phys. stat. sol. (b) 237, No. 1, 301– 307 (2003) / DOI 10.1002/pssb.200301768

InGaAs quantum dot excited states as determined by microphotoluminescence and resonant photoluminescence M. Bissiri1, G. Baldassarri Höger von Högersthal1, D. Ochoa, M. Capizzi*, 1, P. Frigeri2, and S. Franchi2 1 2

Istituto Nazionale di Fisica della Materia and Dipartimento di Fisica, Università degli Studi di Roma “La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy C.N.R. – IMEM Institute, Via Chiavari 18/A, 43100 Parma, Italy

Received 31 October 2002, accepted 18 December 2002 Published online 30 April 2003

Dedicated to Professor Jozef T. Devreese on the occasion of his 65th birthday PACS 63.20.Kr, 71.38.–k, 78.66.Fd, 81.15.Hi Microphotoluminescence and resonant photoluminescence experiments in a variety of InGaAs quantum dots (QD’s) differing for size, shape, indium content, and growth technique are reported. In the case of large QD’s, the excited state energies determined by the above mentioned two experimental techniques show a quite different dependence on the QD ground state energy. Possible causes of this disagreement are discussed.

1 Introduction In the last decade, semiconductor quantum dots (QD’s) have been the subject of intensive studies because of their fascinating physical properties and potential applications in optoelectronics. Due to their small size (typically 6–20 nm), QD’s provide a fully quantized system with a strong three dimensional carrier confinement. In particular, one of the most striking QD features is a discrete, atomiclike density of states (DOS). This feature makes QD’s an extremely attractive system for many optoelectronic devices [1], e.g., lasers with a high gain and a low threshold density weakly depending on temperature [2]. Despite the large number of theoretical and experimental papers published so far, a thorough and wellestablished understanding of DOS in self-assembled QD’s has been achieved only in the case of II–VI colloidal QD’s with a spherical shape [3, 4]. In the case of InxGa1–xAs/GaAs heterostructures, lenticular, conical, and pyramidal QD’s have been found, whose electronic and optical properties are affected strongly by strain distribution [5], indium segregation [6], and electron–phonon interaction [4, 7]. Therefore, the theoretical estimate of the electron and hole states in InxGa1–xAs and InAs QD’s is somewhat cumbersome and/or model dependent [8–11]. On the other hand, the extremely low absorbance of thin QD layers hampers a direct experimental estimate of the QD DOS. This last can be investigated better by photoluminescence (PL) measurements, which also exhibit some drawbacks. A large set of sharp lines have been reported in the PL spectra of single QD’s by several groups and attributed to excitonic and multiexcitonic levels [12]. The single QD approach, however, lacks statistical relevance and detailed structural information on the QD investigated is not easily available. Photoluminescence measurements performed on the whole set of QD’s are af-

*

Corresponding author: e-mail: [email protected]

© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 0370-1972/03/23705-0301 $ 17.50+.50/0

