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Phys. Status Solidi C, 1– 4 (2009) / DOI 10.1002/pssc.200982614

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current topics in solid state physics

Evidence of excitonic transitions by angle-resolved reflectivity for the determination of oscillator strengths in GaN/(Al,Ga)N quantum wells

G. Rakotonanahary*,1, S. Aberra Guebrou1, D. Lagarde1, F. Natali2, F. Reveret1, P. Disseix1, J. Leymarie1, M. Leroux2, and J. Massies2 1 2

LASMEA, UMR 6602 CNRS/Université Clermont-Ferrand II, 63177 Aubière, France CHREA, CNRS, 06560 Valbonne, France

Received 19 June 2009, accepted 1 July 2009 Published online 9 December 2009 PACS 71.35.Cc, 78.55.Cr, 78.66.Fd, 78.67.De * Corresponding author: [email protected]

We report on a study of the excitonic properties of GaN/AlxGa1-xN quantum well samples using continuous-wave reflectivity and photoluminescence measurements. Weak excitonic signals superposed to large oscillations resulting from the interferences in

the buffer layers are highlighted by angle-resolved reflectivity. The quantum well excitonic oscillator strength was determined from the fitting of the experimental spectra and the influence of aluminum concentration of the barrier was also investigated.

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1 Introduction Nitride quantum wells embedded in planar microcavities have been demonstrated to be excellent candidates for the strong light-matter coupling observation [1-3]. However GaN/AlxGa1-xN heterostructures grown along the (0001) axis exhibit an intense internal electric field responsible of the well-known Quantum Confined Stark Effect which significantly weakens the oscillator strength of excitons [4]. The oscillator strength of GaN/(Al,Ga)N quantum wells (QW) is investigated through reflectivity experiments at low temperature for incidence angles varying from 5° to 80°. Several samples grown on silicon and sapphire substrates have been studied in order to explore the influence of the aluminum barrier composition and the well width: (x = 8%, L = 2.5 nm), (x = 10%, L = 2.2 nm), (x = 20%, L = 2.0 nm). We will particularly focus on the angle-resolved experiments which highlight the weak excitonic structures from interferences under particular incidence angles. The reflectivity spectra are compared with transfer matrix calculations which enable to determine the oscillator strengths and transition energies of both A and B excitons in bulk GaN and in the quantum well. Photoluminescence experiments as a function of temperature were performed in order to assess the localization energy of the quantum well excitons.

2 Samples description and experimental details Two samples (labelled 1 and 2) are investigated in this work. The first one was grown by molecular beam epitaxy on a silicon substrate and contains 8 QW of 25 Ǻ thickness with Al0.08Ga0.92N barriers. The latter are grown on a thick Al0.08Ga0.92N deposited on a buffer of AlN (40 nm)/GaN (250 nm)/AlN (250 nm). The second sample was elaborated on a GaN template grown on a sapphire substrate. It consists of thick layers of GaN (3 µm), Al0.12Ga0.88N (1 µm) and a set of 8 GaN quantum wells of 25 Ǻ thickness. The aluminum composition of the barrier is 12%. Angle-resolved reflectivity and photoluminescence measurements were performed at low temperature (T = 5 K). The sample is placed inside a rotating cryostat with quartz cylindrical windows. The excitation beam coming from a halogen lamp is sent through a polarizer on the sample by a mirror positioned at 45°. The whole is mounted on a rotating rail which allows the reflectivity to be detected with an incidence angle varying from 5 to 80°. The sample’s response is focused on the slit of a monochromator and detected by a CCD camera. The photoluminescence spectra were obtained using the continuous excitation of a He-Cd laser at 325 nm.

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3 Results and discussion The angle-resolved reflectivity was investigated for the transverse electric (TE) (electric field perpendicular to the c-axis) and the transverse magnetic (TM) (magnetic field perpendicular to the c-axis) polarizations. The responses of the sample are almost the same in both polarizations. The only significant difference occurs around 65° for which a very weak signal is detected for the TM mode. This is due to the zero reflexion Brewster angle, which in our case occurs at 67° approximately.

peak at 3500 meV. The photoluminescence peak and the reflectivity excitonic structure are splitted by 20 meV due to the excitonic localization. Sample 2 shows very tight oscillations under the bandgap energy of GaN due to the large thickness of the GaN buffer layer. Moreover, the higher quality of the sample offered by the GaN template allows to observe the excitons XA(n=1), XB (n = 1) in bulk GaN respectively at 3494 meV and 3502 meV on the reflectivity spectrum. The free excitonic transitions are evidenced at the same energies on the photoluminescence spectrum where additional lines due to excitons bound to impurity levels are also observed. The excited donor bound state related to n = 2 free excitons is detected a 3512 meV (DBEn=2). The fact that the energies of excitonic transitions are slightly higher than in sample 1 can be explained by a large strain experienced by the GaN layer. The corresponding stress is evaluated to be about 7 kbar [5]. The bandgap energy of the barrier alloy is located around 3760 meV. The transition energy of the exciton in the quantum well is measured at 3580 meV in the reflectivity spectrum.

