1. APPLIED PHYSICS LETTERS VOLUME 82, NUMBER 17 28 APRIL 2003
Percolation-based vibrational picture to estimate nonrandom N substitution
in GaAsN alloys
O. Pagesa) and T. Tite
`
Institut de Physique, 1 Boulevard Arago, 57078 Metz, France
D. Bormann
LPCIA, Rue Souvraz, 62037 Lens, France
´
E. Tournie
CRHEA, Rue Gregory, 06560 Valbonne, France
O. Maksimov and M. C. Tamargo
City College of New York, New York, New York 1003
͑Received 5 August 2002; accepted 14 February 2003͒
The number of N atoms in N-rich regions mostly due to nonrandom N incorporation in GaAsN
͑Nϳ4%͒, referred to as the Nr rate, is studied using a nonstandard Raman setup that addresses
transverse symmetry. The Ga–N optical range shows a two-mode signal which discriminates
between the N-poor (Np ) and N-rich (Nr ) regions. This is discussed via a percolation-based picture
for 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 ϳ30%, i.e., much larger than the corresponding Be rate of ϳ4% in
random Be-based alloys. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1566801͔
The GaAs1Ϫx Nx (xϳ0.03) semiconductor alloy has at- could not be derived using LO-like data. In order to estimate
tracted much attention due to a giant reduction in band gap at the Nr rate we turn to the nonstandard backscattering geom-
small x, corresponding to ϳ300 meV at the N-solubility etry along the ͓110͔-edge axis for which deformation poten-
limit of x s ϳ2%.1 This makes GaAsN-based materials prom- tial scattering by the TO phonon is allowed. This is justified
ising for optoelectronic applications.2 However, one major as follows.
intrinsic limitation may reduce the extent of these applica- Little attention was given to the fact that the reduction in
tions. At xϾx s N ordering3 due to the large lattice-mismatch bond length accompanies a strong increase in the bulk modu-
between GaAs and GaN ͑ϳ20%͒, at the advantage of the lus. The values are 0.756 and 2.054 Mbar for GaAs and
former, is superceeded in or relayed by a more dramatic ef- GaN, respectively. Therefore besides above chemical disor-
fect, i.e., phase separation is believed to occur very easily.1 der, mechanical disorder is expected. This has been observed
This means that N atoms have a propensity to build N-rich recently for random ZnSe–BeSe ͑Ref. 7͒ and ZnTe–BeTe
(Nr -͒ domains with two or more N atoms around an unper- ͑Ref. 8͒ II–VI mixed crystals, which exhibit similar me-
turbed Ga site, instead of remaining mainly isolated in the chanical contrast although a shear instead of bulk modulus is
GaAs-like matrix, as expected in the case of random N sub- then involved. On a Be basis, GaAs1Ϫx Nx in the device
stitution for As at the present N-dilute limit. Phase separation range, i.e., x below the Ga–N bond percolation threshold
degrades the optoelectronic properties, therefore in the de- x c ϳ0.19 associated with the initial formation of an infinite
vice range ͑Nϳ3%͒ it is crucial to estimate the number of N chain of Ga–N bonds in the alloy,9 should consist of a com-
atoms which belong to the Nr domains. This is referred to posite system made of N-rich hard bounded clusters, i.e., Nr
below as the Nr rate (0рNr р1). domains, embedded in a relatively soft GaAs-like host ma-
Raman scattering is the technique of choice to investi- trix with isolated N atoms only. Due to the different me-
gate nonrandom N incorporation, as well as N ordering, chanical properties of the two host media, the Ga–N bonds
since it directly addresses the force constant of the bonds, should vibrate at two separate frequencies, providing thereby
which is highly sensitive to the local atomic environment. a distinctive and quantifiable marker of Nr domains. More
Most of the Raman data from GaAsN in the literature were precisely, the short Ga–N bonds within the N-rich hard clus-
obtained using the usual backscattering geometry along the ters should undergo larger tensile strain to match the sur-
growth axis of ͑001͒-oriented epilayers,4 – 6 corresponding to rounding lattice parameter than those dispersed within the
longitudinal optical ͑LO͒ modes that are allowed and trans- much softer GaAs-like host matrix. The former bonds should
verse optical ͑TO͒ modes that are forbidden. The exception therefore give a mode at lower frequency than that due to the
is the Brewster-angle scattering geometry of the ͑001͒ face isolated Ga–N bonds. It is on this very basis that the atypical
implemented by Mintairov et al.,3 which is still mostly LO Be͑Se,Te͒-like two-mode behavior in Zn–Be chalcogenides
like, and which allowed one to see N ordering in GaAsN via was interpreted.7,8 Accordingly the low- and high-frequency
breakdown of the zinc blende Raman selection rules. The modes were labeled with superscripts h and s, respectively.
