Shell-like formation of self-organized InAs/ GaAs quantum dots

Transcription

1 Shell-like formation of self-organized InAs/ GaAs quantum dots R. Heitz,* F. Guffarth, K. Pötschke, A. Schliwa, and D. Bimberg Institut für Festkörperphysik, TU-Berlin, Hardenbergstrasse 36, Berlin, Germany N. D. Zakharov and P. Werner Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, Halle, Germany Received 26 May 2004; revised manuscript received 20 October 2004; published 20 January 2005 The photoluminescence PL of self-organized InAs/GaAs quantum dots QD s shows a decomposition into a set of eight rather narrow lines upon antimony-surfactant mediated growth. This decomposition results from a shell-like growth mode, which means a discrete variation of the QD size in monolayer steps. Based on the PL monolayer splitting, indicative of structurally and chemically well-defined upper interfaces, structural and optical properties can be correlated much more in detail than previously possible for strongly broadened QD ensembles. A comparison of the spectral positions to predictions of eight-band k p/ configuration interaction model calculations for truncated pyramidal InAs/ GaAs QD s yields excellent agreement only for the shell-like QD growth mode. DOI: /PhysRevB PACS number s : Hc, Cr, La, Qe I. INTRODUCTION Epitaxy of highly strained layers on planar substrates yields a large density of self-similar coherent clusters, dubbed QD s, 1,2 providing a strong three-dimensional confinement for charge carriers. Self-organization controls the growth. 2 Identifying and controlling the structural and chemical properties of such QD s in detail has been proven difficult. Their properties depend intricately on details of the growth and are often substantially inhomogeneous. Equally important, a detailed understanding of the correlation of electronic/optical and structural/chemical properties of self-organized QD s is still rather incomplete. The lattice mismatch, being decisive for the growth, results in a complex inhomogeneous strain distribution, together with chemical inhomogeneity in and around the QD s, which makes intuitive predictions of electronic/optical properties impossible since both the chemical composition and the strain contribute to the local potential. 3,4 Simple box-type or harmonic oscillator potentials fail and realistic modeling is required. Calculations based on eight-band k p Refs. 5 8 or empirical pseudopotential theory 9,10 reflect the strong impact of details of size, shape, and composition and provide quantitative predictions. In particular eight-band k p theory has been successfully applied to discuss quantitatively experimental results on, e.g., the polar exciton-lo-phonon interaction, the permanent dipole moment, the quantum size effect, the exciton oscillator strength, and few-particle effects in QD s The results of such calculations depend largely on structural and chemical properties based on high resolution transmission electron microscopy HRTEM or cross-sectional scanning tunneling microscopy XSTM. Ab initio it is not yet clear how close to quantitative reality the predicted properties of such model QD s are. A precondition for quantitatively linking experimental and calculated results is detailed information on an atomistic level about the investigated QD s. Both structural 15 and optical characterization results of single QD s are typically uncorrelated and still too scarce for a statistical analysis. Presently, at best average properties of QD s can be compared. Instead of using structural input parameters for theory to predict optical properties one could imagine to invert the procedure by using precise results of spectroscopic investigations to predict the QD structure. In recent years a bimodal distribution has been observed repeatedly for the ground state optical transition in QD s and tentatively explained by a bimodal distribution of their size, aspect ratio or composition Here, we report on the observation of a multimodal distribution of the exciton ground state recombination energy in an ensemble of self-organized InAs/ GaAs QD s. Eight clearly resolved peaks will be shown to result from a monolayer variation of the QD size. Observation of such a monolayer splitting implies the existence of structurally and chemically well-defined interfaces. The optical results allow us to draw quantitative conclusions about the shape, composition, and the height of the investigated QD s based on realistic eight-band k p/ configuration interaction model calculations. An evolution of the QD size in monolayer steps caused by a shell-like growth is discovered and analyzed. II. THE INVESTIGATED SAMPLES AND THE EXPERIMENTAL SETUP The investigated