Electron-hole pair generation energy in gallium arsenide by x and γ photonsGiuseppe Bertuccio and Diego Maiocchi Citation: Journal of Applied Physics 92, 1248 (2002); doi: 10.1063/1.1490158 View online: http://dx.doi.org/10.1063/1.1490158 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/92/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Dynamics of carrier generation by photon absorption in semiconductor gallium arsenide AIP Conf. Proc. 1555, 20 (2013); 10.1063/1.4820984 Temperature dependence of the average electron-hole pair creation energy in Al0.8Ga0.2As Appl. Phys. Lett. 102, 181119 (2013); 10.1063/1.4804989 DFT investigations of structural and electronic properties of gallium arsenide (GaAs) AIP Conf. Proc. 1482, 64 (2012); 10.1063/1.4757439 Superfluidity of electron-hole pairs in randomly inhomogeneous bilayer systems Low Temp. Phys. 37, 583 (2011); 10.1063/1.3638141 Diffusion of electron-hole pairs in disordered quantum wires Appl. Phys. Lett. 93, 192101 (2008); 10.1063/1.2970987

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Electron-hole pair generation energy in gallium arsenideby x and g photons

Giuseppe Bertuccioa) and Diego MaiocchiPolitecnico di Milano, Dipartimento di Elettronica e Informazione, Piazza Leonardo da Vinci 32, 20133Milano, Italy

~Received 12 March 2002; accepted for publication 8 May 2002!

The mean energy necessary to generate an electron-hole pair in gallium arsenide byx andg photonshas been measured in the 230–320 K temperature range. The experimental apparatus consists of aSchottky junction on a high-quality epitaxial GaAs, a silicon detector that generates a referencecharge signal and highly stable low-noise electronics. The resolution of the system in measuring thegeneration energy is better than 2 meV. An apparent value of«54.216 eV has been measured at 300K, lower than previously published values of 4.35 and 4.27 eV fora particles and 4.57 eV forelectrons. Charge trapping in the GaAs detector, although very weak~less than 1%!, has beenobserved and a model, based on the Hecht theory, has been developed to derive the true value of«54.18460.025 eV at 300 K. The dependence of« on the temperature, in the 230–320 K range,has been found linear,«54.5520.001223T @eV#. The dependence of« on the band gap has beendetermined«52.763Eg10.257@eV#, in good agreement with the Shockley-Klein theory. At 300K, the found value of« in GaAs, together with those reported for germanium and silicon, yields alinear dependence of« on the band-gap energy«51.833Eg11.6 @eV#, with a correlationcoefficient of 0.9997. ©2002 American Institute of Physics.@DOI: 10.1063/1.1490158#

I. INTRODUCTION

A. Interest in gallium arsenide

Gallium arsenide is a compound semiconductor with fa-vorable physical characteristics for fabricating detectors forxand g photons. The high-atomic number of its constituentsand its wide band gap~1.42 eV! permits to have an high-photon absorption~similar to germanium and ten timeshigher with respect to silicon! and the potentiality to operateat room temperature, not possible for germanium detectors.Moreover, the well-established microelectronic technology isanother advantage of GaAs with respect to other high-Z,wide band gap semiconductors.

Interesting studies on GaAs radiation detectors were car-ried out in the 1970s1–4 but the faster advances in Si and Geslowed down the development of GaAs detectors. In the lastfew years, a quite intensive research activity has been doneto study GaAs as material for radiation detection andspectroscopy.5–9 Recently, it has been proven that excellentresults in x and g ray spectroscopy~200–400 eV energyresolution! can be achieved with a pixel detector made usingepitaxial grown GaAs,10,11 opening perspectives for the useof these devices for fundamental sciences as astrophysics(x-g sky sources study!, x-ray spectroscopy for materialstudy and analysis, medical imaging systems, and many in-dustrial applications.12

B. Motivation for measurement of « in GaAs

Our interest in measuring the electron-hole pair genera-tion energy in gallium arsenide byx and g photons beganwith the observation of an anomalous value of the charge

collection efficiency~CCE! measured in a GaAs detector.The CCE5Qind /Qgen, defined as the ratio between the elec-tric charge induced at the detector output electrode and thecharge generated by the full absorption of the energy of asingle detected photons~or particle!, is an important param-eter to study and characterize radiation detectors, especiallythose made with compound semiconductors. Differentlyfrom Si or Ge detectors, most of compound semiconductordetectors are affected by charge trapping, due to impuritiesand defects, that yield CCE,1 and causes degradation of thedetector energy resolution.13 The measurement of the CCE isa useful parameter to determine the quality of the material, ofthe technology, and of the device, helping to find the factorsimproving all these components, as well.

