Level Repulsion of Localised Excitons Observed in Near-Field Photoluminescence Spectra

Transcription

1 phys. stat. sol. (a) 190, No. 3, (2002) Level Repulsion of Localised Excitons Observed in Near-Field Photoluminescence Spectra A. Crottini (a), R. Idrissi Kaitouni (a), JL. Staehli 1 ) (a), B. Deveaud (a), X. L. Wang (b, c), and M. Ogura (b, c) (a) Department of Physics, Swiss Federal Institute of Technology, PH-Ecublens, 1015 Lausanne, Switzerland (b) Electrotechnical Laboratory, Umezono, Tzukuba, Ibaraki , Japan (c) CREST Japan Science and Technology Corporation (JST), Japan (Received September 4, 2001; in revised form October 5, 2001; accepted October 12, 2001) Subject classification: Hb; Cr; Ea; S7.12 GaAs/GaAlAs quantum wires grown by modulated flow rate metalorganic chemical vapour deposition were investigated by spatially resolved photoluminescence spectroscopy using a scanning near-field optical microscope. It was found that the wires decompose into a series of regions that emit luminescence of varying intensity. The spectra of these regions feature several narrow emission lines, which means that there is a series of more or less localised exciton states inside each region. It is expected that these exciton states are very close to each other and are correlated, which leads to level repulsion. The mean autocorrelation function taken from a series of near-field spectra clearly reveals this level repulsion, which amounts to roughly 2 mev. Introduction One of the most serious problems of the growth of semiconductor nanostructures nowadays concerns the quality of the interfaces. The interfaces of quantum wells (QWs) and quantum wires (QWRs) are in general rough, and in only few cases interfaces of exceptional quality extend over macroscopic distances [1, 2]. Interface roughness strongly affects the electronic properties of nanostructures. It causes fluctuations of the confining electric potential, which in many cases can lead to localisation of the exciton (X) states. A tool for obtaining valuable information on the electronic properties of semiconductor nanostructures is the (scanning) near-field optical microscope (SNOM). It permits one to perform photoluminescence (PL) spectroscopy with a spatial resolution of the order of 100 nm [3, 4]. An important fraction of the light emitted from such a small near-field (NF) spot might come from spatially and energetically correlated X states, and this could also affect the spatially resolved optical spectra. The information extracted from such spectra permits one to draw conclusions concerning the energetic correlation, the wave function overlap, and the localisation to which the X states confined in imperfect nanostructures are exposed. Experimental The samples investigated had structures obtained by flow-modulated metalorganic chemical vapour deposition (MOCVD). The V-grooved GaAs substrate was overgrown by a nominally 3 nm thick GaAs QW embedded between 50 nm wide Al 0.33 Ga 0.67 As barriers. The wires, which form spontaneously at the bottom of the grooves, had a pitch of 4 mm; images obtained using high-resolution electron micro- 1 ) Corresponding author; Phone: ; Fax: ; staehli@dpmail.epfl.ch # WILEY-VCH Verlag Berlin GmbH, Berlin, /02/ $ 17.50þ.50/0

2 632 A. Crottini et al.: Level Repulsion of Localised Excitons Fig. 1. Top: transmission electron microscope image of the QWR cross-section, taken along the crystal plane (01 1). Bottom: PL intensity map obtained by collecting the QWR emission; the laser excitation was at 2.4 ev and 10 W/cm 2 y scopy and a SNOM are shown in Fig. 1. In x the far-field (FF) PL spectra, the emission of 50 nm the QWRs appears some 140 and 250 mev below that of the QWs and the AlGaAs barriers, respectively. 3 FWHM= 200 nm 2 For the SNOM measurements, the sample 1 was cooled to a temperature of about 8 K 2.5 and was illuminated in FF with a laser beam Distance (µm) focused on a spot of 80 mm in diameter. The detected light, collected in NF through an uncoated fibre tip, was detected by a cooled CCD camera or using a photomultiplier tube when acquiring spatially resolved PL spectra 0 A or intensity maps, respectively. For the PL intensity maps, the emission was spectrally inte- B grated over a window of about 10 mev corresponding to the spectral width of the FF 1 µm QWR emission; the spatial resolution was typically 200 nm. In the maps the wires seem to be composed of a series of aligned light-emitting regions (Fig. 1, bottom). The spatially and spectrally resolved emission usually shows several peaks having a width ranging between 0.08 and 0.20 mev. In some exceptional cases, the spectra feature only one single narrow line and remain constant over the whole region. This has been attributed to the emission of an extended X state from a perfectly smooth QWR. In most cases, however, there are several different lines in the spectra, and they change when the fibre tip is moved inside a region. This means that within a NF spot (having a diameter of 200 nm), there are several more or less localised X states with slightly different energies, due to the interface roughness of the QWR. Intensity (a.u.) Discussion It can be expected that an important part of the X states that are within one NF spot are correlated, just because they are close to each other; in fact they might even overlap. If the correlated X states have similar energies, energy level repulsion becomes effective. In other words, the probability of finding, in a single NF PL spectrum, two X emission lines that are energetically at a distance DE from each other is related to the average self-convolution of the normalised PL intensity S(E): hcðs; DEÞi ¼ h Ð SðEÞ SðE DEÞ dei ; ð1þ where Intensity (a.u.) Ð SðEÞ de ¼ 1 ; ð2þ

