Freymann, Georg von

Gerthsen, Dagmar

Klingshirn, Claus

Kurtz, Elisabeth

Litvinov, Dimitri

Schimmel, Thomas

Wegener, Martin

KITopen

Journal of Microscopy, Vol. 202, Pt 1, April 2001, pp. 218–222.Received 28 August 2000; accepted 11 October 2000Autocorrelation spectroscopy on single ultrathin layers ofCdSe/ZnSe: hints for a non-thermal distribution of excitonsin quantum islandsG. VON FREYMANN*, E. KURTZ*, C. KLINGSHIRN*, D. LITVINOV†, D. GERTHSEN†,T. H. SCHIMMEL* & M. WEGENER**Institut fu¨r Angewandte Physik, Universita¨t Karlsruhe (TH), 76128 Karlsruhe, Germany.†Laboratorium fu¨r Elektronenmikroskopie, Universita¨t Karlsruhe (TH), 76128 Karlsruhe,GermanyKey words. Autocorrelation spectroscopy, nanophotoluminescence, near-fieldscanning optical microscopy, quantum islands.SummaryAutocorrelation spectroscopy on the basis of thousands ofindividual near-field photoluminescence spectra of singleultrathin CdSe layers at low temperatures exhibits a strongpositive correlation peak around 18 meV energy with awidth of 5 meV. Using simulations and experiments as afunction of temperature and laser intensity, we can excludeinterpretations along the lines of biexcitons or phononsidebands. We attribute this feature to the splitting ofground state and an excited state in individual quantumislands. This interpretation implies that the potentialminima are rather uniform in size and that the distributionof excitons is nonthermal.IntroductionEpitaxially grown, thin semiconductor layers often lead to aseries of sharp photoluminescence lines in near-field ormicrophotoluminescence experiments (Hess et al., 1994;Zrenner et al., 1994; Flack et al., 1996; Jahn et al., 1997;Robinson et al., 1999; Wu et al., 1999). These individualspectra can exhibit many tens or even hundreds ofindividual lines and usually look, at first sight, like arandom distribution.Autocorrelation spectroscopy allows us to extract moreinformation by focusing on statistically significant featuresin all spectra: calculation of the autocorrelation for eachspectrum and subsequent averaging over all autocorrela-tions allows for global statements about the potentiallandscape. Correlations in the spectrum can arise fromcorrelations in the potential or from a potential which is justnoise. The first case would lead to positive correlations, thelatter to negative correlations, i.e. to the so-called levelrepulsion (Runge & Zimmermann, 1998, 1999).Recent experiments with ultrathin CdSe/ZnSe sampleshave shown a strong positive correlation feature around18 meV energy with a width of 5 meV (von Freymann et al.2000). In this article, we first briefly review the methodcalled autocorrelation spectroscopy and then focus on theorigin of the correlation feature.Statistical analysisAutocorrelation spectroscopy is based on the high lateralresolution achieved in microphotoluminescence or near-field optical experiments combined with the capability tomeasure huge sets of spectra from different locations on thesample within a reasonably short time. The huge amount ofdata is the precondition for the statistical analysis. In vonFreymann et al. (2000) we have extended a proposal byRunge & Zimmermann (1998, 1999) and have made itsuitable for experimental data.Here we summarize this procedure: (1) normalization ofthe individual spectra to equal spectral integral; (2) sub-traction of the average of these normalized spectra; dIn("v)  In ("v) 2 kIn ("v)l; (3) calculation of the individualautocorrelations, C(DE)  R dIn ("v 0) dIn ("v 0 1 DE) dv 0;(4) averaging over all individual autocorrelations; and(5) normalization of the maximum of kC(DE)l at DE  0to unity. For photoluminescence spectra I ("v), whichconsist of a series of sharp lines, i.e. I ("v)  Sn Ind("v 2 ("vn) with arbitrary values of In, one can show that121 kC(DE)ld(DE)  0 holds under these conditions.We test this procedure with different sets of computer-generated random spectra. In these random spectra we haveCorrespondence to: G. von Freymann. Tel: 149 721 608 3407; fax: 149 721607 593; e-mail: georg.freymann@physik.uni-karlsruhe.de218 q 2001 The Royal Microscopical SocietyFirst published in:EVA-STAR (Elektronisches Volltextarchiv – Scientific Articles Repository) http://digbib.ubka.uni-karlsruhe.de/volltexte/4982001 chosen the number of