The CCE is determined by measuring the charge signalat the detector output, assuming that the generated charge isknown asQgen5q(E/«), q being the elementary charge,Ethe energy of the photon or particle, and« the mean energynecessary to generate an electron-hole pair in the semicon-ductor.

In a measurement of the CCE of a state-of-the-art GaAsdetector we have found repetitively CCE.1. Since chargemultiplication have to be excluded due to the relatively low-electric field in the detector (,105 V/cm), we derived thatthe reason was an underestimation of the generated chargeQgen, due to an inaccuracy of the« value.

As will be discussed in Sec. II A, the direct measurementof « is accurate only if CCE51, that is when the measuredinduced charge is equal to the generated charge. A conditionof CCE,1 would bring an overestimation of«. In the caseof GaAs, the lowest« value ~4.27 eV! reported in literaturewas obtained using a detector affected by a critical chargetrapping, since the authors report a significant dependence ofa!Electronic mail: Giuseppe.Bertuccio@polimi.it

JOURNAL OF APPLIED PHYSICS VOLUME 92, NUMBER 3 1 AUGUST 2002

12480021-8979/2002/92(3)/1248/8/$19.00 © 2002 American Institute of Physics

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the signal amplitude on the detector bias, with no evidentsignal saturation~see Ref. 2, Fig. 15!.

The values of« for GaAs reported in literature areshown in Table I. In addition, it can be noted that« has beenmeasured using 5.5 MeVa particles or electrons but no mea-surement has been done usingx andg photons, although it isassumed that« for electrons and forx photons should not bedifferent while, in the case of silicon for example, different«have been found forx-g rays ~3.67 eV! and for 5.5 MeVaparticles~3.62 eV! at 300 K.17

All these reasons justified our aim to perform an accu-rate measurement of the electron-hole pair generation energyin GaAs forx andg photons.

II. EXPERIMENTAL SYSTEM AND METHOD

A. Description

The experimental determination of«GaAs has been ar-ranged as a relative measurement with respect to that one ofsilicon,«Si , which has been measured by several researchersand it can be considered known with a high degree ofaccuracy.16–19

The experimental system is shown in Fig. 1. The GaAsdetector and a silicon detector are connected to the sameinput of the electronic chain, constituted by a charge-sensitive preamplifier, a semigaussian filter, and a multichan-nel analyzer. The two detectors are biased independently, areplaced at a few centimeters of distance from each other, andare irradiated simultaneously by two radioactive sources of241Am. The 241Am source irradiating the GaAs has been

shielded with aluminum foil so that the GaAs detector isirradiated practically with only 59.54 keV photons. An ex-ample of an acquired spectrum is shown in Fig. 2. All the241Am spectral lines are acquired by the silicon detector andare indicated in the figure, while only the 59.54 keV linefrom the GaAs detector is present.

The three monoenergetic lines at 13.94, 26.35, and 59.54keV allow a precise calibration in energy of the channelxaxis for the silicon detector. Relatively to this scale, the59.54 keV line acquired by the GaAs occurs at an energyvalue that we will indicate asEGaAs. It can be easily derivedthat the electron-hole pair generation energy«GaAs can beobtained by~see Appendix A!

«GaAs5«SiS Eph

EGaAsD S CCEGaAs

CCESiD , ~1!

in which Eph is the photon energy~59.54 keV in our case!,CCEGaAs and CCESi are the charge collection efficiencies ofthe GaAs and the Si detectors, respectively. Since«Si andEph

are known,EGaAs is measured on the acquired spectrum andit has been experimentally verified that CCESi51.000, aswill be shown in Sec. II D, from Eq.~1! the apparente-hpairgeneration energy of GaAs«GaAs

a can be derived as

«GaAsa 5

«GaAs

CCEGaAs5«SiS Eph

EGaAsD . ~2!

