Characterization of avalanche photodiodes for calorimetry...

*Corresponding author. Tel.: #33-1-69.33.31.70; fax: #33-1-69.33.30.02.

E-mail address: [email protected] (J.C. Vanel)1On leave from INR, Moscow, Russia.

Nuclear Instruments and Methods in Physics Research A 428 (1999) 413}431

Characterization of avalanche photodiodesfor calorimetry applications

A. Karar!, Y. Musienko",1, J.Ch. Vanel!,*!LPNHE, Ecole Polytechnique, IN2P3-CNRS, 91128 Palaiseau Cedex, France

"Department of Physics, Northeastern University, Boston, MA 02115, USA

Received 10 December 1998

Abstract

Silicon avalanche photodiodes (APDs) have been studied extensively as photosensor candidates for the electro-magnetic calorimeter of the CMS detector at LHC. This work presents the measurements of APDs from Hamamatsu andEG&G, with particular emphasis on multiplication factor, spectral response, excess noise factor as well as theirdependence on wavelength. The results are compared to the theoretical predictions. Results on the stability of APD gainto bias and temperature drift are also presented. ( 1999 Elsevier Science B.V. All rights reserved.

Keywords: Silicon avalanche photodiode; Gain; Excess noise; Calorimetry

1. Introduction

Silicon avalanche photodiodes (APDs) weredeveloped more than 30 years ago and are widelyused in the telecommunication. However their usefor scintillation light detection (especially for HighEnergy Physics calorimetry) has been limited bytheir small size ((1 mm) and poor sensitivity forblue and UV light. During the last decade, a varietyof new large area APDs appeared on the marketand interest in these devices increased for theirapplication in HEP calorimetry. Extensive studiesof these new APDs (from API, EG&G,

Hamamatsu, RMD, etc.) have been carried out andmany interesting results have been published[1}5,19].

Distinctive features of APDs which make themparticularly suitable for scintillation detection are:high quantum e$ciency, internal gain, insensitivityto magnetic "elds, low-power consumption, andcompact size. In addition to these characteristics,a relatively low response to ionizing particles madethem a good candidate for the electromagneticcalorimeter of the CMS detector at the LHC [6].

2. Setup

Two separate setups were used for APD charac-terization. The setup for measurements with con-tinuous light, shown in Fig. 1, uses a broad-bandtungsten halogen lamp (&380 nm to a few lm)

0168-9002/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 1 7 7 - 1

Fig. 1. Setup for measurement with continuous light.

2Hereafter referred to as Hamamatsu HC and HamamatsuLC APDs.

3Hereafter referred to as EG&G APD.

with a stability of light output better than 1% over12 h of operation. A grating controlled by steppingmotor allows us to select wavelengths from 400 to700 nm in steps of 10 nm. The output light issplit between the APD and the calibrated PINphotodiode. The temperature of the deviceunder test is continuously monitored with a plati-num-resistive temperature sensor. With this setupone can measure spectral response (quantume$ciency) and the dependence of the gain on awavelength.

Fig. 2 shows setup for measurement with pulsedlight (it can be also used for measurements witha c-sources). This setup consists of three parts:a pulse light source, an APD with bias circuit andfront-end electronics, and measuring devices. Inorder to produce the light pulse we used a light-emitting diode (LED) driven by a Amtech-AVMR-C fast pulse generator (rise time"3.3 ns, falltime"3.8 ns, minimum width"18.7 ns and max-imum amplitude"21 V in 50 )). Two di!erentskinds of LED are used:

f A fast green LED (produced by Russian indus-try) with a peak emission j

1%!,"570 nm and

a bandwidth (FWMH) *jK20 nm. This LED isable to provide a 20 ns pulse.

f A blue LED from Siemens (type LB5410),j1%!,

"480 nm and *jK75 nm (FWMH). ThisLED provides relatively long pulses of about200 ns. A long shaping time ('500 ns) has to beused in order to ensure that all the photocarrierscreated during the pulse are integrated.

The light is sent to the APD via an optical "ber.The APD is biased through a low-pass "lter and is

AC coupled to the charge preampli"er. At the out-put of the charge preampli"er we use an externalshaper [7]. The pulse from the shaper is sent to anoscilloscope (LeCroy-9450) and to a digital signalanalyser (DSA-602A from Tektronix) connected toa computer. As in the "rst setup the APD temper-ature is permanently monitored. For a detaileddescription of both setups see Refs. [2,3,8].