lines, their width and their(Gaussian) distribution roughly to match both the indivi-dual measured spectra and their average. All data sets aretreated with the same program. For the computer-generatedspectra, we find a maximum at DE  0 and no furtherstructure. The same behaviour is found in many othercomputer-generated sets with different numbers of linesand/or different distributions (not shown). This result isexpected and illustrates that the defined procedure does notlead to artefacts.Experiment and resultsFor the optical experiments we frequency-double about 1 Wpower at 800 nm wavelength from a continuous waveTi:sapphire laser in a 2-mm thick BBO crystal to obtainabout 3 mW power at 400 nm wavelength (3.10 eV photonenergy). The excitation power can be continuously attenu-ated using a sequence of two polarizers. In the parallelpolarized position, 200–300 nW are effectively coupled intoan optical fibre. The light propagates towards a nanometerscale apex which is formed by a two-step selective etchingprocess. Electron micrographs of identical fibre tips havebeen shown in Adelmann et al. (1999). The samples aremounted in a continuous-flow cryostat and can be tem-perature stabilized in a range from 4.2 to 310 K. Thephotoluminescence is collected with the same fibre and sentinto a 0.5-m grating spectrometer (1800 lines/mm grating),which is connected to a liquid nitrogen cooled, back-illuminated, charge-coupled-device camera. The spectralresolution of this system is 0.06 nm, which is equivalent toan energy resolution of 250 meV in the spectral rangeinvestigated. We scan the uncoated fibre tip at a constantheight of 100 nm above the surface, i.e. the feedback loop isinactive. Under these conditions, the measured spatialresolution is better than l/5 of the photoluminescencewavelength (540 nm). The data sets shown in the followingare always based on 1600 individual spectra, each with0.5 s exposure time of the charge-coupled-device camera,taken in a 2-mm  2-mm area with 50 nm (100 nm)separation between adjacent points. For the intensity-dependent measurements, only 400 spectra from the samearea are collected, with exposure times up to 10 s. We havecarefully adjusted the exposure time for each measurementin order to maintain the same signal-to-noise ratio.The four samples A, B, C and D are nominally ultrathinCdSe layers (2.0–3.6 monolayers) between ZnSe barriers.They are described in more detail in von Freymann et al.(2000) and the references therein. The individual photo-luminescence spectra of these samples look very different interms of line density and width of the line distribution. Also,they are shifted in the overall spectral position "v0 (left-hand side of Fig. 1). However, the correlation feature foundby autocorrelation spectroscopy is very similar for manydifferent measurements on samples A, B, C and D (right-hand side of Fig. 1). Therefore, the correlations in thephotoluminescence lines of these CdSe/ZnSe layers seem tobe generic for this material system.DiscussionThe correlations in the spectra can have different origins:Gindele et al. (1999) observed a broad (9 meV) phononreplica in these material systems as a result of the strongcoupling of the exciton to the mixed state of ZnSe andCdSe LO-phonons. Also, they reported a strong biexcitonicemission 20 meV below the exciton peak. In addition,several researchers (Flack et al., 1996; Peranio et al., 2000)have reported islands in this material system with an arealdensity around 1011 cm22 and with sizes of 5–10 nm (seeFig. 2b). Islands of rather uniform size (‘self-organizedquantum dots’) would lead to a rather uniform level spacing(Fig. 2a). The internal motion of the electron and the holewithin the exciton would lead to a further smearing-out,and hence to a broadening, of the potential for the excitons(Runge & Zimmermann (1999) (for bulk CdSe, the excitonBohr radius is 9 nm). The expected level spacing for sucheffective potential wells is roughly consistent with thecorrelation energy of 18 meV observed in our work (theexciton mass of bulk CdSe is 1.3  m0, that of ZnSeFig. 1. One individual spectra of each sample A, B, C and D isshown on the left-hand side. The averaged autocorrelations forthese data are displayed on the right-hand side: raw data (solidline), filtered data with E0 , 0 (dashed line), filtered data withE0 . 