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fected, instead, by an inhomogeneous broadening due to a statistical distribution of the QD size and/or shape, which also hampers a detailed investigation of the QD DOS. Two different kinds of PL techniques are used to investigate the QD DOS: (i) the microphotoluminescence (µPL); (ii) the resonant photoluminescence and the excitation spectroscopy (RPL and PLE, respectively). In µPL, high power excitation densities are reached by focusing the laser spot to a few microns squared and excited states appear in the PL spectrum due to band filling effects [13–15]. In PLE and RPL, a subset of QD’s is selected by using a laser wavelength resonant to a precise QD excited state, thus leading to a PL line narrowing [3] and permitting a more detailed study of the fine structure of the QD DOS [16, 17]. However, the QD excited state energies determined by these two techniques are somewhat different, which has been matter of debate in recent and sometimes controversial papers [15–18]. Many-body interactions and a sizable inhomogeneous broadening have been claimed to affect µPL spectra [15], while carrier relaxation effects [19–21] and the possible insurgence of a phonon bottleneck, often invoked but never fully understood, should make the analysis of RPL/PLE spectra quite troublesome. In this paper, we present a comparison between the DOS estimated by µPL and RPL/PLE in a large set of InxGa1–xAs QD’s grown by molecular beam epitaxy (MBE) or metal-organic chemical vapor deposition (MOCVD). The results achieved by those two techniques are compared with data in the literature. Then, differences among µPL and RPL/PLE results are singled out and discussed. 2 Sample and experimental setup PL, µPL, RPL and PLE measurements have been performed on several InxGa1–xAs/GaAs samples, with the emission energy of QD covering a wide energy range, from 1.31 to 1.07 eV. InAs/GaAs samples have been grown by MBE at TG = 500–520 °C, while In0.5Ga0.5As/GaAs samples have been grown by MOCVD at a temperature varying between 520 °C and 580 °C. MBE grown QD’s have the shape of full pyramids with various aspect ratios, while MOCVD grown QD’s have the shape of truncated pyramids; for further details, see Ref. [22]. PL, RPL, PLE measurements were carried out in a closed cycle, liquid He cryostat at T = 10 K. µPL measurements were performed at T = 77 K in a liquid N cooled cryostat. A tunable Ti-Sapphire laser (Eexc = 1.2 ÷ 1.6 eV) and a Nd-YAG laser (Eexc = 1.165 eV) have been used for RPL and PLE (P ~ 1–10 W/cm2). PL and µPL were performed by means of an Ar+ laser (P = 1–104 W/cm2). The laser spot size in PL (µPL) is about 105 (10) µm2. The signal was spectrally analyzed by a 1 m single or 3/8 double monocromator and detected by a GaAs photomultiplier, an InGaAs detector, or a liquid N cooled Ge detector. 3 Experimental results and discussion PL and µPL spectra for some of the samples investigated here are shown in Fig. 1 by dashed and solid lines, respectively. Exciton recombination from the ground state of QD’s whose size follows a Gaussian distribution leads to PL bands with a full width at half maximum (FWHM) of about 30–55 meV. The peak position of PL spectra measures the average ground state energy of the QD ensemble, 具Eg典. In MBE samples with different amounts of In deposited, L, and/or shape (upper panel) 具Eg典 spans a wide energy range (1.31 – 1.13 eV). On the contrary, 具Eg典 varies weakly with L in MOCVD samples (lower panel), which emit all at low energies (≅1.1 eV). In µPL spectra taken at high excitation density, carrier recombination from QD ground and excited states can be detected. The FWHM of these bands is of the same order of that observed in PL for the ground state recombination at low excitation. The difference 具Ei典 − 具Eg典 between the i-th excited state and the QD ground state average energy can then be determined and is shown in Fig. 2 as a function of 具Eg典 [23]. QD’s excited states, labeled from (I) to (III), are roughly evenly spaced. This justifies previous suggestions that carriers in QD’s experience a simple harmonic oscillator potential [13]. 具Ei典 − 具Eg典 steadily decreases with increasing 具Eg典, in good agreement with previous µPL results [14, 15]; see open symbols in the figure. In the µPL experiments reported in the literature [13–15], up to five excited states have been measured although a higher number of QD excited states have been predicted on the ground of the removal of

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Fig. 1 Non resonant PL (dashed lines) and µPL (continuous lines) spectra in InAs MBE grown (top) and In0.5Ga0.5As MOCVD grown (bottom) QD’s. The growth temperature TG and the amount of In deposited L are given for each sample.

