Giant LO oscillation in the Zn1yxBex(Se,Te) multi-phonons percolative alloys
Thin Solid Films 450 (2004) 195–1980040-6090/04/$ - see front matter ᮊ 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.tsf.2003.10.071Giant LO oscillation in the Zn Be (Se,Te) multi-phonons percolative1yx xalloysT. Tite , O. Pages *, M. Ajjoun , J.P. Laurenti , O. Gorochov , E. Tournie , O. Maksimov ,a a, a a b c d` ´M.C. TamargodInstitut de Physique, 1 Bd. Arago, 57078 Metz, FranceaLPSC, 1 Place A. Briand, 92195 Meudon, FrancebCRHEA, Rue Gregory, 06560 Valbonne, FrancecCity College of New York, New York, NY 10031, USAdAbstractWe enrich a percolation-based picture for the basic understanding of the atypical two-modes behavior observed by Ramanscattering in the Be-VI optical range of Zn Be (Se,Te) alloys, with contrast in the bond stiffness. The attention is focused on1yx xthe longitudinal optical (LO) Be-VI spectral region within the percolation regime (0.19-x-0.81). Three apparent anomalies arediscussed. First the low-frequency component is systematically overdamped. Also, the high-frequency component exhibits amarked red-asymmetry which goes with an apparent blue-shift with respect to the theoretical predictions derived on a conventionalone-bondlone-mode basis. All three apparent anomalies are accounted for by considering a discrete multi-mode description foreach of the low- and high-frequency Be-VI components. They basically arise from inter- and intra-component transfer of oscillatorstrength resulting in the building up of a quasi-unique giant LO oscillation. The transfer comes from coupling via the commonLO macroscopic polarization field.ᮊ 2003 Elsevier B.V. All rights reserved.Keywords: ZnBe(Se,Te); Percolation phenomena; Multi-mode behavior; Raman1. IntroductionWide band-gap Be-chalcogenides have recentlyattracted considerable attention because they exhibit alarge amount of covalent bonding w1x, which is quiteunique among II–VI semiconductor materials. Thisresults 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, whichfinds direct expression in a remarkably high shearmodulus C *. Values of 0.478 and 0.510 were estimatedSin BeSe and BeTe, respectively, i.e. roughly twice thevalues for ZnSe (0.277) and ZnTe (0.319) w2x. Preciselythe main aim of Be incorporation in ZnSe and ZnTe isto strengthen latter highly ionic lattices, with concomi-tant impact on defect generation and propagation, andthereby device lifetime.*Corresponding author. Tel.: q33-3-8731-5873; fax: q33-3-8731-5801.E-mail address: firstname.lastname@example.org (O. Pages).`However, it is feared that besides chemical disorderthe sharp contrast between the stiffness of the covalent-like Be-VI and the other ionic-like Zn-VI bonds resultsin a large-scale mechanical disorder in theZn Be (Se,Te) alloys when x goes above the critical1yx xvalues associated with the first formation of pseudo-continuous wall-to-wall chains of the Be-VI and Zn-VIbonds. These are defined as the bond percolation thresh-olds, and are estimated at x s0.19 and x s0.81Be-VI Zn-VIin zinc-blende systems from computer simulations basedon random atomic substitution w3x. Vibrational spectro-scopy is the first choice technique for investigation ofsuch percolation effects because it addresses directly theforce constant of the bonds, which is highly sensitive tothe mechanical properties of the host matrix.Previous Raman studies w4,5x of transverse (TO) andlongitudinal (LO) optical modes have shown that withinthe percolation regime the Zn Be (Se,Te) alloys can1yx xbe described in terms of composite systems mainlymade of two interlaced pseudo-continuous sub-matrices:a Be-rich region with relatively large stiffness coeffi-
196 T. Tite et al. / Thin Solid Films 450 (2004) 195–198cient, and a relatively soft Zn-rich region. A pertinentmacroscopic marker for this percolation effect is theactivation of a specific two-mode behavior for the Be-VI bonding. Our view is that due to the differentmechanical properties of the two host media, the Be-VIbonds should vibrate at two separate frequencies, pro-viding thereby distinct Be-VI modes from the Be-richhard-like region (h) and the Zn-rich soft-like one (s).More precisely, the former Be-VI bonds in h-regionundergo a larger internal tensile strain to match thesurrounding lattice parameter than those dispersed withinthe much softer ZnVI-like host s-matrix. Accordinglythe low- and high-frequency Be-VI modes, labelled withsuperscript ‘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-richh-region basically expands while the Zn-rich one shrinksat increasing Be-content. Accordingly the TO modehgrows at the cost of the TO mode; they have identicalsintensities at x;0.5. In contrast the LO yLO strengthh sratio remains invariant when x varies, apparently due tosystematic overdamping of the LO mode (i). As ahmore refined effect we observe an unexplained red-asymmetry (ii) of the LO mode in the percolationsregime. Interestingly this reduces when x enlarges w4x.In earlier work, TO- and LO-multi-mode lineshapeswere modelled by using separate dielectric functions forthe h- and s-regions, i.e. by considering the overallRaman signal as the simple addition of the contributionsfrom the two regions, weighted by their relative scatter-ing volume. This model provided a reasonable agree-ment with experimental TO lines only; in LO symmetryneither point (i) nor point (ii) could be explained. Asan additional puzzling behavior we observe that (iii),within the percolation regime the LO -mode appears atsmuch higher frequency than is predicted. This is referredas the apparent blue-shift of the LO line.sIn this work our attention is focused on LO modes inthe percolation regime (0.19-x-0.81), in search ofpossible explanations for the puzzling behaviors (i)–(iii). First, care is taken to verify that these apparentLO-anomalies are intrinsic in character. One decisiveimprovement is to consider a single dielectric functionfor our composite alloys. Also, contour modelling ofthe LO lineshapes requires multi-mode description foreach of the h-and s-signals. Basically the apparent LO-anomalies would result from inter- and intra-couplingbetween the s- and h-series of elementary LO modesvia their common macroscopic polarization field. Similareffect is not expected for TO modes as they do notcarry any macroscopic polarization.2. ExperimentWe use ;1 mm-thick (0 0 1) Zn Be Te and1yx xZn Be Se layers with x(0.5 grown by molecular1yx xbeam epitaxy on GaInAs buffer layers lattice-matchedwith the underlying InP substrates and on GaAs, respec-tively. The Raman spectra are recorded in backscatteringgeometry along either the conventional w0 0 1x-growthor the non-standard w1 1 0x-edge crystal axis. The firstgeometry (I) is LO-allowed and TO-forbidden; thesituation is reversed in the second geometry (II). TheDilor microprobe set-up was used since high spatialresolution was needed for geometry II. All the spectrawere recorded, at room temperature by using the 514.5-nm excitation.3. Results and discussionOne key question is to decide whether the apparentLO-anomalies (i–iii) are intrinsic or not. Let us considerthe representative TO and LO data at xs0.50, inZnBeTe. The typical mechanisms responsible for thebuilding 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 layersappear fully relaxed in the percolation regime by high-resolution X-ray diffraction. Internal strain due to themechanical disorder at the interface between the S andH interlaced pseudocontinua, is also excluded becausein this case the asymmetry will be maximum at xs0.5,corresponding to the closest intermixing of the tworegions, in contradiction with our experimental findingsw4x.Major disorder-induced effects concern the activationof theoretically-forbidden symmetry-insensitive zone-edge modes. This is ruled out because ideal selectionrules are observed. Minor disorder effects typicallyrelated to topological disorder concern lineshape asym-metry of allowed modes. They are currently treated viathe 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 antagonistsblue-shift (iii), which is not compatible with an SCMapproach. Additional support to exclude SCM is that itcurrently fails to describe low-energy asymmetries aslarge as 30 cm .y1At last fluctuations in the composition may ariseduring the growth process, i.e. when the layer thicknessincreases. Decisive insight upon latter point arises fromdetailed Raman analysis in geometry I, along the;(0 0 1)-slope of several bevelled Zn Be Te samples.1yx xThe results at xs0.5 are shown in the insert of Fig. 1.Neither the lineshape of LO modes nor the asymmetryparameter G yG (ratio between the widths at high-A Band low-frequency sides) change significantly from theinterface to the surface. In addition, the inertia of theLO Be–Te mode, highly sensitive to x-variations, indi-scates negligible x-fluctuations when the ZnBeTe layergrows.
