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Speed and sensitivity limitations of extrinsic photoconductors†
Infrared Physics, 1969, Vol. 9, pp. 37-40. Pergamon Press. Printed in Great Britain
Speed and Sensitivity
Limitations
of Extrinsic Photoconductorst
(Receiced 23 October 1968)
Abstract-For extrinsic photoconductors with gain in excess of unity there is a minimum response time determined by the background flux. Combining this concept with conventional D* arguments leads to
This sensitivity bandwidth manium for 12.5 microns.
product has a value of 2 x 101* cm Hz: W set for extrinsic ger-
INTRODUCTION the study of mercury- and copper-doped germanium photoconductors it has been shown that the speed of response is determined not only by the carrier lifetime but also by the resistivity of the photoconductor.c’s 2, Further the response time component determined by resistivity-the dielectric relaxation response timeappears only as the gain of the photoconductor approaches and exceeds unity.c”) For the high gain conditions, when the response time is set by the dielectric relaxation time, the sensitivity and speed are interrelated. IN
DETECTOR SPEED-DIELECTRIC RELAXATION TlME CONSTANT The response of the detector always contains a dielectric relaxation component. This component is usually small or is sufficiently fast to be of no concern. In two situations, high speeds and low backgrounds, it can be the dominant response time. In the latter situation, the reduced background increases the dielectric relaxation time to values as long as seconds. The dielectric relaxation time is given by 7p = EE0fJ (1) where p is the resistivity of the material, c the dielectric constant, and E” the permitivity of free space. The dielectric relaxation effects are delays so that the total response time T of a detector is the sum of the carrier lifetime TJ and T,,. Thus, 7=71+7 (2) P For extrinsic photoconductors the resistivity of detector materials is determined by the background flux fpe, namely
In this expression 7 is the efficiency with which the radiation is absorbed, t the sample thickness, pp the hole mobility and q the electronic charge. Combining equations (2) and (3) yields (4) The principal features of equation (4) are illustrated by plotting the reponse time as a function of carrier lifetime for several values of the background flux 9~. Such curves are reproduced in Fig. 1. Note that for lifetime values shorter than a certain value the response time not only stops decreasing but starts to increase. This increase is the onset of dielectric relaxation effects. The curve for P)B= 10~s/sec/cm2 corresponds approximately to the 3GO”K, 180” field of view situation for a 14 micron detector such as Ge : Hg. For this situation the minimum response time is approximately 2 x 10-s sec. tThis work was supported in part by the Office of Naval Research
under
37
Contract
No. NOOO14-67-C-0497
Letters to the Editors
I
10-L
f\
I
I
I +B
1 = lO”/SEC/
I
I
V
V
I
cm2
10-4 1014
1016
10-6 1018
E cot 3
TZT.4
/
10-8
I
1
10
-2
I
I
I
1o-4
10
I
‘Fe RECOMBINATION
I
I
-6
10
-8
LIFETIME
lo-lo
I lo-l2
(SEC)
FIG. I. Variation of response time with recombination lifetime. For a particular background flux the response time depends on the carrier lifetime, being long if 7~ is too short or too long. The fastest response time requires a specific carrier lifetime for each background value. To achieve speeds faster than this value excess radiation must illuminate the detector as well as 71 being short. At reduced values of pn an anomalous situation arises for to achieve the fastest speed the lifetime must not be short. De-SPEED OF RESPONSE CONSIDERATIONS A consequence of the response time arguments in the above paragraph is that D* and the fastest speed ot response are related, that is for each background flux there is an optimum carrier lifetime. This is immediately apparent from the plot of equation (4) in Fig. 1. For the fastest response time 7min there is an optimum carrier lifetime ant. The value of 7mtn is calculated for a particular background by equating the two terms of equation (4) namely Thus,
%1pt
71when T,, = 7,
(5)
Recognizing that TmtII = 71 + $ = 2710pt is the minimum response time,
The background-limited
infrared performance (BLIP) of a detector is given by the following D*
The D* bandwidth
,llaiX
relationship Pj
(8)
product is then ?LF&X Tmin
__ h 7 he 4
(9)
Letters to the Editors
39
It is apparent that the D*-bandwidth product is independent of background flux. Further, if high D* values are to be obtained,c4) speed must be sacrificed. Conversely, if speed is required, D* must be sacrificed. The value of D*/T~~~ is easily calculated since the only significant parameter to be determined is pP, Taking c(~ = 2 x lo5 cm2/V-set, l C~= 1.4 x lo-l2 F/cm, I = 0.5 cm, A = 12.5 pm and 7 = 0.5, we have for extrinsic germanium in the 10-30” K range. D*,,Xl 7mrn = 1.7 x 10lscm (Hz)a/W-set The operating limits described by equation (9) are best illustrated by plotting both equations (7) and (8) on the same graph. This has been done in Fig. 2 with abscissa axis units of photons/sec/cm2 and W/cm?. Included are 7min values for 4 cm and 5 micron absorption length detectors.