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symmetry degeneracies and the breakdown of the dipole selection rules in InxGa1–xAs/GaAs QD’s [9, 10]. This lack 500 ºC 3.2 ML of full symmetry is supported by single QD spectroscopy, where several sharp transitions are commonly observed. 520 ºC 2.1 ML [12] This DOS fine structure, however, cannot be determined by µPL experiments where the whole distribution of 2.5 ML 520 ºC QD’s is excited simultaneously. Therefore, µPL mimics some averaged, smoothed DOS. 3.1 ML T = 520 ºC G Let us compare present µPL results with those previously In Ga As obtained by RPL and PLE in these same samples [17], 0.5 0.5 where a large number of peaks and shoulders has been L = 6 ML T = 535 ºC observed by selectively exciting a subset of QD’s. PLE G (top) and RPL (bottom) spectra of some typical samples 6 ML differing for ground state energy, indium concentration and 580 ºC growth technique are shown in Fig. 3. It is worth noting that RPL and PLE are complementary experiments and there is 8 ML a perfect correspondence between excited state energies 580 ºC obtained by the two different techniques [24]. The 具Ei典 − 5 ML 具Eg典 values determined from RPL and PLE spectra like 535 ºC those in Fig. 3 are shown in Fig. 4 by full dots. Despite the 1.0 1.1 1.2 1.3 1.4 1.5 QD’s largely differ in Eg’s, data groups into well defined Photon energy (eV) clusters corresponding to different sets of optical transitions and labeled from (0) to (5) in the Figure. It should be mentioned that no major difference can be found in this plot between MBE and MOCVD samples despite the two different In concentration (x = 1 and x = 0.5, respectively) [25]. The data spread reflects the experimental uncertainty as well as the large variety of investigated samples. The lowest energy resonance (0) corresponds to local modes or to hole excited state energies. Resonance (1) at 28–35 meV, which does not depend on 具Eg典, corresponds to phonon sidebands due to an enhanced electron-phonon interaction [4, 26]. All other resonances are attributed to QD excited electronic states and their energy varies with 具Eg典 in a continuous way. Transition (3), which exhibits the larger spread in the measured peak position, has a more complicated and not well resolved fine structure. Finally, the light hole (LHE) and heavy hole (HHE) excitonic recombinations from the InAs wetting layer [27] are reported for the sake of completeness. For further details, see Ref. [17]. In Fig. 4, 具Ei典 − 具Eg典 values determined by µPL and reported in Fig. 2 are shown by open symbols. The grey areas show the regions where most of the excited state energies detected by µPL fall. µPL spectra could be obtained from RPL and PLE spectra by taking into account the inhomogeneous broadening, as attempted in Ref. [15]. However, we have not tried this approach, which requires a careful analysis of the spectra, beyond the aim of this work. Anyhow, a comparison of the results obtained by the two techniques can be made already on a qualitative ground. At a first sight, the dependences on Eg for the QD excited state energies obtained by the two techniques agree each other for small QD’s (high 具Eg典 values) and substantially disagree for large QD’s (low 具Eg典

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M. Bissiri et al.: InGaAs quantum dot excited states as determined by microphotoluminescence Fig. 2 Resonance energies for all investigated samples, as determined by µPL spectra at medium-high excitation intensity are shown by full symbols as a function of the average QD ground state energy 具Eg典. Labels (n) refer to different clusters of data for QD excited states. Data taken from µPL spectra reported in Refs. [14] and [15] are shown for comparison by open symbols.

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values). For small QD’s, the energy differences between the excited states and the ground state decrease for increasing 具Eg典, independently on the experimental 0 technique. This dependence cannot be attributed to 1.10 1.20 1.30 1.40 quantum size effects, which should give rise to an (eV) opposite behavior. In fact, the smaller the QD, the higher 具Eg典, and the more spaced the QD excited states should be. It has been already suggested [17] that this behavior could be attributed, instead, to quantum shape effects, since structural characterization shows that these QD’s have the shape of pyramids with a lower aspect ratio than that of QD’s emitting at ~1.1 eV [22]. Moreover, In interdiffusion gives rise to a blueshift of the PL band and a reduced intersublevel spacing in InAs QD’s [14]. It should be pointed out here, however, that the agreement between µPL and PLE/RPL results is largely qualitative for these small QD’s. In fact, PLE/RPL resonances (2) and (3) should contribute to the µPL band (I), while the µPL band (II) results from the superposition of resonances (4) and (5), at least. However, band (I) in µPL has an energy closer to that of resonance (2) in PLE/RPL than to that of resonance (3). On the contrary, the intensity of the latter resonance is always much stronger than that of the former resonance; see Fig. 3. An even stronger disagreement can be found in the case of large QD’s emitting at 具Eg典 less than 1.2 eV. In this case, 具Ei典 − 具Eg典 decreases with 具Eg典 in µPL while it increases with 具Eg典 in PLE and RPL. The difference is stronger in the case of high energy excited states, like those of band (II). Therefore, quantum size effects seem to determine the energy of excited states in large QD’s, as suggested in Refs. [16] and [17] on the ground of RPL and PLE measurements, while µPL measurements seems to lead to quite different conclusions. The reasons for such major discrepancies for large (and minor for small) QD’s can be several. PLE and RPL techniques are optimal candidates to investigate the single particle QD DOS, because of the low excitation density used in these measurements. However, efficient carrier relaxation toward the ground state and their optical detection should only take place if excited states differ in energy by multiple of a LO-phonon energy. In turn, PLE and RPL resonances should appear equally spaced by multiples of LOphonon energies, thus hampering a precise investigation of the whole QD DOS. However, this is not the case for excited states reported in Fig. 4, which indicates a negligible phonon bottleneck in these systems. It has been suggested that an enhanced coupling with acoustic phonons may enlarge the optical window of phonon energy available for an efficient carrier relaxation [28, 29]. RPL and PLE spectra would provide then an accurate measure of the QD DOS. It should also be mentioned here that the Raman and fluorescence spectra in colloidal CdSe QD’s have been very well described provided the electron-phonon interaction in a non-adiabatic approach has been taken into account properly [4, 7]. For what concerns the different dependences of 具Eg典 – 具Ei典 on 具Eg典 obtained by µPL and PLE or RPL in large QD’s, they cannot be accounted for by a dependence of the various PLE or RPL resonance intensities on Eg’s, not observed in our samples. Alternatively, one should remember that single particle DOS may not be investigated in µPL, because of the high excitation intensities achieved by this technique. Many-body effects have indeed been claimed to give rise to a 16 meV red-shift of the ground state