key point is that decisive information upon phase separation Basically, our view is that in ͑N,Be͒-based systems, which
constitute a class of semiconductor alloys made of parent
a͒
Author to whom correspondence should be addressed; electronic mail: materials with mechanical contrast, the short-bond frequen-
pages@ipc.sciences.univ-metz.fr cies are primarily determined by the mechanical properties of
0003-6951/2003/82(17)/2808/3/$20.00 2808 © 2003 American Institute of Physics
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2. Appl. Phys. Lett., Vol. 82, No. 17, 28 April 2003 `
Pages et al. 2809
the surrounding medium, not by the local composition. The
two effects are opposite.
Nonrandom N substitution should facilitate the forma-
tion of hard clusters, so we expect clear (Ga–N) h activation
even at the present N-dilute limit. More precisely we expect
that the Nr rate in nonrandom GaAsN is larger than the Ber
rate in the random Be-based alloys.
No Ga–N multimode was reported in GaAsN; additional
In incorporation is believed to be needed to split the Ga–N
mode.5,10 However, we have shown that the reference
(Be–VI) h mode is screened to the advantage of the FIG. 1. Geometry ͑1͒ ͑LO͒ Raman spectra of GaAs1Ϫx Nx obtained by off-
(Be–VI) s mode in LO symmetry.7,8 Therefore actual Ga–N resonant 514.5 nm excitation. Open squares refer to LO modeling via the
splitting may exist in GaAsN, but barely in LO symmetry. In spatial correlation model. The L values derived are indicated. The two LO-
modes calculated by taking C GaNϭϪ1.5 at xϭ0.03 are also shown ͑thin
contrast the (Be–VI) h mode appears strongly in TO symme- line͒. Polarized spectra at xϭ0.03 are shown in the inset. I R and ␻ are
try. Accordingly, for (Ga–N) h -mode detection we use non- notations for the Raman intensity and wave number.
standard backscattering analysis along the ͓110͔-edge layer
axis, corresponding to TO allowed only modes. This requires
produce a minor signal at ϳ475 cmϪ1 between second-order
ϳ1 ␮m thick layers and high spatial resolution of the Raman
GaAs-like modes, 2ϫGa–As,3 i.e., at much higher frequency
microprobe. On a Be basis, ͑i͒ the (Ga–N) h mode should be
than the dominant Ga–As signal, close to the GaAs optical
TO–LO degenerate, noted as Oh , and frequency stable when
band, i.e., 268 –292 cmϪ1 . The poor structural quality due to
x varies (xрx c ). Moreover ͑ii͒ it should emerge below the dӷd c is seen by the emergence of the polarization-
usual GaAs:N local mode (xϳ0) at ϳ470 cmϪ1 . insensitive disorder-activated TOGa–As ͑DATO͒ mode, which
The study is supported by a quantitative treatment based is theoretically forbidden ͑inset of Fig. 1͒. Further degrada-
on our extension of the Hon and Faust dielectric formalism tion occurs with an increase of x. In the present DATO re-
to the equations of motion and polarization given by the gime the build up of clear asymmetry on the low-frequency
modified random-element-isodisplacement model.11 The lat- side of LOGa–As mode is an indication of degradation. Basi-
ter is the usual description for the two-mode A–B and A–C cally, structural defects limit the distance L, the so-called
qϭ0 oscillators in AB1Ϫx Cx alloys. Further three-mode ex- phonon correlation length, over which the phonons propa-
tension is derived by adding one oscillator in the mechanical gate freely. This leads to the contribution of q 0 phonons to
equations. We use the two- and three-mode Raman cross the Raman line shape. In GaAs the LO dispersion curve has