samples were grown by metal-organic chemical vapor deposition MOCVD on GaAs 001 substrates. Trimethylindium, trimethylgallium, and tertiarybutylarsine were used as precursors. At 625 C a 300 nm thick GaAs buffer layer followed by a 60 nm Al 0.6 Ga 0.4 As diffusion barrier and 90 nm GaAs were grown. For the growth of the QD layer of type A the growth temperature was reduced to 485 C before depositing about 1.9 ML InAs followed by a 5 s growth interruption. Subsequently, the QD s were capped by 50 nm GaAs. The first 5 nm were grown at 485 C, then the temperature was ramped up to 600 C during growth. Finally, a 20 nm Al 0.33 Ga 0.67 As diffusion barrier and a 10 nm GaAs capping layer were deposited /2005/71 4 / /$ The American Physical Society

2 HEITZ et al. FIG. 1. Typical cross section high resolution transmission electron micrograph of an InAs/ GaAs quantum dot. Evaluation of the shape yields a truncated pyramid with a height of six monolayers. Triethylantimony was added for sample of type B during the deposition of the InAs layer and the growth interruption. Antimony is hardly incorporated due to its large size, but acts as a surfactant modifying the evolution of the InAs QD s. 25,26 Part of sample B were ex situ annealed under an As atmosphere. Transmission electron microscopy investigations of such samples type A reveal a truncated pyramidal see Fig. 1 shape of InAs/GaAs QD s with a density of about cm A detailed study on structural properties dependent on varying growth conditions will be subject to an extra publication. 27 For photoluminescence PL and PL excitation PLE experiments the samples were mounted in a continuous-flow He cryostat, giving access to temperatures between 5 K and 315 K. A tungsten lamp dispersed by a 0.27 m doublegrating monochromator served as low-density, tunable excitation source. The luminescence was spectrally dispersed by a 0.3 m double-grating monochromator and detected by a cooled Ge-diode using lock-in technique. III. MONOLAYER SPLITTING FOR SELF-ORGANIZED InAs/ GaAs QD S Figure 2 compares low-temperature PL spectra of samples A and B excited at ev in the GaAs barrier. The excitation density is about 5 mw cm 2, being well in the linear regime, with an average occupation of the QDs with less FIG. 2. Photoluminescence spectra of samples A and B recorded at 7 K at an excitation density below 5 mw cm 2. than one exciton. Both samples show QD related emission between 1.02 and 1.37 ev. Detailed growth investigations suggest the large overall full width at half maximum FWHM to result from the fact that the morphology of the InAs layer is far from equilibrium under the chosen growth conditions. 26 Extending the growth interruption time shifts the PL maximum to lower energies and reduces the overall FWHM as shown in Ref. 26. Though both spectra show multimodal decomposition of the PL, the decomposition is particularly pronounced for sample B, showing eight peaks. The presence of antimony seems to have a large impact on the surface kinetics, 26 resulting in an enhanced PL modulation contrast and larger QD s, emitting at lower energies. Additionally, the individual subensemble peaks are shifted by 15 mev to lower energies. In the following we will concentrate on B-type samples. We first turn to explain the multimodal PL. Interference effects can be safely excluded. The modulation is independent of the orientation of the sample and depends on the active QD layer. In addition, the peak positions shift with increasing temperature as expected for InAs/ GaAs QD s, in contrast to what would be expected for an interference pattern. A second possibility could be a nonequilibrium population of the QD s due to complex carrier dynamics, e.g., restricted relaxation. However, the energy spacings between individual peaks, varying between 29 and 51 mev, do neither agree with the LO-phonon nor excited state energies. Furthermore, PLE spectra Fig. 3 do not show corresponding excitation channels. Therefore emission from excited QD states can be neglected in our spectrum. The third explanation is based on the assumption of a heterogeneous and well defined distribution of QD sizes. Here, we resolve eight clearly distinguished peaks, suggesting that the very large overall inhomogeneous broadening 200 mev is dominated by a discrete, steplike variation of the size of the QD s. We test first whether the various lines are caused by a variation of the QD height in monolayer steps. The energy shift between subsequent peaks is expected to decrease with increasing height, in qualitative agreement with the experimental results Fig. 4. Although the absolute thickness is not self-evident, we tentatively assume that the peak at 1.36 ev corresponds to a