Resonant Rayleigh scattering in quantum well structures

Resonant Rayleigh scattering in quantum well structures

Solid State Communications, Vol. 97, No. 5, pp. 389-394, 1996 Elsevier Science Ltd Printed in Great Britain 0038-1098196 $12.00+.00 Pergamon 0038-10...

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Solid State Communications, Vol. 97, No. 5, pp. 389-394, 1996 Elsevier Science Ltd Printed in Great Britain 0038-1098196 $12.00+.00


0038-1098(95)00663-X RESONANT



M. Gurioli, F. Bogani, A. Vinattieri, Department

of Physics,

of Applied Physics,


and M. Colocci

Unitb INFM and LENS, University liO125 Firenze, Italy

V. I. Belitsky, A. Cantarero, Department

9 May

of Florence, Lnrgo E. Fermi 2,

and S. T. Pavlov

University of Vufencia,

1995; accepted


22 August





1995 by E. Molinari)

We report continuous wave experiments on resonant Rayleigh scattering (RRS) performed on high quality GaAslAlGaAs quantum weil structures. The simultaneous measurement of the resonant Rayleigh scattering and of the photoluminescence excitation (PLE) allows us to resolve very small differences between the two spectra. We show that, even in very good samples, there is a small but detectable Stokes shift of the RRS profile with respect to the PLE. It is also found that the RRS profile has a smaller linewidth and is sensitive to bound exciton transitions which are not detectable in the PLE. We compare our data with previous findings and discuss possible origins of the Stokes shift.

It is well known that in optical experiments the elastic diffusion of light in the whole solid angle (or Rayleigh scattering (RS)) gives rise to an unwanted effect, to be minimized in order to resolve the signal. However, resonant excitation near the fundamental excitonic resonance results in a strong enhancement of the elastic light scattering1 (usually referred to as resonant Rayleigh scattering (RRS)) that, as shown more than ten years ago for quantum well (QW) heterostructures*t3, contains useful information on the optical properties of the samples. In fact, being the RRS related to the coherent polarization driven by the external field, it should provide a simple and powerful tool, at least in principle, for the optical investigation of the dephasing processes in solids. Moreover RRS is a linear technique and therefore simpler to realize, even if less direct, than the standard non-linear methods (four-wave mixing, hole burning, etc.) used for studying the coherence relaxation. Nevertheless, in spite also of the enormous quantity of optical studies of QWs, with tens of different experimental techniques reported in the last years, scarce attention has been devoted to RRS; only recently a revival of interest on RRS has been originated in connection with time-resolved experimzi&6. A tentative explanation for this can be retraced in the absence of a clear picture of the origin of RRS. Even within the few experimental data reIk)rted so far there are discrepancies from differen: groups. One of the most relevant is connected with the presence, or lack thereof, of a

low energy shift of the RRS profile with respect to th.2 absorption band. In fact in Ref.[2,31 this shift has bee;. correlated to the presence of a mobility edge, while in Ref.[4-61 its absence has been interpreted as a signature of the localized nature of all the excitonic states in real QWs. in this letter we present data on continuous wilve (cw) RRS experiments performed on extremely good GaAs/AlGaAs QW structures. Our data c!early show a difference between absorption and US. .4s a consequence of a simultaneous measurement of the RRS and of the photoluminescence excitation (PLE) we are able to show tn-t even in very good samples there is a smali but detectable Stokes shift (SS) of the RRS profile with respect to the PLE. Moreover we find in the RRS spectrum a low energy band corresponding to a bound exciton transition which is not detectable in the PLE. We compare our data with previous findings and discuss possible origins for the SS, showing the relevance of our results in the interpretation of the time-resolved experiments as well. Let us start with a brief qualitative analysis of the origin of RRS in QW heterostructures; a more detailed theory, including microscopic calculations, will be presented in a forthcoming paperT. Two typical scales of lengths are to be considered: (a) the spatial extension of the microscopic scattering center and (b) the coherence length of the macroscopic collection of these centers. The excitonic wavefunctions of an ideal crystal are 389