3. Structure of APD investigated

Three di!erent types of APD have been exten-sively studied for this work. Two types are fromHamamatsu (high capacitance and lowcapacitance2 type S5345), made by epitaxial growthon a low resistivity silicon substrate. The third typeis from EG&G3 (C30626E) made by ion implanta-tion and di!usion technology.

The sensitive area of the Hamamatsu APDs iscircular and 5 mm in diameter, while that of theEG&G APD is 5]5 mm2 square. The schematicstructure as well as the presumed electric "eld pro-"les of these APDs are shown in Fig. 3. All of theseAPDs have a structure, which is `reverseda in com-parison to the standard n`}p}p}p` structure ofAPDs used for telecommunication [1]. The mainjunction, where the avalanche gain takes place, ofthe `reverse structurea is located 4}20 lm insidethe APD. This allows short wavelength light(&450}550 nm) to be absorbed before the ava-lanche region to obtain maximum possible multi-plication (see Section 4). The results on capacitancemeasurements as a function of applied bias arepresented in Figs. 4 and 5. Measurements are per-formed using an HP4270A automatic capacitancebridge at 1 MHz. These measurements give in-formation about the thickness of the depletionlayer and about the relative doping pro"le. Due tothe additional p and p layers of the Hamamatsu LCand EG&G APD respectively, these two APDshave smaller capacitance and thicker depletionregions than the Hamamatsu HC APD. More

414 A. Karar et al. / Nuclear Instruments and Methods in Physics Research A 428 (1999) 413}431

Fig. 2. Setup for measurement with pulsed light and c-sources.

Fig. 3. Electric "eld pro"le and internal structure of APDsinvestigated.

Fig. 4. Capacitance vs. bias voltage for the Hamamatsu APDs.

detailed discussion of these APDs structures isgiven in Refs. [2,3,8,9].

4. Measurement of the gain

The evaluation of all APD parameters (such asspectral response, noise, excess noise factor, re-sponse to charged particles, etc.) requires preciseand correct measurement of the gain. To performthese measurements, di!erent signal sources havebeen used:

f continuous light, 400}700 nm (spectrophoto-meter);

f pulsed light (blue or green LED);f gamma sources (241Am, 55Fe, 57Co, etc.).

A. Karar et al. / Nuclear Instruments and Methods in Physics Research A 428 (1999) 413}431 415

Fig. 5. Photocurrent and capacitance vs. bias voltage for the EG&G APD.

Fig. 6. Photocurrent vs. bias voltage for the Hamamatsu APDs.

The simplest way to evaluate the gain of an APD isto measure the photocurrent I

1)versus bias voltage

under continuous illumination:

I1)

(<)"I*--(<)!I

$!3,(<) (1)

where I*--

is the total current measured when theAPD is illuminated with continuous light, andI$!3,

is the dark current (the current when thisillumination is switched o! ). For this type ofmeasurement, it is necessary for the light to beabsorbed before the high electric "eld region (multi-plication region). If the light is not fully absorbedbefore the multiplication region, some of the pri-mary photoelectrons will undergo smaller multipli-cation. If one uses 520 nm wavelength light theabsorption length is about 1 lm and most of thelight is absorbed within the "rst 3 lm of silicon.The high electric "eld region must then be locateddeeper than 3 lm from the surface.

The measured photocurrent versus bias forthe EG&G APD is shown in Fig. 5. There is a`plateaua at small biases which also exists forHamamatsu APDs (Fig. 6). Although the APD isnot fully depleted with low-voltage bias, the risein photocurrent from 1 V up to biases where the

gain starts is very small. This enables us to makea hypothesis that the gain at the `plateaua isclose to unity and can be used as a reference. Thegain at bias voltage < can be calculated using theequation

M(<)"I1)

(<)

I1)

(10 <)(2)


Fig. 7. Ratio of gains measured using continuous and pulsed LED (450 nm) light vs. gain measured with continuous light.

Fig. 8. 241Am spectrum measured with the Hamamatsu LCAPD.

where I1)

(10 <) is the photocurrent measured at10 V (as it is seen from Figs. 5 and 6, 10 V biascorresponds to the `plateaua for all APDs studied).For the calculation of the pulsed light gain mea-sured with an LED pulse, the value of the gainmeasured with continuous light at the bias wherethe APD is fully depleted is used as a reference. Thegain measured with the pulsed LED light at higherbias coincides within 1.5% accuracy with the valuesfound using continuous light (Fig. 7).

