1. Introduction

Exciton-polaritons, generated by the strong coupling between light and excitons, are attracting tremendous attentions in the last decades due to the unique properties exhibited in both the physics of quantum coherence and the novel optical devices. Great advances in this field have been achieved, e.g., polariton lasing, Bose-Einstein condensation of exciton-polaritons, super〉uidity, vortices, et al [1–4]. These interesting macro quantum phenomena arise from dense polaritons involving free excitons which show extended propagating waveform. Another interesting system is defect-induced localized excitons (bound-excitons) coupling with light, which would be potential for studying the optical evolvement of polaritons from collective to single emitter excitation. It is expected that the strong coupling between bound-excitons and light is realized by a series of virtual coherent emitting and reabsorption process of bound-excitons [5,6]. However, the experimental showing the anticrossing for strong coupling of light-bound exciton is yet to be demonstrated, and the cavity confined bound-exciton polaritons have not been reported before. We note that introducing microcavity to the subject of bound-exciton polaritons would pave a new way for revealing the physical mechanism of bound-exciton polaritons and extends its potential application in photonic storage and communications.

ZnO as a wide band gap material has large exciton binding energy (: 60 meV) and giant exciton oscillator strength, which is ideal semiconductor for the study of light-matter interaction. The slowdown of light due to exciton-polariton propagation in ZnO has been reported [7]. The strong coupling between cavity modes and free excitons in ZnO have been successfully observed in nanowire, of which hexagonal cross section functioned as a WG microcavity [8,9]. In this letter, A tapered ZnO nanowire with radius gradually decreasing from the root to the tip top, is used as a testbed. Resonant modes (WGMs) are clearly observed in the CL spectra. The scanning CL mapping along the tapered nanowire is performed at low temperature (5 K). We find that a clear anticrossing trend appears at energy range of the cavity modes resonating with the bound exciton states. This unambiguously indicates bound-exciton strongly coupled with cavity modes. The plane wave formula for WGMs combined with the multi-oscillators coupled model for polaritons give a good fit to the experimental results. The experimental obtained energy splitting of bound exciton-cavity mode strong coupling is about 2.6 meV.

2. Experimental details

The high quality ZnO tetrapod with tapered nanowire arms are fabricated by using vapor phase transport method [8]. To prepare a single nanowire for CL measurement, we first disperse nanowires in ethanol by sonicating and transfer them onto a Si substrate. The CL system includes a SEM (FEI Quanta 200, resolution 3-4 nm) and a grating monochromator equipped with a liquid nitrogen cooled CCD camera (Jobin Yvon, HR460, 0.3 meV/pixel). CL is collected by the parabolic mirror which has been mounted in the chamber of SEM and then analyzed by the monochromator [10]. For the CL mapping along a single nanowire, the accelerating voltage of 20 kV and the excitation spot of 100 nm are chosen. The CL scanning step is set to ~1 µm, and the diameters of nanowire at different scanning points are measured simultaneously. To observe the emission peaks of bound excitons clearly and suppress the thermal broadening of linewidth of the peaks, the sample, which is placed on a copper holder of a He-〉ow-type cryostat in the chamber of SEM, is cooled to 5 K.

3. Results and discussion

Figure 1(a) shows the SEM image of ZnO tetrapods with tapered arms (nanowire) dispersed on Si substrate. One can see that the arms of ZnO tetrapods usually have a length of tens of micrometers. The tapered arm marked by a white rectangle in the Fig. 1(a), is used for CL measurement. Its enlarged SEM image is shown in Fig. 1(b), from which we can see that the radius of tapered nanowire gradually decreases from:400 nm at the root to:270 nm at the tip top. The CL spectra, measured on both the middle part of nanowire (P1) and the root part (P2) at 5 K, are depicted in Fig. 1(c). The typical spectrum is characterized by excitonic transitions in the ultraviolet energy region. The free excitons (X_A, X_B) are visible at 3.370 eV and 3.375 eV. The donor-bound excitons (DXs) are responsible for the several sharp peaks at energy region from 3.355 eV to 3.364 eV. The more detailed peak features of these bound excitons are shown in Fig. 1(d). The main peaks I₈ (3.360 eV), I₉ (3.355 eV) can be identified as the emission from the shallow donors Indium and Ga_Zn [11]. The I_8a has not been identified yet. The peaks around 3.364 eV labeled as D⁰X_B are assigned to the same donors as those for I_8a and I₈, but with the hole derived from the B valence band [12]. In addition, two-electron-satellite transitions (TES, 3.324 eV and 3.308 eV) of the DXs and the first order of phonon replica of DX (DX-1LO, 3.289 eV) can be also observed [13]. Compared to the spectrum (P2), a shoulder-like peak appeared at 3.357 eV in the spectrum (P1) is clearly observed. This distinctive peak is actually a resonant mode, which comes from a natural formed WG microcavity in the hexagonal cross section plane of ZnO nanowire due to the total internal re〉ection effect [14].

 

Fig. 1 (a) The SEM image of dispersed ZnO tetrapods on Si substrate. (b) The enlarged SEM of a single ZnO tapered nanowire (one arm of tetrapod) extracted from the white rectangle region from (a). (c) The CL spectra measured on the position P1 (middle part of nanowire) and P2 (the root part of nanowire). (d) Cavity mode (WGM) with linewidth:1.6 meV is clearly observed in the spectrum (P1).