197T. Tite et al. / Thin Solid Films 450 (2004) 195–198Fig. 1. Raman spectra of a Zn Be Te epitaxial layer above the per-0.5 0.5colation threshold, using the TO-allowed and LO-allowed backscat-tering geometries as schematically indicated. The correspondingtheoretical 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 0.5Identical decompositions of eight elementary modes per 1 cm (a)y1and 3 cm (b) are considered for the h- and s-series. The corre-y1sponding two-mode predictions are shown as dotted lines, forcomparison.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 theHon and Faust formalism w7x to the equations of motionand polarization given by the modified-random-elementisodisplacement model w8x, which is the standarddescription for the long wavelength two-mode AC- andBC-like phonons in A B C alloys. Only the LO mode1yx xis accompanied by a macroscopic polarization due tothe ionic nature of the bond. This is responsible for theTO–LO splitting, which gives the oscillator strength Sof the bond; and also for an additional Frohlich-like¨scattering mechanism for LO modes. The interferencewith the TO-like deformation potential mechanism isfixed the Faust–Henry coefficient C. For a given bondin the alloy S and C scale linearly with respect to thebulk values, when the volume fraction of this bondvaries. Further three-modes ((Zn-VI, (Be-VI) , (Be-sVI) ) extension is derived by adding one oscillator inhthe mechanical equations. The key question is then toestimate at a given composition x the proportion p ofBe-VI bonds within the h-region for example. OurZnBe(Se,Te) alloys are random in character since thepercolation threshold observed from Raman singularitiescoincide with the theoretical predictions derived on abasis of a random substitution. Simple considerationsguarantee p;0.5 at x;0.5 because the h- and s-regionshave identical volumes. Also p;0 at x;0, since thehost matrix is all ZnVI-like at this limit, i.e. soft-like incharacter. At last p;1 at x;1 since the alloy turns intoa full h-matrix. The simplest generalization is p;x. Thetheoretical TO lineshapes derived on this basis are ingood agreement with the experimental data, as shownin the body of Fig. 1 for the representative compositionxs0.5. The LO curve derived on the above TO-basis isalso shown. The LO overdamping is well-reproduced.hThis is valid throughout the whole percolation regime.Somewhat surprisingly the frequency ranges coveredby the experimental LO line and the corresponding TO-sbased prediction do coincide. More precisely they aretied up at the same ends. This strongly suggests that themarked red-energy asymmetry of the s-line can beregarded as a blue-shift of the experimental line withrespect to the single-mode prediction, i.e. the result of a‘transfer’ of oscillator strength from the lower towardsthe upper end of the frequency domain that the modecovers. The notion of transfer basically supposes a multi-mode description for the s-component, namely a decom-position into a collection of elementary modes withdifferent frequencies. Similar ‘transfer’ was already sug-gested by Brafman and Manor w9x. The key point is thatthey suppose a continuous collection of frequencies,resulting from local x-fluctuations.Simulations of the multi-mode BeVI-like TO and LORaman responses from Zn Be Se assuming a collec-0.5 0.5tion of eight elementary modes for the h- and s-series,are presented in Fig. 2a. The frequencies are close so asto mimic continuity. The three-modes ((Zn–Se), (Be–Se) , (Be–Se) ) are also shown (dotted lines), forh scomparison.
