Room-Temperature Observation of Trapped Exciton-Polariton

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Room temperature observation of trapped exciton-polariton emission in GaN/AlGaN microcavities with air-gap/III-nitride distributed Bragg reflectors Renchun Tao, Kenji Kamide, Munetaka Arita, Satoshi Kako, and Yasuhiko Arakawa ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00003 • Publication Date (Web): 21 Jun 2016 Downloaded from http://pubs.acs.org on June 25, 2016

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Room temperature observation of trapped exciton-polariton emission in GaN/AlGaN microcavities with air-gap/III-nitride distributed Bragg reflectors Renchun Tao,∗,† Kenji Kamide,‡ Munetaka Arita,†,‡ Satoshi Kako,†,‡ and Yasuhiko Arakawa∗,†,‡ †Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo, 153-8505, Japan ‡Institute for Nano Quantum Information Electronics, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo, 153-8505, Japan E-mail: [email protected]; [email protected]

Abstract We demonstrate trapped exciton-polariton emission at room temperature from nonpolar GaN/AlGaN cavities sandwiched between air/AlGaN distributed Bragg reflectors. Nanoscale thickness fluctuations characteristic to the non-polar AlGaN cavity layer create deep potential traps, giving rise to a strong (in-plane) localization of exciton-polaritons. The observed quantized exciton-polariton states exhibit a large quantized energy of up to 6 meV, which benefits from the wide bandgap of III-nitrides. The experimental results are well explained by numerical simulations.

III-nitride

exciton-polaritons in such deep traps will be useful for practical exciton-polariton

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lasers with high degrees of coherence, and high-repetition rate Josephson oscillators with multi-component condensates.

Keywords air-gap DBR microcavity, GaN, III-nitrides, room temperature, trapped exciton-polariton, real-space pinhole In distributed Bragg reflector (DBR) semiconductor microcavities (MCs), photons can become strongly coupled to excitons, resulting in the generation of two normal modes of exciton-polaritons. The higher-energy branch is called the upper polariton (UP), and the lower-energy branch is called the lower polariton (LP). 1 Due to their half-light and halfmatter nature, exciton-polaritons exhibit many interesting properties, such as Bose Einstein condensation (BEC), exciton-polariton lasing, 2–5 parametric amplification, 6,7 bistability, 8,9 and superfluidity. 10 In recent years, exciton-polaritons confined laterally by potential traps have also been attracting increased attention due to their prospective applications such as bistability, 11,12 optical parametric oscillation using multiple scattering channels, 13–15 light squeezing with reduced intensity noise, 16 single photon emitters using exciton-polariton blockade effects, 17–19 coherent exciton-polariton lasers, 20 and polariton cascade lasers in the terahertz regime. 21 The potential traps provide lateral photonic confinement and to date have been created using laser excitation, 22,23 strain modulation, 24,25 external defects 26 or gratings 27 and low-dimensional microstructures which include micropillars, 16,19,28,29 photonic wires, 14,30 and planar cavity region with thickness variations. 31–33 Such low-dimensional structures can be fabricated with relative ease using today’s technology, especially for IIIarsenide materials. However, to date, the room temperature observation of trapped excitonpolaritons has not been reported in inorganic DBR microcavities. 26 III-nitride microcavities are one of the most promising inorganic candidates for the study of exciton-polaritons at room temperature, because the material exhibits large exciton bind-


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ing energies and exciton oscillator strengths. Indeed, exciton-polariton luminescence 34–36 and even lasing/condensation 37–40 has been realized at room temperature in GaN-based cavities. However, trapped exciton-polariton states and trapped photon states have not yet been reported in III-nitride DBR MCs, due to difficulties in both the patterning process and obtaining a sufficient degree of trapping when using III-nitride DBR MCs. Very recently, air-gap/III-nitride DBR MCs have been realized by employing a GaN thermal decomposition technique. 41,42 Due to their high refractive index contrast, such DBR MCs have been shown to exhibit superior properties such as relatively high quality factors 42 and strong exciton-photon coupling. 43 In this work, we report the room temperature observation of trapped exciton-polariton emission from naturally formed thickness fluctuations in m-plane air-gap/AlGaN DBR MCs. We use momentum space spectroscopy to perform our measurements. Due to the anisotropic oscillator strength of excitons in non-polar (m-plane) nitride cavity layers, the coupling condition depends on the polarization: either along the crystal a-axis and c-axis, respectively. Moreover, an energy spacing of up to 6 meV is observed in the trapped exciton-polariton

