APPLIED PHYSICS LETTERS VOLUME 82, NUMBER 17 28 APRIL 2003

Percolation-based vibrational picture to estimate nonrandom N substitutionin GaAsN alloys

O. Pagesa) and T. TiteInstitut de Physique, 1 Boulevard Arago, 57078 Metz, France

D. BormannLPCIA, Rue Souvraz, 62037 Lens, France

E. TournieCRHEA, Rue Gregory, 06560 Valbonne, France

O. Maksimov and M. C. TamargoCity College of New York, New York, New York 1003

~Received 5 August 2002; accepted 14 February 2003!

The number of N atoms in N-rich regions mostly due to nonrandom N incorporation in GaAsN~N;4%!, referred to as the Nr rate, is studied using a nonstandard Raman setup that addressestransverse symmetry. The Ga–N optical range shows a two-mode signal which discriminatesbetween the N-poor (Np) and N-rich (Nr) regions. This is discussed via a percolation-based picturefor Be-chalcogenide alloys, which exhibit mechanical contrast with regard to the shear modulus.This applies to GaAs–GaN even though the contrast is in the bulk modulus. The balance of Nr /Np

strength provides a Nr rate of;30%, i.e., much larger than the corresponding Be rate of;4% inrandom Be-based alloys. ©2003 American Institute of Physics.@DOI: 10.1063/1.1566801#

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The GaAs12xNx (x;0.03) semiconductor alloy has atracted much attention due to a giant reduction in band gasmall x, corresponding to;300 meV at the N-solubilitylimit of xs;2%.1 This makes GaAsN-based materials proising for optoelectronic applications.2 However, one majorintrinsic limitation may reduce the extent of these applictions. At x.xs N ordering3 due to the large lattice-mismatcbetween GaAs and GaN~;20%!, at the advantage of thformer, is superceeded in or relayed by a more dramaticfect, i.e., phase separation is believed to occur very eas1

This means that N atoms have a propensity to build N-r(Nr-! domains with two or more N atoms around an unpturbed Ga site, instead of remaining mainly isolated inGaAs-like matrix, as expected in the case of random N sstitution for As at the present N-dilute limit. Phase separatdegrades the optoelectronic properties, therefore in thevice range~N;3%! it is crucial to estimate the number of Natoms which belong to the Nr domains. This is referred tobelow as the Nr rate (0<Nr<1).

Raman scattering is the technique of choice to invegate nonrandom N incorporation, as well as N orderisince it directly addresses the force constant of the bowhich is highly sensitive to the local atomic environmeMost of the Raman data from GaAsN in the literature weobtained using the usual backscattering geometry alonggrowth axis of~001!-oriented epilayers,4–6 corresponding tolongitudinal optical~LO! modes that are allowed and tranverse optical~TO! modes that are forbidden. The exceptiis the Brewster-angle scattering geometry of the~001! faceimplemented by Mintairovet al.,3 which is still mostly LOlike, and which allowed one to see N ordering in GaAsN vbreakdown of the zinc blende Raman selection rules.key point is that decisive information upon phase separa

a!Author to whom correspondence should be addressed; electronicpages@ipc.sciences.univ-metz.fr

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could not be derived using LO-like data. In order to estimthe Nr rate we turn to the nonstandard backscattering geetry along the@110#-edge axis for which deformation potential scattering by the TO phonon is allowed. This is justifias follows.

Little attention was given to the fact that the reductionbond length accompanies a strong increase in the bulk molus. The values are 0.756 and 2.054 Mbar for GaAs aGaN, respectively. Therefore besides abovechemicaldisor-der,mechanicaldisorder is expected. This has been observrecently for random ZnSe–BeSe~Ref. 7! and ZnTe–BeTe~Ref. 8! II–VI mixed crystals, which exhibit similar me-chanical contrast although a shear instead of bulk moduluthen involved. On a Be basis, GaAs12xNx in the devicerange, i.e.,x below the Ga–N bond percolation threshoxc;0.19 associated with the initial formation of an infinichain of Ga–N bonds in the alloy,9 should consist of a composite system made of N-rich hard bounded clusters, i.e.r