198 T. Tite et al. / Thin Solid Films 450 (2004) 195–198Fig. 3. Raman spectra of Zn Be Se epitaxial layers below and just1yx xabove the percolation threshold in the LO-allowed backscatteringgeometry. The corresponding theoretical curves are superimposed assolid line.The multi- (plain line) and three-mode (dotted line)TO descriptions are equivalent, as expected. Indeed theelementary TO modes do not couple, as they do notcarry any macroscopic polarization. In contrast, in eachof the LO and LO components the whole oscillatorh sstrength is channeled into a single giant oscillation. Thekey point is that this is blue-shifted with respect to thesingle-mode predictions, which accounts for (iii). Ourview is that LO overdamping, i.e. (i), results from ahsimilar h™s inter-component transfer of oscillatorstrength, which mirrors the h and s intra-componenttransfers.The LO red-asymmetry, i.e. (ii), suggests incompletestransfer. Basically more separate are the energies of theelementary LO modes, the weaker should be the LO-coupling. On this basis let us try a discrete rather thanquasi-continuous multi-mode decomposition of the s andh. We take the same number of elementary modes butwe increase the spacing from 3 to 10 cm , so that they1density of mode decreases. As shown in Fig. 2b, theLO overdamping as well as the apparent blue-shift andhred-asymmetry of LO are eventually accounted for. Onesremaining matter then is to determine the proper numberof modes to use in each of the s- and h-series. Onepossible support is the model of clustering developedby Verleur and Barker w10x. This is under currentinvestigation.Clearly we observe in Fig. 3 that the red-asymmetryand the blue-shift on the LO -mode appear only abovesthe percolation threshold (xs0.19), i.e. when both thes- and h-regions have a fractal geometry. Therefore, thediscrete multi-mode approach seems inherent to thecomplexity in the alloy mesostructure.4. ConclusionIn this work we enrich a percolation-based picture forthe basic understanding of the atypical two-modesbehavior observed by Raman scattering in the BeVIoptical range of Zn–Be chalcogenide alloys, which openthe 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 ofthe LO -mode, and red-asymmetry plus blue-shift of thehLO -mode. All are checked to be intrinsic. We showsthat they can be accounted for by using a discrete multi-mode approach, for each of the s and h modes. Wesuggest that they arise from inter- and intra-mode trans-fer of oscillators strength. Mediated by the LO macro-scopic polarization. Multi-mode description is requiredonly in the percolation regime, and appears therebyintimately related to topological complexity at the localscale.Referencesw1x C. Verie, in: B. Gil, R.L. Aulombard (Eds.), Semiconductors´ ´Heteroepitaxy, World Scientific, Singapore, 1995, p. 73.w2x R.M. Martin, Phys. Rev. B 1 (1970) 4005.w3x D. Stauffer, Introduction to Percolation Theory, Taylor andFrancis, London, 1985, p. 17.w4x O. Pages, M. Ajjoun, D. Bormann, C. Chauvet, E. Tournie,` ´J.P. Faurie, Phys. Rev. B 65 (2001) 35213.w5x O. Pages, T. Tite, D. Bormann, O. Maksimov, M.C. Tamargo,`Appl. Phys. Lett. 80 (17) (2002) 3081.w6x H. Richter, Z.P. Wang, L. Ley, Solid State Commun. 39 (1981)625.w7x D.T. Hon, W.L. Faust, Appl. Phys. 1 (1973) 241.w8x I.F. Chang, S.S. Mitra, Phys. Rev. 149 (1966) 715.w9x O. Brafman, R. Manor, Phys. Rev. B 51 (1995) 6940.w10x H.W. Verleur, A.S. Barker, Phys. Rev. 149 (1966) 715.