AP-Aa", 7C0 ItI

THE'TEMPERATURE DEP'ENDENC OF A LARGEDYILMIC RANGE PHOTODE , T'E"TOIt, S.TRUICTU."RE (U)

by,Robert J., Inkol

DEOFENCE RESEARCH ESTABLISHMENT OTTAWATECHNICAL NOTE 91-35

Cand~Rest Available Copy December 1991Canada ttawa

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THE TEMPERATURE DEPENDENCE OF A LARGEDYNAMIC RANGE PHOTODETECTOR STRUCTURE (U)

by

" Robert J. Inkol* Radar E" Section

Elearonic Warfare Division

DEFENCE RESEARCH ESTABLISHMENT OTTAWATECHNICAL NOTE 91-35

PCN December 19910111B Ottawa

ABSTRACT

A recently developed photodetector circuit exploits theexponential voltage-to-current characteristic of a MOSFEToperated in the subthreshold region to achieve a logarithmicsteady state response. This paper analyzes the temperaturedependence of the circuit operation and presents experimentalresults demonstrating the capabilities and limitations of themodel.

RESUME

La reponse logarithmique en regime permanent d'un nouveaucircuit pour photodetecteur est obtenue grace a la relationexponentielle entre la tension et le courant d'un MOSFET operantsous le seuil. Cette publication contient une analyse del'operation du circuit en fonction de la temperature. Desresultats experimentaux demontrent les capacites et leslimitations du modele presente.

iii

EXECUTIVE SUMMARY

A recently developed photodetector circuit exploits theexponential voltage-to-current characteristic of a MOSFEToperated in the subthreshold region to achieve a logarithmicsteady state response. This paper analyzes the temperaturedependence of the circuit operation and presents experimentaldata which is generally consistent with the model. It isobserved that the behaviour of the photodetector is similar insome respects to that of a photodiode operated in the solar cellmode, but has a greater sensitivity to fabrication processparameters. A test circuit which would facilitate accuratemeasurements at low illumination levels is proposed.

v

TABLE OF CONTENTSPAGE

ABSTRACT/RESUME iiiEXECUTIVE SUMMARY vTABLE OF CONTENTS viiLIST OF FIGURES ix

1.0 INTRODUCTION 1

2.0 CIRCUIT MODEL 1

2.1 MOSFET Model 12.2 Photodiode Model 6

3.0 ANALYSIS OF CIRCUIT MODEL FOR TEMPERATURE DEPENDENCE 7

4.0 EXPERIMENTAL RESULTS 9

5.0 DISCUSSION 12

6.0 REFERENCES 15

APPENDIX 1: IMPROVED TEST CIRCUIT FOR DC CHARACTERIZATION, OF THE DYNAMIC RANGE PHOTODETECTOR CIRCUIT A-I

vii

LIST OF FIGURES

PAGE

FIGURE 1: LARGE DYNAMIC RANGE PHOTODETECTOR CIRCUIT 2

FIGURE 2: EXPERIMENT SET-UP 10

FIGURE 3: Vas (VOLTS) VS LIGHT ILLUMINATION ATTENUATION(INCREMENTS OF 0.3 dB/UNIT) 11

FIGURE Al: IMPROVED PHOTODETECTOR TEST CIRCUITFOR DC CHARACTERIZATION A-2

i

ix

1.0 INTRODUCTION

The dynamic range of photodetectors is important in manyapplications. One solution is to operate a photodiode in thesolar cell mode. The steady state open circuit output voltage isgiven by

V - mkT in !P +!o (1q ( o I0

where m is a constant between 1 and 2, k is Boltzmann's constant,T is the absolute temperature in degrees Kelvin, q is the chargeof an electron, I0 is the reverse saturation current of thephotodiode and I_ is the photocurrent. Since the photocurrent isproportional to the intensity of the illumination, the steadystate response is logarithmic for I_ >> I0. Unfortunately,operation of photodiodes in the solar cell mode on a monolithicarray requires dielectric isolation techniques to electricallyisolate the photodiodes.

The recently developed photodetector circuit illustrated inFigure 1 uses the exponential voltage to current characteristicof a MOSFET operated in the subthreshold region to achieve asimilar behaviour [1]. It is attractive for the implementationof monolithic arrays since it is compatible with standard MOSprocessing technology.