L
WATTSlClll 10‘8
I
10
-b
10
10-4
I
-2
1
I
I
IO2
1’0
I
10b
10’
I
lIO
c> 1
-4
IO -5
IO
-b
10-7 3
\ T&(5,)
\ \
" F
\
10
\
\
-*
\
\
\
\
\
\
‘\ \
\\
\
10
\
-9
IO-'0
-I
;0-"
10,?
FIG. 2. Maximum D* and minimum response time. Under operating conditions with photoconductive gain in excess of unity, dielectric relaxation determines speed of response. Then for background-limited operation both D* and the minimum response time are determined by the background photon flux density.
CONCLUSIONS High gain extrinsic photoconductors are limited in performance by dielectric relaxation effects. If high speeds are to be achieved sensitivity must be sacrificed by adding an additional photon flux to the detector; for example, a speed of lo-i0 set requires a flux of 100 W/cm2. Conversely for high sensitivities such as a D* of 1014cm Hz*/W, the speed cannot be faster than 3 x IO-5 sec. In all the above discussion of speed and sensitivity the photoconductive gain is greater than unity. For
40
Letters to the Editors
gains significantly less than unity dielectric relaxation effects are absent. (1) This is the operating condition utilized by several workers when performing heterodyne detection experiments.(5-” Acknowledgements-The search for a relationship Werner Beyen and George Pruett
between sesntivity and speed arose from discussions with Ii. L.
Texas Iiutruments Research Building I3500 North Central Expresswla) Dallas, Texas 75201
WILLIAMS
REFERENCES
I. WILLIAMS,R. L., J. appl. Phys. 38, 4802 (1967). 2. WILLIAMS,R. L., submitted for publication and also a part of Final Technical Report for High-Speed, Long Wavelength Coherent Radiation Detectors, June 1968, Contract NOOO14-67-C-0497, Office of Naval Research-Advanced Research Projects Agency, Texas Instruments Incorporated Report No. 08-68-38. 3. KRUSE, P. W., L. D. MCGLAUCHLINand R. B. MCQUISTAN,Elements ofInfrared Technology. John Wiley (1968); Handbook of Military Infrared Technology, edited by W. L. WOLFE. U.S. Government Printing Office (1965). 4. QUIST, T. M. Proc. IEEE 56, 1212 (1968). 5. TEICH. M. C.. R. KEYESand R. KINGSTON,Appl. Phyc. Lett. 9, 357 (1966); M. C. TEICH, Proc. IEEE56, 37 (1568). 6. BUCZECH,C. S. and G. S. Rcus, Appl. Phys. Lett. 10, 125 (1967); G. S. PICUS, private communication. 7. ARAMS,F. R., E. W. SARD, B. S. PEYTONand F. P. PACE, IEEE J. Qcrantam Electron. QJS, 484 (1967).
Speed and Sensitivity
Limitations
of Extrinsic Photoconductorst
(Receiced 23 October 1968)
Abstract-For extrinsic photoconductors with gain in excess of unity there is a minimum response time determined by the background flux. Combining this concept with conventional D* arguments leads to
This sensitivity bandwidth manium for 12.5 microns.
product has a value of 2 x 101* cm Hz: W set for extrinsic ger-
INTRODUCTION the study of mercury- and copper-doped germanium photoconductors it has been shown that the speed of response is determined not only by the carrier lifetime but also by the resistivity of the photoconductor.c’s 2, Further the response time component determined by resistivity-the dielectric relaxation response timeappears only as the gain of the photoconductor approaches and exceeds unity.c”) For the high gain conditions, when the response time is set by the dielectric relaxation time, the sensitivity and speed are interrelated. IN
DETECTOR SPEED-DIELECTRIC RELAXATION TlME CONSTANT The response of the detector always contains a dielectric relaxation component. This component is usually small or is sufficiently fast to be of no concern. In two situations, high speeds and low backgrounds, it can be the dominant response time. In the latter situation, the reduced background increases the dielectric relaxation time to values as long as seconds. The dielectric relaxation time is given by 7p = EE0fJ (1) where p is the resistivity of the material, c the dielectric constant, and E” the permitivity of free space. The dielectric relaxation effects are delays so that the total response time T of a detector is the sum of the carrier lifetime TJ and T,,. Thus, 7=71+7 (2) P For extrinsic photoconductors the resistivity of detector materials is determined by the background flux fpe, namely
In this expression 7 is the efficiency with which the radiation is absorbed, t the sample thickness, pp the hole mobility and q the electronic charge. Combining equations (2) and (3) yields (4) The principal features of equation (4) are illustrated by plotting the reponse time as a function of carrier lifetime for several values of the background flux 9~. Such curves are reproduced in Fig. 1. Note that for lifetime values shorter than a certain value the response time not only stops decreasing but starts to increase. This increase is the onset of dielectric relaxation effects. The curve for P)B= 10~s/sec/cm2 corresponds approximately to the 3GO”K, 180” field of view situation for a 14 micron detector such as Ge : Hg. For this situation the minimum response time is approximately 2 x 10-s sec. tThis work was supported in part by the Office of Naval Research