Another method to determine the gain is toexpose the APD to c-rays from 241Am, 55Fe, 57Coand other sources. Some c-rays are absorbed in thelayer before the avalanche region. A typical spec-trum obtained with the Hamamatsu LC APD ispresented in Fig. 8. From the position of the c-peaks in the spectrum, it is then possible to calcu-late the gain, assuming that 3.62 eV of incidentenergy are required to produce an electron/holepair. For gains smaller than 5, gains measuredusing c-rays coincide with good accuracy withthose measured with continuous light. However,for high gains, the values found with c-sources aresmaller than those found with continuous light.The higher the gamma energy the greater the e!ectbecomes (see Fig. 9). This phenomena is also re-

ported in Refs. [4,5]. This is also the case for theHamamatsu HC APD. Fig. 10. shows the ratiobetween the gain measured with c-sources and withlight as a function of the gain measured with a pul-sed blue LED. To "rst order this ratio is one at


Fig. 9. Measured gain with di!erent kinds of sources vs. bias voltage for the Hamamatsu LC APD.

Fig. 10. Ratio of the gain measured with c-sources to measured with light.

unity gain and then drops linearly with the gain.A reasonable explanation of this phenomena is anattenuation of the multiplication process bya `screening e!ecta reducing the electric "eld whenthe density of primary electron/hole pairs is high, asis the case for c absorption. In fact, a decrease of

1% of the electric "eld could cause a decrease ofabout 20}30% of the gain [10].

For the EG&G APD, we found an even morecomplicated e!ect [2,3,5]. For calibration of thegain a 5.9 keV55Fe c-source has been used due tothe thinness of the depleted region in front of the


Fig. 12. Ratios of the gain measured with 55Fe c-source to gain measured with pulsed light as functions of bias voltage.

Fig. 11. 55Fe spectrum measured with the EG&G APD.

multiplication region (see Fig. 3). In Fig. 11, a typi-cal 55Fe spectrum is shown. It was surprising to"nd two peaks at biases higher than 300 V. Tocompare the gain measured with a c-source(M

cv1%!,4) and with continuous light (de"ned by

M-*')5

"I1)

(<)/I1)

(10 V)) we have calculated theratio M

-*')5/M

cv1%!,4as shown in Fig. 12. For biases

from 160 to 300 V the two peak are not resolved.The peak with higher amplitude, further referred toas the `second peaka, follows the gain measuredwith continuous light up to biases where saturatione!ects start (as for the Hamamatsu APDs). Thepeak with smaller amplitude (the `"rst peaka)drops with bias much faster than the second peak.From Fig. 12 it is seen that M

-*')5di!ers not more

than 4% from the gain measured with the 55Fec-source for biases from 160 to 200 V. The existenceof this plateau in the ratio M

4%#0/$1%!,to M

-*')5leads

us to use the second peak as a reference forM

-*')5for small bias values. The origin of the two

peaks in the 55Fe spectrum is probably due to thefact that a c can be converted either in the non-depleted or the depleted region in front of themultiplication zone (the size of those two regionsare roughly the same). In addition, di!usion,screening and/or trapping and de-trapping e!ects,probably di!erent for the two regions, must playsome role.

We also checked another hypothesis: that a verylarge non-uniformity of the gain across the sensitive


Fig. 13. Gain for electrons and holes as function of bias voltage.

area of APD can cause such an e!ect. We per-formed a scan of the APD with collimated c-sour-ces (the diameter of the hole was 1 mm) and we didnot "nd large non-uniformity, but found the sametwo peaks across the full 5]5 mm2 area of APD.

An interesting feature of the EG&G APD is thatone can measure the ampli"cation of holes. Thethin sensitive and ampli"cation regions are almosttransparent for 60 keV c's from 241Am which areabsorbed in the relatively thick (100 lm) drift re-gion. These c's create electron}hole pairs which areseparated by electric "eld. Electrons drift towardthe anode contact and holes toward the multiplica-tion region. The dependence of the multiplicationfactor for holes versus bias is shown in Fig. 13,where the curve for electron multiplication is alsoshown for comparison. One can see that at bias of390 V, the electron gain is 50 and the hole gain is2.5. Multiplication by holes increases the signalfrom minimum ionizing particles traversing theAPD and is not negligible.

