Thin Solid Films 450 (2004) 195–198

1. Thin Solid Films 450 (2004) 195–198
0040-6090/04/$ - see front matter ᮊ 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2003.10.071
Giant LO oscillation in the Zn Be (Se,Te) multi-phonons percolative1yx x
alloys
T. Tite , O. Pages *, M. Ajjoun , J.P. Laurenti , O. Gorochov , E. Tournie , O. Maksimov ,a a, a a b c d
` ´
M.C. Tamargod
Institut de Physique, 1 Bd. Arago, 57078 Metz, Francea
LPSC, 1 Place A. Briand, 92195 Meudon, Franceb
CRHEA, Rue Gregory, 06560 Valbonne, Francec
City College of New York, New York, NY 10031, USAd
Abstract
We enrich a percolation-based picture for the basic understanding of the atypical two-modes behavior observed by Raman
scattering in the Be-VI optical range of Zn Be (Se,Te) alloys, with contrast in the bond stiffness. The attention is focused on1yx x
the longitudinal optical (LO) Be-VI spectral region within the percolation regime (0.19-x-0.81). Three apparent anomalies are
discussed. First the low-frequency component is systematically overdamped. Also, the high-frequency component exhibits a
marked red-asymmetry which goes with an apparent blue-shift with respect to the theoretical predictions derived on a conventional
one-bondlone-mode basis. All three apparent anomalies are accounted for by considering a discrete multi-mode description for
each of the low- and high-frequency Be-VI components. They basically arise from inter- and intra-component transfer of oscillator
strength resulting in the building up of a quasi-unique giant LO oscillation. The transfer comes from coupling via the common
LO macroscopic polarization field.
ᮊ 2003 Elsevier B.V. All rights reserved.
Keywords: ZnBe(Se,Te); Percolation phenomena; Multi-mode behavior; Raman
1. Introduction
Wide band-gap Be-chalcogenides have recently
attracted considerable attention because they exhibit a
large amount of covalent bonding w1x, which is quite
unique among II–VI semiconductor materials. This
results in a reduced lattice parameter from 6.103 A for˚
ZnTe and 5.669 A for ZnSe down to 5.626 A for BeTe˚ ˚
and 5.037 A for BeSe. More important the covalent˚
character corresponds to increased bond stiffness, which
finds direct expression in a remarkably high shear
modulus C *. Values of 0.478 and 0.510 were estimatedS
in BeSe and BeTe, respectively, i.e. roughly twice the
values for ZnSe (0.277) and ZnTe (0.319) w2x. Precisely
the main aim of Be incorporation in ZnSe and ZnTe is
to strengthen latter highly ionic lattices, with concomi-
tant impact on defect generation and propagation, and
thereby device lifetime.
*Corresponding author. Tel.: q33-3-8731-5873; fax: q33-3-8731-
5801.
E-mail address: pages@sciences.univ-metz.fr (O. Pages).`
However, it is feared that besides chemical disorder
the sharp contrast between the stiffness of the covalent-
like Be-VI and the other ionic-like Zn-VI bonds results
in a large-scale mechanical disorder in the
Zn Be (Se,Te) alloys when x goes above the critical1yx x
values associated with the first formation of pseudo-
continuous wall-to-wall chains of the Be-VI and Zn-VI
bonds. These are defined as the bond percolation thresh-
olds, and are estimated at x s0.19 and x s0.81Be-VI Zn-VI
in zinc-blende systems from computer simulations based
on random atomic substitution w3x. Vibrational spectro-
scopy is the first choice technique for investigation of
such percolation effects because it addresses directly the
force constant of the bonds, which is highly sensitive to
the mechanical properties of the host matrix.