3 phys. stat. sol. (a) 190, No. 3 (2002) 633 and where the average is taken over an important number of spectra. For an ensemble where all X levels are correlated, it is expected that for small DE, C(S, DE) vanishes as [5] jdej CðS; DEÞ! ; ð3þ DE!0 D S where D S is the average energy separation. In a FF spectrum taken from a large spot, or in the average hs(e)i of a series of NF spectra, the emission stems from X levels that are uncorrelated, and the corresponding self-convolution CðhSi; DEÞ ¼ Ð hsðeþi hsðe DEÞi de ð4þ has no particular behaviour for DE close to zero. A series of 69 spectra of the PL emitted by NF spots were recorded using the SNOM (Fig. 2). The excitation density was kept as low as possible, at 0.01 W/cm 2. We analysed these spectra applying the following procedure: (i) each individual spectrum, after background subtraction, was normalised according to Eq. 2; (ii) the average spectrum hs(e)i and its self-convolution C(hSi, DE) were calculated (Eq. (4), Figs. 3a and c); and (iii) the self-convolution of each individual spectrum and its mean hc(s, DE)i was calculated (Eq. (1), Figs. 3a and 3c). The mean self-convolution of the individual spectra features a strong peak at DE = 0. This peak is due to the self-convolution of each emission line of finite width with itself, and to the self-convolution of the noise in the spectra. However, the self-convolution of the mean spectrum does not show this peak at DE = 0 because the average spectrum consists of a spectrally broad emission, and because the signal-to-noise ratio is much improved in comparison to the individual spectra. Fig. 2. Samples (A, B, C, and D) of PL spectra, collected in NF with 200 nm resolution. The excitation density is 0.01 W/cm 2. hsi is the average of all recorded spectra

4 634 A. Crottini et al.: Level Repulsion of Localised Excitons Fig. 3. a) Mean self-convolution hc(s, DE)i of the individual PL spectra (solid line), and self-convolution C(hSi, DE) of the average PL spectrum (dashed line). b) Autocorrelation function DC(DE). c, d) Enlarged parts of the plots in a) and b), respectively. The effect of level repulsion is clearly visible in hc(s, DE)i as well as in DC(DE) Apart from the central peak, there is a shoulder at DE 2 mev in hc(s, DE)i that is absent in C(hSi, DE). We believe that this shoulder is a signature of level repulsion. Because we carefully normalised our spectra, we can also plot the autocorrelation function DC(DE), i.e. the difference DCðDEÞ hcðs; DEÞi CðhSi; DEÞ : ð5þ Since C(hSi, DE) represents an ensemble of mostly uncorrelated X states, and hc(s, DE)i one for which a sizeable fraction of these states is, on the contrary, correlated, the effects of level repulsion become strongly visible in DC(DE) (Figs. 3b and d). At DE =0, again a strong peak appears, caused by the self-convolution of the single emission lines and by the spikes in the noise. At DE 1.8 mev, there is clearly a visible dip, at DE 2.4 mev a small side peak. At this energy, the expected drop towards zero with decreasing DE of the autocorrelation starts (Eq. (3)). However, this drop is partly covered by the self-convolution of the single emission lines. Fortunately they are narrow enough and the effect of level repulsion is not completely hidden. We estimate that the mean level separation D S caused by repulsion amounts to about 2 mev. The presence of such a quantitatively significant level repulsion indicates that the X states strongly overlap in the QWRs studied here, and thus that they are only weakly localised. Detailed knowledge of the X states is needed to translate the mean level separation D S into a wave function overlap length [5]. For higher DE, the effect of level repulsion (which is a characteristic feature of quantum mechanics) vanishes, and the autocorrelation function behaves as expected from

5 phys. stat. sol. (a) 190, No. 3 (2002) 635 classic theory: for DE 7 mev, DC is positive, i.e. the probability that X states that are close in space have similar energy is enhanced with respect to that of distant ones. For still higher energy differences, DC becomes negative and approaches zero for DE 40 mev. Recently, NF PL spectra measured on GaAs/AlGaAs QWs at a bath temperature of 20 K have been investigated [6]. The observed features are qualitatively quite similar to what we observed on QWRs. In particular, the autocorrelation function DC(DE) has a shoulder at DE 2.5 mev which is very close to our observation. This means that X localisation and wave function overlap are quite similar for the two cases investigated, and we note that the inhomogeneous broadening observed in the average NF PL spectra is similar in both cases. In any case, the numerical analysis and simulations presented in Ref. [6] indeed confirm the picture of overlapping, weakly localised X states. Acknowledgements This work was supported in part by the Fonds National Suisse de la Recherche Scientifique. The authors acknowledge interesting discussions with V. Savona and R. Zimmermann. References [1] See, for example, Q. Wu et al., Phys. Rev. Lett. 83, 2652 (1999); and references therein. [2] A. Crottini et al., Phys. Rev. B 63, (2001). [3] H. F. Hess et al., Science 264, 1740 (1994). [4] A. Crottini et al., Ultramicroscopy, in press. [5] E. Runge and R. Zimmermann, phys. stat. sol. (b) 206, 167 (1998). [6] F. Intonti et al., Phys. Rev. Lett. 87, (2001).

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