delocalized Bloch states; even considering the interaction with phonons the translational invariance is not destroyed and then the elementary excitations are still described by a well defined Kvector that produces only the transmitted and reflected beams and, at least to the lowest orde?, no Ra_vleigh scattering occurs at all. However in real samples the interaction with random potentials, due to impurity contamination or interface disorder, leads to a finite mean free path 3, the states maintain a propagating character, although with a reduced mobility due to the probability of scattering. For the case of localized states, K-conservation is relaxed and the radiation pattern of the scattered light will be related, through the Heisenberg’s uncertainty relation between position and momentum, to the spatial extension of the center of mass excitonic wavefunction. In summary, at least to the lowest orderg, only localized states can produce RRS and the fact that the scattered light from each individual center is more or less isotropic depends on the localization extension of the excitonic wavefunction. The scale length (b) must be considered in a real experiment because the sample is illuminated by a large spot (>>A) of coherent light. All the indiv:dunl scattering centers inside the excitation spot dre coherently excited and the macroscopic scattered signal comes out from the coherent sum of each individual scattered field. The macroscopic collection of the individual radiators strongly modifies the scattering pattern. Assuming, for instance, that all the individual radiators are identic.21 .lnd distributed in a regular lattice, the coherent sum exactly cancels the scattered signal, independently of the radiation pattern of the indivi*dl.ta! scattering center, except in the transmission and reflection directions (apart from diffraction due to the finite dimension of the excitation spot). As a matter of fact, a given amount of disorder is indeed necessary to produce elastic scattering in all directions. If only the spatial distribution of the scattering centers is random, at least to a certain degree, their density fluctuations produce Rayleigh scattering, as it is well known in sy..!cms like gases or liquids. On the other hand, RRS can also arise from a regular lattice of inhomogeneous scattering centers, that is with different transition energies. The inhomogeneous distrib:tion does not allow for a complete destructive interference in directions different from reflection and transmission. In real samples the spatidl and energy disorder are very often directly correlate,1 and a clear distinction between the two is not possible. However it can be shown that in the limit of large inhomogeneous broadening the spatiil distribution of the individual scattering cen?,.~rsis not relevant7.

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We have investigated two nominally undoped, G-?As/Alo,3Gao,7As single QWs, 120 and 180 8, thick, grown by molecular beam epitaxy on ti:;!oped substrates at a temperature of the order of 66’) “C The wells are separated by thick barriers (300 A) in order to decouple the carrier wavefunctions. The measurements have been perforil;cd using a cw Ar+ pumped Ti:Sapphire laser as excitation source; the excitation power used in all the measurements presented here was 0.1 W/cnt2. The scattering geometry was chosen so as to have incidence near the Brewster angle with the linear polarization of the incoming light in the incident plane, while the detection was normal to the sample surface; this choice reduces the intensity of t!le non-resonant Rayleigh scattering signal. The emitted signal was dispersed through a 60 cm double-gratmg monochromator (spectral resolution of 0.16 meV) and detected by standard photon colinting techniques. In Fig.1 we report a series of PL spectra of the 1801i QW obtained by scanning the CW excitation



1.527 Energy



Fig.1 Emission spectra of the 180 8, QW at TL=1.8 K for different excitation energies showing a resonant enhancement of the RS (hatched areas) when the excitation is tuned across the HH exciton band. The shoulder at low energy corresponds to a bound exciton transition.