The temperature dependence of the circuit operation has notbeen considered in published analysis, but is potentiallyimportant in some applications. This is discussed in thisreport.

2.0 CIRCUIT I4ODELFor unloaded steady state operation, the MOSFET source and

photodiode currents, Is and ID respectively, satisfy the equality

is - ID (2)

With appropriate analytic behavioral models for ID and Is, thisrelationship can be evaluated to determine the circuit behaviouras a function of environmental and circuit parameters.

2.1 MOSFET Model

The behaviour of MOSFETs in the subthreshold region is ofconsiderable significance in a number of applications. MOSFETsmay be operated in the subthreshold region in low power analogcircuits where the relatively high ratio of transconductance to

VD

VGM1

vs

VBS

VB

FIGURE 1: LARGE DYNAMIC RANGE PHOTODETECTOR CIRCUIT

2

drain current achievable is desirable (2]. Another applicationis found in analog neural networks which exploit the exponentialrelationship between gate-source bias and drain current [3].However, most published analysis of the temperature dependence ofMOSFETs operated in the subthreshold region concerns the designimplications for digital VLSI circuits where it is important toensure that a transistor biased in the OFF condition does notconduct a significant current over the operating temperaturerange (4].

The wide dynamic range photodetector circuit is analyzedusing an expression for the current given in [5],

1

is- (W/L)DqNDL9(ni/N')2exp(V,,)e [l-exp(_VDs) ] (2lsa '-2 (3)

where

L = channel lengthW = channel widthD = diffusion constant (kT/q)g, where g = carrier

mobilityND = channel dopant impurity concentratiFni = intrinsic carrier concentration a T exp

(-Eg/2kT), where Eg = bandgap potential (-1.1 eVfor Silicon) 1

= (thermal voltage) = q/kTVa = source to substrate voltageVs D = source to drain voltage

= extrinsic Debye length = [ESE,16qND]s = relative permittivity of Silicon = 11.76 = permittivity of free space(sat = band bending potential at the channel - gate

dielectric interface for channel pinch off.

Equation (3) can be solved explicitly as a function of theMOSFET terminal potentials since the term Psat is a function ofVBS and of the effective source to gate voltage VGS. Therelationship is

P ,sa " - VGs + P VBs a'/2 - a (P (VBs+ VGs) +a'/4) (4)

with the parameter a given by

a-V r(es/e ox) (tOx/LB) (5)

3

where

tox= gate dielectric thicknessand o = relative permittivity of the gate dielectric

(- 3.7 for SiO2).

Equation (3) can be rewritten to explicitly show the temperaturedependence:

exp[(-E./kr) + (qV,3s/kr+-_ ( T) T/lT)2

-apTl (V/kT ) + _ q~ /T+ 2 ' T/T

is /2-a(T")To/( (s+Va)+ aT 0 4 (l-exp(-qVDs/kT) (6)

qVGs/kT+qVBs/kT+ a 2 (T) (T0/T))

v'-T 2 ~11-a (T ) To()(Vs+V /(T) 2) 2v s,6s) / kT,+ a! }

where

wD k 5 e o oL [3N

contains parameters which are relatively insensitive to terminalvoltages or temperature and a(T,) is the value of a at atemperature To. Although some parameters such as Eg and D areknown to be dependent on temperature [6]-[7], the resultant erroris not significant over the range of operating temperaturesencountered in most practical applications.

For the wide dynamic range photodetector circuit, Equation(6) can be greatly simplified with minimal errors. First, thephysical short circuit between the MOSFET gate and sourceterminals constrains VGS to be equal to -VFB. VFB is the flatbandvoltage which is necessary to account for surface states, oxidecharge and the metal-semiconductor potential Oms. Theoreticalestimates of VFS are very inaccurate, consequently, it is usuallydetermined experimentally [5].

Second, the term (l-exp(-qVos/kT)) in the numerator can beneglected if the circuit is biased for normal operation.Finally, as the gate to source threshold voltage VTS of theMOSFET must be negative with Vs 2 0 for correct circuitoperation, it can be shown that the upper limit for the parametera is approximately 2.5 for the usual ranges of silicon pro~essparameters [5]. Since (qVss/kT) wil be much larger than a , theterms in Equation (6) containing a can be neglected with minimalerror.