sections to model the LO and TO line shapes, respectively. a negative slope near qϭ0, which accounts for the observed
GaAs1Ϫx Nx layers are grown by molecular beam epitaxy asymmetry. L values between 15.5 and 11.5 are derived from
͑MBE͒ on ͑001͒ GaAs substrates. Relatively large x of LOGa–As-contour modeling via the usual spatial correlation
3%– 4% is considered because of potentially large Nr do- model with Gaussian distribution ͑see Fig. 1͒.11 A decrease in
mains. x is measured within an accuracy of 0.25% by double L of ϳ25% is a lot for so small a variation in composition as
x-ray diffraction. The layer thickness dϳ1 ␮m required is far 1%, and indicates nonstandard structural degradation. As a
above the threshold, d c ϳ105 nm, for full relaxation at comparison the relaxed ZnBeTe layers have LOZn–Te line
Nϳ3%,12 and gives rather poor crystalline quality. Raman shapes which ideally superimpose for Be variation of 2%–
analysis is first performed with the usual ͑LO-allowed, TO- 3%. Above all they exhibit a ZnTe-like strength ratio be-
forbidden͒ backscattering geometry along the ͓001͔-growth tween the DATO mode at ϳ176 cmϪ1 and the allowed LO at
axis ͑1͒ to provide an overview of the Ga–As and Ga–N ϳ205 cmϪ1 below 10Ϫ2 ͑inset of Fig. 3͒, even at larger
¯
two-phonon system. The LO-activated z(x,y)z and LO- substitution of 14%.8 At this stage it is feared that the requi-
¯
extinct z(x,x)z polarized setups are considered, according to sed condition of dӷd c for Raman analysis of GaAsN in TO
the usual notations. The nonstandard ͑TO-allowed, LO- symmetry generates such poor crystalline quality that the
forbidden͒ backscattering geometry along the ͓110͔-edge intrinsic Nr rate is altered. This is ruled out below.
axis ͑2͒ is also used, with unpolarized excitation, for Possible (Ga–N) h -mode activation is investigated using
(Ga–N) h -mode detection. This is optimized by taking the geometry ͑2͒, corresponding to TO data. The Ga–N range is
near-resonant 623.8 nm HeNe excitation. In geometry ͑1͒ the shown in detail in Fig. 2. The LO data at xϭ0.04 are added
514.5 nm Arϩ line is preferred in order to avoid activation of for comparison. From the usual Ga–N mode at ϳ475 cmϪ1 ,
the resonance of the parasitic TOGa–As mode.13 The penetra- which blueshifts when x increases, there is clear evidence of
tion depth of ϳ100 nm is small with respect to d, so no an extra mode. This emerges at fixed frequency, i.e., ϳ428
signal comes from the substrate. Reference fully relaxed ϳ1 cmϪ1 , and appears to be TO–LO degenerate ͑see the upper
␮m thick ͑001͒ Zn1Ϫx Bex Te layers with xϭ4% and 14% are spectra in Fig. 2͒. In the sample with xϭ0.035 the LO-like
grown by MBE on a GaInAs buffer lattice matched to InP. component of the extra mode is large enough for reliable
Raman analysis is performed in geometries ͑1͒ and ͑2͒ with analysis of the symmetry ͑inset in Fig. 2͒. The usual LOGa–N
nonresonant 647.1 nm Arϩ excitation, which is relevant at mode and the extra mode undergo similar extinction with
low x. 8 respect to the polarization-insensitive 2ϫGa-As bands3 when
The spectra in geometry ͑1͒ obtained with GaAs1Ϫx Nx changing from the z(x,y)z LO-activated ͑labeled 1͒ to the
¯
are shown in Fig. 1. Due to small x, and to the small mass of z(x,x)z¯ LO-extinct ͑labeled 1͒ polarized setups. The same
N in comparison with As, in a ratio of 1:5, Ga–N bonds holds true for the Be reference.7,8 This establishes that the
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3. 2810 Appl. Phys. Lett., Vol. 82, No. 17, 28 April 2003 `
Pages et al.