Figure 1: (a) Schematic image of the cavity structure, with three-period AlGaN/air-gap DBRs at the top and four-period air-gap/AlGaN DBRs at the bottom; (b) the 2λ cavity region with three GaN active layers at antinodes; (c) AFM image scanned over the AlGaN cavity layer surface of one bare cavity sample without top DBRs; (d) the surface profile over the area indicated by the dashed black line in (c). 3 ACS Paragon Plus Environment

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spectrum. Theoretical calculations show good agreement with our experimental observations. The samples were grown on m-plane free-standing GaN substrates by metalorganic chemical vapor deposition. Using thermal decomposition, 41 2λ-MC structures sandwiched by airgap DBRs were fabricated as shown schematically in Figure 1(a). The structures consist / 3λ ) DBR layer at the top, a four-period DBR layer at the of a three-period AlGaN/air ( 3λ 4 4 bottom, and a 2λ-cavity in between them. The cavity region has three GaN (34 nm) layers at anti-node positions. These layers are separated by two AlGaN (34 nm) layers as shown in Figure 1(b). Further details on the growth and fabrication processes can be found in our previous work. 42,43 We note that, as shown by atomic force microscopy (AFM) in Figure 1(c) and Figure 1(d), the AlGaN cavity surface is covered with striations formed by giant bunched steps that often appear on non-polar III-nitride layers. 44,45 The striations formed by these bunched steps lie typically along the a-axis in our samples, as can be seen in Figure 1(c). An optical image of the cavity layer surface in a large size scale is shown in Figure S1 in the Supporting Information, from which the elongated striations along a-axis are clearly seen. Momentum space spectroscopy was performed on the samples using angle-resolved photoluminescence (PL) measurements at room temperature. A kinematic lens could be inserted into the setup to allow for real space measurement. 43 Samples were excited using a frequencyquadrupled continuous-wave 266 nm laser at 16 mW (∼ 2 kW/cm2 ), and the PL emission was collected from the sample surface at different emission angles (θ) using an objective lens with a numerical aperture of 0.55. The collection angle is related to the in-plane momentum wavevector of the light as kin plane =

2π sinθ. λ

(1)

A spatial filter (pinhole) was used to select a detection spot of ∼ 5 µm in diameter on the sample surface, and a polarizer was used to resolve the polarization of the PL emission. The PL emission was finally detected using a cooled charge-coupled device at the exit of a 750 mm spectrometer. The samples were oriented with their a-axis perpendicular to the 4 ACS Paragon Plus Environment

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Figure 2: PL emission from trapped states in (a) momentum space and (b) real space; both were measured from the same spot of the same cavity (Cavity A), with k k c and E k c. spectrometer entrance slit. We first present the PL emission from trapped states in both momentum space and real space from a cavity (hereafter labelled Cavity A). Figure 2(a) shows the angle-resolved PL results measured for an electric field polarization (E) along the c-axis (E k c). The discrete energy states, with flat dispersion in momentum (or angle), are clearly visible up to the 6th level. The quantized states can also be observed in real space, as shown in Figure 2(b). Due to the fact that the discrete modes span over a length scale of several microns, which is comparable to the in-plane size of the giant bunched steps in the cavity surface as shown in Figure 1, we suggest that these trapped states originate from the cavity thickness fluctuations caused by the giant bunched steps in the AlGaN layer. In fact, the trapped state emission can only be observed when the a-axis of the samples is perpendicular to the entrance slit of the spectrometer (a-axis ⊥ e slit ), and we do not observe any obvious trapped states when the c-axis of the sample is perpendicular to the entrance slit of the spectrometer (c-axis ⊥ e slit ). This is likely due to an inherent anisotropy in the traps (cavity thickness fluctuations), which typically have dimension sizes of Lka ' 40 µm, Lkc ' 5 µm and Lkm ' 0.27 µm, where Lka and Lkc are the in-plane sizes of the traps and Lkm is the cavity thickness in between the top and the bottom DBRs (see Figure S1 in Supporting Information). The size and aspect ratio of the traps are similar to previously reported one dimension (1D) systems in as-grown ZnO nanorod structures 14 and GaAs DBR caivties. 23,32 In our samples, the smaller trap size along c-axis leads to stronger confinement effects. Therefore, in this work we only


