10
Frequency
I
102
I
I
103
[Hz]
F1.g 5 NEP m thm-film pyroelectrx the same as m Fig 4
detectors
The parameters
are
Borut B LavrenEzE received his Ph D m physics from the University of LJublJana in 1973 Ha mam interests are melastlc scattering of laser light, ferroelectnc phase transitions, pyroelectnc detectors, and recently thm ferroelectrlc films