1. Introduction

ZnO has attracted much interest as an important technological material. Physically, it is well-known for its wide band gap (3.3 eV), large free-exciton binding energy (60 meV), and ability to emit a wide spectrum in visible range that originates from numerous extrinsic and intrinsic deep-level impurities and complexes [1–5]. Recently, ZnO-based micro resonator has been considered as a good candidate for ultraviolet (UV) micro laser. It is a result of a unique combination between stable emission layer and good optical confinement. Lasing properties of those resonators was first reported in [6] for Fabry-Perot cavity. After that, countless efforts have been devoted on WGM in ZnO micro resonator to improve the lasing performance (see [7] and reference therein).

Among different morphologies that support WGMs, microsphere (MS) is the simplest 3D resonator. In spite of this, its WGM behavior exhibits very complicated behavior and possesses extraordinary high Q values of 10⁸ - 10⁹ [8]. ZnO microsphere resonator would be a promising system for many photonic applications. However, there are very few studies till now because of limitation for preparing smooth surface, perfect spherical symmetry and high crystalline quality. Two major methods for obtaining ZnO MSs (with size up to 10μm) are laser ablation [9] and hydrothermal synthesis [10].

Those studies have revealed unique WGM properties in ZnO MS, such as photo-induced UV, white light lasing [11–13] and field-induced UV lasing [14]. In our previous work [10], ZnO MSs with sizes from 1.52 μm to 2.7 μm were successful synthesized by hydrothermal techniques. Those spheres show sharp WGM peaks in wavelengths of 400nm – 800nm, and significant redshift of the exciton emission peak (with Δε ~0.3 eV) from the ZnO bulk value (3.3 eV). After careful analysis, it was deduced that a change in refractive index of bulk ZnO, Δn needs to be introduced to explain the data [10]. Those unique behaviors could not be observed in ZnO MSs fabricated by laser ablation [9,11–14]. The current work is therefore devoted to explain such behaviors. Photoluminescence (PL) spectrum and SEM picture for single ZnO MS were investigated systematically. PL spectra of ZnO MSs of various sizes were collected. As a result, the correlation between Δε, Δn and inner morphology can be analyzed.

2. Experimental and theoretical analysis

2.1 Synthesis of ZnO microspheres

ZnO MSs were synthesized by hydrothermal techniques described in our previous work [10]. It was optimized for the surface smoothness, and the size of such MS strongly depends on the molar ratio between Zn(NO₃)₂.6H₂O and sodium citrate in reactant solution [15,16]. In order to obtain larger size (up to 10 µm) and smooth surface, this ratio should be in the range of 2.6 to 2.9 in our case. The as-prepared samples were dropped to Si substrate and then annealed at 550 °C for 12 hours in the ambient atmosphere before characterization.

The size of ZnO MSs on a Si substrate is measured by a scanning electron microscope (SEM-Nano Nova). The WGM behavior in PL spectrum of ZnO microcavities of various sizes is observed using a Horiba Jobin Yvon HR-800 UV setup with a He-Cd laser source (325 nm line). X-ray photoelectron spectroscopy (XPS) analyses were carried out in a XPS spectrometer (ULVAC-PHI 5000 Versaprobe) with a monochromatic Al Kα X-ray source (1486.6 eV). More information about X-ray diffraction (XRD), Raman properties and composition can be found in [10].

2.2 Modified Refractive Index model

In order to investigate the WGM behavior in spherical micro resonator, we applied the scheme previously described in [10,17]. Our scheme was modified based on similar scheme proposed elsewhere [18], where another iteration of Newton-Rapshon scheme was added after implementing Sellmeier’s dispersion relation [19] in order to solve the characteristic equation [20]. The refractive index n, cavity radius R, angular momentum mode number l and complex roots of resonance position k were then calculated in a self-consistent way. Then, those values were redefined again after modifying the refractive index.

Such modifications would produce Δn = |n_g,exp(λ_l) − n_g,bulk(λ_l)| where n_g,exp(λ_l), n_g,bulk(λ_l) are experimental and calculated group indices, respectively. On the other hand, the assignment of angular momentum mode number l is made by optimizing the indicator function D (l, l’) [10].

As shown in previous studies, the modified refractive index (MRI) scheme worked well in evaluating the refractive index shift in hydrothermally-grown ZnO microcavities. However, this shift is negligible for MSs fabricated by laser ablation [9,13]. In the following studies, we will explain the physical mechanism of Δn and confirm the validity of MRI to reproduce the universal relation (UR) between n, R, l and k for hydrothermally-grown ZnO MSs.

3. Results and discussions

3.1 Mechanisms for redshift of the center wavelength of the WGM band in UV range

In order to explain the significant red shift of UV peak in the ZnO spherical microcavities grown by hydrothermal method, one needs to consider carefully their inner morphology and chemical bonding. Figure 1 shows the PL spectrum of a 3.7μm ZnO MS before and after it is damaged by laser illumination. Interestingly, the cavity effect of WGM is linked to the shift of UV peak of the ZnO MS. It is observed that when the ZnO MS crumbles due to laser heating, the WGM behavior disappears while the main UV peak would blue shift and split into two peaks at energies around 3.16 eV and 3.25 eV, and its intensity would also be enhanced significantly. The high-energy peak is close to the typical UV peak in polycrystalline ZnO, suggesting that part of the crumbled MS is polycrystalline ZnO. The difference in the two spectra reveals the cavity effect of MS. In comparison, the main UV peak of the PL spectrum of ZnO MS made by laser ablation is near 3.20 eV, about 0.05 eV lower than the UV peak of polycrystalline ZnO target [13]. The small red shift in that study could be due to cavity effect, excitons trapped by defects near surface, or the electron-hole plasma induced band gap renormalization effect. It has been shown that for ZnO micro cavities, higher laser power would cause a redshift of the center wavelength of the WGM lasing band [21].