4

The simplified equation for Is(T,Ves) is therefore given by

is(T, V s ) - GT 7/2exp[-Eg/kT+qVs!kT-a(T 0 ) (T/T) (q(VGs+VBs) /kT ) 2]

1 1

V2( qVGs/kT+qV~s/kT-a(To) (T 0/T) (q(VGs+VBs)/kT) 2) 2

(7)

Equation (3) for the MOSFET subthreshold current is derivedfrom a one dimensional model of the MOSFET channel potential.The accuracy of this model is dependent on the channel length; asthis is reduced, various additional phenomena degrade thevalidity of the model. These include the effects of the sourceand drain potentials on the MOSFET channel potential, transporteffects such as carrier velocity saturation, and high electricfield effects such as the injection of electrons into the gateoxide and thereby shifting the flatband voltage [5].

The effect of the MOSFET drain potential on the subthresholdcurrent is useful in the photodetector circuit since it permitsthe DC operating point for V to be modified by varying thedrain voltage VD. Furthermore, the dependence of thesubthreshold current on the source potential Vss providesadditional compression which may be useful in avoiding excessivesignal voltage swings for operation over a large dynamic range.

Consequently, the standard implementations of thephotodetector circuit use relatively short gate lengths whosenominal values are bracketed in each wafer fabrication run.

Exact analysis of short channel effects requires numericalsimulation since the three dimensional geometry of the device anddopant impurity profiles must be considered. However, a twodimensional model is of some use provided its limitations areunderstood.

A particularly simple relationship between VDS and thesource-drain current of a short channel MO FET is given in[4],[6]

Is - IsLexp(qvDsl/6kT) , (8)

where ISL is the source current given by Equation (3) for thelong channel MOSFET model and 6 is a parameter having a weakdependence on V and determined by numerical or empirical means.Note that 8 = corresponds to the long channel model.

Consequently, Equation (7), the explicit temperaturedependent for the subthreshold current Is in the photodetectorcircuit, can be modified to include the short channel effects ofthe drain and source voltages

5

IS (T, VBso 8) -

[GT /2exp [-Eg/kT+qVs/ kT+q(VDB-VB) /6kT-a (T o ) (T 0/T) (q(VGS+VBs,) /kT) 21 1

v'- (qVGs/kT+qV~s/kT-a (T) (T/T) (q(VGs+Vs) /kTo) 2 ) 2

(9)

where VDB is the MOSFET drain to substrate voltage.

2.2 Photodiode Model

Under reverse bias conditions, the photodiode current IDconsists of a photocurrent I and a dark current ILi I isnormally proportional to light intensity and is ven gy

IP- PLnq/hc , (10)

where

n = quantum efficiencyP = incident illumination powerI = wavelength of the lighth = Planck's constantc = velocity of light in free space

Previously reported measurements confirm that thephotocurrent has a low sensitivity to temperature and biasvoltage [7]-[8].

The photodiode dark current IL is largely the result of thethermal generation of carriers in the semiconductor. Twocomponents, a generation current produced by the generation ofcarriers in the reverse biased depletion layer, and a diffusioncurrent caused by the diffusion of carriers generated in thesemiconductor bulk to the depletion layer, can be identified.They are given by [8]:

Igen -I/2qniW(V) A/T o, (i

where

W(V) = depletion layer width proportional to V", where Vis the reverse bias voltage and ]/3 ! x S 1/2

to = average carrier lifetime

and

6

Idiff - qDAni/NALnlqDAnI/N DL P , (12)

where

Dn = diffusion constant for electronsDP = diffusion constant for holesNA = dopant impurity concentration for p-type

semiconductor materialND = dopant impurity concentration for n-type

semiconductor materialLn = diffusion length of electron in p-type semiconductor

material= diffusion length of holes in n-type semiconductor

material.

For a photodiode fabricated as a n+ diffusion on a p-typesubstrate, the second term in Equation (12) can be neglected.

The temperature dependence of Equatiogs (11) and (12) islargely determined by that of the ni and ni parametersrespectively. Consequently, the temperature dependence of thedark current has the form

IL (T) -Igen (T) + Idif(T). (13)

- H1exp (-Eg/2kT) +H2exp (-Eg/kT)

For silicon diodes reverse biased by more than a few volts,the Igen component is usually dominant at temperatures up to atleast 400°K with the exact crossover temperature being a functionof bias voltage and the dopant impurity profile [9]-[10].