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Thanks to the natural formed nanowire with a tapered radius, we can perform a scanning CL mapping along the c-axis of nanowire to further examine the origin of the shoulder-like peak, because the WG modes would be strongly affected by the radius of the nanowire. And the most important is that by this strategy we can control precisely the energy of the cavity mode to be in resonance with the donor-bound exciton states, and to explore the strong interaction behavior of bound exciton and cavity modes. In our experiment, by scanning the excitation spot with a step of 1 µm, the CL mapping is obtained as shown in Fig. 2. It is obvious that at least four cavity modes are visible and they gradually shift to high energy side with decreasing the radius of nanowire (white belts labeled by yellow stars). The energy shift is not linear versus the radius, but shows an anticrossing-like behavior against the excitons states. This result is similar to the PL mapping of ZnO tapered nanowires at room temperature [7]. The strong coupling between cavity modes and excitons at UV region should be considered to explain this off-linear behavior of WG modes. In addition, we can also clearly resolve several linear white belts being independent on radius (labeled by red lines), which are ascribed to the intrinsic exciton-related transitions as we have analyzed in Fig. 1(c). However, at the bound-excitons energy region, as shown in Fig. 3, one can see a dislocation of cavity modes at bound excitons energies, showing an anticrossing dispersion. To make this dispersion more visible, we extract cavity mode peaks carefully with multi-peaks fitting and second-order differential method, as shown in Fig. 3(b). The anticrossing behavior is undoubtedly observed by eliminating the strong affection of bound excitons emission. This provides a straightforward evidence for the strong coupling between cavity modes and bound-exciton states.

 

Fig. 2 The scanning CL mapping along the c-axis of ZnO nanowire, the modulated WG modes (N = 9 −12, yellow stars) can be clearly observed. Excitons-related transitions are also labeled by red lines.

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Fig. 3 (a) The scanning CL mapping along the c-axis of ZnO nanowire at bound-excitons energy region. A log-scale for intensity is used. (b) The expanded view of anticrossing region is shown. The cavity modes peaks are carefully extracted by multi-peaks fitting and second-order differential treatment. The dashed red curves (colored curves in (b)) are calculated by multi-oscillators coupling model with both free and bound excitons included.

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To further understand this phenomenon, a theoretical simulation is performed. We can use a plane wave model to describe the WG modes in ZnO hexagonal cross section. The resonant energy E_c as a function of the circumscribing radius of the hexagonal cavity R can be written as [8,14]

Here, n_bg is the background refractive index, h and c are the Plank constant and the speed of light in vacuum. The integer N is the mode number. The factor β denotes polarization. For TE polarization (E⊥c-axis), β = n, and for TM polarization (E//c-axis), β = 1/n. In UV region, the polarization of emission mainly shows TE preference because A- and B-excitons are TE polarized, and their recombination and phonon replicas would dominate the emission [15]. Therefore, the observed cavity modes here can be assigned to the TE polarized WG modes.

At room temperature, these TE polarized cavity modes will strongly interact with A- and B-excitons, and thus form hybrid quasi-particles, excitonic polaritons. A simple coupled oscillators model including A-, B-excitons, and cavity modes can well describe this blueshifted behavior of TE polarized resonant modes (the lower branch of TE polarized exciton polaritons) in ZnO. However, at low temperature, most of free excitons are captured by localized donors, and become bound excitons, as we have observed at CL spectra. These localized states will play an important role in the strong coupling of cavity modes and excitons, and thus finally determine the eigenstates of system. For TE polarized dispersions, both bound excitons (I₉, I_8a, I₈, D⁰X_B) and free excitons (X_A, X_B) should be included in the fitting. Here, the quasi-degenerated I_8a and I₈ are simplified to an effective bound exciton I_8eff. Therefore, the eigenstates of system can be obtained from the diagonalization of the Hamiltonian matrix, which is given by

Without the free excitons and other bound excitons, the Rabi splitting (Ω) of I_8eff can be calculated from fitting parameter g₂ with Ω = 2g₂, which is 0.018 eV. To further verify the reasonability of the fitting parameter. We compared our value with the oscillator strengths (f) of I_8a and I₈, which is obtained by using time-of-flight spectroscopy [7]. The Rabi splitting can be written as$\Omega =\sqrt{2{\omega }_{ex}{\omega }_{LT}}$, where ${\omega }_{ex}$and ${\omega }_{LT}$ are exciton energy and bulk value of longitudinal-transverse splitting, respectively [16]. According to the expression of dispersion of exciton polariton in [7], Chen et al., and [8], Sun et al., oscillator strength f can be described as$f=2{\omega }_{LT}/{\omega }_{ex}$, thus we can get the relationship between Ω and f as$\sqrt{f}=\Omega /{\omega }_{ex}$. With this equation, the f (I_8ef) is calculated as 2.86 × 10⁻⁵. Considering the f (I_8ef) here contains both oscillator strengths of I_8a and I₈, this value is almost consistent with f (I₈) = 2.6 × 10⁻⁵ and f (I_8a) = 1.3 × 10⁻⁵ in [7], Chen et al.. A little bit deviation may be due to much higher bound exciton-light coupling induced by improved light confinement in ZnO WG microcavity or higher density of donor impurities in ZnO nanowire.

Here we note that the CL from bound excitons is much stronger than that of bound-exciton polariton modes. This can be easily understood by considering the unique properties of WG microcavity formed by total internal re〉ection. In this kind of cavity, only light with specific wave vectors can couple into the WG modes and forming bound-exciton polaritons, as depicted in [8], Sun et al., and in [15], Sun et al.. Most of photons emitted by bound excitons escape directly from nanowire and contribute a very strong CL of bound excitons.

4. Conclusions

In conclusion, we have shown the direct evidence for bound exciton-cavity mode strong coupling in ZnO WG microcavity. By performing CL scanning along a tapered ZnO nanowire, the anticrossing behavior between cavity modes and bound excitons are clearly observed. The plane wave formula for WG modes combined with multi-oscillators coupling model for light-exciton strong interaction gives a good fit to the experimental results. An energy splitting of about 2.6 meV is obtained from experiments.