height of 2 ML. The peaks in Fig. 2 are labeled accordingly. If monolayer steps in the QD height cause the multimodal PL, some conclusions can be immediately drawn. The QD s must have a flat truncated shape with well-defined upper 001 interfaces. Indeed, QD s with such interfaces have been observed in XSTM of similarly grown QD s. 29 Spectral broadening caused by variations of the base length, the interface roughness, or composition fluctuations must be smaller than the energy shift caused by the addition of one monolayer to the height. Figure 4 depicts the evolution of the peak separation and FWHM as a function of the height of the QD s, showing the FWHM of the individual peaks to decrease from above 33 mev to about 25 mev with increasing thickness. The peak separation decreases from 51 to 29 mev with increasing thickness. The existence of well-defined upper interfaces suggests In/ Ga interdiffusion as negligible. Indeed, the observation of a large substate splitting of 120 mev shown in Fig. 5 sup

3 SHELL-LIKE FORMATION OF SELF-ORGANIZED FIG. 3. PL and PLE spectra shifted vertically of sample B recorded at T=7 K and excitation densities below 5 mw cm 2. The detection energies of the PLE spectra are marked by arrows. ports strongly small InAs QD s. Ex situ annealing experiments, degrading the definition of the interfaces by In/ Ga interdiffusion, demonstrate the crucial role of the interfaces of the QD s. Figure 6 compares normalized PL spectra of as-grown and two annealed samples 10 min at 700 C and 730 C, respectively. The decreasing contrast of the modulation with increasing annealing temperature is due to the degradation of the interfaces by In/Ga interdiffusion. The PL shows no influence of the annealing on the PL peak positions. PLE spectra, however, recorded at a given ground state transition energy see inset of Fig. 6, show a slight reduction of the substate splitting upon annealing, resulting either from FIG. 4. Energy separation and FWHM of emission peaks observed for sample B as a function of the height of the QD s. The data have been obtained by a multi-gaussian fit to the PL spectrum see Ref. 28. an increasing effective size of the QD s or an increasing Ga concentration within the QD s. Information on exciton localization and lateral confinement is obtained from PLE spectra. Figure 3 compares PLE spectra detected at the maximum of the different subensemble peaks, showing the impact of a ML increase of the height of the QD s. All PLE spectra have a common excitation resonance at 1.45 ev, which is attributed to absorption in the wetting layer. Thus, all QD s are surrounded by a one ML thick wetting layer, which limits exciton localization in the QD s. The exciton localization increases from 100 mev for QD s with a height of 2 ML to 360 mev for QD s with a height of 9 ML. Figure 5 depicts a contour plot of the PL intensity as a function of the detection and excess excitation energies. The intensity is given on a logarithmic scale. The plot was generated from a series of PLE spectra. The y axis presents the energy difference between excitation and detection energy. Modulation upon resonant excitation is clearly resolved, e.g., in the n=1 state at 120 mev, proving unambiguously a multimodal distribution of the QD ground state transition as origin of the observed modulation of the PL intensity. With increasing exciton localization energy the number of excited exciton states increases. Especially the large separation of the n=1 resonance, appearing 120 mev above the ground state, provides additional guidance in view of internal QD composition and QD size. This peak originates from an excited exciton, composed of the first excited electron and hole state. 3,12 The large splitting to the ground state transition, which mainly results from the large ground to first excited electron splitting, again is a result of pure InAs QD s with a rather small lateral extension. The apparent decrease of the quantization for the flattest QD s of 3 ML and 2 ML height is attributed to a delocalization of the excited state into the wetting layer