To conclude, coincidence of the gain values in therange of small gains (where APDs are already fullydepleted) measured with light and gamma sourcecon"rms the hypothesis that the `plateaua of photo-current versus bias can be used as a reference(gain"1) for calculation of the gain. Thus we can

use the simple, fast, accurate and reproducible `con-tinuous light methoda for determination of the gain.

5. Spectral measurement

The quantum e$ciency (QE) of Hamamatsu andEG&G APDs has been measured at the biasof 10 V using a commercially available spectro-photometer `Graseby Optronix S370a [2,3]. Theresults are shown in Fig. 14. Values of QE found forthe Hamamatsu LC APD coincide with 2% accu-racy with those of the HC type. Because EG&GAPDs have Si

3N

4(n"2) antire#ective layer, their

QE in the range of 420}640 nm is a bit higher thanthe QE of Hamamatsu APDs which are coatedwith SiO

2(n"1.5). The thickness of the Si

3N

4layer (50 nm) has been choosen by the manufac-turers to increase the QE at 450 nm. Below thiswavelength, QE starts to drop o! because of thethin (0.1 lm) dead p`` layer located near the sur-face of the EG&G APD. For the Hamamatsu APDthis p`` layer is probabaly very thin and the dropof QE below 450 nm is not very sharp. ForHamamatsu H.C. and EG&G APDs the avalancheregions are located close to surface (4}6 lm behindit). The light absorbed behind the junction


Fig. 14. Quantum e$ciency of the three APDs.

Fig. 15. Gain vs. wavelength. Nominal gain is 50.

produces electrons and holes but only holes go toavalanche region and multiply, while electrons drifttowards the back contact without multiplication.The multiplication factor for holes is much smaller

than that for electrons (because of smaller ioniz-ation coe$cient), and as a result, the gain for lightwith long wavelengths is smaller than for shortones (see Fig. 15). The avalanche region of the


4Here we neglected the intrinsic resolution of the calorimeter,which can be very small for some crystals [6].

Fig. 16. Excess noise factor of the three APDs.

Hamamatsu LC APD is 20}25 lm deep andthe gain does not depend on wavelength up to700 nm. The depleted region in front of the ava-lanche region is sometimes called as the `sensitiveregiona. The thickness of this region is ratherimportant for calorimetry applications: it must bethick enough to absorb all the scintillation lightand multiply generated photocarriers with a max-imum gain, and must be as thin as possible tominimize the nuclear counter e!ect [11] andthe leakage current generated in this region afterirradiation.

6. Excess noise factor

6.1. Measurement of excess noise factor

One of the most important parameters of theAPDs is their excess noise factor. The excess noiseis due to the statistical nature of the multiplicationprocess, which causes additional #uctuation of themeasured signal. The deterioration of the stochasticterm in the energy resolution of electromagneticcalorimeter due to multiplication noise can be sig-ni"cant if the light yeild coming from the calori-

meter is relatively small. In this case the stochasticterm can be expressed as follows:4

Ap5

EB2"

F

N(3)

where N is the number of primary photoelectrons,E is the energy per incident particle, and F is theexcess noise factor of the APD.

Standard techniques have been used to measurethe excess noise factor [2,3]. APDs have been illu-minated with pulsed blue LED light and the signalamplitude and its variance measured with an ADC.The normalized total variance of the signal iscomposed of statistical and electronic noise#uctuations:

Ap5

AB2"

F

N#A

p%-

A B2

(4)

with N"Q/M, where Q is the charge in electronsmeasured at the input of preampli"er, M is the gainof the APD, A is the signal amplitude, p

5is the r.m.s.


of the signal, and p%-

is the r.m.s. of the electronicnoise. Using Eq. (4), one can calculate the values ofF in terms of measured variances of the signal andelectronic noise and in terms of the amplitude of thesignal and the gain. Fig. 16 shows measured valuesof the excess noise factor as a function of gain for allof the APDs tested.

These results are obtained by what we call the`direct methoda. This method uses only the de"ni-tion of the excess noise factor (see Eqs. (3) and (4))without any additional theoretical considerations.The main di$culty of the direct method is that weneed a very accurate measurement of the gain.

