phys. stat. sol. (c) 4, No. 1, 108 – 111 (2007) / DOI 10.1002/pssc.200673562

Strong coupling in bulk GaN microcavities grown on silicon F. Réveret*, 1, I. R. Sellers2, P. Disseix1, J. Leymarie1, A. Vasson1, F. Semond2, M. Leroux2, and J. Massies2 1 2

LASMEA, UMR 6602 UBP/CNRS, 24 Avenue des Landais, 63177 Aubière Cedex, France CRHEA-CNRS, rue Bernard Gregory, 06560 Valbonne, France

Received 31 May 2006, revised 29 June 2006, accepted 3 July 2006 Published online 11 January 2007 PACS 42.55.Sa, 71.35.–y, 71.36.+c, 78.66.Fd We have studied GaN microcavities grown on silicon by angle resolved reflectivity at 5 and 300 K. A Bragg mirror made up of λ/4 AlGaN and AlN layers has been grown on a silicon substrate. The GaN active layer whose thickness is equal to λ/2 is covered by a 100 Å thick aluminium layer which acts as the top mirror. Transfer matrix simulations are carried out to interpret the reflectivity spectra from which crucial parameters of the active layer such as the oscillator strengths, the excitonic energies and the associated broadenings of A and B excitons are deduced. At low temperature the strong coupling regime between with A and B excitons and the cavity photonic mode is clearly observed. At room temperature the splitting is evaluated to 45 meV. In order to get further insight in the physics of nitride-based microcavities and especially to improve the exciton-photon coupling, the influence of the Bragg or metallic mirrors on the cavity is analysed. The inhomogeneous broadening of excitons together with the strain gradient experienced by the active layer along the growth axis are also investigated. All of these effects on the Rabi splitting are analysed and discussed. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction In the field of physics of light matter coupling and since the first observation and measurement of the Rabi splitting in bulk GaN microcavities at low and room temperature, the main goal is now to improve the quality of both GaN active layer and Bragg mirrors in order to obtain the largest photon-exciton coupling [1–5]. New optoelectronics devices such as polariton light emitters or ultra-fast micro-optical amplifiers could be then investigated in a near future [6, 7]. In this paper, we present both experimental and theoretical results of angle-resolved reflectivity for GaN microcavities and the exciton parameters are deduced from the best fit to the reflectivity spectra at 5 K and room temperature.

2 Sample description and experimental setup We studied λ/2 GaN microcavities grown by molecular beam epitaxy, λ being the resonance wavelength of the cavity mode. The structure consists of a silicon substrate and a λ/4 AlGaN/AlN Bragg mirror which contains first seven (A714), ten (A808) and fifteen (A771) pairs respectively for the three investigated samples and an active λ/2 GaN layer. A 100 Å thick aluminium layer is then deposited and acts as the top mirror. The sketch of the structure is presented on Fig. 1. A thickness gradient is naturally introduced during the growth so that the cavity mode can be tuned with the excitonic transition energy along the sample. *

Corresponding author: e-mail: [email protected], Phone: +33 473 407 333, Fax: +33 473 407 262

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phys. stat. sol. (c) 4, No. 1 (2007)

109 100 Å Al mirror λ/2 GaN λ/4 AlGaN λ/4 AlN

Bragg mirror 7, 10 or 15 pairs

Si Substrate

Fig. 1 Sketch of structure of the studied samples.

Microcavities were studied by angle resolved reflectivity experiments. The sample is placed inside a cryostat with cylindrical windows and measurements can be performed at 5 K, 77 K and room temperature (300 K). The light source is an halogen lamp. The incidental beam crosses a polarizer and is then reflected by a mirror positioned at 45° in order to illuminate the sample. The reflectivity is focused on the slit of a monochromator and the signal is detected by a photodetector. The system (halogen lamp + polarizer + mirror) is on a mobile rail to allow measurements with incidence angles from 5° to 75°.

3 Results and discussions For the three samples, angle resolved reflectivity experiments have been performed at 5 K and at room temperature in transverse electric (TE) and transverse magnetic (TM) polarization. In TE (TM) configuration, the electric field is perpendicular (parallel) to the incident plane which is defined by the direction of the light and the normal direction of the sample. The experimental data and the simulation for the A714 sample at 5 K in TE polarization are reported in Fig. 2. We can clearly identify the cavity mode and the A and B excitons. The increase of the incident angle corresponds to the tuning of the structure which consists in moving the cavity mode towards the excitonic energy. When the incident angle increases, the cavity mode moves to the high energy side as it can be seen on the experimental spectra. Between 35 and 40°, we observe an anticrossing between the photonic mode and the A and B excitons which demonstrates the strong coupling. By plotting the energy of the different dips as a function of the incident angle in Fig. 3a, a Rabi splitting equal to 54±2 meV is deduced. For larger angles, the increase of the broadening of the polaritonic mode is attributed to the near band-edge absorption of GaN. For the simulations of the reflectivity spectra, we use the transfer-matrix formalism developped by Azzam and Bashara [8]. The excitonic resonances are taken into account by classical harmonic oscillators which are distributed around A and B exciton energies through a Gaussian distribution. The latter allow to describe the inhomogeneous broadening which microscopic origin is mainly due to the inhomogeneous distribution of lattice strain. The dielectric constant is then given by the following expression: εr (E) = εb + Ú www.pss-c.com