domains, embedded in a relatively soft GaAs-like host mtrix with isolated N atoms only. Due to the different mechanical properties of the two host media, the Ga–N boshould vibrate at two separate frequencies, providing thera distinctive and quantifiable marker of Nr domains. Moreprecisely, the short Ga–N bonds within the N-rich hard cluters should undergo larger tensile strain to match therounding lattice parameter than those dispersed withinmuch softer GaAs-like host matrix. The former bonds shotherefore give a mode at lower frequency than that due toisolated Ga–N bonds. It is on this very basis that the atypBe~Se,Te!-like two-mode behavior in Zn–Be chalcogenidwas interpreted.7,8 Accordingly the low- and high-frequencmodes were labeled with superscriptsh ands, respectively.Basically, our view is that in~N,Be!-based systems, whichconstitute a class of semiconductor alloys made of pamaterials with mechanical contrast, the short-bond frequcies are primarily determined by the mechanical propertieil:

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2809Appl. Phys. Lett., Vol. 82, No. 17, 28 April 2003 Pages et al.

the surrounding medium, not by the local composition. Ttwo effects are opposite.

Nonrandom N substitution should facilitate the formtion of hard clusters, so we expect clear (Ga–N)h activationeven at the present N-dilute limit. More precisely we expthat the Nr rate innonrandomGaAsN is larger than the Ber

rate in therandomBe-based alloys.No Ga–N multimode was reported in GaAsN; addition

In incorporation is believed to be needed to split the Gamode.5,10 However, we have shown that the referen(Be–VI)h mode is screened to the advantage of(Be–VI)s mode in LO symmetry.7,8 Therefore actual Ga–Nsplitting may exist in GaAsN, but barely in LO symmetry.contrast the (Be–VI)h mode appears strongly in TO symmtry. Accordingly, for (Ga–N)h-mode detection we use nonstandard backscattering analysis along the@110#-edge layeraxis, corresponding to TO allowed only modes. This requ;1 mm thick layers and high spatial resolution of the Rammicroprobe. On a Be basis,~i! the (Ga–N)h mode should beTO–LO degenerate, noted as Oh, and frequency stable whex varies (x<xc). Moreover~ii ! it should emerge below theusual GaAs:N local mode (x;0) at ;470 cm21.

The study is supported by a quantitative treatment baon our extension of the Hon and Faust dielectric formalito the equations of motion and polarization given by tmodified random-element-isodisplacement model.11 The lat-ter is the usual description for the two-mode A–B and A–q50 oscillators in AB12xCx alloys. Further three-mode extension is derived by adding one oscillator in the mechanequations. We use the two- and three-mode Raman csections to model the LO and TO line shapes, respective

GaAs12xNx layers are grown by molecular beam epita~MBE! on ~001! GaAs substrates. Relatively largex of3%–4% is considered because of potentially large Nr do-mains.x is measured within an accuracy of 0.25% by doux-ray diffraction. The layer thicknessd;1 mm required is farabove the threshold,dc;105 nm, for full relaxation atN;3%,12 and gives rather poor crystalline quality. Ramanalysis is first performed with the usual~LO-allowed, TO-forbidden! backscattering geometry along the@001#-growthaxis ~1! to provide an overview of the Ga–As and Ga–two-phonon system. The LO-activatedz(x,y) z and LO-extinctz(x,x) z polarized setups are considered, accordingthe usual notations. The nonstandard~TO-allowed, LO-forbidden! backscattering geometry along the@110#-edgeaxis ~2! is also used, with unpolarized excitation, f(Ga–N)h-mode detection. This is optimized by taking thnear-resonant 623.8 nm HeNe excitation. In geometry~1! the514.5 nm Ar1 line is preferred in order to avoid activation othe resonance of the parasitic TOGa–As mode.13 The penetra-tion depth of;100 nm is small with respect tod, so nosignal comes from the substrate. Reference fully relaxed;1mm thick ~001! Zn12xBexTe layers withx54% and 14% aregrown by MBE on a GaInAs buffer lattice matched to InRaman analysis is performed in geometries~1! and ~2! withnonresonant 647.1 nm Ar1 excitation, which is relevant alow x.8