Additional mechanisms contributing to dark current such assurface states exist, but these can usually be neglected for highquality silicon photodiodes.

3.0 ANALYSIS OF CIRCUIT MODEL FOR TEMPERATURE DEPENDENCE

Since the steady state photodiode and MOSFET currents areequal, it is possible to set up the equality

Up + IL(T)) - I.(VBs,T, ) (14)

7

This is a useful relationship for analyzing the circuitoperation. Since the circuit is operated so that Vss has asubstantial DC bias or offset relative to both the drain voltageof the MOSFET and the substrate potential, the temperaturedependence of V8S for constant illumination is of criticalimportance. It determines the need for temperaturecalibration/compensation techniques and affects the design of theinterface electronics which must be able to operate properly overthe range of VBS that can result from the worst case combinationof illumination and temperature extremes.

The dependence of VBs with respect to temperature is foundby evaluating the differential

dVss a VS ()IL ( T) 81s(T; Vs' 8) (15)

dT T(Is(T, Vs,) ) aT aT

By neglecting the weak temperature dependence of G, Equation (15)can be evaluated to yield

dVsdT

I II1 L 7/2+-1l (E/k-qVs/k-q(Vs-Vss)/8k+a(To) To(q(Vcs+Vs)/kT)

(P +IL(T)) @T T T 2

1

-(kT/q) (q(Vs+VssV)/kTr) 2X 1 ' (16)(1/6) (q(VGs+VBs)/kTo) - la(T)

2

where

OIL kT . Eg/2qT: (IL : IP) (17)

,T qls

-I 0: (I L -C IP) (18)aT qI s

8

From the examination of these results, dVBs/dT has only amild dependence on temperature and is virtually constant overrestricted temperature ranges. They also indicate that dVBs/dTdecreases with increasing Ip due to the dependence of VBS on Ip,except for very small values of Ip where IL is important.

Another important performance parameter is the logarithmicslope of the response given by

Se" -~ x 19a'ln I,

SR represents the change in output voltage resulting from achange in I_ by one decade. It is desirable that SR has a lowsensitivity to temperature and Ip, as complex calibration andcorrection schemes would otherwise be necessary in applicationswhere accurate measurements of illumination intensity aredesirable.

Using Equation (9) yields

V 'N

SR - -2.3 '_ _ (q(V'T+V..) /kT0 ) 2 (20)

(1/6) (q(V~s+Vas)/kT) 2 +-a (T:)2

Except for very low values of I where the ratio IL(T)/Ipbecomes significant, this result has a weak inverse dependence onIp since VSs is a logarithmic function of Ip. The temperaturedependence of SR consists of an explicit component linearlyproportional to T and implicit non-linear components resultingfrom the temperature dependence of IL(T) and VBS.

4.0 EXPERIMENTAL RESULTS

The output voltage from a photodetector structure on theDALSA D4-100 evaluation device was measured for differentcombinations of illumination intensity and temperature.Illumination was obtained using a HeNe laser having a wavelengthof 632.8 nanometers. Uniform illumination over the photodiodeand non-critical requirements for its alignment were ensured bythe use of a beam expander. An optical attenuator allowedillumination intensity to be varied over a range of 45 dB. Thevoltage was directly measured by switching on the reset 12MOSFETand using a low input bias current amplifier (ibias Z 10 A) to

9

V010oV 12V PRECISION

VOLTMETER

OFF ON

1.Skfl

VD RSTG ASTS 1 2V

Ili0 BUFFERED

0-2 DC OUTPUT0-ADC

POWER 3'PLY*SUPPLY

1059

8.00

VDB =9V-4

7.00---4 V 8 T-305*K-VDB =8V T--325"K

~T--325"K

0.00 -,

Z 5.00 -.

4.00 TEST DEVICE: DALSA D4-100(TK07 Element)

-.4

3.005-1

C.00 40.00 80.00 20.0 ",0.C 2.,CG1T ATTEiuA-7"O

FIGURE 3: VBs (VOLTS) VS LIGHT ILLUMINATION ATTENUATION

(INCREMENTS OF 0.3 dB/UNIT)

11

monitor the voltage at the open circuited reset bias line asshown in Figure 2. Typical results, given in Figure 3, aregenerally consistent with the analysis.

