Index grating lifetime in photorefractive GaAs

Li-Jen Cheng and Afshin Partovi

The index grating lifetime in liquid encapsulated Czochralski-grown undoped semi-insulating GaAs wasmeasured using a beam coupling technique. The largest lifetime measured was -8 s under a read beamintensity of 0.7 mW/cm 2 with the grating periodicity being 0.63 jum. The measured value decreases tomilliseconds as the read beam intensity and the grating periodicity increase to '10 mW/cm2 and 4 im,respectively. This range of grating lifetime in this material is adequate for its use in real-time spatial lightmodulators, reconfigurable beam steering devices, and dynamic memory elements for optical computing. Inaddition, the results suggest that the lifetime is sensitive to residual imperfections in the crystal.

1. Introduction

The lifetime of the index grating determines theinformation storage time in a photorefractive material.This is a critical parameter needed for evaluating thematerial's potential for optical computing and imageprocessing applications. Gallium arsenide (GaAs) is apotential photorefractive material as a real-time spa-tial light modulator and a volume holographic element.The advantages of this photorefractive compoundsemiconductor include fast response,1-3 high sensitiv-ity,1'4 and operation at infrared wavelengths compati-ble with semiconductor lasers.5 In addition, its pho-torefractive devices operate with photons of energysmaller than the band gap energy which do not affectthe operation of GaAs circuits. Recently, the poten-tial of photorefractive GaAs for spatial light modula-tion was demonstrated.6-8

The photorefractive effect is based on the net trans-port of electrical charge from one location to anotherthrough uneven photoexcitation and carrier trappingat localized energy levels in the band gap, therebycreating a space-charge field which gives rise to achange of refractive index via the electrooptic effect.The index grating is due to the periodic space-chargefield created by illumination of two coherent beams.The index grating lifetime depends on how fast thespace-charge field disappears. If the space chargeswere in the conduction band, the characteristic timefor the disappearance would be the dielectric relaxationtime. However, if the charges are trapped at impurity

When this work was done both authors were with CaliforniaInstitute of Technology, Jet Propulsion Laboratory, Pasadena, Cali-fornia 91109; A. Partovi is now with University of Southern Califor-nia, Center for Laser Studies, Los Angeles, California 90089-1112.

Received 17 July 1987.0003-6935/88/091760-04$02.00/0.© 1988 Optical Society of America.

and defect levels located deep in the energy band gap,the process for the disappearance is dominated by thethermal emission of trapped carriers, the periodicity ofthe charge distribution, and the intensity of light illu-minating the crystal.910 For a given periodicity, thegrating lifetime in the dark is at its maximum and isdetermind mainly by the thermal emission rate. Thethermal emission rate is an exponential function of thetrapping level location in the band gap with respect tothe conduction band. The energy band gap of GaAs is-1.4 eV and the deep levels responsible for the photo-refractive effect are known to be located near the mid-dle of the band gap. The recent observation of tem-perature and intensity dependence of the photorefrac-tive effect in GaAs has illustrated that the thermalemission plays a significant role in the determinationof the magnitude of the effect.4 It is known that theresponsible levels in the conventional photo-refractive oxides such as barium titanate and bismuthsilicon oxide, are located deeper in the band gap. 1

Therefore, their grating lifetimes are much longer thanthat of GaAs, as is evident by experimental observa-tions.

In this paper we report results of an investigation ofthe index grating lifetime in liquid encapsulatedCzochralski (LEC)-grown semi-insulating GaAs crys-tals at room temperature. The results reveal that thelifetime can vary from milliseconds to seconds, de-pending on the illuminating intensity and the gratingperiodicity. The results also suggest that the lifetimeis sensitive to residual defects in the material.