4 HEITZ et al. FIG. 5. Contour plot of the PL intensity in dependence on the detection and excess excitation energies. The plot was generated from a series of PLE spectra and the intensity is given on a logarithmic scale. IV. PREDICTED ABSORPTION SPECTRA OF TRUNCATED PYRAMIDAL InAs/ GaAs QD S FIG. 7. The five steps involved in modeling the electronic and optical QD properties see text. Excitonic properties are now calculated for self-organized QD s based on a three-dimensional implementation of the eight-band k p model and a configuration interaction scheme. 3,5,6 The calculations account for the inhomogeneous strain distribution, the piezoelectric potential, interband mixing and Coulomb interactions. A schematic presentation of the five steps involved is shown in Fig. 7 and works in the following way: a The modeling process starts with an assumption on shape, size, and composition guided either by structural investigations of a QD sample or as in this work suggested only by peculiarities of the optical spectra. b Next, the strain distribution and the piezoelectric potential are calculated which enter c the strain-dependent eightband k p Hamiltonian. By solving the Schrödinger equation we obtain single-particle wave functions. The parameters entering this Hamiltonian are based on experimental values for the required bulk material -point band structure parameters. Free, adjustable parameters are not present in this model. d The single-particle states provide a basis for the configuration interaction model which is applied to calculate excitonic properties, including correlation and exchange. e Finally the optical absorption spectra are computed. By using this procedure good agreement between experiment and prediction has been demonstrated for pyramidal InAs/GaAs QD s, with regard to exciton properties 12 as well as single-particle localization energies. 30 Here, the model is applied to flat truncated InAs/ GaAs QD s surrounded by a one ML thick InAs wetting layer, as implied by the structural FIG. 6. Normalized PL spectra of three pieces of sample B, which are as-grown or have been annealed for 10 min at 700 C and 730 C, respectively. The inset shows corresponding PLE spectra detected at ev. FIG. 8. Absorption spectra calculated in an eight-band k p model for InAs/GaAs QD s as a function of the height. A truncated pyramidal shape with 110 -side facets and base lengths of 13.6 nm was assumed

5 SHELL-LIKE FORMATION OF SELF-ORGANIZED FIG. 9. a Predicted solid symbols and observed open symbols energies of the ground n=0 and first excited n=1 exciton transition in truncated pyramidal InAs/ GaAs QD s as a function of height. b The corresponding energy separation between the n=0 and n=1 transitions. data inferred from the optical results. The base length of the QD s up to this stage was not yet discussed, but will be now determined from comparison to the experimental results in the following. Figure 8 displays calculated exciton absorption spectra for QD s of different height with a base length of 13.6 nm. The spectra show a blueshift of 145 mev for the ground state transition energy upon reducing the QD height from a pointed pyramid down to 3 ML truncated one. The dependence of the transition energies and first excited state splitting on the height of the QD s are summarized for constant base lengths of 10.2 and 13.6 nm gray solid symbols in Figs. 9 a and 9 b, respectively. Open symbols are experimental results obtained by multi-gaussian fits to the PL spectrum and PLE spectra measured at the maximum of the respective PL peak. The impact of height variations on the inhomogeneous broadening decreases for larger QD s leading to smaller narrower FWHMs and peak separations see Fig. 4. The energetic positions of the ground and excited states Fig. 9 a as well as the substate splitting Fig. 9 b show good agreement between theory and experiment for a QD base length of 10.2 nm and a QD height of 3 ML or a base length of 13.6 nm and a QD height of 9 ML. This agreement suggests the base length to increase in 2 ML steps with increasing QD height in monolayer steps. Qualitative correlations between width and height have been reported previously based on AFM Refs. 31 and 32 and optical experiments. 33,34 Variation of theoretical lateral confinement dramatically improves the agreement with the experimental results. The solid black symbols in Figs. 9 a and 9 b take into account stepwise increasing the QD lateral extension with increasing QD height, corresponding to a shell-like evolution of the QD volume see inset of Fig. 9 a. Based on

6 HEITZ et al. this assumption experiment and theory show absolutely excellent agreement. Therefore, the average base length and height of the QD s are correlated for the investigated samples. With increasing volume of the QD s the height-to-base length aspect ratio becomes larger. Calculations predicted such a correlation as a consequence of the size-dependent balance between surface/interface energies and the strain energy. 