Within the past three decades, Tager [12] anda little later McIntyre [13,14] published a theoret-ical model of the multiplication process and multi-plication noise in semiconductor devices. The mostpopular is the theory of McIntyre. In this theory,the ionization process is described as a continuousprocess, characterized by ionization probabilitiesper unit of length, a(x) for the electrons and b(x) forthe holes. This theory assumes that the region ofthe gain is very long, or, equivalently, that thenumber of ionizing collisions per primary carriertransit is very large, and that the electric "eld ismore or less uniform in the avalanche region. Theexpression for the excess noise factor (when themultiplication is initiated by electrons) given byMcIntyre is then

F"kM#A2!1

MB(1!k) (5)

with k"b/a. To take into account that the k factoris a function of the electric "eld, McIntyre proposedto use a weighted value of k called k

%&&[10,14]. So, if

M is greater than 10, it is possible to rewrite Eq. (5)as follows:

F"2#k%&&

M. (6)

Webb [15] proposed the use of Eq. (6) and mea-sured values p

5and p

%-for calculation of the gain

and the excess noise factor. From Eqs. (4) and (6),and assuming that M"A/N, where A is the signalamplitude in number of electrons, we can obtainthe following equation:

p25!p2

%-A

"

2

N#A

k

N2. (7)

The plot of the left-hand side of this relation asa function of A then gives a linear relationship. Theintercept on the vertical axis of a linear "t to thedata points gives the number of primary photo-electrons N and the slope gives the k factor.

Fig. 17 show this `Webb plota for HamamatsuHC and EG&G APD (M'10). A linear relation-ship can be seen for these APDs, and calculatedvalues of N and k are also shown in the same"gures.

The dependence of F on gain using Eq. (5) andcalculated values of k is shown in Fig. 18. One cansee that values of F found using the Webb methodare 35}40% larger than ones found using `directmethoda. On the other hand, the values of gainsfound were 35}40% lower. If one assumes that theWebb method (based on the McIntyre theory) givesthe correct result, then the `direct methoda under-estimates F and overestimates the gain. This meansalso that it underestimates QE (which was mea-sured at the `plateaua) and the real QE is 35}40%higher. Measured values of QE at the `plateaua forHC and EG&G APDs were 72% and 81%, respec-tively, so the `truea QE (480 nm) would be 101%for HC and 109% for EG&G APDs. Even if wetake into account inaccuracies of our measure-ments, 1% for the gain and 5% for QE, it is clearthat these values exceed any reasonable expectationfor QE.

Our results on F could be understood in theframe of the more recently developed theory ofmultiplication noise in avalanche devices (see VanVliet et al. [16,17]). This theory takes into accountthat the number of ionizations that occur percarrier transit through the avalanche region issmall and predicts a value of F smaller than theMcIntyre theory. The experimental check of VanVliets theory needs very accurate measurements ofthe dependence of F versus gain and is planned forfuture tests.

6.2. Excess noise factor versus wavelength

As shown in Section 5, the gain of an APDdepends on the wavelength of the incident light. Itis easy to understand that excess noise factor(which depends on gain) is also dependent on thelight's wavelength. To understand this dependence,


Fig. 17. Webb plot for calculation of k factor.


Fig. 18. Excess noise factor measured with direct method compare with McIntyre calculation.

Fig. 19. Schematic representation of generated photocarriers(electrons and holes) inside an APD (simple model).

let us consider a simple model for the multiplica-tion of carriers inside of the APD. It is clear thatlight with short wavelengths (optical absorptioncoe$cient A1/¸

j, where ¸

jis the distance between

the junction and the APD front surface) will be fullyabsorbed before the multiplication region and gen-erated carriers will all have the same multiplicationcoe$cient and excess noise factor. Light withlonger wavelength (optical absorption coe$cient(1/¸

j) will be absorbed not only before the junc-

tion but also partly inside and even behind it. Let usassume that the avalanche region is in"nitely thinwhere the carrier generation (due to absorbed light)can be neglected (see Fig. 19). So at small biases(M"1) the total photocurrent can be expressed as

I0"I

%#I

)with M"1 (8)

where I0

is total current generated by light at gain1, I

%and I

)the currents generated respectively by

electrons and holes. At higher biases (M'1) wecan de"ne a mean gain SMT, which is a functionof j, as

SMT(j)"SMT"I1)

(;, j)

I0*M/1+

. (9)