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energy across the HH exciton transition at 1.8 I(; a’ similar behaviour is found in the case of the 120 A QW. The half width at half maximum of the PL and PLE lines turns out to be as small as - 0.22 meV and = 0.35 meV for the 180 A and 120 A QWs, respectively, that is, two among the smallest values ever reported in the literature. Beside the main peaks, the PL spectra show a shoulder on the low energy side, related to bound exciton recombination, that is enhanced when the laser frequency is tuned at resonance, in agreement with the the findings of Ref. [lo] and denoting an energy dependent capture process. The hatched peaks represent the contribution from RS, as easily recognized from the lineshape which reflects, as expected, the instrumental resolution. Very small contributions from RS are found outside the resonance region due to a careful choice of the point on the sample surface. On the other hand, a dramatic enhancement of the RS intensity is observed when the excitation approaches the HH exciton resonance, making the RS to dominate the optical spectra as soon as the excitation energy is nearlv resonant with the fundamental exciton transition. In the figure are also reported the scale factors of each spectra; note that the maximum of the RRS, corresponding to the profile with a unit scale factor, is red shifted with respect to the PL maximum. A series of spectra similar to the ones reported in Fig.1 has been performed by tuning the laser energy inside the excitonic resonance by steps of about 0.1 meV for both the 120 A and 180 A QWs. The measurement of the complete emission spectrum for each laser frequency allows a very accurate comparison of the PL, PLE and RRS proiiles. In fact the three spectra are acquired simultaneously, so as to avoid the standard problems connected with the calibration of the laser tuning and/or the spatial inhomogeneity of the samp!ec. Moreover the excitation spectrum of the PL is monitored simultaneously over the whole PL band. The separation of the RRS contribution from PL is rather simple due to their different lineshape: the XRS signal has a full width at half maximum (FW’rIM) of 0.16 meV while the PL FWHMs are larger by n factor 3 to 4. The results of the deconvolution of the two signals is reported in Fg.2 and Fig.3 for the 180 A and 120 A QW, respectively; in the figures the full lines are the RRS spectra, the dashed iines are the PLE spectra at the low energy side of the bound exciton shoulder, the dots are the PLE spectra of the main PL band and the arrows indicate the energy of the PL maxima We have chosen to report also the bound exciton PLE spectra bec:.use it is free from the deconvolution problem when the laser is exactly in resonance with the l’ree exciton, on one side, and because, on the other, we wanted to investigate the PLE profile for resonant exci tion at the bound exciton itself. It should be







3.t: cl .


s .



1.5265 Energy





Fig.2 Intensities of RRS (full line), PLE at the bound exciton emission (dashed line; E,,=1.5252 eV) and PLE at the PL maximum (dots; E,,=1.52692 eV1 as a function of the laser excitation energy in the case of the 180 A QW. The arrow marks the energy position of the PL maximum

noted that there are no major differences in the PLE profile at the two different emission wavelengths. The prcfiles reported in Figs.(2)-(3) clearly show that RRS is different from PLE, which is commonly assumed to reflect the absorption. In particular we

: ......--. PLE (1.5377




1.541 Energy





Fig.3 Intensities of RRS (full line), PLE at the bound exciton emission (dashed line; E,,=l.5377 eV1 and PLE at the PL maximum (dots; E,,=1.5423 eV) as a function of the laser excitation energy in the case of the 120 8, QW. The arrow marks the energy position of the PL maximum



note that there is a small but measurable Stokes shifi between the RRS and the PLE (0.3kO.05 meV and 0.18*0.03 meV for the 120 8, and 180 8, QW, respectively). It is worth stressing that only the simultaneous measurement of PLE and RRS allows US to be confident of the reliability of our experimental data. In this way, in fact, our resolution is much better than in standard experiments where the PL and PLE spectra are acquired separately and the main source of error is the laser calibration. As a matter of fact we have also found very small Stokes shifts between the PL and PLE spectra, of the order of 0.15 meV and 0.05 meV for the 120 A and 180 8, QW, respectively, values that are well below our experimental resolution in a previous work (- 0.3 meVl1). Finally, as noted when discussing Fig. 1, we found that the RRS spectrum is red shifted even with respect to the PL profile. Other important features can be extracted from the comparison of the RRS, PL and PLE. First of all, the RRS profile turns out to have a smaller linewidth than both the PL and PLE spectra; we find a FWHM of .35 meV and .55 meV for the RRS of the 180 8, and 120 8, QWs to be compared with 0.45 meV and 0.7 meV of the PL and PLE spectra. In addition to that, a low energy structure is found in the RRS profile, corresponding to the bound exciton transition, which, due to its extrinsic nature, is missing in the PLE curve, especially in the 180 8, QW. This last observation agrees with the findings of Ref.1121 where it was shown that RRS is sensitive to v clearly show that RRS and absorption derive from different mechanisms. We find a Stokes shift bc!ween RRS and PLE, a smaller FWHM of the RRS ;,,i!‘, rcapect to the PL and PLE profiles and in addition the presence of an extrinsic rf?SOnaIVX in