The spectra in geometry~1! obtained with GaAs12xNx

are shown in Fig. 1. Due to smallx, and to the small mass oN in comparison with As, in a ratio of 1:5, Ga–N bond

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produce a minor signal at;475 cm21 between second-ordeGaAs-like modes, 23Ga–As,3 i.e., at much higher frequencthan the dominant Ga–As signal, close to the GaAs optband, i.e., 268–292 cm21. The poor structural quality due tod@dc is seen by the emergence of the polarizatioinsensitive disorder-activated TOGa–As ~DATO! mode, whichis theoretically forbidden~inset of Fig. 1!. Further degrada-tion occurs with an increase ofx. In the present DATO re-gime the build up of clear asymmetry on the low-frequenside of LOGa–As mode is an indication of degradation. Bascally, structural defects limit the distanceL, the so-calledphonon correlation length, over which the phonons progate freely. This leads to the contribution ofqÞ0 phonons tothe Raman line shape. In GaAs the LO dispersion curvea negative slope nearq50, which accounts for the observeasymmetry.L values between 15.5 and 11.5 are derived frLOGa–As-contour modeling via the usual spatial correlatimodel with Gaussian distribution~see Fig. 1!.11A decrease inL of ;25% is a lot for so small a variation in composition1%, and indicates nonstandard structural degradation. Acomparison the relaxed ZnBeTe layers have LOZn–Te lineshapes which ideally superimpose for Be variation of 2%3%. Above all they exhibit a ZnTe-like strength ratio btween the DATO mode at;176 cm21 and the allowed LO at;205 cm21 below 1022 ~inset of Fig. 3!, even at largersubstitution of 14%.8 At this stage it is feared that the reqused condition ofd@dc for Raman analysis of GaAsN in TOsymmetry generates such poor crystalline quality thatintrinsic Nr rate is altered. This is ruled out below.

Possible (Ga–N)h-mode activation is investigated usingeometry~2!, corresponding to TO data. The Ga–N rangeshown in detail in Fig. 2. The LO data atx50.04 are addedfor comparison. From the usual Ga–N mode at;475 cm21,which blueshifts whenx increases, there is clear evidencean extra mode. This emerges at fixed frequency, i.e.,;428cm21, and appears to be TO–LO degenerate~see the upperspectra in Fig. 2!. In the sample withx50.035 the LO-likecomponent of the extra mode is large enough for reliaanalysis of the symmetry~inset in Fig. 2!. The usual LOGa–N

mode and the extra mode undergo similar extinction wrespect to the polarization-insensitive 23Ga-As bands3 whenchanging from thez(x,y) z LO-activated~labeled 1! to thez(x,x) z LO-extinct ~labeled 1! polarized setups. The samholds true for the Be reference.7,8 This establishes that th

FIG. 1. Geometry~1! ~LO! Raman spectra of GaAs12xNx obtained by off-resonant 514.5 nm excitation. Open squares refer to LO modeling viaspatial correlation model. TheL values derived are indicated. The two LOmodes calculated by takingCGaN521.5 at x50.03 are also shown~thinline!. Polarized spectra atx50.03 are shown in the inset.I R and v arenotations for the Raman intensity and wave number.

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2810 Appl. Phys. Lett., Vol. 82, No. 17, 28 April 2003 Pages et al.

extra mode observed in geometry~1! can be safely regardeas a true LO mode with regard to the symmetry, whichcludes activation by structural disorder. Incidentally thhelps to decide about point~i!. In summary, the extra modat ;428 cm21 depicts an intrinsic feature, which satisfiepoints ~i! and ~ii ! in the h-mode picture above.