II. Experimental

A beam coupling (two-wave mixing) technique wasused to measure the grating lifetime of three differentLEC-grown undoped-semi-insulating GaAs crystals.All the samples were cut in the same way, with rectan-gular surfaces parallel to the (001), (110), and (110)crystalline planes. Figure 1 shows a sketch of theexperimental setup. The output of a 1.7-mW, 1.15-gumHe-Ne laser was split into two beams of the sameintensity. One of the beams (pump beam Ip) was

1760 APPLIED OPTICS / Vol. 27, No. 9 / 1 May 1988

incident on an electronically controlled shutter. Theother beam (signal beam Is) passed through a variableneutral density filter for varying intensity. When theshutter is open, the two beams interfere in the crystalto form an index grating via the photorefractive effect.The plane of the two incident beams was parallel to the(110) crystal plane. The crystal was arranged in such away that the intensity of I, was increased due to beamcoupling in the crystal. When the shutter was closed,the energy transfer from p to I, stopped immediately.However, the grating was still present because of itsfinite lifetime. Its amplitude started to decay with acharacteristic lifetime, depending on I, and the ther-mal emission rate of trapped carriers at defect levels.During this turn-off period of p, I, was still illuminat-ing the sample as a simulated read beam. If the closedduration of the shutter was shorter than the gratinglifetime under illumination, a significant amplitude ofthe grating still remained in the crystal when the shut-ter was reopened. A fast rise of I, was observed due tothe diffraction of the remaining grating, as illustratedby oscilloscope traces of I, in two photographs of Fig. 2.After this fast rise, I increased at a slower rate, asillustrated by its oscilloscope traces. This was due tothe increase of the grating amplitude caused by two-beam interference in the crystal. As the shutter wasleft closed for longer times, the magnitude of the fastrise decreased since the grating had a longer time todecay (see the difference between the two oscilloscopetraces in Fig. 2). The observation led us to concludethat the measurement of the amplitude of the fastcomponent as a function of shutter closed duration cangive the index grating lifetime.

Ill. Results and Discussion

Figure 3 shows experimental data on the amplitudeof the fast rise component as a function of shutterclosed duration for two different values of I, Thisillustrates that the amplitude of the fast rise decreasesexponentially with shutter closed duration. Namely,the diffraction efficiency decays exponentially withtime under constant illumination. Therefore, the dif-fraction efficiency decay time, defined as the timerequired for the diffraction to decrease to the lie valueof the original, is a meaningful parameter that can bemeasured. Since the diffraction efficiency is propor-tional to the square of the amplitude of the indexgrating for small amplitudes (as is the case in GaAs),the index grating lifetime is twice the measured dif-fraction efficiency decay time.9 By changing the neu-tral density filter value, the grating lifetime can bemeasured as a function of I. Also, by varying theincident angle of two beams, the grating lifetime can bedetermined as a function of grating periodicity.

Figure 4 shows the measured grating lifetime r insample A as a function of I, and grating periodicity,illustrating two interesting general features. The life-time decreases with increasing Is and grating periodici-ty. This is consistent with the theoretical predic-tions.10 -13 The periodicity dependence can beexplained by the fact that the carrier hopping range,

GE/ PHOTODIODE

1. 15SHe-Ne

LASER out

1. 7mW Is

-- , - GaAs, A,- , ~~~~~CRYSTAL

VARIABLE / CNEUTRAL DENS ITY / ,FILTER

BS ELECTRONICSHUTTER

Fig. 1. Experimental setup for measuring index grating lifetime inGaAs.

Ip ONI OFF ON ON OFF I ON

1, ON!ON: ON ON ON ON

Fig. 2. Two oscilloscope traces of Is with different close durations of

I,. The Is signals were biased with a dc voltage so that the effect of Ipcould be observed.

0 0.5 1.0 1.2

SHUTTER CLOSED TIME (sed

Fig. 3. Decay of the fast rising component in sample A as a function

of shutter closed duration under two different I,. The incidentangle of two beams was 94°.

0. X '.60.1 * 894 0.79

. 45 1. 50

0 18° 3. 68 0.01

0. 0010 0.01 0. 1 10

INTENS ITY (mW/ cm2)

Fig. 4. Measured index grating lifetime in sample A as a function of

I, intensity and grating periodicity. The solid curves are calculatedgrating lifetimes using Eqs. (1) and (2) with known material parame-

ters and fitting factors of x and s0 being 0.8 and 0.15, respectively.