The term ‘‘apparent’’ derives from the fact that what is mea-sured is the charge induced at the detector electrode (Qind),which can be different by the chargeQgen generated by thephoton because of the charge loss due to trapping and recom-bination. When CCE5Qind /Qgen,1, it results«GaAs

a .«GaAs

and the true generation energy«GaAs can be determined onlyif the condition CCEGaAs51 can be reached or derived.

B. Discussion of method

The presented measurement technique, reference detec-tor method~RDM!, allows the relative measurement of«GaAs

with respect to«Si , whose value is assumed to be known.The value of«Si has been repetitively measured in the pastusing the standard method~SM!, which compares the chargegenerated by the radiation with a known charge injected at

TABLE I. Published data of the electron-hole pair generation energy ingallium arsenide. In the last row the data presented in this paper is reported

Radiation EnergyTemperature

range Value at 300 K

e2¯ 300 K ,4.6 eVa

a 5.5 MeV 300 K 4.5 eVb

a 5.5 MeV 87–340 K 4.27 eVc

a 5.5 MeV 195–330 K 4.35 eVd

e2 115 keV 300 K 4.57 eVd

x-g 14–60 keV 230–320 K 4.18 eVe

aReference 14bReference 15cReference 2dReference 4ePresent work.

FIG. 1. Experimental apparatus. The GaAs is connected in parallel with asilicon detector to the same signal processing electronics, which consist of alow-noise charge amplifier, a shaper~band-pass filter!, a 13 bit analog todigital converter and a multichannel analyzer.

FIG. 2. Spectrum of241Am acquired with the silicon and GaAs detectorsarranged as in Fig. 1.

1249J. Appl. Phys., Vol. 92, No. 3, 1 August 2002 G. Bertuccio and D. Maiocchi

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the preamplifier input by means of a calibrated capacitor anda calibrated voltage pulse.17 It is worthwhile to observe thatboth methods~SM, RDM! derive the apparent generationenergy because only the induced charge can be measured.The difference between the two methods is the mode to gen-erate the reference charge: by a silicon detector~RDM! or bya calibrated capacitor and pulse~SM!.

If the knowledge of«Si is assumed to be accurate, theRDM has several peculiarities that make it preferable to theSM for measuring«GaAs

~a! It does not require an injection capacitor, whosevalue must be measured with high accuracy and precision atall the temperatures at which the measurement is done.

~b! It does not require generating voltage steps whoseamplitude must be known with high accuracy, and demandrepeated controls and recalibration during the experiments.

C. GaAs detector

The GaAs detector used in the measurements was de-signed and fabricated at the IAF Institute in Ju¨lich.20 Thedetector is a Schottky diode realized on a 100-mm-thick un-doped GaAs grown by vapor phase epitaxy. The substrate isa GaAs wafer grown by Horizontal Bridgeman with a dopingdensity of 1018 Si/cm3. The Schottky junction~Ti/Pt/Au met-allization! has an area of 1 mm2 and is surrounded by anotherSchottky contact acting as guard to reduce the reverse andsurface currents. The ohmic contact on the backside is con-stituted by a Ni/AuGe/Ni/Au metallization.

From capacitance measurements, a doping of 3.331014 cm23 of the epitaxial layer has been derived. Themeasured reverse current density has been found below 10nA/cm2 at room temperature up to about the maximum re-verse bias voltage of 110 V, above which junction breakdownoccurs.21

D. Characterization of silicon reference detector

The silicon detector has been fabricated at BrookhavenNational Laboratories using a high-resistivityn-type 400-mm-thick wafer. A 2.25 mm2 pn junction with a guard ringhas been realized on the front side while an ohmic contact ismade on the backside of the wafer. Then side of the junctioncan be fully depleted with a reverse bias of 80 V.22

We have verified the full collection of the generatedcharges in the silicon device (CCESi51). This test can bedone by examining if the amplitudes of the charge signalsdelivered by the detector, irradiated by a monoenergetic ra-diation, do not depend on the electric field inside the detec-tor. In fact, if trapping exists (CCE,1), a monotonic in-crease of the signal amplitude with the detector bias isalways observed, because the increase of the carrier driftvelocity reduces the collection time of the charges, and sothe probability to be trapped.