Previous Raman studies w4,5x of transverse (TO) and
longitudinal (LO) optical modes have shown that within
the percolation regime the Zn Be (Se,Te) alloys can1yx x
be described in terms of composite systems mainly
made of two interlaced pseudo-continuous sub-matrices:
a Be-rich region with relatively large stiffness coeffi-

2. 196 T. Tite et al. / Thin Solid Films 450 (2004) 195–198
cient, and a relatively soft Zn-rich region. A pertinent
macroscopic marker for this percolation effect is the
activation of a specific two-mode behavior for the Be-
VI bonding. Our view is that due to the different
mechanical properties of the two host media, the Be-VI
bonds should vibrate at two separate frequencies, pro-
viding thereby distinct Be-VI modes from the Be-rich
hard-like region (h) and the Zn-rich soft-like one (s).
More precisely, the former Be-VI bonds in h-region
undergo a larger internal tensile strain to match the
surrounding lattice parameter than those dispersed within
the much softer ZnVI-like host s-matrix. Accordingly
the low- and high-frequency Be-VI modes, labelled with
superscript ‘h’ and ‘s’ in the following, refer to the Be-
VI vibrations within the h- and s-regions, respectively.
Regarding the strength aspect we notice that the Be-rich
h-region basically expands while the Zn-rich one shrinks
at increasing Be-content. Accordingly the TO modeh
grows at the cost of the TO mode; they have identicals
intensities at x;0.5. In contrast the LO yLO strengthh s
ratio remains invariant when x varies, apparently due to
systematic overdamping of the LO mode (i). As ah
more refined effect we observe an unexplained red-
asymmetry (ii) of the LO mode in the percolations
regime. Interestingly this reduces when x enlarges w4x.
In earlier work, TO- and LO-multi-mode lineshapes
were modelled by using separate dielectric functions for
the h- and s-regions, i.e. by considering the overall
Raman signal as the simple addition of the contributions
from the two regions, weighted by their relative scatter-
ing volume. This model provided a reasonable agree-
ment with experimental TO lines only; in LO symmetry
neither point (i) nor point (ii) could be explained. As
an additional puzzling behavior we observe that (iii),
within the percolation regime the LO -mode appears ats
much higher frequency than is predicted. This is referred
as the apparent blue-shift of the LO line.s
In this work our attention is focused on LO modes in
the percolation regime (0.19-x-0.81), in search of
possible explanations for the puzzling behaviors (i)–
(iii). First, care is taken to verify that these apparent
LO-anomalies are intrinsic in character. One decisive
improvement is to consider a single dielectric function
for our composite alloys. Also, contour modelling of
the LO lineshapes requires multi-mode description for
each of the h-and s-signals. Basically the apparent LO-
anomalies would result from inter- and intra-coupling
between the s- and h-series of elementary LO modes
via their common macroscopic polarization field. Similar
effect is not expected for TO modes as they do not
carry any macroscopic polarization.
2. Experiment
We use ;1 mm-thick (0 0 1) Zn Be Te and1yx x
Zn Be Se layers with x(0.5 grown by molecular1yx x
beam epitaxy on GaInAs buffer layers lattice-matched
with the underlying InP substrates and on GaAs, respec-
tively. The Raman spectra are recorded in backscattering
geometry along either the conventional w0 0 1x-growth
or the non-standard w1 1 0x-edge crystal axis. The first
geometry (I) is LO-allowed and TO-forbidden; the
situation is reversed in the second geometry (II). The
Dilor microprobe set-up was used since high spatial
resolution was needed for geometry II. All the spectra
were recorded, at room temperature by using the 514.5-
nm excitation.
3. Results and discussion
One key question is to decide whether the apparent
LO-anomalies (i–iii) are intrinsic or not. Let us consider
the representative TO and LO data at xs0.50, in
ZnBeTe. The typical mechanisms responsible for the
building of a LO red-asymmetry are strain effects,
disorder effects and fluctuations in the composition.
External strain due to a lattice-mismatch at the sub-
strateylayer interface is excluded since our thick layers
appear fully relaxed in the percolation regime by high-
resolution X-ray diffraction. Internal strain due to the
mechanical disorder at the interface between the S and
H interlaced pseudocontinua, is also excluded because
in this case the asymmetry will be maximum at xs0.5,
corresponding to the closest intermixing of the two
regions, in contradiction with our experimental findings
w4x.