Thus total photocurrent I5is then given by

I5"SMTI

0"I

%M

%#I

)M

), (10)

where M%

and M)

are the multiplication coe$-cients of electrons and holes respectively (for siliconM

%*M

)). The photocurrent noise spectral density

p(I5) is given by [1,18]

p2(I5)"2qI

0SMT2F(j) (A2/Hz), (11)

where F(j) is the excess noise factor of the APD atone wavelength and q the electronic charge. It is


Fig. 20. Ratio of gain measured at di!erent wavelengths vs. gain measured with blue light (Hamamatsu HC APD).

also possible to write p2(I5) in terms of M

%, M

), F

%and F

):

p2(I5)"2qI

%M2

%F%#2qI

)M2

)F)

"2qI%M2

%F%#2q(I

0!I

%)M2

)F), (12)

where F%and F

)are the excess noise factors of the

APD in the case of electron- and hole-initiatedavalanches, respectively.

From Eqs. (10)} (12) we obtain then

F(j)"I%

I0

M2%

SMT2F

%#A1!

I%

I0B

M2)

SMT2F

). (13)

Taking into account that [1]

M)"k(M

%!1)#1, (14)

let us consider the case when I%'I

)and k@1

(which is true for silicon), then we can "nd (usingEq. (13) and neglecting the second term of thisequation)

F(j)KI%

I0A

M%

SMTB2F%. (15)

Eq. (15) shows that if we know how the excess noisefactor depends on gain at short wavelengths, andwe also know the ratio I

%/I

0, then by measuring the

ratio of gains at short and long wavelengths we can"nd the excess noise factor of the APD at longwavelengths. The ratio I

%/I

0can be found from the

measurements of the gain of the APD. Indeed, fromEq. (10) we have

I%

I0

"

SMT!M)

M%!M

)

. (16)

In the case when I%'I

), k@1 and M

%PR,

I%

I0

P

SMTM

%

. (17)

We can then take the ratio SMT/M%, measured at

high gain, as a good estimate for I%/I

0. Fig. 20

shows the ratio of gains of the Hamamatsu HCAPD measured with di!erent LEDs (green(560 nm) and red (650 nm)) compared to that mea-sured with a blue LED (480 nm). The APD hasbeen kept at a constant temperature (20$0.13C)


Fig. 21. Excess noise factor vs. gain at di!erent wavelength: measured and calculated (Hamamatsu HC APD).

during these measurements. One can see that atM'50 the ratios almost do not depend on thegain. For green light the ratio saturates at 0.894; forthe red one, at 0.78. Excess noise factors of the APD(using blue, green and red light) have been mea-sured using the technique described in previoussection (Section 6.1). Results of measurementsand calculations using Eq. (16) are shown inFig. 21. One can see excellent agreement betweenthe measurements and the predictions of ourmodel.

7. Leakage current

Leakage current is an important parameter ofthe APD since it determines the noise. It consists oftwo components: surface current (I

4) and current

generated in the bulk region of APD (I"). Surface

current does not go into the avalanche region andcan be described by a resistor connected in parallelto the APD. The surface current rises linearly withthe applied bias. On the other hand, the bulk cur-

rent goes into the avalanche region and undergoesmultiplication. If one assumes that I

"0is the bulk

current at unity gain then the total current (I5)

will be

I5"I

4(<)#I

"(<)"

<

R#I

"0M(<) (18)

where < is the bias applied to the APD and I4the

surface leakage current.When the contribution of the surface current

is small in comparison to the bulk current (athigh gain, for example), one can write I

5/MKI

"0.

This works quite well for both Hamamatsu APDs(Fig. 22). At small biases (M(10) the APDsare not fully depleted and this is the reason thatthe I

5/M ratio rises with the gain. The sur-

face current dominates in the case of EG&GAPD (Fig. 23). The dark current rises linearlywith the bias up to 420 V (M"120) and onlynear breakdown does the bulk current becomethe dominant contributor to the overallcurrent.


Fig. 22. Dark current divided by gain vs. gain for two Hamamatsu APDs.

Fig. 23. Dark current vs. bias for the EG&G APD.

8. Voltage and temperature sensitivity of the gain

Gain stability depends mainly on the stabilityof the applied bias and the temperature. Todescribe the dependence of the gain versus bias

and temperature one can introduce voltage andtemperature coe$cients of the gain as follows:

kV(M)"

1

M

dM

d<(19)


Fig. 25. Gain vs. temperature for the Hamamatsu HC APD.