The silicon detector, connected to the same electronicsdescribed in Sec. II A, has been so irradiated with241Am.Spectra have been acquired at different bias voltages of thedetector, ranging from 50 to 150 V. Ten consecutive acquisi-tions have been also taken at the constant bias voltage of 120V. For each spectra, the 59.54 keV line, with more than 104

integral counts, has been accurately fitted to a gaussian func-tion to determine the channel number corresponding to theline peak. Figure 3 shows the result of the measurements. Itcan be seen that the peak channel position does not show anytrend with the increasing of the detector bias voltage, and itis stable to a mean value of channel 582.35 within60.2channel, which corresponds to a deviation from the meanvalue within 60.04%. It can be concluded that the CCE ofthe reference silicon detector is CCESi51.000, with an un-certainty of less than 531024.

It has been also verified that the repeated measurementsmade at constant detector bias~120 V! are affected by aneven lower uncertainty~60.02%! in the peak channel posi-tion ~crosses in Fig. 3!. Due to the relatively long time re-quired for all these acquisitions~several hours!, this resultalso indicates the high degree of the system stability.

III. RESULTS AND DISCUSSION

A. Measurements of apparent generation energy

The apparente-hpair generation energy in GaAs, as de-fined in Eq.~2!, has been measured at temperatures rangingfrom 230 to 320 K with 10 K step, and at different biasvoltages of the GaAs detector. The silicon detector has beenalways biased at 120 V. The two detectors and the preamp-lifier were placed in dry air inside a thermostatic chamberwith an automatic temperature control. The temperature wascontinuously measured in proximity to the detectors using athermocouple, with 1 K accuracy and 0.1 K resolution. Dur-ing each set of measurements, at a given nominal tempera-ture, the minimum and the maximum temperature have beenrecorded, showing a maximum excursion of 0.4 K as worsecase.

The generation energy«Si in silicon, that has been usedin Eq. ~2!, is that one measured by Pehlet al.17 for x-gphotons:

«Si53.870120.0006673T @eV#. ~3!

FIG. 3. Peak position~left axis! of the 59.54 keV line acquired with thesilicon detector biased at different voltages~circles!. The right axis showsthe deviation with respect to the mean value. The maximum displacement ofthe peak channel is less than60.04%~about60.2 channels! and does notshow any increasing trend with the bias voltage. The crosses are the resultsof repetitive acquisitions at the constant bias of 120 V. This measurementproves that CCE51.000 for the silicon detector.

1250 J. Appl. Phys., Vol. 92, No. 3, 1 August 2002 G. Bertuccio and D. Maiocchi

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Figure 4 shows the apparent energy«GaAsa measured at

300 K. As expected,«GaAsa decreases with the increasing of

the detector bias voltageVb , due to the increase of the CCEof the GaAs detector@see Eq.~2!#. The high resolution of thesystem~,2 meV! and the expandedy scale of Fig. 4~14meV is the maximum variation of«GaAs

a ! allows us to ob-serve that no saturation of«GaAs

a occurs, indicating that theCCE does not reach the unity value in the tested voltagerange. Anyway, the spectrum acquisitions forVb.110 Vwere not possible due to the occurrence of frequent and pe-riodical current spikes at the detector output.

It can be noted that all the measured values are lowerthan the lowest value of thee-h pair generation energy re-ported in literature fora particles, equal to«54.27 eV.2

This evidence will be discussed in Sec. III C.Figure 5 shows the apparent generation energy measured

at fixed bias (Vb5100 V) as a function of the temperature.Also in this case, the high resolution and the expanded scale~0.16 eV! allows us to observe that«GaAs

a does not show alinear dependence onT. This can be explained noting that thevariation of «GaAs

a with T is affected by both the dependen-cies of «GaAs and CCE onT @see Eq.~2!#. The variation of

«GaAswith T is expected to be linear, as observed for those ofother semiconductors~Si, Ge! in the same temperature range@see Eq.~3! and Refs. 16–19#. The dependence of CCE onTis not known, but it can be said that CCE depends on severalparameters such as: the capture cross section of the differenttraps, the activity of the traps~which depends on the Fermi-level position!, the thermal velocity of the carriers, the re-emission of the trapped carriers, so that it seems reasonableto expect a nonlinear CCE versusT function.