0 (dotted line). Filter function is f("v) / exp ("v/E0).AUTO CORRELATION SPECT ROSCOPY OF U LTRAT HIN CD SE/ZNSE LAYERS 219q 2001 The Royal Microscopical Society, Journal of Microscopy, 202, 218–2221.9  m0) (see Fig. 2(a)). Also, the number of lines in eachspectrum is roughly consistent with an areal density ofislands of 1011 cm22.The correlations are consistent with individual photo-luminescence spectra, which consist of sets of pairs of lines.For each pair the energy spacing has to be around 18 meV.For an interpretation along the lines of a phonon sidebandor of biexcitonic emission we would like to know whetherthe second peak lies on the low or on the high energy side ofthe first peak. To achieve this information, we multiply theindividual photoluminescence spectra with filter functionsf("v) before performing step (1). Exponential functions,i.e. f("v) / exp("v/E0), are especially simple to interpret.For the case of E0 , 0 and for spectra that consist of pairsof lines with one main line and a weaker, low-energy side-band, the sideband would be enhanced by a certain factor(independent on its absolute energetic position). Conse-quently, the correlation function kC(DE)l would exhibitenhanced correlations. Similarly, a high-energy sidebandwould be suppressed for E0 , 0 and vice versa for E0 . 0.This idea has been verified explicitly by numerical simula-tion (not shown). Applying this procedure to the data leadsto the curves shown in Fig. 1 on the right-hand side and inFig. 3(b) (full lines correspond to the raw data, dotted linesto E0  1 18 meV, dashed lines to E0  2 18 meV).Obviously, the determined height of the correlation peak isroughly the same for E0  ^ 18 meV. This implies that wehave pairs of lines with comparable strength – on average.This can either mean that the two lines in the pairs haveidentical strength in each case or that they fluctuatestrongly independently. By additional simulations we havefound that the latter scenario would lead to a correlationpeak in kC(DE)l, which is definitely too weak to be consistentwith the experiment (not shown). For lines of identicalstrength, our simulations (Fig. 3c) give results which areconsistent with the experiment (Fig. 3b). Here we havechosen the parameters for the simulations such that thegenerated spectra match the experimental ones regardingline width, Gaussian distribution and spectral position(Fig. 3(a)).Pairs of lines with comparable strength makes an inter-pretation along the lines of a phonon sideband unlikely (theLO-phonon energy of bulk CdSe is 26 meV, that of ZnSe is32 meV. The observed correlation energy is below 20 meVfor each sample). Furthermore, phonon sidebands in thisFig. 2. (a) Simple model for a potential minimum in a quantumisland of type A that results in a level spacing of about 18 meV. Theground state and the second excited state of the exciton areoptically allowed. (b) The lateral dimensions are consistent withthe sizes found for real islands in the sample by cross-section high-resolution transmission electron microscopy. The images areanalysed by the composition evaluation by lattice fringe analysis(CELFA) routine described in detail by Rosenauer & Gerthsen(1999). The analysis yields the local Cd concentration that isdisplayed in a colour-coded map. Islands consisting of Cd-richregions with sizes below 10 nm are clearly visible.Fig. 3. (a) Individual simulated spectrum consisting of pairs oflines of equal strength. The energy spacing is chosen to match theexperimental results. (b) Averaged autocorrelations for raw data(solid line), filtered data with E0 , 0 (dashed line), filtered datawith E0 . 