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Fig. 3 Top: PLE spectra taken at different values of Edet for a few representative InAs and In0.5Ga0.5As QD’s are shown as a function of Eexc – Edet. Bottom: RPL spectra for the same samples shown in the top of figure, taken for different values of Eexc. Different resonances in PLE and RPL spectra are labeled by numbers (dashed lines are guides to the eye). The amount of In deposited L and the average QD ground state energy 具Eg典 are given for each sample.

energy and to a blue-shift of the excited states in 18 excitons populated QD’s with an 具Eg典 = 1.05 eV [15]. These results were in qualitative agreement with theoretical predictions of a few tens meV decrease of the ground state energy based on the two-dimensional harmonic oscillator [30] or the box-like approximation [31] for QD’s with 18 excitons. We suggest that µPL and PLE or RPL results qualitatively agree in the case of small QD’s, where kinetic confinement energy dominates and renormalization effects become negligible [32]. In the case of large QD’s emitting below 1.2 eV, instead, many-body effects dominate µPL spectra and give rise to a sizable energy renormalization of both ground and excited states, as also reported previously [15]. Therefore, difference between the excited state energies as determined by µPL and by PLE and RPL may provide a rough estimate of the sum of the red-shift of the QD ground state and the blue-shift of the QD shell of excited states [15]. This difference is ≈10 meV for µPL band (I) and ≈40 meV for µPL band (II), see Figs. 2 and 4. The former value agrees well with the value of

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M. Bissiri et al.: InGaAs quantum dot excited states as determined by microphotoluminescence 180

Fig. 4 Resonance energies for all investigated samples as determined by PLE and RPL spectra at different excitation and detection energies are shown by full symbols as a function of the average QD ground state energy 具Eg典. The resonance energies determined by µPL spectra, see Fig. 2, are shown by open symbols. Labels (n) refer to different clusters of data for QD excited states as determined by PLE and RPL or µPL spectra. Isolated points on the left are data taken by means of Nd-YAG laser. Energy regions that correspond to QD excited state resonances as determined by µPL are highlighted in gray. The light hole (LHE) and heavy hole (HHE) excitonic recombinations from the InAs wetting layer are reported for the sake of completeness.

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(eV) 17 meV found for the red-shift of band (I) in Ref. [15]. (In the present µPL experiments, lower excitation intensities than in Ref. [15] have been used.) In conclusion, a comparison between excited and ground state energies derived by µPL and PLE or RPL supports previous evidence that many-body effects affect high excitation µPL spectra in large QD’s, preventing in that case a straightforward determination of the single particle and single exciton DOS. In the case of small QD’s these discrepancies are reduced but do not vanish, suggesting that further experimental and theoretical studies are needed before reaching a full understanding of how the QD DOS reflects on µPL and PLE or RPL spectra. Acknowledgements This work was supported by the European Commission GROWTH program, within the framework of the NANOMAT project, Contract no. G5RD-CT-2001-00545.

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