Freymann, Georg von

Klingshirn, Claus

Kurtz, Elisabeth

Wegener, Martin

English

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APPLIED PHYSICS LETTERS VOLUME 77, NUMBER 3 17 JULY 2000First published in:Statistical analysis of near-field photoluminescence spectraof single ultrathin layers of CdSeÕZnSeG. von Freymann,a) E. Kurtz, C. Klingshirn, and M. WegenerInstitut für Angewandte Physik, Universita¨t Karlsruhe (TH), 76128 Karlsruhe, Germany~Received 13 March 2000; accepted for publication 26 May 2000!The statistical analysis of thousands of near-field photoluminescence spectra of single ultrathinCdSe layers at 20 K exhibits a strong positive correlation peak around 20 meV energy with a widthof 5 meV. Our data are consistent with individual spectra which consist of sets of many pairs oflines. In each pair, the two lines must have comparable strength. We speculate about the origin ofthese pairs. ©2000 American Institute of Physics.@S0003-6951~00!03229-0#adduhttioomlatrnsiotiosothrixlstialalhsetshiouvincapswmnv5atce,ns,setsalera,ntraAwnnmts.ndSei-tealffer-atsameEpitaxially grown, thin semiconductor layers often leto a series of sharp photoluminescence lines in near-fielmicrophotoluminescence experiments.1–6 These individualspectra can exhibit many tens or even hundreds of individlines and usually look like a random distribution at first sigWhat can be learned from this type of spectra? This queswas first investigated theoretically in Refs. 7 and 8 for phtoluminescence of excitons which move in a truly randopotential, i.e., a potential which in itself shows no corretions. They proposed to measure a set of individual speccalculate the individual spectral autocorrelation functioand average over many such autocorrelations. In this fashthey demonstrated that one can hope to observe correlain the energy spectrum. In their case, they found thecalled level repulsion, i.e., a negative correlation close tozero energy difference, which is known from random mattheory. It is clear that correlations in the spectrum can aarise from correlations in the potential, i.e., from a potenwhich is not just noise. This would lead to positive corretions.In this letter, we first modify and extend the proposa7,8in order to make it suitable for measured spectra. Tcomplements recent experiments using time-resolvedondary emission.9 As an example, we investigate large seof near-field photoluminescence spectra of single ultratCdSe layers clad between ZnSe barriers.For the optical experiments, we frequency double ab1 W power at a 800 nm wavelength from a continuous-waTi:sapphire laser in a 2-mm-thick BBO crystal to obtaabout 3mW power at a 400 nm wavelength~3.10 eV photonenergy!. 200–300 nW are effectively coupled into an optifiber. The light propagates towards a nanometer-scale awhich is formed by a two-step selective etching proceElectron micrographs of identical fiber tips have been shoin Ref. 10. The photoluminescence is collected with the safiber and sent into a 0.5 m grating spectrometer~1800lines/mm grating!, which is connected to a liquid-nitrogecooled back-illuminated charge-coupled-device~CCD! cam-era. The spectral resolution of this system is a 0.06 nm walength, which is equivalent to an energy resolution of 2meV in the spectral range investigated. We scan the uncoa!Electronic mail: georg.freymann@physik.uni-karlsruhe.de3940003-6951/2000/77(3)/394/3/$17.00Downloaded 06 Mar 2009 to 129.13.72.198. Redistribution subject to AIPEVA-STAR (Elektronisches Volltextarchttp://digbib.ubka.uni-karlsruhe.de/volloral.n--a,,n,ns-eol-isc-ntelexs.ne-e-0edfiber tip in a constant height of 100 nm above the surfai.e., the feedback loop is inactive. Under these conditiothe measured spatial resolution is 200 nm. The datashown in the following are always based on 1600 individuspectra, each with 0.5 s exposure time of the CCD camtaken in a 2mm32 mm area with 50 nm separation betweeadjacent points.Four examples of individual photoluminescence specat a sample temperature ofT520 K from four differentsamples, A, B, C, and D, are shown in Fig. 1. Samplestems from the Ioffe institute in St. Petersburg and is groby molecular-beam epitaxy~MBE!.11 The nominal averageCdSe layer thickness is 3.6 ML, the top ZnSe layer is 10thin, which is suitable for optical near-field experimenSamples B, C, and D are grown by mixed elemental acompound-source MBE in-house.12 The nominal averageCdSe layer thickness of sample B is 2 ML, the top Znlayer is 20 nm thin. Samples C~2.3 ML, 20 nm ZnSe!and D~3 ML, 45 nm ZnSe!are thermally annealed at 320 °C drectly after CdSe deposition~i.e., prior to cap growth!for aduration of 5 and 10 min, respectively. This is to initiaOswald ripening of CdSe islands. Obviously, the individuphotoluminescence spectra of these samples look very diFIG. 1. Individual photoluminescence spectra of samples A, B, C, and Da sample temperature of 20 K. For clarity, the spectra are shown on thescale.