Fig. 24. Voltage coe$cient of the gain vs. gain.

kT(M)"

1

M

dM

d¹. (20)

Knowing the dependence of these parameterson the gain we can compare di!erent APDs andcalculate requirements which we should apply toour bias and temperature to get the desired stabilityof measured signal.

Voltage coe$cients of the gain versus gain forHamamatsu and EG&G APDs have been cal-

culated from measured gain curves (Fig. 24). Forgain higher than 20, Hamamatsu APDs exhibita linear increase of the voltage coe$cient. ForEG&G APD this dependence is more complicatedbecause of the reach-through structure of theEG&G APD, but for gain higher than 20 (APDfully depleted) the dependence is also linear. Thevoltage coe$cient for the Hamamatsu HC APD ishigher than that for Hamamatsu LC and EG&GAPD. This is caused by the thickness of the de-pleted region: the thinner the depleted region, thelarger the change of the electric "eld for the samechange in bias.

As the temperature increases, the ionization co-e$cient of carriers decreases, due to increase ofphonon scattering, and thus the gain decreaseswhen the temperature increases. Fig. 25 shows thevariation of the gain of the Hamamatsu HC APDversus temperature. At M"50 the temperaturecoe$cient of the gain for this APD is 2.3%/3C.Using the same technique, the temperature coe$c-ient of the gain was found to be 2.5%/3C (atM"50) for the Hamamatsu LC APD.

For the EG&G APD gain mesurements wereperformed over the whole range of HV bias at twodi!erent and stable temperatures (21.6 and 24.63C).


Fig. 26. Temperature coe$cient of the gain vs. gain for the EG&G APD.

The temperature coe$cient of the gain was thencalculated as

kT(M)"

2

M1#M

2

M1!M

2¹

1!¹

2

, (21)

where M"(M1#M

2)/2. The results are shown

in Fig. 26. For gains higher than 10, kT(M) rises

linearly with the gain and reaches 3.5%/3Cat M"50.

It is interesting to notice that the HamamatsuAPDs which have smaller excess noise factors alsohave a smaller temperature coe$cients. This is re-lated to the fact that the dependence of ionizationcoe$cients on the gain decreases with a decrease ofthe peak value of the electric "eld inside of the APD(see Ref. [1]). Hamamatsu APDs have thicker ava-lanche regions and a smaller maximum value of theelectric "eld (for the same gain) than that of theEG&G APD.

9. Conclusion

We have presented systematic studies of perfor-mances of three di!erent APDs (two APDs from

Hamamatsu and one from EG&G) which haveenhanced sensitivities for short wavelength lightand are good candidates for High Energy Physicsapplications. The basic properties of these APDs(gain, spectral response, dependence of the excessnoise factor versus gain and wavelength, etc.) havebeen measured with light (continuous and pulsed)or gamma (55Fe, 241Am) sources. Existence ofspace charge e!ects (`screeninga), which decreasethe gain in the case of a nearly point `clouda ofcharge delivered by low energy gammas in siliconhas been demonstrated. However, from the com-parative measurements of the gain with gammasources and continuous light, we conclude that theplateau in dependence of the photocurrent versusbias (at small biases) corresponds to unity gain withan accuracy better than 5%. Only light with shortwavelength ((500 nm) can be used for correctmeasurement of the gain to prevent the injection ofthe light into and beyond the avalanche region.This avoids underestimation of the gain and sub-sequent introduction of the error into the calcu-lation of the other parameters of the APDs. Theresults on the measurements of the excess noisefactor shows that the values of the excess noisefactor measured by the `directa method are


30}40% lower than ones found using approachbased on the theory of McIntyre. This e!ect wasobserved for all tested APDs and could not beexplained by mismeasurement of the gain. The de-pendence of the excess noise factor versus gain forthree di!erent wavelength of light (blue, green andred) has been measured. The results are in excellentagreement with a simple model proposed.

Acknowledgements

We would like to acknowledge encouragementsand continuous support given to the present workby J. Badier. We also thank R. Tanaka for impor-tant and stimulating suggestions all along our workand D. Renker, R. Rusack, B. Ille, P. Denes, S.Reucroft, J. Swain, J.P. Pansart, J.E. Bateman, R.Stephenson for the fruitful discussions of the resultsand their interpretation.

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