B. Determination of generation energy „real …

In this section, we present the analysis that can allow thedetermination of the real«GaAs from the measured values ofthe apparent energy. At a fixed temperature, it has been ob-served that the apparent electron-hole pair generation energydecreases as the detector bias voltageVb is increased, be-cause of the increase of the CCE,@see Eq.~2! and Fig. 4#.Under the hypothesis thatVb can be increased enough so thatCCEGaAs saturate to the unity value, this would bring to thecondition«GaAs

a 5«GaAs. Since no spectra can be acquired forVb higher than 110 V, the extrapolation method, describednext, has been derived to determine«GaAs.

We will search, on a theoretical basis, to derive the de-pendence of the CCE onVb , then compare it with the ex-perimental data. This can permit us to determine theasymptotic limit of«GaAs

a for Vb approaching infinity, so de-termining«GaAs.

A theoretical basis for extrapolating«GaAscan be derivedby the expression for the charge collection efficiency of aradiation detector derived by Hecht.23 This theory is basedon the determination of the mean distance a charge carrier,generated at a coordinatexo inside the detector, drifts beforebeing trapped. The mean induced charge at the detector elec-trode can be consequently calculated by summing all thecontributions of the generated carriers by means of the Ramotheorem. The CCE for a planar detector can be written as24

CCE~xo!51

W S Exo

W

expF21

teE

xo

x dz

ne~z!Gdx

1E0

xoexpF2

1

thE

x

xo dz

nh~z!GdxD , ~4!

in which it has been assumed that the electric field is orientedin the positivex direction,W is the thickness of the depletionregion, andxo is the coordinate at which the charges aregenerated by the radiation.te andth are the mean lifetime ofthe electrons and holes, respectively, starting from their gen-eration until they are trapped;ne(x) andnh(x) are the driftvelocities of the carriers.

If ne(x) andnh(x) can be assumed constant with respectto x, due to a constant electric field inside the detector~asfound for semi-insulating liquid-encapsulated Czochralski~LEC! GaAs detectors!,25 or due to the saturation of the ve-locity, Eq. ~4! simplifies to the Hecht equation23

FIG. 4. Apparent electron-hole pair generation energy in GaAs measured at300 K. Equations~2! and ~3! have been used to derive the values from themeasurement. Two adjacent values differ about 2 meV and the full excursionof the measured values is within 14 meV. The right axis reports«GaAs

a /«Si

@Eq. ~2!# that is independent on the value«Si .

FIG. 5. Apparent electron-hole pair generation energy in GaAs measured atdifferent temperature. The detector bias voltage is constantVb5100 V.

1251J. Appl. Phys., Vol. 92, No. 3, 1 August 2002 G. Bertuccio and D. Maiocchi

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CCE~xo!5le

W F12expS xo2W

leD G

1lh

W F12expS 2xo

lhD G , ~5!

in which le5nete andlh5nhth are the mean drift length ofelectrons and holes, respectively. Equation~5! can be appliedto our case because of the almost saturated carrier drift ve-locities due to the high-electric field (E.104 V/cm) presentin nearly the whole depletion region of the detector.

It has to be observed that Eq.~5! gives the CCE asfunction of the positionxo at which the charge is generated.In the case ofx or g photons impinging the detector alongthe x direction, the interactions can occur at any coordinatewith a probability distribution determined by the absorptioncoefficient. If the photon energy is high enough so that theabsorption is uniform in all the detector thickness~as in ourcase for 59.54 keV photons!, it can be shown that the CCE,as experimentally measured on a spectrum, is given by themaximum value of the CCE(xo) function, that is26

CCE5le1lh

W F12expS 2W

le1lhD G . ~6!

Since our aim is to express CCE as function of the ap-plied voltageVb , it is now necessary to express the depen-dence ofW and of (le1lh) on Vb in Eq. ~6!.

The W(Vb) expression has been experimentally deter-mined by means of junction capacitance measurements. Fig-ure 6 shows that the measured capacitance can be well fittedby the following equation, valid for a planar Schottky junc-tion on a uniformly doped semiconductor:

C5A«s

W1Cp , ~7!

W5A2«s

qNd~Vb1Vbi!, ~8!

in which A is the junction area,«s is the semiconductor di-electric constant,Cp is the stray capacitance,Nd is the dop-ant concentration, andVbi is the junction built-in voltage.