© 2000 American Institute of Physics license or copyright; see http://apl.aip.org/apl/copyright.jsphiv – Scientific Articles Repository) texte/5992000 n.onmanbethdeesaiocprte-t ohAuhenenrae-ugwesthicrgbongcner-naytaoneak395Appl. Phys. Lett., Vol. 77, No. 3, 17 July 2000 von Freymann et al.ent in terms of line density and width of the line distributioAlso, note the large shift in the overall spectral positi\v0 .Back to our initial question: What can be learned frosuch spectra? We first tried to apply the idea of Refs. 78 directly. This leads to difficulties, which can alreadyanticipated from the spectra shown in Fig. 1. Besidemany resolved lines, one also has a broad backgrouneach individual spectrum. The autocorrelation of this undired contribution is so prominent that it overwhelms all othfeatures by far~not shown!. Consequently, we eliminate thibackground by calculating the average and subtract thiserage from each individual spectrum of this set. In additto this, we normalize each individual photoluminescenspectrum to equal the integral before starting the abovecedure. For photoluminescence spectraI (\v), which consistof a series of sharp lines, i.e.,I (\v)5(nI nd(\v2\vn)with arbitrary values of I n , one can show tha*0`^C(DE)&d(DE)50 holds under these conditions. Wsummarize the complete procedure:~1! normalization of theindividual spectra to equal the spectral integral;~2! subtrac-tion of the average of these normalized spectra,dI n(\v)5I n(\v)2^I n(\v)&; ~3! calculation of the individual autocorrelations, C(DE)5*dI n(\v8)dI n(\v81DE)dv8; ~4!averaging over all individual autocorrelations; and~5! nor-malization of the maximum of̂C(DE)& at DE50 to unity.Figure 2 illustrates this procedure for two examples: A semeasured spectra of sample A~left column! and a set ofcomputer-generated random spectra~right column!. In theserandom spectra we have chosen the number of lines, twidth, and their~Gaussian! distribution to roughly matchboth the individual measured spectra and their average.data sets are treated by the same program. For the compgenerated spectra, we find a maximum atDE50 and nofurther structure. The same behavior is found in many otcomputer-generated sets with different numbers of liand/or different distributions~not shown!. This result is ex-pected and illustrates that the defined procedure doeslead to artifacts. In contrast to the computer-generateddom spectra, the experimental data show a correlation paroundDE518 meV @arrow in Fig. 2~e!#.Amazingly, this correlation is very similar for many different measurements on samples A, B, C, and D—althothe individual spectra~see Fig. 1! look considerably differ-ent. This is shown in Fig. 3, where, for each sample,depict two data sets~Nos. 1 and 2! from different areas onthe sample. Obviously, the correlations in the photolumincence lines of these CdSe/ZnSe layers are generic forparticular material system.These correlations are consistent with spectra whconsist of sets of pairs of lines. For each pair the enespacing has to be around 18 meV. Can we learn more athe relative strength of the two lines in the pairs? FollowiRef. 13, one can multiply the individual photoluminescenspectra with filter functionsf (\v) @before performing step~1!#. Exponential functions, i.e.,f (\v)}exp(\v/E0), are es-pecially simple to interpret. For the case ofE0.0 and forspectra which consist of pairs of lines with one main line aa weaker high-energy sideband, the sideband would behanced by a certain factor~independent on its absolute eneDownloaded 06 Mar 2009 to 129.13.72.198. Redistribution subject to AIPdeins-rv-neo-feirllter-rsotn-akhe-ishyutedn-getic position!. Consequently, the correlation functio^C(DE)& would exhibit enhanced correlations. Similarly,low-energy sideband would be suppressed forE0.0 andvice versa forE0,0. This idea has been verified explicitlby numerical simulation. Applying this procedure to the daFIG. 2. Illustration of the statistical procedure for experimental datasample A~left column! and for computer-generated random spectra~rightcolumn!. ~a! Individual spectra, normalized to equal spectral integral;~b!average; (c)5(a)-(b); ~d! autocorrelation of~c!; and~e! averaged autocor-relation ^C(DE)& ~normalized to unity!.FIG. 3. Correlation function̂C(DE)& of two areas~Nos. 1 and 2! on eachof the samples A, B, C, and D. Note that the position of the correlation paround 15–20 meV does not vary much. license or copyright; see http://apl.aip.org/apl/copyright.jspe-letwthlaocateulotteuakraiaolutsiurmofofb-tri-onottheisingheregedit2 to95,nn,t,.er-e,. B.