1 B e 2 2 x E + j
Γ E π∆

- ( x - Eexc 0 )2 ∆2

dx

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F. Réveret et al.: Strong coupling in bulk GaN microcavities grown on Si

reflectivity (a.u)

where εb, Γ, 2 ln 2∆ and Eexc0 are respectively the background dielectric constant, the homogeneous (Lorentzian) and inhomogeneous (Gaussian) linewidths and the excitonic resonance energy. The value of the excitonic oscillator strengths used in the simulation is (35 000 ± 5000) meV2 for A and B exciton. The C exciton is not considered due to its weak oscillator strength (less than 2000 meV2) in the GaN layer under highly compressive strain [9, 10]. The value of the energy separation between A and B exciton (15±2 meV) corresponds to the influence of this large biaxial strain on the valence band states. In this model the fitting values of homogeneous and inhomogeneous broadenings are respectively Γ = 0.1 meV (at 5 K) and ∆ = 13±3 meV. For the complex index of GaN, AlN and AlGaN, we use previous determinations obtained by ellipsometry [11]. To take into account the strain gradient of the Experimental Simulation GaN active layer along the growth axis, the latter is divided is several layers (5) in which a progres60° sive strain is applied from the surface to the bot55° tom of the sample [4]. This parameter enables us more precisely to adjust simulations with experi50° ments, especially the anticrossing between the 45° photonic mode and the A and B exciton. The deduced value of the Rabi splitting is reliable. 40° The position of the polariton modes as function 35° of the incidence angle at 5 K for sample A714 is reported in Fig. 3a. The solid squares correspond 30° to the upper polariton branch (UPB), circles to 25° the middle polariton branch (MPB) and triangles to lower polariton branch (LPB). The solid line 20° corresponds to the result from the simulation by 15° using the transfer-matrix method; calculation follows the tendency for the LPB and the MPB. 10° Nevertheless the calculated UPB deviates from 5° the experimental data after 35°. This fact is probably related to the broadening previously mentioned. It is possible to refine the model by A B A B theoretically calculating the GaN complex index in order to take into account the effect of the strain on the conduction and the valence bands. 3400 3500 3600 3700 3400 3500 3600 3700 This would certainly improve the simulations. The reflectivity and photoluminescence specEnergy (meV) Energy (meV) tra related to sample A808 (10 pairs) are reFig. 2 Experiment and simulated reflectivity specported on Fig. 3b at low temperature and for an tra at 5 K from 5° to 60° in TE polarization for incidence angle of 40°. The reflectivity spectrum A714 sample. clearly evidences the light-matter strong coupling. Whatever the incidence angle, the photoluminescence line does not follow the evolution of the lower polariton branch (LPB) and is constant in energy. This result can be explained by the fact that the polaritonic effect is inhibited by localized exciton at this low temperature. We performed simulations in order to determine the influence of the reflectivity of the lower mirror on the Rabi splitting. When the reflectivity of the lower mirror is high, we observe a narrow photonic mode but a small Rabi splitting. However, as the number of pairs decreases, the reflectivity of the Bragg mirror decreases and the Rabi splitting is improved. This effect probably comes from the balance of the cavity. Indeed, when the reflectivity of the two mirrors is identical, a larger Rabi splitting is obtained. This result is in good agreement with the measurements performed on the samples with various Bragg mirrors (ħΩRabi = 45±2 meV, ħΩRabi = 39±4 meV and ħΩRabi = 30±5 meV at 300 K for samples A714, A808 and A771, respectively). © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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phys. stat. sol. (c) 4, No. 1 (2007)

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(a)

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Simulations 3600

3550

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Aware of is issue, we finally propose an optimal structure in order to improve the strong coupling. To efficiently confine the photons inside the cavity we must balance the mirrors correctly. The Rabi splitting increases with the increase of the thickness of the active layer; however when GaN thickness is too large, light is absorbed and the Perot-Fabry effect is no more effective. So the later would be constituted of a 3λ/2 bulk GaN microcavity grown on silicon with 5 pairs of λ/4 AlGaN/AlN Bragg mirror and a 100 Å thick aluminium layer. The simulation leads theoretically to a Rabi splitting value of 70 meV. (b) θ=40°

3300

R Diffusion of laser light

θ=40°

PL

θ=30° 3400

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Fig. 3 (a) Polariton dispersion curve at 5 K for sample A714, (b) for sample A808 at 5 K, reflectivity (R) spectrum is displayed for an incident angle (θ) of 40° while photoluminescence (PL) spectra correspond to θ = 30° and 40°.

4 Conclusion Three GaN hybrid microcavities grown on a silicon substrate and constituted of a λ/2 GaN active layer embedded between a nitride-based Bragg bottom mirror and an aluminium top mirror have been studied by angle resolved reflectivity. A Rabi splitting value varying from 30 to 45 meV and depending on the number of AlGaN/AlN pairs in the Bragg mirror has been determined. These experimental results are in good agreement with numerical simulations which account well for the observed Rabi splitting values. These simulations are also useful to design the optimal structure in order to obtain the largest Rabi splitting values. The challenge is now to evidence the cavity polariton emission at room temperature by angle resolved photoluminescence. Acknowledgements The authors would like to acknowledge Tatiana Shubina for fruitful discussions.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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