FIG. 3. Geometry ͑1͒ ͑LO, inset͒ and ͑2͒ ͑TO͒ Raman spectra of
FIG. 2. Geometry ͑1͒ ͑LO͒ and ͑2͒ ͑TO͒ Raman spectra of GaAs1Ϫx Nx Zn1Ϫx Bex Te obtained by off-resonant 647.1 nm excitation. The calculated
obtained by resonant 623.8 nm excitation. The calculated TO multimodes BeTe-like TO multimodes are shown by thin lines. The Ber values derived
are shown by thin lines. The Nr values derived are indicated. The z(x,y)z ¯
are indicated. The two LO modes calculated at xϭ0.04 by taking
LO-activated ͑1͒ and z(x,x)z LO-extinct ͑1Ј͒ polarized spectra at xϭ0.035
¯
C Be–TeϭϪ0.2 are shown in the inset. I R and ␻ are notations for the Raman
are shown in the inset. I R and ␻ are notations for the Raman intensity and intensity and wave number.
wave number.
reference, for example. The TO spectra in the Be–Te range
extra mode observed in geometry ͑1͒ can be safely regarded for xϭ4% and 14% are shown in Fig. 3. The h and s modes
as a true LO mode with regard to the symmetry, which ex- appear at ϳ386 and ϳ415 cmϪ1 , respectively. The optical
cludes activation by structural disorder. Incidentally this band of BeTe is 461–503 cmϪ1 , 8 which gives R. C Be–Te is
helps to decide about point ͑i͒. In summary, the extra mode estimated to be Ϫ0.2 via the same procedure as that above,
at ϳ428 cmϪ1 depicts an intrinsic feature, which satisfies S
i.e., from the strength of the LOZn–Te /LOBe–Te ratio at xϭ4%,
points ͑i͒ and ͑ii͒ in the h-mode picture above. ͑inset in Fig. 3͒. The Ber rates derived from contour model-
The number of Ga–N bonds in the H domains, i.e., the ing of the TO multimodes at xϭ4% and 14% are 0.04 and
Nr rate, is directly derived from the amount of sharing of 0.15, respectively. Identical values are found for ZnBeSe.
GaN-like oscillator strength (R) and Faust–Henry coeffi- Even the latter value is much smaller than the GaAsN one
cient (C) between the two kinds of Ga–N bonds in the TO although it corresponds to a much larger substitution, as ex-
multimode cross section. R is fixed by the optical band in pected.
cubic GaN, i.e., ϳ555–740 cmϪ1 . The most recent estimate We have shown by using a nonstandard TO-like Raman
of C of Ϫ3.8 refers to hexagonal GaN.14 This might differ setup that the percolation picture used for basic understand-
from the value used with the present Ga–N bonds dispersed ing of atypical Raman multimodes in Be-chalcogenide al-
in a GaAs-like zinc blende lattice. Therefore C is derived loys, with contrast in the shear modulus, basically applies to
from the balance of strength between the LOGa–As and GaN–GaAs mixed crystals, with contrast in the bulk modu-
S
LOGa–N modes at xϭ0.03, corresponding to quasisymmetric lus. This allows one to discriminate between the signals from
broadening of the Ga–As mode and still significant Ga–N N-poor and N-rich regions in GaAsN ͑Nϳ3%– 4%͒. The
signal. Fair contour modeling is obtained by taking CϳϪ1.5 number of N atoms in the latter domains is derived from the
͑solid line in Fig. 1͒. Slight misestimation due to possible balance of strength via curve fitting of the TO multimodes.
s
disorder activation of the theoretically forbidden TOGa–N We find a value of ϳ30% which is much larger than the
mode close to the allowed-LO mode has basically no influ- corresponding Be rate of ϳ4% in random Be-based alloys.
ence on the final Nr value ͑see below͒. Finally R and C are
injected in the TO multimode cross section, and Nr is ad- J. Neugebauer and C. G. Van De Walle, Phys. Rev. B 51, 10568 ͑1995͒.