Major disorder-induced effects concern the activation
of theoretically-forbidden symmetry-insensitive zone-
edge modes. This is ruled out because ideal selection
rules are observed. Minor disorder effects typically
related to topological disorder concern lineshape asym-
metry of allowed modes. They are currently treated via
the well-known spatial correlation model (SCM) w6x.
However, one key point in our case is that the red-
asymmetry of the LO line (ii) goes with an antagonists
blue-shift (iii), which is not compatible with an SCM
approach. Additional support to exclude SCM is that it
currently fails to describe low-energy asymmetries as
large as 30 cm .y1
At last fluctuations in the composition may arise
during the growth process, i.e. when the layer thickness
increases. Decisive insight upon latter point arises from
detailed Raman analysis in geometry I, along the
;(0 0 1)-slope of several bevelled Zn Be Te samples.1yx x
The results at xs0.5 are shown in the insert of Fig. 1.
Neither the lineshape of LO modes nor the asymmetry
parameter G yG (ratio between the widths at high-A B
and low-frequency sides) change significantly from the
interface to the surface. In addition, the inertia of the
LO Be–Te mode, highly sensitive to x-variations, indi-s
cates negligible x-fluctuations when the ZnBeTe layer
grows.

3. 197T. Tite et al. / Thin Solid Films 450 (2004) 195–198
Fig. 1. Raman spectra of a Zn Be Te epitaxial layer above the per-0.5 0.5
colation threshold, using the TO-allowed and LO-allowed backscat-
tering geometries as schematically indicated. The corresponding
theoretical curves in solid line are superimposed for comparison.
Microprobe scanning along a bevelled face is shown in insert.
Fig. 2. Simulations of the multi-mode TO (bottom) and LO (top)
Raman responses from Zn Be Se in the Be–Se spectral region.0.5 0.5
Identical decompositions of eight elementary modes per 1 cm (a)y1
and 3 cm (b) are considered for the h- and s-series. The corre-y1
sponding two-mode predictions are shown as dotted lines, for
comparison.
The whole of this indicates that the apparent LO-
anomalies (i)–(iii) in the percolation regime are intrin-
sic. Recently, we have proposed an extension of the
Hon and Faust formalism w7x to the equations of motion
and polarization given by the modified-random-element
isodisplacement model w8x, which is the standard
description for the long wavelength two-mode AC- and
BC-like phonons in A B C alloys. Only the LO mode1yx x
is accompanied by a macroscopic polarization due to
the ionic nature of the bond. This is responsible for the
TO–LO splitting, which gives the oscillator strength S
of the bond; and also for an additional Frohlich-like¨
scattering mechanism for LO modes. The interference
with the TO-like deformation potential mechanism is
fixed the Faust–Henry coefficient C. For a given bond
in the alloy S and C scale linearly with respect to the
bulk values, when the volume fraction of this bond
varies. Further three-modes ((Zn-VI, (Be-VI) , (Be-s
VI) ) extension is derived by adding one oscillator inh
the mechanical equations. The key question is then to
estimate at a given composition x the proportion p of
Be-VI bonds within the h-region for example. Our
ZnBe(Se,Te) alloys are random in character since the
percolation threshold observed from Raman singularities
coincide with the theoretical predictions derived on a
basis of a random substitution. Simple considerations
guarantee p;0.5 at x;0.5 because the h- and s-regions
have identical volumes. Also p;0 at x;0, since the
host matrix is all ZnVI-like at this limit, i.e. soft-like in
character. At last p;1 at x;1 since the alloy turns into
a full h-matrix. The simplest generalization is p;x. The
theoretical TO lineshapes derived on this basis are in
good agreement with the experimental data, as shown
in the body of Fig. 1 for the representative composition
xs0.5. The LO curve derived on the above TO-basis is
also shown. The LO overdamping is well-reproduced.h
This is valid throughout the whole percolation regime.