Figure 1 Low temperature reflectivity and photoluminescence spectra at normal incidence on (a) sample 1 and (b) sample 2.

Figure 1 presents reflectivity and photoluminescence spectra of samples 1 and 2. The reflectivity spectra are characterized by oscillations whose amplitude decrease when the photon energy approaches the GaN bandgap and vanishes above the gap of (Al,Ga)N. These oscillations are due to the interferences inside the epitaxial layers. For sample 1, the exciton energy in GaN was found at 3475 meV in reflectivity and the alloy’s bandgap energy around 3640 meV. The latter is more difficult to point on the spectra but corresponds approximately to the vanishing of the oscillations. An additional excitonic structure is observed at higher energy, around 3520 meV and attributed to the transition energy of the free exciton in the quantum well. This is confirmed by the photoluminescence spectrum with a © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Figure 2 (a) Evolution of the reflectivity spectra of sample 1 as a function of the incidence angle at T = 5 K. (b) Measured and simulated reflectivity spectra for an incidence angle varying from 5° to 35°. Solid and dashed lines correspond to experiments and simulations, respectively.

Figure 2 presents the reflectivity spectra of sample 1 in the region related to the GaN quantum well for various incidence angles from 5° to 80° for the TE polarization. Not only one but two excitonic features which are independent of the incidence angle can be distinguished. They are attributed to excitonic transitions in the quantum well. As shown in Fig. 2, both structures can be clearly separated around 35°, while it is more difficult under normal incidence. They are located at 3517 meV and 3529 meV and www.pss-c.com

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are labelled by A1 and B1, respectively. We will discuss about their nature below. Whereas reflectivity spectra exhibit two excitonic structures, photoluminescence displays only one peak at 3503 meV. This is explained by the fact that the emission linewidth (20 meV) is larger than the difference between the transition energies deduced from the reflectivity spectrum (12 meV). Simulations of reflectivity are performed using standard transfer matrix formalism where the contribution of excitons to the dielectric function can be modeled by harmonic oscillators: εr = εb + Σi Ai / (E²-E0i²+jγiE) [6], where εb is the background dielectric function, E0i the excitonic resonance energy, γi the broadening parameter and Ai a parameter proportional to the oscillator strength. The band-to-band absorption in the GaN well is taken into account through a sigmoidal function centered on the bandgap energy. The fitting parameters are the energy, the oscillator strength and the broadening of excitons and also the bandgap energies of GaN and (Al,Ga)N. The thickness of the various layers in the structure has also been adjusted in order to fit the interference oscillations (thickness gradient along the sample). Figure 2b displays the evolution of theoretical and experimental spectra for various incidence angles, for sample 1. The solid and dotted lines represent the experimental data and the fit, respectively. A good agreement is found between experimental and calculated spectra. The oscillator strength values related to A1 and B1 are respectively found to be equal to 90000±12000 meV² and 50000±7000 meV² with broadenings equal to 12±2 meV and 11±2 meV, respectively.

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in Fig. 3 but only one quantum well signature was detected from 5° to 80°. For the thick GaN layer, the same oscillator strength of 50000±7000 meV² and inhomogeneous broadening of 3 meV for both excitons A and B were determined. Concerning the quantum wells, although only one excitonic resonance is detected, the experimental spectra were fitted considering two excitons. The best fit led to 3580 meV and 3585 meV for the excitonic energies A1 and B1 and to 50000±7000 meV² and 40000±6000 meV² for their respective oscillator strengths. The inhomogeneous broadenings are 16±2 meV and 15±2 meV, respectively. 3.1 Photoluminescence experiments

Figure 4 Temperature dependence of the photoluminescence peak energies of sample 2. Solid lines correspond to Varshni fits. Transition energies measured in reflectivity are also displayed.

Figure 3 Measured and simulated reflectivity spectra for incidence angle varying from 5° to 30°. Solid lines are the experiments and dashed lines are the simulation.

These values are consistent with those obtained by Zamfirescu et al. in Al0.07Ga0.93N quantum wells [7]. The reflectivity spectra corresponding to sample 2 have been plotted

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At low temperature, free excitonic transitions are detected in reflectivity. It is not the case in photoluminescence where extrinsic transition involving impurity levels or transitions associated to localized excitons are often observed. However, when no excitonic signal corresponding to the quantum well transitions can be detected by reflectivity, it is always possible to perform temperature dependent photoluminescence experiments in order to determine the localization energy of the quantum well excitons. Without localization effect, the temperature behavior of the photoluminescence energies can be described by the Varshni empirical formula (Fig. 4). The fit of the latter to the experimental energies leads to E(T) = E0 – 0.87 T²/ (T+900 ) for the bulk GaN excitons (XA, XB) and for the quantum well transition energies (E0 = 3495 meV and 3505 meV for the bulk GaN excitons A and B and 3578 meV for the quantum well). Concerning the (Al, Ga)N barriers, the formula is slightly different: E(T) = 3762 – 0.92 T² / (T+806). It is then possible to extrapolate the free excitonic quantum well transition at low temperature which is found in very good agreement with the reflectivity. It has to be noted that for sample 2, the luminescence peak correspond-