1
2
justed so as to mirror the balance of strength between the h- D. J. Friedman, J. F. Geisz, S. R. Kurtz, and J. M. Olson, J. Cryst. Growth
and s-like Ga–N modes. The best fits are shown in Fig. 2. A 195, 409 ͑1998͒.
3
A. M. Mintairov, P. A. Blagnov, V. G. Melehin, N. N. Faleev, J. L. Merz,
typical Nr rate is ϳ30% at xϳ3%– 4%. We want to mention Y. Qiu, S. A. Nikishin, and H. Temkin, Phys. Rev. B 56, 15836 ͑1997͒.
that Nr varies less than 5% when C assumes a value of Ϫ3.8. 4
T. Prokofieva, T. Sauncy, M. Seon, M. Holtz, Y. Qiu, S. Nikishin, and H.
Also, we have checked that the balance of strength between Temkin, Appl. Phys. Lett. 73, 1409 ͑1998͒.
5
the h and s modes is stable with resonant ͑632.8 nm͒ and ¨
J. Wagner, T. Geppert, K. Kohler, P. Ganser, and N. Herres, J. Appl. Phys.
90, 5027 ͑2001͒.
off-resonant ͑514.5 nm͒ excitations; only the signal-to-noise 6
M. J. Seong, M. C. Hanna, and A. Mascarenhas, Appl. Phys. Lett. 79,
ratio varies. Therefore Nr misestimation due to possible 3974 ͑2001͒.
7
¨
parasitical resonance-induced Frohlich scattering by LO ` ´
O. Pages, M. Ajjoun, D. Bormann, C. Chauvet, E. Tournie, and J. P.
modes from the ͑110͒ side face is excluded. The key point is
5 Faurie, Phys. Rev. B 65, 35213 ͑2002͒.
8 `
O. Pages, T. Tite, D. Bormann, O. Maksimov, and M. C. Tamargo, Appl.
that while the structural quality degrades with an increase of Phys. Lett. 80, 3081 ͑2002͒.
x ͑refer to L values in Fig. 1͒, Nr remains quasistable. Our 9
L. Bellaiche, S.-H. Wei, and A. Zunger, Phys. Rev. B 54, 17568 ͑1996͒.
10
Nr estimate can therefore be taken as chiefly representative S. Kurtz, J. Webb, L. Gedvilas, D. Friedman, J. Geisz, J. Olson, R. King,
D. Joslin, and N. Karam, Appl. Phys. Lett. 78, 748 ͑2001͒.
of intrinsic nonrandom N substitution, in spite of the poor 11 ` ´
O. Pages, M. Ajjoun, D. Bormann, C. Chauvet, E. Tournie, J. P. Faurie,
structural quality. and O. Gorochov, J. Appl. Phys. 91, 43211 ͑2002͒.
Let us compare with the corresponding Ber rate in 12
R. Srnanek, A. Vincze, J. Kovac, I. Gregora, D. S. Mc Phail, and V.
Zn–Be chalcogenides. Here the atomic substitution is truly Gottschalch, Mater. Sci. Eng., B 91, 87 ͑2002͒.
13
H. M. Cheong, Y. Zhang, A. Mascarenhas, and J. F. Geisz, Phys. Rev. B
random since the x c value detected with good accuracy from 61, 13687 ͑2000͒.
vibrational singularities7,8 coincides with the theoretical one 14
F. Demangeot, J. Frandon, M. A. Renucci, N. Grandjean, B. Beaumont, J.
calculated on a random basis.9 Let us take Zn1Ϫx Bex Te as a Massies, and P. Gibart, Solid State Commun. 106, 491 ͑1998͒.
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