Somewhat surprisingly the frequency ranges covered
by the experimental LO line and the corresponding TO-s
based prediction do coincide. More precisely they are
tied up at the same ends. This strongly suggests that the
marked red-energy asymmetry of the s-line can be
regarded as a blue-shift of the experimental line with
respect to the single-mode prediction, i.e. the result of a
‘transfer’ of oscillator strength from the lower towards
the upper end of the frequency domain that the mode
covers. The notion of transfer basically supposes a multi-
mode description for the s-component, namely a decom-
position into a collection of elementary modes with
different frequencies. Similar ‘transfer’ was already sug-
gested by Brafman and Manor w9x. The key point is that
they suppose a continuous collection of frequencies,
resulting from local x-fluctuations.
Simulations of the multi-mode BeVI-like TO and LO
Raman responses from Zn Be Se assuming a collec-0.5 0.5
tion of eight elementary modes for the h- and s-series,
are presented in Fig. 2a. The frequencies are close so as
to mimic continuity. The three-modes ((Zn–Se), (Be–
Se) , (Be–Se) ) are also shown (dotted lines), forh s
comparison.

4. 198 T. Tite et al. / Thin Solid Films 450 (2004) 195–198
Fig. 3. Raman spectra of Zn Be Se epitaxial layers below and just1yx x
above the percolation threshold in the LO-allowed backscattering
geometry. The corresponding theoretical curves are superimposed as
solid line.
The multi- (plain line) and three-mode (dotted line)
TO descriptions are equivalent, as expected. Indeed the
elementary TO modes do not couple, as they do not
carry any macroscopic polarization. In contrast, in each
of the LO and LO components the whole oscillatorh s
strength is channeled into a single giant oscillation. The
key point is that this is blue-shifted with respect to the
single-mode predictions, which accounts for (iii). Our
view is that LO overdamping, i.e. (i), results from ah
similar h™s inter-component transfer of oscillator
strength, which mirrors the h and s intra-component
transfers.
The LO red-asymmetry, i.e. (ii), suggests incompletes
transfer. Basically more separate are the energies of the
elementary LO modes, the weaker should be the LO-
coupling. On this basis let us try a discrete rather than
quasi-continuous multi-mode decomposition of the s and
h. We take the same number of elementary modes but
we increase the spacing from 3 to 10 cm , so that they1
density of mode decreases. As shown in Fig. 2b, the
LO overdamping as well as the apparent blue-shift andh
red-asymmetry of LO are eventually accounted for. Ones
remaining matter then is to determine the proper number
of modes to use in each of the s- and h-series. One
possible support is the model of clustering developed
by Verleur and Barker w10x. This is under current
investigation.
Clearly we observe in Fig. 3 that the red-asymmetry
and the blue-shift on the LO -mode appear only aboves
the percolation threshold (xs0.19), i.e. when both the
s- and h-regions have a fractal geometry. Therefore, the
discrete multi-mode approach seems inherent to the
complexity in the alloy mesostructure.
4. Conclusion
In this work we enrich a percolation-based picture for
the basic understanding of the atypical two-modes
behavior observed by Raman scattering in the BeVI
optical range of Zn–Be chalcogenide alloys, which open
the class of mixed crystals with contrasted bond stiff-
ness. Special attention is awarded to the puzzling appar-
ent anomalies in the LO lineshapes, i.e. overdamping of
the LO -mode, and red-asymmetry plus blue-shift of theh
LO -mode. All are checked to be intrinsic. We shows
that they can be accounted for by using a discrete multi-
mode approach, for each of the s and h modes. We
suggest that they arise from inter- and intra-mode trans-
fer of oscillators strength. Mediated by the LO macro-
scopic polarization. Multi-mode description is required
only in the percolation regime, and appears thereby
intimately related to topological complexity at the local
scale.
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