At 305-K, SR and dVss/dT are approximately 0.76V/decade and10 mV/OK over a large range of illumination levels. Using thea = 1.74 determined from the nominal process parameters (13],Equations (20) and (16) can be fitted to the data correspondingto settings of the optical attenuator between 80 and 140 bysetting VGS = 1.6 V and 6 = 36 (Vas = 6V).

At low illumination levels SR and dVss/dT decreasesubstantially, as expected from the analysis, but the accuracy ofthe results is uncertain due to the likelihood that leakagecurrent in the experimental setup is significant.

The dependence of VBS on VDB also demonstrates a good fit tothe analysis. The 1 volt change in VDB from 8.0 to 9.0 voltsshifts VBs by approximately 0.7 volts for a wide range ofillumination levels. This is reasonable since the substitutionof the two sets of values for VD8 and Vas in Equation (9) resultsin little change in current.

One area of discrepancy concerns the temperature dependenceof SR which varies by approximately half the amount predicted bythe kT/q term in Equation (20) for a 200C temperature change.However, this may be a result of the limitations of theexperimental test setup, which did not permit a large temperaturerange to be used or an accurate direct measurement of the chiptemperature of the photodetector device.

5.0 DISCUSSION

It is interesting to compare the analytical behaviour of thelarge dynamic range photodetector circuit with that of aphotodiode operated in the solar cell mode. The logarithmicslope of the response of the latter can be derived from Equation(1) as,

SR - 2 . 3 mkT( ..§ (21)

This is similar in form to Equation (20), but differs inmagnitude by approximately an order of magnitude due to thedifference between m which is between 1 and 2 and the last termin brackets.

The photodiode output voltage V has a temperature dependence

given by

12

dV _ _ 1 3 T q m g q( P (22)

Equations (16) and (22) both have a relatively weak (=I/T)dependence on temperature and tend to decrease with increasingillumination. The behaviour for the large dynamic rangephotodetector is more complex in that it is dependent onfabrication process parameters (which affect VGS, a(T0 ) and 6),operating conditions (VDB) and the MOSFET geometry (L, dopantprofile). If the results of Equations (16) and (22) arenormalized with respect to the appropriate SR, a useful figure ofmerit is obtained.

F 1 (23)dT S R (3

F can be regarded as the temperature change corresponding to anoutput voltage change that would indicate a change in current byan order of magnitude. For the large dynamic rangephotodetector, this can be evaluated to yield

2. 3IPF-IP+ IL (T)

7 /2/T+ 12(E-qk-qV~s/k-q(VDBV~s) /8k-a (T) T(q(V~s+ VBs) /kr) 2) (24)

[_1 a.IL1 -

(IP+IL(T)) aT

Similarly, for the photodiode operated in the solar cell mode

F - 2I I(T) (3kT/qmEg/q) IP (25)

13

For operation at 300 0K with moderate illumination, typicalvalues of F would be approximately 680K and 330K for Equations(24) and (25) respectively.

A more complete treatment of the problem would involve thegeneration of a model for 6 which would include its voltagedependence, the collection of data from a larger number of sampledevices whose process parameters have been independentlyevaluated and a more accurate test setup as proposed in Appendix1.

14

6.0 REFERENCES

(1] S.G. Chamberlain and J.P.Y. Lee, "A Novel Wide Dynamic RangeSilicon Photodetector and Linear Imaging Array", IEEE Trans.Electron Devices, Vol. ED-31, No. 2, February 1984.

(2) E. Vittoz and J. Fellrath, "CMOS Analog Integrated CircuitsBased on Weak Inversion Operation", IEEE Journal of SolidState Circuits, Vol. SC-12, No. 3, June 1977.

[3] A.G. Androu et al, "Current-Mode Subthreshold MOS Circuitsfor Analog VLSI Neural Systems", IEEE Trans. on NeuralNetworks, Vol. 2, Mar. 1991.

[4] R.R. Troutman, "Subthreshold Design Considerations forInsulated Gate Field Effect Transistors", IEEE Journal ofSolid State Circuits, Vol. SC-19, No. 02, April 1974.