-d B.J.andndng396 Appl. Phys. Lett., Vol. 77, No. 3, 17 July 2000 von Freymann et al.shown in Fig. 3, leads to the curves shown in Fig. 4~fulllines correspond toE05118 meV, dashed lines toE05218 meV!. Obviously, the determined height of the corrlation peak is roughly the same forE05618 meV. This im-plies that we have pairs of lines with comparabstrength—on the average. This can either mean that thelines in the pairs have identical strength in each case orthey strongly fluctuate independently. By additional simutions we have found that the latter scenario would lead tcorrelation peak in̂C(DE)&, which is definitely too weak tobe consistent with the experiment. For lines of identistrength, our simulations give results which are consiswith the experiment~Fig. 3!.We have already concluded that our experimental resare consistent with individual spectra which consist of setspairs of lines. The last section has shown that in each pairtwo lines must have comparable strength. This makes inpretations along the lines of a phonon sideband quitelikely ~the LO-phonon energy of bulk CdSe is 26 meV, thof ZnSe is 32 meV!. Phonon sidebands are usually weaIslands of rather uniform size~‘‘self-organized quantumdots’’! would lead to a rather uniform level spacing. Severesearchers3,14 have indeed reported islands in this matersystem with an areal density around 1011cm22 and with sizesof 5–10 nm. The internal motion of the electron and the hwithin the exciton would lead to a further smearing ohence to a broadening, of the potential for the excitons8 ~forbulk CdSe, the exciton Bohr radius is 9 nm!. The expectedlevel spacing for such effective potential wells seems conFIG. 4. Correlation function̂C(DE)& of the same two areas~Nos. 1 and 2!as in Fig. 3. Filters withE05118 meV ~full lines! and E05218 meV~dashed lines!. Note that the height of the correlation peak does not chamuch.Downloaded 06 Mar 2009 to 129.13.72.198. Redistribution subject to AIPoat-alnttsfher-n-t.lle,s-tent with the correlation energy of 18 meV observed in owork ~the exciton mass of bulk CdSe is 1.33m0 , that ofZnSe 1.93m0!. Also, the number of lines in each spectruis roughly consistent with an areal density of islands1011cm22. If this interpretation concerning sets of pairslines from rather uniform islands is correct indeed, our oservations would be evidence for a highly nonthermal disbution of excitons in these islands~due to the ‘‘phononbottleneck’’!. Biexcitonic effects in these dots could alslead to the observed positive correlations. While we havefound any clear intensity dependence when attenuatingincident laser intensity from 200 nW down to 20 nW, itinteresting to note that the quantum-dot biexciton bindenergy of'20 meV observed in single-dot experiments15 iclose to the numbers seen here. This would imply a ratuniform biexciton binding energy in the quantum dots.Note added in proof: Additional recent experiments havshown that the positive correlation peak remains unchanfor incident laser intensities even down to 2 nW. Also,remains unchanged for temperatures in the range of 4.80 K.This research has been supported by the DFG-SFB 1the DFG-GK 284, and is performed within the Institut fu¨rNanotechnologie der Universita¨t Karlsruhe ~TH!. The re-search of one of the authors~M.W.! is funded by the DFGLeibniz price. The authors thank E. Runge, R. Zimmermaand Th. Schimmel for stimulating discussions.1H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. WesScience264, 822 ~1994!.2A. Zrenner, L. V. Butov, M. Hagn, G. Abstreiter, G. Bo¨hm, and G. We-imann, Phys. Rev. Lett.72, 3382~1994!.3F. Flack, N. Samarth, V. Nikitin, P. A. Crowell, J. Shi, J. Levy, and DAwschalom, Phys. Rev. B54, 17312~1996!.4U. Jahn, M. Ramsteiner, R. Hey, H. T. Grahn, E. Runge, and R. Zimmmann, Phys. Rev. B56, R4387~1997!.5L. M. Robinson, H. Rho, J. C. Kim, H. E. Jackson, L. M. Smith, S. LeM. Dobrowolska, and J. K. Furdyna, Phys. Rev. Lett.83, 2797~1999!6Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, Phys. Rev. Lett.83,2652 ~1999!.7E. Runge and R. Zimmermann, Phys. Status Solidi B206, 167 ~1998!.8E. Runge and R. Zimmermann, Ann. Phys.~Leipzig! 8, 229 ~1999!.9V. Savona, S. Haacke, and B. Deveaud, Phys. Rev. Lett.84, 183 ~2000!.10Ch. Adelmann, J. Hetzler, G. Scheiber, Th. Schimmel, M. Wegener, HWeber, and H. v. Lo¨hneysen, Appl. Phys. Lett.74, 179 ~1999!.11S. V. Ivanov, A. A. Toropov, T. V. Shubina, S. V. Sorokin, A. V. Lebedev, I. V. Sedova, P. S. Kop’ev, G. R. Pozina, J. P. Bergmann, anMonemar, J. Appl. Phys.83, 3168~1998!.12E. Kurtz, M. Schmidt, M. Baldauf, S. Wachter, M. Gru¨n, D. Litvinov, S.K. Hong, J. X. Shen, T. Yao, D. Gerthsen, H. Kalt, and C. Klingshirn,Cryst. Growth214-215, 712 ~2000!.13E. Runge~private communications!.14N. Peranio, A. Rosenauer, D. Gerthsen, S. V. Sorokin, I. V. Sedova,S. V. Ivanov~unpublished!.15G. Bacher, R. Weigand, J. Seufert, V. D. Kulakovskii, N. A. Gippius, aA. Forchel, Phys. Rev. Lett.83, 4417~1999!.e license or copyright; see http://apl.aip.org/apl/copyright.jsp

Statistical analysis of near-field photoluminescence spectra of single ultrathin layers of CdSe/ZnSe

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Statistical analysis of near-field photoluminescence spectra of single ultrathin layers of CdSe/ZnSe

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