1 May 1988 / Vol. 27, No. 9 / APPLIED OPTICS 1761

E

<1

e11

952��0

from one trapping site to the other via the conductionband in GaAs, is much larger than the Debye screeninglength.12 It should be noted that the I value in thefigure is the averaged intensity in the crystal estimatedfrom the measured incident beam intensity with cor-rections due to reflection losses, beam cross-sectionalchanges due to refraction at the surface, and lightabsorption in the bulk. The largest T value measuredis -8 s at I = 0.7 mW/cm 2 with grating periodicity Ag= 0.63 Aim. The lifetime decreases to millisecondswhen the read beam intensity and the grating periodic-ity increase to -10 mW/cm 2 and 4 um, respectively.Shorter lifetimes are possible, when higher read beamintensity and larger grating periodicity are used.23

Because of the limited shutter speed, we are not able tomeasure any lifetime below milliseconds. The dataillustrate the tunability of the grating lifetime frommilliseconds to seconds, which provides flexibility forapplications.

Without an applied electric field, the lifetime of agrating in GaAs can be written as9

___ /IkbT 22(1

[ erANA (Ag) ]

with

(a + sI)ND3no = ~~~~~~~~~~(2)

rANA

where o is the vacuum permittivity constant, e is thedielectric constant, e is the electron charge, Ai is thecarrier mobility, NA is the acceptor density, no is thecarrier density, kB is Boltzmann's constant, T is tem-perature, rA is the carrier trapping rate at the acceptor,Ag is the grating periodicity, s is the photoionizationcross section of the donor, is the thermal emissionrate of trapped carrier, and ND is the neutral donordensity. The combination of Eqs. (1) and (2) repre-sents the grating lifetime as a function of materialparameters, read beam intensity, and grating periodic-ity. The grating periodicity dependence appears inthe second term in parentheses in Eq. (1). Equation(2) is derived in the condition that a quasiequilibriumcondition between the carrier band and the trappinglevels exists.

In LEC-grown undoped GaAs, the dominant deeplevel is a donor state designated as EL2, which is be-lieved to be responsible for the photorefractive effectin this material. The neutral (filled) EL2 level acts asthe donor and the empty EL2 level acts as the acceptor.The properties of sample A are the same as thosereported in Ref. 2 (i.e., the electron mobility is 5800cm2 /V s, the absorption coefficient at 1.15 jim is 0.7/cm, NA is 1.4 X 101 5/cm2 , NO is 1.0 X 1016/cm3 , and thedark resistivity is 6.5 X 107 Q - cm). The thermalemission rate of trapped electrons from the EL2 level isreported to be 0.01/s.14

The eno and eoe/ejino are the electrical conductivityand the dielectric relaxation time of the material, re-spectively. Both values in the dark can be estimatedfrom the measured dark resistivity. The dielectic re-laxation time is estimated to be -70 s, which is much

smaller than the measured grating lifetimes shown inFig. 4. It is noted that the grating lifetime also de-pends on the time required for the removal of spacecharges from the deep level traps to the conductionband which is much slower than the dielectric relax-ation time. Therefore, we can conclude that the valueof the second term in parentheses of Eq. (1) is muchlarger than unity for the GaAs samples under investi-gation. As a consequence, a combination of Eqs. (1)and (2) can be written as

eoekbT (27r\2

e2(o + sI) r \Ag) (3)

This equation reveals that the lifetime in GaAs de-pends mainly on three material parameters, i.e., thethermal emission rate of trapped carriers, the photo-ionization cross section, and the donor concentration.Among them, only the photoionization cross section isnot known. We tried to fit the data in Fig. 4 with Eq.(3) using s as a fitting parameter. But, we failed toobtain a satisfactory result. It is found that, as Iincreases, the decreasing rate of the calculated gratinglifetime is always faster than that of the measuredvalue.