[5] J.R. Brews, "Physics of the MOS Transistor", Applied SolidState Science, Silicon Integrated Circuits, Part A, AcademicPress, 1981.

[6] R.R. Troutman and S.N. Chakravarti, "SubthresholdCharacteristics of Insulated Gate Filed Effect Transistors",IEEE Transactions on Circuit Theory, Vol. CT-20, No. 6,November 1973.

[7] W. Bludau et al, "Temperature Dependence of the Bandgap ofSilicon", Journal of Applied Physics, Vol. 45, pg. 1846,1974.

(8] L. Vadasz and A.S. Grove, "Temperature Dependence of MOSTransistor Characteristics Below Saturation", IEEE Trans. onElectron Devices, Vol. ED-13, No. 12, December 1966.

[9] M.D. Jack and R.H. Dyck, "Charge-Transfer Efficiency in aBuried-Channel Charge Coupled Device at Very Low SignalLevels", IEEE Journal of Solid State Circuits, Vol SC-ll,No. 1, February 1976.

[10] R. Kohler et al, "Temperature Dependent Nonlinearity Effectsof a QED-200 Detector in the Visible", Applied Optics, Vol.29, No. 28, October 1990.

(11] A.S. Grove, "Physics and Technology of SemiconductorDevices:, Wiley, 1967.

(12] S. Cheng and P. Manos, "Effects of Operating Temperature onElectrical Parameters in an Analog Process", IEEE Circuitsand Devices Magazine, 1989.

[13] W. Washkurak, private communication.

15

APPENDIX 1

IMPROVED TEST CIRCUIT FOR DC CHARACTERIZATION

OF THE DYNAMIC RANGE PHOTODETECTOR CIRCUIT

The test circuit used in the work described in this reporthas several deficiencies which result from the constraint ofhaving to use a standard production photodetector device.Usually the photodetector circuit is interfaced to an amplifierwhich is typically a MOSFET operated as either a common source orcommon drain amplifier or is multiplexed via a CCD Parallel-Input-Serial-Output shift register. However, it becomesdifficult to determine what the actual voltage Vs in thephotodetector circuit is since the amplifier transfer functionwill not be accurately known. Consequently, the directmeasurement of the DC voltage from the photodetector must be donevia the reset bias voltage input with the reset transistor tunedon. This has the fundamental disadvantage that loading effectswill be introduced at low illumination levels. Even if a lowinput bias current amplifier is used to buffer the signal, as wasdone for the experimental work described in the report,significant leakage currents can result from contamination of theinterconnection between the photodetector and amplifier.

An attractive solution is shown in Figure A-1. Thisinvolves the use of a special test device with a pair of matchingcommon drain amplifiers Al and A2. Amplifier Al buffers thephotodetector voltage and amplifier A2 is used inside thefeedback loop of an operational amplifier A3 to compensate forthe input to output offset voltage and non-ideal transferfunction of amplifier Al. Since the input of amplifier Al needsnot be accessible externally, it has no need for electrostaticprotection circuitry which will introduce leakage currents.Consequently, the photodetector circuit operates with negligibleDC loading and high accuracy should be achievable.

The test device could also have additional test structuresto allow the accurate measurements of the fabrication processparameters.

-A-l -

r - ----

I ml

I Vs

L LI B

PHOTO- AlA

NOTAil and A2

0 as ift PhotodetectorVB Circutt

FIGURE Al: IMPROVED PHOTODETECTOR TEST

CIRCUIT FOR DC CHARACTERIZATION

- A-2

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THE TEMPERATURE DEPENDENCE OF A LARGE DYNAMIC RANGE PHOTODETECTOR

STRUCTURE (U)

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INKOL, ROBERT J.

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DECEMBER 1991 Annexes, Appendices. etc.)22 13

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(U) A recently developed photodetector cricuit exploits theexponential voltage-to-current characteristic of a MOSFET operatedin the subthreshold region to achieve a logarithmic steady state response.This paper analyzes the temperature dependence of the circuit operationand presents experimental results demonstrating the capabilities andlimitations of the model.

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PHOTODIODETEMPERATURE DEPENDENCEPHOTOCURRENTSUBTHRESHOLD EFFECT

OPERATIONAL AMPLIFIER

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