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RRS which can be resolved in PL but not in PLE. This phenomenology clearly demostrates that the RR: is selectively sensitive to the low energy tail of the .iSsorption band. As previously noted, similar findings have been already reported in the literature but differem conclusions have been drawn from the diCerent authorsl,lo. We believe that the difference b&ween absorption and RRS is associated with the diiierent nature of the two processes; the RRS derives from the coherent interaction of the medium with thp hght and is selectively sensitive to the localizeci states, while absorption is an incoherent process proportional to the optical density. This is an intrinsic feature, even if the quantitative diffei,er,t,e between the two spectra is obviously sample dependent. Let us now discuss the possible origin of the SS through a comparison with previous findings for the RRS in QWs. In the pioneering works of Heglrty et a1.2,3 a red shift of the RRS profile with respect to the absorption was found, in agreement with our results. The RR’Sdata were interpreted in the framework of a simple model based on the disorder in the energy distribution (i.e. inhomogeneous broadening). However the authors did not clearly point out the qualitative difference between localized and propagating excitonic states. It was assumed that all the excitonic states contribute to RRS and shown that the RRS profile corresponds to the absorption weighted by the ratio between the inhomogeneous broadening r, and the homogeneous broadening Th of the resonant transition2r3. Then the dispersion of l-h was estimated by comparing the measured RRS and absorption and, due to the presence of the SS, a sharp increase of l-h near the energy corresponding to the maximum absorption was found2,3. This was interpreted as a signature of the presence of a mobility edge near that energy since delocalized states are expected to have larger rh with respect to localized states. The authors concluded that below the ,&scrrption maximum the states are localized and dominate the RRS signal, while, above, the states are propagating and give only rise to a small col:tr;bution to RRS due to their large rh. The final statement by Hegarty et al. is substantially in agreement with our previous discussion: RRS comes from localized states. However, it is surprising that it has been derived a\xuming that both propagating and localized states can give rise to RRS through the same mechanism and that the only difference between these two kinus of states is the ratio rh/rx. Actually we believe rilat, at least at the lowest order, delocalized statps do not contribute to RRS because their microscopic radiation pattern is peaked around the reflectioil and transmission directions; therefore RRS essentially contains information on the homogeneous broadening l-h of the localized exciton states.

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A new generation of experiments for RR’S in QWs has been recently developed in connection with the time-resolved exciton dynamic&6. One of the main features of these experiments is the lack of an! Stokes shift between the RRS and absorption profiles, contrary to both ours and Hegarty’s et al. findings2J. In agreement with our previous statement that the RRS is originated from localized states, it was concluded13 that all the excitonic states in a real QW are localized due to the interface disorder and, consequently, that there is no mobility edge within the exciton absorption band. This fact allows the authors to use time-resolved RRS for extracting information on the dephasing time of the “intrinsic excitonic states” (i.e. corresponding to the energy of the maximum absorption) to which they refer to as free excitons4,5, even if they are, by assumption, localized statest3. Obviously there is a disagreement with the results of Hegarty et a1.2,3 and, in particular, with the presence of a Stokes shift as the signature of a mobility edge. It should be also noted that the samples investigated in Ref.[4,51 are of better quality than those used in Ref.[2,31. This argument could possibly be used for explaining the lack of SS in airalogy to the standard case when the PL spectra are compared to the PLE spectra. However our results in QWs of better quality than those so far investigatedI-5 contradict this argument. At the sa!lie time, following the picture of the SS as a signature of the presence of a mobility edge, one would expect exactly the opposite: only in good samples it is possible to have propagating states. We believe, indeed, that a possible explanation. of this disagreement lies in the fact that in good quality samples the SS can be so small that only a simultaneous measurement of both RR’S and I’LE can aliow for its reliable determination. Finally it has been also foundI that RRS is sensitive to bound exciton transitions which are not visible in absorption or reflection, in agreement with Iour findings. This necessarily implies that RRS enhances the extrinsic transitions with respect to the intrinsic resonances. According to the conclusions of Ref.[2,3] we