The number of Ga–N bonds in the H domains, i.e.,Nr rate, is directly derived from the amount of sharingGaN-like oscillator strength (R) and Faust–Henry coefficient (C) between the two kinds of Ga–N bonds in the Tmultimode cross section.R is fixed by the optical band incubic GaN, i.e.,;555–740 cm21. The most recent estimatof C of 23.8 refers to hexagonal GaN.14 This might differfrom the value used with the present Ga–N bonds dispein a GaAs-like zinc blende lattice. ThereforeC is derivedfrom the balance of strength between the LOGa–As andLOGa–N

S modes atx50.03, corresponding to quasisymmetrbroadening of the Ga–As mode and still significant Gasignal. Fair contour modeling is obtained by takingC;21.5~solid line in Fig. 1!. Slight misestimation due to possibdisorder activation of the theoretically forbidden TOGa–N

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mode close to the allowed-LO mode has basically no inence on the final Nr value ~see below!. Finally R andC areinjected in the TO multimode cross section, and Nr is ad-justed so as to mirror the balance of strength between thh-ands-like Ga–N modes. The best fits are shown in Fig. 2typical Nr rate is;30% atx;3%–4%. We want to mentionthat Nr varies less than 5% whenC assumes a value of23.8.Also, we have checked that the balance of strength betwthe h and s modes is stable with resonant~632.8 nm! andoff-resonant~514.5 nm! excitations; only the signal-to-noisratio varies. Therefore Nr misestimation due to possiblparasitical resonance-induced Fro¨hlich scattering by LOmodes5 from the~110! side face is excluded. The key pointthat while the structural quality degrades with an increasex ~refer toL values in Fig. 1!, Nr remains quasistable. OuNr estimate can therefore be taken as chiefly representaof intrinsic nonrandom N substitution, in spite of the postructural quality.

Let us compare with the corresponding Ber rate inZn–Be chalcogenides. Here the atomic substitution is trrandom since thexc value detected with good accuracy frovibrational singularities7,8 coincides with the theoretical oncalculated on a random basis.9 Let us take Zn12xBexTe as a

FIG. 2. Geometry~1! ~LO! and ~2! ~TO! Raman spectra of GaAs12xNx

obtained by resonant 623.8 nm excitation. The calculated TO multimoare shown by thin lines. The Nr values derived are indicated. Thez(x,y) zLO-activated~1! andz(x,x) z LO-extinct ~18! polarized spectra atx50.035are shown in the inset.I R andv are notations for the Raman intensity anwave number.

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reference, for example. The TO spectra in the Be–Te rafor x54% and 14% are shown in Fig. 3. Theh ands modesappear at;386 and;415 cm21, respectively. The opticaband of BeTe is 461–503 cm21,8 which givesR. CBe–Te isestimated to be20.2 via the same procedure as that aboi.e., from the strength of the LOZn–Te/LOBe–Te

S ratio atx54%,~inset in Fig. 3!. The Ber rates derived from contour modeing of the TO multimodes atx54% and 14% are 0.04 an0.15, respectively. Identical values are found for ZnBeEven the latter value is much smaller than the GaAsN oalthough it corresponds to a much larger substitution, aspected.

We have shown by using a nonstandard TO-like Ramsetup that the percolation picture used for basic understaing of atypical Raman multimodes in Be-chalcogenideloys, with contrast in the shear modulus, basically appliesGaN–GaAs mixed crystals, with contrast in the bulk modlus. This allows one to discriminate between the signals frN-poor and N-rich regions in GaAsN~N;3%–4%!. Thenumber of N atoms in the latter domains is derived frombalance of strength via curve fitting of the TO multimodeWe find a value of;30% which is much larger than thcorresponding Be rate of;4% in random Be-based alloys.

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FIG. 3. Geometry ~1! ~LO, inset! and ~2! ~TO! Raman spectra ofZn12xBexTe obtained by off-resonant 647.1 nm excitation. The calculaBeTe-like TO multimodes are shown by thin lines. The Ber values derivedare indicated. The two LO modes calculated atx50.04 by takingCBe–Te520.2 are shown in the inset.I R andv are notations for the Ramanintensity and wave number.

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