under
37
Contract
No. NOOO14-67-C-0497
Letters to the Editors
I
10-L
f\
I
I
I +B
1 = lO”/SEC/
I
I
V
V
I
cm2
10-4 1014
1016
10-6 1018
E cot 3
TZT.4
/
10-8
I
1
10
-2
I
I
I
1o-4
10
I
‘Fe RECOMBINATION
I
I
-6
10
-8
LIFETIME
lo-lo
I lo-l2
(SEC)
FIG. I. Variation of response time with recombination lifetime. For a particular background flux the response time depends on the carrier lifetime, being long if 7~ is too short or too long. The fastest response time requires a specific carrier lifetime for each background value. To achieve speeds faster than this value excess radiation must illuminate the detector as well as 71 being short. At reduced values of pn an anomalous situation arises for to achieve the fastest speed the lifetime must not be short. De-SPEED OF RESPONSE CONSIDERATIONS A consequence of the response time arguments in the above paragraph is that D* and the fastest speed ot response are related, that is for each background flux there is an optimum carrier lifetime. This is immediately apparent from the plot of equation (4) in Fig. 1. For the fastest response time 7min there is an optimum carrier lifetime ant. The value of 7mtn is calculated for a particular background by equating the two terms of equation (4) namely Thus,
%1pt
71when T,, = 7,
(5)
Recognizing that TmtII = 71 + $ = 2710pt is the minimum response time,
The background-limited
infrared performance (BLIP) of a detector is given by the following D*
The D* bandwidth
,llaiX
relationship Pj
(8)
product is then ?LF&X Tmin
__ h 7 he 4
(9)
Letters to the Editors
39
It is apparent that the D*-bandwidth product is independent of background flux. Further, if high D* values are to be obtained,c4) speed must be sacrificed. Conversely, if speed is required, D* must be sacrificed. The value of D*/T~~~ is easily calculated since the only significant parameter to be determined is pP, Taking c(~ = 2 x lo5 cm2/V-set, l C~= 1.4 x lo-l2 F/cm, I = 0.5 cm, A = 12.5 pm and 7 = 0.5, we have for extrinsic germanium in the 10-30” K range. D*,,Xl 7mrn = 1.7 x 10lscm (Hz)a/W-set The operating limits described by equation (9) are best illustrated by plotting both equations (7) and (8) on the same graph. This has been done in Fig. 2 with abscissa axis units of photons/sec/cm2 and W/cm?. Included are 7min values for 4 cm and 5 micron absorption length detectors.
L
WATTSlClll 10‘8
I
10
-b
10
10-4
I
-2
1
I
I
IO2
1’0
I
10b
10’
I
lIO
c> 1
-4
IO -5
IO
-b
10-7 3
\ T&(5,)
\ \
" F
\
10
\
\
-*
\
\
\
\
\
\
‘\ \
\\
\
10
\
-9
IO-'0
-I
;0-"
10,?
FIG. 2. Maximum D* and minimum response time. Under operating conditions with photoconductive gain in excess of unity, dielectric relaxation determines speed of response. Then for background-limited operation both D* and the minimum response time are determined by the background photon flux density.
CONCLUSIONS High gain extrinsic photoconductors are limited in performance by dielectric relaxation effects. If high speeds are to be achieved sensitivity must be sacrificed by adding an additional photon flux to the detector; for example, a speed of lo-i0 set requires a flux of 100 W/cm2. Conversely for high sensitivities such as a D* of 1014cm Hz*/W, the speed cannot be faster than 3 x IO-5 sec. In all the above discussion of speed and sensitivity the photoconductive gain is greater than unity. For
40
Letters to the Editors
gains significantly less than unity dielectric relaxation effects are absent. (1) This is the operating condition utilized by several workers when performing heterodyne detection experiments.(5-” Acknowledgements-The search for a relationship Werner Beyen and George Pruett
between sesntivity and speed arose from discussions with Ii. L.
Texas Iiutruments Research Building I3500 North Central Expresswla) Dallas, Texas 75201
WILLIAMS
REFERENCES
I. WILLIAMS,R. L., J. appl. Phys. 38, 4802 (1967). 2. WILLIAMS,R. L., submitted for publication and also a part of Final Technical Report for High-Speed, Long Wavelength Coherent Radiation Detectors, June 1968, Contract NOOO14-67-C-0497, Office of Naval Research-Advanced Research Projects Agency, Texas Instruments Incorporated Report No. 08-68-38. 3. KRUSE, P. W., L. D. MCGLAUCHLINand R. B. MCQUISTAN,Elements ofInfrared Technology. John Wiley (1968); Handbook of Military Infrared Technology, edited by W. L. WOLFE. U.S. Government Printing Office (1965). 4. QUIST, T. M. Proc. IEEE 56, 1212 (1968). 5. TEICH. M. C.. R. KEYESand R. KINGSTON,Appl. Phyc. Lett. 9, 357 (1966); M. C. TEICH, Proc. IEEE56, 37 (1568). 6. BUCZECH,C. S. and G. S. Rcus, Appl. Phys. Lett. 10, 125 (1967); G. S. PICUS, private communication. 7. ARAMS,F. R., E. W. SARD, B. S. PEYTONand F. P. PACE, IEEE J. Qcrantam Electron. QJS, 484 (1967).