One still unexplained anomaly in the photorefrac-tive effect of oxides is the observation that the gratingerase rate is proportional to light intensity to a frac-tional power between 0.5 and 1.0.15 To understandthe grating lifetime data as a function of intensity andgrating periodicity, we made a modification of Eq. (3)to accommodate the anomaly as the following:

eoekbT /2

e2 ( + saIx)N )2 (4)

where Sa and x are fitting factors. Figure 4 shows afamily of -vs-I, curves with grating periodicity as theparameter which were calculated using Eq. (4) withknown material parameters stated above and fittingfactors x and being 0.8 and 0.15, respectively. Thesa value depends on the unit used for the intensity. Inthe present case, we used mW/cm2. Here x and Sa haveno clear physical meaning except that they can be usedto fit the experimental data well. The fitted value of xbeing 0.8 is similar to those anomalies observed inphotorefractive oxide crystals, which is still unex-plained.15 Clearly, more studies are needed on thissubject.

Figure 5 shows measured grating lifetimes as a func-tion of I in LEC-grown undoped GaAs samples fromthree different suppliers. They were Hughes, M/A-COM, and Airtron for samples A, B, and C, respective-ly. Sample A was a research grade material and theother two were commercial products. The absorptioncoefficients of samples B and C were measured to be1.0/cm and 1.1/cm, respectively. The data clearly il-lustrate that the lifetime is sensitive to material prop-erties. It is known that the residual imperfection inGaAs crystals grown by state-of-the-art technologyvaries considerably from one part to the other withinone ingot.16 Thus, it is not surprising to observe thedifference in grating lifetime among samples from the

1762 APPLIED OPTICS / Vol. 27, No. 9 / 1 May 1988

Is (mW/cm2)

Fig. 5. Measured index grating lifetime in samples from three

different suppliers as function of Is.

different suppliers. Recently, the measurement ofgrating lifetime using a nondegenerate four-wave mix-ing technique was suggested for mapping the distribu-tion of material properties in semi-insulating GaAswafers.17 It is interesting to note that the dependenceof the grating lifetime of sample B on I, is differentfrom those of samples A A and C. This could suggestthat the anomaly of the grating lifetime is also sensitiveto the residual imperfection in the crystals. Obvious-ly, further studies are needed before any conclusioncan be made.

In our experiments, the 1.15-jim beam was used tosimulate the reading beam. If the beam of a 1.3- or 1.5-jim injection semiconductor laser is used as the readingbeam, the storage time for a given intensity can belonger. This is due to the fact that the cross section ofthe EL2 level for photoionization at these wavelengthsis much smaller. For example, the cross section at 1.5jum is about a factor of 10 smaller. 14

It is interesting to note that the index grating life-time in photorefractive Fe-doped InP was reported tobe only about several hundred microseconds. 9 Theshort index grating lifetime observed could be attrib-uted to the fact that energy band gap of InP is smallerthan that of GaAs.

IV. Summary

The results demonstrate that the information storedin a volume holographic element of GaAs can vary frommilliseconds to seconds, depending on the read beamintensity and the grating periodicity. This range ofgrating lifetime in this material is adequate for its usein real-time spatial light modulators, reconfigurablebeam steering devices, and dynamic memory elementsfor some optical computing applications.

The authors would like to acknowledge valuablediscussions with E. M. Garmire, G. Gheen, J. Katz, M.B. Klein, R. A. Mullen, and G. C. Valley. Sample Aused in this study was kindly supplied by M. B. Kleinof Hughes Research Laboratories. The work de-

scribed in this paper was carried out by the Jet Propul-sion Laboratory, California Institute of Technology,and was sponsored by the Defense Advanced ResearchProjects Agency and the Strategic Defense InitiativeOrganization/Innovative Science & Technologythrough an agreement with the National Aeronauticsand Space Administration.

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Ballman, "Four-Wave Mixing in Semi-Insulating InP Using thePhotorefractive Effect," Appl. Phys. Lett. 44, 948 (1984).

2. M. B. Klein, "Beam Coupling in Undoped GaAs at 1.06 vm

Using the Photorefractive Effect," Opt. Lett. 9, 350 (1984).3. G. C. Valley, A. L. Smirl, M. B. Klein, K. Bohnert, and T. F.

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lating GaAs," J. Appl. Phys. 60, 169 (1986).17. R. B. Bylsma and A. M. Glass, "Photorefractive Image of the

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