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ing to the quantum well transition energy remains intense in the whole temperature range. This is due to the high quality of the sample improved by the GaN template grown on sapphire substrate. 3.2 Analysis By considering envelope function calculations including the confined Stark effect, the quantum well excitonic transitions (A1 and B1) observed for sample 1 are attributed to the recombinations between electrons and holes confined in Γ9 and Γ7 valence bands (generally labelled A and B). The Γ9 - Γ7 crossover of AlxGa1-xN can be calculated when x varies [8, 9]. Nevertheless, the x value for which it occurs is directly influenced by the crystal field and spinorbit term values which can be chosen [10]. For values linearly interpolated between those of the binary compounds ( Δcr(GaN) = 20 meV and Δcr(AlN) = -150 meV, Δso(GaN) = 13 meV and Δso(AlN) = 17.5 meV [10,5] ), the Γ9 - Γ7 crossover occurs at x = 11%. For the quantum well transitions (A1 and B1), the crossover does not necessary occur at the same aluminum composition because of the confinement effect. This can be shown by envelope function calculations. Nevertheless, due to the large scatter in the parameters entering in the calculation (valence band offset, effective masses, bowing parameter, see reference [11] for a review) it is difficult to estimate accurately the value of the aluminum composition corresponding to the quantum well transition Γ9 - Γ7 crossover. Our experimental results show that this crossover is not very far from x = 0.12 in agreement with Leroux et al. [10]. This can explain the difficulty to separate the two excitonic transitions in the well for sample 2 in addition to their larger broadening and their lower energy difference. The internal electric field F in the quantum well (|F| = ΔP/εr ε0 where ΔP is the difference between the polarizations in the barrier and in the quantum well, and εr is the static dielectric constant which is supposed to be the same in AlN and GaN) increases with the aluminum composition of the barriers. A linear dependence was demonstrated: F = α x where α lies between 5.5 and 6 MV/cm [12-14] in agreement with our results. Consequently, the overlap of the electron and hole wave functions which is proportional to the oscillator strength decreases also with the aluminum composition. This is coherent with the lower oscillator strength values obtained for sample 2 in comparison with sample 1.

quantum well thicknesses or high aluminum barrier compositions. These limitations were overcome by using angle-resolved reflectivity experiments together with transfert-matrix simulations. Two excitonic transitions involving confined electrons and confined holes, relative to the Γ9 and Γ7 valence bands, were identified for an aluminum composition of 8% in the barriers. The oscillator strengths of these transitions were determined. In addition, our results corroborated by envelope function calculations show that the Γ9 - Γ7 crossover can be expected around 12%. References [1] A. Kavokin, J. Baumberg, G. Malpuech, and F. Laussy, Microcavities (Oxford University Press, New York, 2007). [2] G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Rev. B 73, 153305 (2006). [3] Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, Appl. Phys. Lett. 93, 051102 (2008). [4] J.S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, Phys. Rev. B 57, R9435 (1998). [5] O. Aoudé, P. Disseix, J. Leymarie, A. Vasson, M. Leroux, E. Aujol, B. Beaumont, A. Trassoudaine, and Y. André, Phys. Rev. B 77 045206 (2008). [6] L. C. Andreani, in Confined Electrons and Photons, edited by E. Bunstein and C. Weisbuch (New York, 1995), p. 57. [7] M. Zamfirescu, B. Gil, N. Grandjean, G. Malpuech, A. Kavokin, P. Bigenwald, and J. Massies, Phys. Rev. B 64, 121304 (R) (2001). [8] J. J. Hopfield, Phys. Rev. 112, 1555 (1958). [9] S. L. Chuang and C. S. Chang, Phys. Rev. B 54, 2491 (1996). [10] M. Leroux, F. Semond, F. Natali, D. Byrne, F. Cadoret, B. Damilano, A. Dussaigne, N. Grandjean, A. Le Louarn, S. Vézian, and J. Massies, Superlattices Microstruct. 36, 659–674 (2004). [11] M. Leroux, Matériaux semi-conducteurs III-V, II-VI et nitrures pour l’optoélectronique (Hermes, Science Publications, Paris, 2003), Chap 5, p 169. [12] M. Leroux, N. Grandjean, M. Laügt, J. Massies, B. Gil, and P. Lefebvre, Phys. Rev. B 58, R13371 (1998). [13] V. Fiorentini, F. Bernardini, F. Della Sara, A. Di Carlo, and P. Lugli, Phys. Rev. B 60, 8849-8858 (1999). [14] F. Natali, D. Byrne, M. Leroux, B. Damilano, F. Semond, A. Le Louarn, S. Vezian, N. Grandjean, and J. Massies, Phys. Rev. B 71, 75311 (2005).

4 Conclusion In conclusion, we have presented an experimental procedure to highlight excitonic transitions in GaN/(Al,Ga)N quantum well reflectivity spectra for the determination of their oscillator strength. The main limitations for this determination is the presence of interferential oscillations in the reflectivity spectra due to the buffer layers required to improve the quality of quantum wells. Moreover, the Stark effect weakens the excitonic features particularly for large

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