0 (dotted line). (c) same as (b) but for simulated data.Filter function is f("v) / exp("v/E0).220 G. VON FREYMANN ET AL.q 2001 The Royal Microscopical Society, Journal of Microscopy, 202, 218–222material system are not strong enough to explain theobserved correlation feature (ILO 0.04IX, Gindele et al.,1999). Biexcitonic effects could also lead to pairs of lines ofcomparable strength. A clear signature of biexcitonic effectswould be an intensity dependence. We have not found anyintensity dependence when attenuating the incident laserintensity by two orders of magnitude, i.e. from 200 nWdown to 2 nW excitation power (Fig. 4). However, it isinteresting to note that the quantum dot biexciton bindingenergy of < 20 meV observed in single-dot experiments(Bacher et al., 1999; Gindele et al., 1999) is close to thenumbers seen here. We interpret the pairs of lines as groundand excited state of individual quantum islands. If this inter-pretation is correct, our observations would be evidence for ahighly nonthermal distribution of excitons in these islands(resulting from the ‘phonon bottle-neck’). In this case thereshould be no temperature dependence of the correlationfeature; this is indeed the case. The correlation featureremains unchanged for temperatures in the range of4.2 2 80.0 K (Fig. 4). Note that the correlation feature isstill present at high temperatures even though the sharplines in the spectra have disappeared. All averaged auto-correlations are normalized to the value at DE  0. Lookingat the raw autocorrelation data the total strength of thecorrelation feature decreases with decreasing photolumi-nescence intensity (for increasing temperatures). In additionto the energetic correlations, we also find spatial corre-lations in the photoluminescence maps. Numerical inte-gration over each line in such a pair separately, shows adistribution rather lacking in order (Fig. 5). However,multiplication of the two photoluminescence maps witheach other pointwise shows regions (marked by the dottedcircles in Fig. 5) where both lines are present. The lateralresolution, determined by a cross-section in one of thephotoluminescence maps, is better than 110 nm (Fig. 5).ConclusionIn conclusion, we have shown by simulations and directexperiments that the positive correlation feature found byFig. 4. Temperature dependence (left hand side) and intensitydependence at T  10 K (right-hand side) of the correlationfeature. The correlation feature remains unchanged even thoughthe line width increases with increasing temperature and the sharplines vanish (inset).Fig. 5. One individual experimental spectrum after normalizationand background subtraction. The photoluminescence maps of thered and the green highlighted areas are shown on the left, respec-tively, right-hand side. Pointwise multiplication of the photo-luminescence maps clearly shows two areas where both lines canbe found (dotted circles). The blue marked cross-section reveals alateral resolution of 107 nm full width at half maximum, which isbetter than l/5 of the photoluminescence wavelength.AUTO CORRELATION SPECT ROSCOPY OF U LTRAT HIN CD SE/ZNSE LAYERS 221q 2001 The Royal Microscopical Society, Journal of Microscopy, 202, 218–222autocorrelation spectroscopy on ultrathin CdSe layers cladbetween ZnSe is not consistent with interpretations basedon phonon sidebands or on biexcitonic emission. An inter-pretation along the lines of a nonthermal population ofground and an excited state in rather homogeneousquantum islands is consistent with the data.AcknowledgementsThis research has been supported by the DFG-SFB 195, theDFG-GK 284 and is undertaken within the Institut fu¨rNanotechnologie der Universita¨t Karlsruhe (TH). Theresearch of M.W. is funded by the DFG Leibniz-Preis.ReferencesAdelmann, Ch., Hetzler, J., Scheiber, G., Schimmel, Th., Wegener,M., Weber, H.B. & von Lo¨hneysen, H. 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(1999) Level repulsion andwavefunction statistics in semiconductor quantum systems withlocalized excitons. Ann. Phys. 8, 229–232.Wu, Q., Grober, R.D., Gammon, D. & Katzer, D.S. (1999) Imagingspectroscopy of two-dimensional excitons in a narrow GaAs/AlGaAs quantum well. Phys. Rev. Lett. 83, 2652–2655.Zrenner, A., Butov, L.V., Hagn, M., Abstreiter, G., Bo¨hm, G. &Weimann, G. (1994) Quantum dots formed by interfacefluctuations in AlAs/GaAs coupled quantum well structures.Phys. Rev. Lett. 72, 3382–3385.222 G. VON FREYMANN ET AL.q 2001 The Royal Microscopical Society, Journal of Microscopy, 202, 218–222

Autocorrelation spectroscopy on single ultrathin layers of CdSe/ZnSe: hints for a non-thermal distribution of excitons in quantum islands

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Autocorrelation spectroscopy on single ultrathin layers of CdSe/ZnSe: hints for a non-thermal distribution of excitons in quantum islands

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