believe that the physical origin of the SS can be ascribed to the presence of a mobility edge between propagating and localized states. However this is not the only possible explanation; in fact, even if all the exciton states are localized as suggested in Ref.[lSj, we can still use the old picture of Hegarty et al. of the inhomogeneous broadening as the origii: o1 RRS if we assume that the SS reflects a dispersion of the homogeneous broadening of the loca!ized states. In fact the lower is the energy in the absorption tail the more localized is the corresponding state. At the same time, the more Gcaliied is the state the longer is the corresponding dephasing time, as predicted in Ref.[l4] and observed in CdSSe mixed crystals’5. These two pictures are not necessarily alternative; in principle both can contribute to explain the differences between RRS and absorption and we are not at the momzni able to determine which of the two plays a major role in QW structures. In fact, even if there are several papers claiming the observation of a mobility edge inside the excitonic absorption band in QWs on the basis of four wave mixing and hole burning experiments lh,17, they essentially report an increase of the dephasing rate inside the inhomogeneous absorption band, a result that, at least in principle, agrees with both the previous 1:yFothesis. In any case the main purpose of our work is to point out that RRS is selectively sensitive to the low energy tail of the absorption band, that is, to the more localized states. As a consequence, we believe !hat the information obtained from timeresolved RRS measurements is, a priori, different from what can be obtained from other experimental techni:tu?s like hole burning or four wave mixing, Achnowledgments - Work at LENS has been performed in the frame of a ECC contract GEr*CT92-0046. V. I. B. and S. T. P. thank the Europe Union, and Ministerio de Education y Ciencia de Espaiia and the Russian Fundamental Investigaticn Fund (93-02-2362) for financial support. This project has been supported by the Arione Integrata Dipartimento di Fisica, Universitd di Firenze/ Departament de Fisica Aplicada, Universitat de Valencia.


D. L. Huber, Phys. Rev. 170, 418 (1968); Phys. Rev. 178,93 (1969); Phys. Rev. B 1,3409 (1970). J-Hegarty, M.D.Sturge, C.Weisbuch, A.C.Gossard, and W.Wiegmann., Phys.Rev.L.ett. 49,930 (1982). J.Hegarty, L. Goldner, and M.D.Sturge, Phys. Rev. B 30,7346 (1984). H.Stolz, DSchwarze, W.von der Osten, and G.Weimann, Superlattices and Microstruct. 9, 511(1991). H.Stoiz, DSchwarze, W.von der Osten, and GWeimann, Phys.Rev. B 47,9669 (1993).


H. Stolz in T&e-Resolved Light Scattering from , Springer Tracts in Modern Physics, Volume 130 (Springer-Verlag, Berlin Heidelberg 1994). V. I. Belitsky, A. Cantarero, S. T. Pavlov, M. Gurioli, F. Bogani, A. Vinattieri, and M. Colocci, to be published N. F. Mott and E.A. Davies, Electronic Properties in Non-Crystalline Materials (Claredon Press, Oxford 1971). The elastic scattering by defects of the propagating exciton intermediate states in the Exiiton”






light scattering process indeed leads to RRS, but only at higher orders in the perturbation theory7. It is also found that the RRS from propagating exciton states goes to zero in both limits of weak and strong disorder 7. 10 J. Martinez-Pastor, A. Vinattieri, L. Carraresi, M. Cnlocci, Ph. Roussignol, and G. Weimann, Phys. Rev. B 47,10456 (1993). 11 ?4. Gurioli, A. Vinattieri, J. Martinez-Pastor, and i,:!. Colocci, Phys. Rev. B 50, 11817 (1994).

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I2 see Ref.[6] pages 173-175. t3 see Ref.[6] pages 169-170. l4 T. Tagakahara Phys. Rev. B 32,7013, (1985). 15 11. Schwab, V. G. Lyssencko, J. M. Hvam, and C. Klingshirn, Phys. Rev. B 44,3413 (1991). t6 J.Hegarty and M. D Sturge, J. Opt. Sot. Am. B 2,li43 (1985). I7 M. D. Weeb, S. T. Cundiff, D. G. Steel Phys. Rev. B 43,12658 (1991)