Figure 6 shows the fit curve withNd and Cp as freeparameters. After subtraction ofCp'1 pF to the experimen-tal data, the 1/C2 versusVb has confirmed a constant dopingof the epitaxial layerNd53.331014 cm23. Figure 6 alsoshows theW versusVb curve@Eq. ~8!#, derived by the mea-surements, which will be used in the CCE Eq.~6!.

For what concernle1lh , Hecht found a linear depen-dence of the mean drift length of carrier on the electric fieldfor AgCl crystals.23 For GaAs, no theory and only a fewexperimental results are available. Measurements of CCE insemi-insulating LEC GaAs detectors, with a depletion regionequal to the device thickness, can be well explained withle1lh proportional toVb , or, in one case, with an exponen-tial dependence ofle1lh with Vb .26 In the following analy-sis, for simplicity, we will assumele1lh5kVb with k con-stant. This hypothesis will be verified in Sec. III C.Substituting Eq.~6! into Eq. ~2!, we obtain

«GaAsa 5

«GaAs

kVb

W F12expS 2W

kVbD G , ~9!

with W given by Eq.~8!. It can be verified that«GaAsa ap-

proaches«GaAs asVb increases. Equation~9! has been usedto fit the experimental data of«GaAs

a having «GaAs and k asfree parameters. The continuous lines in Fig. 4 is the fit to thedata at 300 K using Eq.~9!. A good agreement with theexperimental data can be observed. In Fig. 7, the same fit isrepresented as function of 1/AVb in order to put in evidencethe asymptotic value«GaAs54.187 eV asVb tends to infinity.The almost straight line is due to the fact that, since (le

1lh)@W, Eq.~9! gives«GaAsa approximately proportional to

1/AVb . The found value«GaAs is about 0.7% lower than theminimum value of the apparent energy«GaAs

a 54.216 eVmeasured atVb5110 V, revealing that the CCE of the de-tector is higher than 0.993~see, also, the next section!.

FIG. 6. Measured capacitance of the Schottky junction~left axis!. The fitusing Eq.~7! is shown. The width of the depletion region, derived from thecapacitance-voltage measurement using Eq.~8! is shown~right axis!.

FIG. 7. Experimental apparent electron-hole pair generation energy in GaAsmeasured at 300 K. The fitting curve using Eq.~9! is shown as a function ofthe reciprocal of the bias voltage 1/AVb . For 1/AVb50 the value of the realgeneration energy is extrapolated.

1252 J. Appl. Phys., Vol. 92, No. 3, 1 August 2002 G. Bertuccio and D. Maiocchi

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Excellent fit has been found at all the temperatures andthe results of the extrapolation of«GaAs at all the availabletemperatures are shown in Fig. 8. A linear interpolation ofthe data yields

«GaAs5~4.5560.017!2~0.0012266.331025!T@eV#.

~10!

The correlation coefficient isR50.982, the displacements ofthe points from the fitting line is less than60.2%, exceptthat for the point at 260 K~20.42%! as shown in the inset ofFig. 8.

C. Comparison with data for a particles

Figure 9 shows the comparison of our results with thosepresented by Eberhardtet al.2 and by Kobayashiet al.,4 bothobtained using 5.5 MeVa particles. It can be observed thatthe slopeD«GaAs/DT'0.001 @eV/K# agrees in all the threeexperiments. The difference in the«GaAsvalues fora andx-gradiation is about 2% and 4% with respect to Eberhardtet al.or Kobayashiet al. values, respectively.

This difference needs a comment since it is opposite ofthe case of silicon, for which the pair generation energy fora~3.62 eV atT5300 K! has been measured to be about 1%lower than forx-g rays ~3.67 eV!, and also differs from thecase of germanium for which the values have been foundidentical.17

It cannot be excluded that the difference in«GaAs for aand x-g shown in Fig. 9 be mainly due to the difference inthe CCE of the detectors used. In fact, the detectors used byEberhardtet al. and Kobayashiet al. were affected by sig-nificant signal charge loss when irradiated bya particles, asevident from the relevant variation~.5%! in the pulse am-plitudes with the detector bias.2

The CCE5«GaAsa /«GaAs@Eq. ~2!# at 300 K of our detector

as a function of the detector bias is shown in Fig. 10. Itexceeds 99% for bias above 70 V. The continuous line is thefit to Eq. ~6!, with a linear dependence ofle1lh from thebias voltage. A value ofle1lh51.4 mm is derived at 110 V.