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focus on the cases when the a-axis of the samples is perpendicular to the entrance slit of the spectrometer (we fix kka ∼ 0 µm−1 ). However, we emphasize that the bunched steps are not uniformly distributed in the sample and we observe exciton-polariton modes with continuous dispersions from cavities with a smoother morphology. 43 In order to acquire information at higher angles (or larger momentum), the c axis of the sample was tilted by around 15◦ toward the objective lens. The measured momentum space results from Cavity A for E k c and E k a are shown in Figures 3(a) and (c) respectively. In these figures, the angles have been converted to momentum wavevectors according to Eq. (1).

Figure 3: Experimental PL results in momentum space (a) for E k c and (c) for E k a; (a) and (c) were measured at the same spot of the same cavity (Cavity A). Simulation results in (b) for a weak coupling case to fit (a), with A = 80 meV, R = 3.36 µm, g = 0 meV, EC (0) = 3.422 meV and a Lorentzian energy linewidth γL = 3.18 meV (equal to the linewidth of the ground state in (a)); simulation results in (d) for a strong coupling case to fit (b), with A = 80 meV, R = 3.36 µm, g = 33 meV, EC (0) = 3.465 meV and γL = 3.60 meV (equal to the linewidth of the ground state in (c)). In the simulations of (b) and (d), the same trap was used, because (a) and (c) were measured from the same spot. 6 ACS Paragon Plus Environment

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Firstly, we can see the similarities between Figures 3(a) and (c). Both have a strong emission band at large momentum (|kin plane | > 10 µm−1 ), which are formed by Bragg modes (BMs). In air-gap DBR MCs, the average refractive index is very small (close to the value of air), such that the Bragg modes have a strong dispersion, appearing almost vertical in these figures. Most importantly, both plots clearly reveal emissions from discrete trapped states, and these trapped states have flat dispersions along the momentum axis, which is the evidence for confinement in real space, as exemplified in Figure 2(b). Beside these similarities, clear differences can also be found. In Figure 3(a), the large momentum modes in each energy level form a dispersion (DSP1 in Figure 3(a)) that seems to cross with the exciton line EXkc , while the dispersion in Figure 3(c) (DSP2) appears to level off when approaching exciton line EXka (the exciton lines EXka (for E k a) and EXkc (for E k c) were measured from a reference sample 43 ). It is well known that in a homogeneous cavity system the leveling-off of the dispersion reveals a strong coupling between the cavity photons and excitons. Therefore, the discrete states shown in Figure 3(c) are ascribed to trapped exciton-polaritons. Furthermore, the energy difference between the ground state and the first excited state in Figure 3(c) is 4 meV, which is smaller than that in Figure 3(a) (6 meV). Since Figure 3(a) and Figure 3(c) were measured on the same spot of the same cavity, the trap potential in both cases is the same. Thus, this energy difference can only originate from the properties of the trapped particles themselves, i.e., their different masses. The different masses of the trapped states shown in Figures 3(a) and (c) are due to the different coupling conditions for E k c and E k a. In the strong coupling case, because of the involvement of exciton part, the effective mass of an exciton-polariton becomes larger than that of a pure cavity photon. In fact, in our m-plane air-gap DBR MCs, the coexistence of strong coupling for E k a and weak coupling for E k c has been observed for extended states, 43 which makes it reasonable to assume that the quantized states for E k c in Figure 3(a) are trapped photon states and those for E k a in Figure 3(c) are trapped excitonpolariton states.