35 Note that the reported results might be bound to the used growth conditions. However, we believe that similar effects take place in a larger range of growth conditions, though the interface quality and the overall height variation might be too small to observe the ML splitting, which is the basis of the present paper. V. CONCLUSION A distinct multimodal decomposition of the PL of InAs/GaAs QD s grown by MOCVD with antimony as surfactant is reported for the first time. The multimodality is unambiguously attributed to a shell-like growth mode leading to ML-steps of the QD size. Based on the optical data we deduce a flat shape with both a structurally and chemically well-defined upper InAs/GaAs 001 interface. The large splitting between the exciton ground and excited state of 120 mev supports a practically ideal InAs composition of small QD s. The conclusions are based on a comparison to predictions of an eight-band k p/ configuration interaction model for exciton states. ACKNOWLEDGMENTS Parts of this work are supported by the SANDiE Network of Excellence of the European Commission, Contract No. NMP4-CT , by the NANOMAT project of the European Commission s Growth Programme, Contract No. G5RD-CT , and by Deutsche Forschungsgemeinschaft in the framework of SFB 296. Parts of the electronic structure calculations were performed on the IBM p690 computer of the HLRN within Project No. bep In addition we want to thank Volker Türck and Udo Pohl for many fruitful discussions. *Deceased. Electronic address: florian@sol.physik.tu-berlin.de 1 D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures Wiley, Chichester, V. A. Shchukin, N. N. Ledentsov, and D. Bimberg, Epitaxy of Nanostructures Springer, Berlin, M. Grundmann, O. Stier, and D. Bimberg, Phys. Rev. B 52, F. Guffarth, R. Heitz, A. Schliwa, O. Stier, N. N. Ledentsov, A. R. Kovsh, V. M. Ustinov, and D. Bimberg, Phys. Rev. B 64, O. Stier, M. Grundmann, and D. Bimberg, Phys. Rev. B 59, O. Stier, A. Schliwa, R. Heitz, M. Grundmann, and D. Bimberg, Phys. Status Solidi B 224, W. Sheng and J.-P. Leburton, Phys. Rev. B 63, R C. Pryor, Phys. Rev. B 57, L.-W. Wang, J. Kim, and A. Zunger, Phys. Rev. B 59, A. J. Williamson and A. Zunger, Phys. Rev. B 59, R. Heitz, I. Mukhametzhanov, O. Stier, A. Madhukar, and D. Bimberg, Phys. Rev. Lett. 83, R. Heitz, O. Stier, I. Mukhametzhanov, A. Madhukar, and D. Bimberg, Phys. Rev. B 62, F. Guffarth, R. Heitz, A. Schliwa, O. Stier, M. Geller, C. M. A. Kapteyn, R. Sellin, and D. Bimberg, Phys. Rev. B 67, S. Rodt, A. Schliwa, R. Heitz, V. Türck, O. Stier, R. L. Sellin, M. Strassburg, U. W. Pohl, and D. Bimberg, Phys. Status Solidi B 234, H. Eisele, O. Flebbe, T. Kalka, F. Heinrichsdorff, A. Krost, D. Bimberg, and M. Dähne-Prietsch, Phys. Status Solidi B 215, J. J. Finley, A. D. Ashmore, A. Lemaitre, D. J. Mowbray, M. S. Skolnick, I. E. Itskevich, P. A. Maksym, M. Hopkinson, and T. F. Krauss, Phys. Rev. B 63, D. V. Regelman, E. Dekel, D. Gershoni, E. Ehrenfreund, A. J. Williamson, J. Shumway, A. Zunger, W. V. Schoenfeld, and P. M. Petroff, Phys. Rev. B 64, F. Findeis, M. Baier, A. Zrenner, M. Bichler, G. Abstreiter, U. Hohenester, and E. Molinari, Phys. Rev. B 63, R S. Anders, C. S. Kim, B. Klein, M. W. Keller, R. P. Mirin, and A. G. Norman, Phys. Rev. B 66, M. Colocci, F. Bogani, L. Carraresi, R. Mattolini, A. Bosacchi, S. Franchi, P. Frigeri, M. Rosa-Clot, and S. Taddei, Appl. Phys. Lett. 78, G. Saint-Girons, G. Patriarche, L. Largeau, J. Coelho, A. Mereuta, J. M. Moison, J. M. Gerard, and I. Sagnes, Appl. Phys. Lett. 79, Y. C. Zhang, C. J. Huang, F. Q. Liu, B. Xu, J. Wu, Y. H. Chen, D. Ding, W. H. Jiang, X. L. Ye, and Z. G. Wang, J. Appl. Phys. 90, H. Lee, R. Lowe-Webb, T. J. Johnson, W. Yang, and P. C. Sercel, Appl. Phys. Lett. 73, L. Brusaferri, S. Sanguinetti, E. Grilli, M. Guzzi, A. Bignazzi, F. Bogani, L. Carraresi, M. Colocci, A. Bosacchi, P. Frigeri, and S. Franchi, Appl. Phys. Lett. 69, X. Yang, M. J. Jurkovic, J. B. Heroux, and W. I. Wang, Appl. Phys. Lett. 75, K. Pötschke, L. Müller-Kirsch, R. Heitz, R. L. Sellin, U. W. Pohl, D. Bimberg, N. D. Zakharov, and P. Werner, Physica E Amsterdam 21, K. Pötschke, U. W. Pohl, R. Heitz, L. Müller-Kirsch, R. L. Sellin, D. Bimberg, N. D. Zakharov, and P. Werner unpublished. 28 F. Guffarth, R. Heitz, A. Schliwa, K. Pötschke, and D. Bimberg, Physica E Amsterdam 21, H. Eisele, O. Flebbe, T. Kalka, C. Preinesberger, F. Heinrichs

7 SHELL-LIKE FORMATION OF SELF-ORGANIZED dorff, A. Krost, D. Bimberg, and M. Dähne-Prietsch, Appl. Phys. Lett. 75, S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, Phys. Rev. B 68, I. Mukhametzhanov, Z. Wei, R. Heitz, and A. Madhukar,Appl. Phys. Lett. 75, H. Saito, K. Nishi, and S. Sugou, Appl. Phys. Lett. 74, R. Heitz, A. Kalburge, Q. Xie, M. Grundmann, P. Chen, A. Hoffmann, A. Madhukar, and D. Bimberg, Phys. Rev. B 57, M. Grundmann, N. N. Ledentsov, O. Stier, J. Böhrer, D. Bimberg, V. M. Ustinov, P. S. Kopev, and Z. I. Alferov, Phys. Rev. B 53, R L. G. Wang, P. Kratzer, N. Moll, and M. Scheffler, Phys. Rev. B 62,