D. Dependence of «GaAs on photon energy

Our measurement of«GaAs has been made using the59.54 keV line of241Am. A spontaneous question can be if«GaAs depends or does not depend on the photon energy. Asmall dependence of« on the radiation type and energy hasbeen observed and reported for silicon: it has been shownthat «a for a particles are about 1% lower that« for g pho-tons and for electrons.17,19Ryan observed similar differencesin the « values measured using electrons at two differentenergies~481 and 975 keV! and also fora particles at 5.5and 8.78 MeV.19 For x andg photons, it is generally acceptedthe assumption that« does not depend on the photonenergy.17–19 In our case, a demonstration of this hypothesisfor GaAs can be derived verifying experimentally the linearrelationship between the generated chargeQgen and the pho-ton energyEph, that is

Qgen5S q

«GaAsDEph. ~11!

If «GaAs would not be constant with respect toEph thenQgen, and so the amplifier output signal, would be a nonlin-

FIG. 8. Electron-hole pair generation energy in GaAs as extrapolated fromEq. ~9! to correct the apparent values affected by the charge trapping. Thelinear fit, Eq. ~10!, is shown. The inset graph represents the residuals ofthe fit.

FIG. 9. Comparison between the data available for the electron-hole pairgeneration energy in GaAs.

FIG. 10. Charge collection efficiency of the GaAs detector calculated afterthe determination of the true« of GaAs@Eq. ~2!#. The continuous line is thefit of the experimental data to Eq.~6!.

1253J. Appl. Phys., Vol. 92, No. 3, 1 August 2002 G. Bertuccio and D. Maiocchi

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ear function ofEph. We have found that this is not the case:Fig. 11 shows the relationship between the photon energyand channel number of the pulse-height analyzer at whichthe corresponding spectral line peak is found. Thex and gray lines at 13.94, 20.8, 26.35, and 59.54 keV from241Amhave been used. The linear fit has a correlation coefficientRpractically equal to one (12R51028) and the linearity er-rors are below 0.06%, consistent with the limit of the elec-tronics. This spectra has been acquired using a GaAs pixeldetector having a very high-energy resolution@'500 eV, fullwidth at half maximum# and a unity charge collection effi-ciency, but not suitable for the measurement of« because ofits very low-detection efficiency due to the small area andthickness, that imply several hours for a single spectrum ac-quisition. Details and spectra taken with this detector can befound in Ref. 10. This result demonstrates the validity of Eq.~11! assuming«GaAs constant with respect toEph within theexplored energy range.

E. Fano factor

Recently, the Fano factor in GaAs has been experimen-tally evaluated at 295 K, findingF50.1260.0110 assuming«54.27 eV.2 If the value«54.19 eV at 295 K is considered,the derived Fano factor isF50.122. However, it has to beobserved that the difference with the previous value is notsignificant because well below the uncertainty of the mea-sured value.

F. Band-gap energy dependence

In 1961, W. Shockley proposed a theoretical model forthe secondary ionization in semiconductors,27 predicting alinear relationship between the electron-hole pair averagegeneration energy and the band-gap energyEg given by

«5aEg1r ~\v r !, ~12!

in which a52.2 is a calculated constant,r and\v r are theaverage number and the energy of the Raman phonons gen-

erated per ionization, respectively. In 1968, C. A. Klein re-vised the Shockley theory calculating a new value fora52.8, which agrees well with the available experimental«for various semiconductors, from which Klein derived alsothat 0.5 eV,r (\v r),1 eV.28

From the experimental«GaAs versusT data presented inthis paper and the ThurmondEg versusT relationship,29 the«GaAs versusEg relationship has been determined and it isshown in Fig. 12. The linear fit to the experimental pointsgives

«GaAs5~2.7660.15!Eg1~0.25760.21! @eV#, ~13!