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To further confirm our observation and analysis, theoretical calculations were performed, using two coupled Schrödinger equations for photons and excitons: X

→ − → − Hkk ,k0 ψ k0 = E ψ kk , k

0 kk

where





→ − ψC,kk  ψ kk =  , ψX,kk and Hkk ,k0

k

(2)

k

    EC (kk ) g  1 0 = δkk ,k0  + Vkk −k0   . k k g EX 0 0

(3)

(4)

In above equations, ψC,kk (ψX,kk ) is wavefunction of cavity photon (exction), EC (kk ) = q hc ¯ ( nC E¯hCc (0) )2 + kk2 (where c is the speed of light in vacuum, and nC the refractive index nC of the cavity), kk = kin plane , EX the exciton energy, g the exciton-photon coupling strength. Vq=kk −k0 is the q-component of the trapping potential, V (x), which is induced by the cavity k

thickness fluctuation and modelled by

V (x) = −Aexp(−x2 /R2 ),

(5)

where A and R represent the trap’s depth and effective size, respectively. Solving the equation in Eq. (2), for the n-th exciton-polariton mode with energy E(n), the → − wavefunction ψ n (kk ) could be calculated. Then the normalized emission intensity, defined as I(E, kk ) =

X→ − | ψ˜ n (kk )|2 ρn n

π −1 γL /2 , (E − En )2 + (γL /2)2

(6)

could be calculated and plotted in an E–kk map to allow direct comparison with the experimental results. When calculating the spectrum, a Lorentzian energy line-shape with linewidth γL is assumed for all trapped states. In fact, since all the trapped states are de-


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tuned away from the exciton resonance, it is expected that their linewidths mainly come from a constant cavity linewidth. This assumption is also justified by experimental results shown in Figure S3(a) (in Supporting Information), where no obvious differences in linewidth can be found among the three lowest-energy peaks. In the calculation, a Boltz0 ) at T = 300 K is assumed for the occupation number mann distribution ρn ∝ exp(− EknB−E T

in each state (this assumption reasonably agrees with the observed state energy distribution of ∼ 30 meV in Figures 3(a) and (c)). A spatial filter (whose effective diameter is 5 µm) is also included in our calculation to try to match the experimental conditions. The inclusion of the filter in the calculation is done through a filter function, F (x), after the Fourier transformation (F.T.) of wavefunctions from momentum space to real space → − → − → − − → − F.T. → filter F.T. ( ψ n (kk ) −−→ ψ n (x) −−→ ψ˜ n (x) = F (x) ψ n (x) −−→ ψ˜ n (kk )). We would like to emphasize that for a more precise comparison of calculated results with observed PL data, particle relaxation dynamics should also be considered. The calculation results shown in Figure 3 are obtained using parameters A = 80 meV, R =3.36 µm, and with g values of 0 meV and 33 meV for the weak and strong coupling cases, respectively. Here according to a simple relation δL ≈

A L EC (0) C

(where LC stands for the

cavity thickness), a trap with depth A = 80 meV corresponds to a cavity thickness fluctuation δL of 6.3 nm, which is consistent with the AFM measurement of the AlGaN layer surface shown in Figures 1(c) and 1(d). It is clear that the energy and momentum positions of the intensity peaks in Figure 3(b) (calculated using g = 0 meV) are in good agreement with that in Figure 3(a). The dispersion DSP1 formed by the large momentum states in Figure 3(a) is also reproduced in Figure 3(b). This confirms that the quantized modes in Figure 3(a) are trapped photon states. As for the strong coupling case in Figure 3(d), the calculated positions in energy and momentum space (calculated using g = 33 meV) are also in good agreement with the experimental data in Figure 3(c). The calculated dispersion formed by the large momentum states levels off in the same manner as experimentally observed dispersion (DSP2), confirming the observation of trapped exciton-polariton states. The


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obtained Rabi-splitting (Ω) for the result shown in Figure 3(c) is Ω = 2g = 66 meV, which is relatively larger than previous reports 35–40 and is mainly attributed to the usage of air-gap DBRs. 43 Next we estimate the exciton oscillator strength, B, using a simple equation modified from a bulk-active-layer case, 46,47 s Ω'