with a correlation coefficientR50.989. The angular coeffi-cient is in good agreement with the theoretical Klein’s value(a52.8) and with the experimental value determined byEberhardt (a52.7) in GaAs irradiated usinga particles. Forcomparison with silicon, Ryan founda52.87 irradiatingwith electrons whilea52.15 anda51.83 have been foundby Canali et al. and Ryan, respectively, for 5.5 MeVaparticles.18,19

In Fig. 13, the e-h pair generation energies atT5300 K for x-g photons in germanium, in silicon17 together

FIG. 11. Channel number of the pulse height analyzer vs the photon energy.The x-g ray at 13.94, 20.8, 26.35, and 59.54 keV from241Am have beenused. The linear fit has a unity correlation coefficient showing that a linearrelationship exists between the generated charge and the photon energy. Thisdemonstrates that« is a constant within this energy range.

FIG. 12. « as function of the band-gap energy in GaAs as derived from theexperimental values and theEg vs T relationship by Thurmond.29

FIG. 13. Experimental electron-hole pair generation energy in Ge, Si, andGaAs at 300 K vs the band gap energy. The linear fit to the data is shown,giving a correlation coefficient of 0.9997.

1254 J. Appl. Phys., Vol. 92, No. 3, 1 August 2002 G. Bertuccio and D. Maiocchi

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with the value for GaAs («54.184 eV) as determined in thispaper, have been plotted as function of the band gap at 300K. The three data are fitted with a straight line

«51.83Eg11.6 @eV#, ~14!

with a correlation coefficient of 0.9997.

IV. CONCLUSIONS

The mean energy necessary to generate an electron-holepair in GaAs byx andg photons has been measured using adetector made with high-purity epitaxial GaAs and a systemwith a resolution better than 2 meV. The value at 300 K,«54.18460.025 eV, is between 2% and 8% lower than thevalues reported in literature fora particles or electrons~4.27and 4.57 eV, respectively!. These differences can be mostlyattributed to the high purity of the GaAs used in this paper,as demonstrated by the extremely low-charge trapping ob-served in the detector used in the experiments. A theoreticalmodel has been derived to determine the fraction of the gen-erated charge that it is trapped in the detector~,1%!. Theexcellent agreement between the model and the experimentaldata allowed to extrapolate the true value of«. In the tem-perature rangeT5230– 320 K a linear dependence of« on Tand on the band-gap energy (Eg) has been found, in goodagreement with the Shockley-Klein theory. The« versusEg

dependence for Ge, Si, and GaAs has been derived, showinga linear fit with a correlation coefficient very close to one.

ACKNOWLEDGMENTS

The authors thank J. Lauter, C. Rente, A. Fo¨rster, and H.Luth of IAF Institute in Ju¨lich for device design and realiza-tion, S. Masci of Politecnico di Milano for front-end assem-bly, H. Kraner of Brookhaven National Laboratories for thesilicon device, and A. Pullia of University of Milano forhelpful discussion.

APPENDIX A

The electronic chain used and shown in Fig. 1 is sup-posed to be linear so that the relationship between the chargeQ delivered by the detector and the channel numberch atwhich the multichannel analyzer record the event is

ch5a3Q1b, ~A1!

in which a andb are constants. From a spectra with at leasttwo monoenergetic line, it is possible to calculate the coeffi-cient a andb of the system.

The chargeQ delivered by the Si and by the GaAs de-tectors, when a photon of energyEph is fully absorbed are,respectively,

QSi5qS Eph

«SiDCCESi , ~A2!

QGaAs5qS Eph

«GaAsDCCEGaAs. ~A3!

Substituting Eq.~A2! into Eq. ~A1! the relationship betweenthe energyEph and the channel number can be derived.

Eph5S 1

a3qD S «Si

CCESiD ch2S b

a3qD S «Si

CCESiD . ~A4!

The peak of the line acquired by the GaAs detector appearsat a channel chGaAs derived by Eqs.~A3! and ~A1!

chGaAs5a3qEph

«GaAsCCEGaAs1b. ~A5!

This channel, on the scale calibrated with the Si detector,corresponds to energyEGaAs that can be calculated by sub-stituting Eq.~A5! into Eq. ~A4!, which brings to us Eq.~1!.

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1255J. Appl. Phys., Vol. 92, No. 3, 1 August 2002 G. Bertuccio and D. Maiocchi

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