Nac Lac B , 2 nC (LC + LDBR )

(7)

where Nac and Lac are the number and thickness of the active layers in the cavities, respectively. In the estimation, for our

3λ 3λ /4 4

DBRs, LDBR is equal to

are the refractive index of DBRs and λC =

2π¯ hc ). EC (0)

3λC n1 n2 2nC |n1 −n2 |

(where n1 and n2

From this, the exciton oscillator strength

B is estimated to be 22000 (meV)2 , which agrees reasonably well with the values reported in the literature. 48 As the traps originate from thickness fluctuations in the cavity layers, each cavity can be expected to have different trap sizes and depths (and therefore different trapped states). Figure 4(a) shows the measurement result of another cavity (hereafter labelled Cavity B). An obvious difference between Figure 4(a) and Figure 3(c), is that both the extended LP states and discrete trapped states were observed in the case of Cavity B. From the corresponding simulation shown in Figure 4(b), the estimated trap size (2R) in Cavity B is 2.0 µm, which

Figure 4: (a) Momentum space measurement in Cavity B, for E k a; (b) calculated results for a strong coupling regime to fit (a), with A = 30 meV, R = 1.0 µm, g = 29 meV, EC (0) = 3.397 meV, EX = 3.420 meV and γL = 2.52 meV (equal to the linewidth of the ground state in (a)). 10 ACS Paragon Plus Environment

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is smaller than the experimentally used pinhole size of 5 µm. The small size of the trap means that the emission from the extended LP states outside the trap could be also collected though the pinhole. Indeed, in the simulation result shown Figure 4(b), the contribution from extended LP states is clearly seen. A slight difference in the extended LP dispersions around kin plane = 0 µm−1 between the experimental observation and the theoretical simulation could be due to the simplicity of our model. For example, in the calculation, the same linewidth is assumed for both the trapped states and extended states; whereas, in the experimental spectra shown in Figure 4(a), the linewidth of the extended states is larger than that of trapped states, because the extended states are closer to the exciton resonance than the trapped states. Moreover, as shown in Figure 4(a), due to the smaller size of the confinement trap, not only is the flat dispersion in momentum of each discrete state further elongated, but also the quantized energy between the ground state and the first excited state is enlarged to 6 meV. Indeed, the trap amplitude is proportional to the material bandgap, and the measured large energy spacing in our samples is enhanced by the wide-bandgap III-nitride materials from which they are made. Such a large quantized energy will be advantageous for coherent exciton-polariton lasers due to a possible reduced mode competition between trapped states. 20 In summary, trapped exciton-polariton and photon states were observed in m-plane air/III-nitride DBR MCs at room temperature. These results show the promising prospectives of III-nitrides for the application and research of trapped exciton-polaritons at room temperature. Moreover, with trapped exciton-polaritons, a quantized energy up to 6 meV was observed. This large quantized energy of trapped exciton-polaritons could be useful for practical exciton-polariton lasers with high degrees of coherence, 20 high-repetition rate Josephson oscillators with multi-component condensates, 49 ultrafast mode-locked excitonpolariton lasing, 50 etc. Finally, we would like to remark that, the trap potentials in our cavities have a strong anisotropy, for which the trapped exciton-polaritons can exhibit quasi-one


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dimensional motion. However, it would be unpersuasive to claim that our current systems are ideal 1D cavities, as the thickness fluctuations were naturally formed with irregular morphology. Rapid advancement in III-nitride processing technology will enable us to intentionally engineer the trap size and shape, allowing systematic studies such as 1D exciton-polariton transport properties 13 with III-nitrides.

Acknowledgement The authors thank Mark Holmes for discussions. This work was supported by Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

Supporting Information Available Firstly, we give more details about the anisotropies of the traps. Then we explain the absence of PL emission from high-energy trapped states at small momentum by discussing the relation between the trap size and spatial pinhole size. Finally, we show our attempts to study the exciton-polariton populations at each discrete state. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Room-Temperature Observation of Trapped Exciton-Polariton

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