 

Fig. 1 PL spectrum of 3.7μm ZnO MS before (up) and after (down) laser damage with SEM images shown in insets.

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The SEM picture of the damaged MS reveals a porous structure inside our MS made by hydrothermal synthesis. During the growth process, it was observed that the MS is usually porous with tiny voids formed inside the MS. The formation of mesoporous structures by hydrothermal synthesis is rather typical, as reported in [22]. The surface of MS becomes smooth only after a long time growth followed by thermal annealing. The main UV peaks at 3.16 eV and 3.25eV for damaged MSs remain different from the 3.3 eV for single crystalline ZnO. Based on this study, we conclude that the interior of our MS may be comprised by polycrystalline ZnO and some sheet-like ZnO structures as observed in [16], where the main peak appears at around 3.17 eV. The larger shift (Δε ~0.3 eV) than in [13] might be the results of porous structure inside MSs. The more direct evidence would show in section 3.2

To confirm this assumption, the XPS spectrum of ZnO MS was measured, and results were given in Fig. 2. As shown in Fig. 2, the Zn 2p_3/2 and O 1s peaks are composed by three main peaks. The typical binding values of Zn²⁺ and O^2- ions in wurtize structure is 1021.80 eV ~1022.30 eV for Zn 2p_3/2 and 530.90 eV ~531.5 eV for O 1s. In Zn(OH)₂, these values are 1021.80 eV and 1022.70 eV for Zn 2p_3/2 and 532.20 eV for O 1s. All above data were taken from [23]. On the other hand, recent investigation in 2D graphite-like ZnO (g-ZnO) also showed value of 1020.76 eV for Zn 2p_3/2 [24]. Based on the comparison of our XPS data (see Fig. 2) with the above, it is concluded that our sample may contain wurtzite ZnO, g-ZnO and Zn(OH)₂ crystal structures. It is worth to note that bonding related to Zn(OH)₂ structures may be excluded as a result of very high annealing temperature [25]. Hence, our ZnO MS could be composed by polycrystalline and graphite-like ZnO structures. The existence of graphite-like and plate-like nanostructures in porous microstructures synthesized by similar reactants with difference reaction conditions was reported in [16].

 

Fig. 2 XPS spectra of Zn 2p3/2 (a) and O 1s (b) in annealed ZnO MSs on silicon substrate.

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3.2 Revisiting universal relation behavior in ZnO microcavities by experimental data

Figure 3 illustrates the linear relation between the parameter KR and angular-momentum mode number l, where K = n2𝜋/𝜆 and R is the radius (edge length) of spherical (hexagonal) cavity. The data of hexagonal cavities were obtained from [26]. By doing so, the universal relation (UR) between cavity size, refractive index (including the MRI correction, Δn), resonance wavelength and mode number l can be established. Moreover, it is clearly shown that the UR has morphology dependence (Fig. 3(a)). The slopes of linear fitting of the UR line for hexagonal and spherical resonators are α_hex = 1.230 ± 0.004 and α_sph = 1.081 ± 0.001, respectively.

 

Fig. 3 (a) KR values extracted from WGM peak positions observed experimentally (with MRI correction for spherical MSs) as functions of mode number for our ZnO spherical cavities (solid squares) and hexagonal microcavities (open objects) taken from [26]. (b) Illustration of the failure of constructing UR for KR values extracted from WGM peak positions observed experimentally (with the use of a constant refractive index of 2.2) for our ZnO MSs. The data with MRI correction as shown in (a) (which satisfy the UR) are plotted again for comparison. Note that same cavity size was denoted by the same color, and the width a (twice the edge length R) of hexagonal cavities is related to the diameter d of a circle with the same enclosed area via a = 1.0996 d [27].

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For hexagonal dielectric resonators, the UR was implied using numerical or semi-classical analysis [28] for lowest-loss modes, 20 ≤ Re(KR)/n ≤ 60. From such calculation, we could get α_num = 1.236 and α_semi = 1.237 with n = 2.2, in good agreement with the above α_hex.

For a certain size, the slope of KR line is independent of refractive index. However, it is not the case for its intercept (see Fig. 3(b)). For ZnO MSs in this current work, without utilizing corrected refractive index in MRI model the UR could not be established. In Fig. 3(b), the deviation of KR lines from the UR line for different sizes of spherical cavities indicates the importance of adding Δn and dispersion effect. The existence of Δn is a result of porous structure in hydrothermal-based ZnO MS. For ZnO microcavities prepared by other methods, such as thermal evaporated ZnO microwires [26] and laser ablated ZnO MSs [9,13], implementation of Δn for calculating WGM resonances is negligible. The ZnO synthesized by latter methods might be more robust than the first one: no damage occurs even at high laser power [29,30].

The size independence of Δn as shown in Table 1 is therefore explained by the arbitrary character of intrinsic porosity concentration inside hydrothermal-based MSs. There is a correlation between Δn and deviation from the standard UR line of the line calculated with $n=2.2$ for each size. On the other hand, there might be an existence of correlation between Δn and the UV peak shift. This is consistent with the observation in [13]. When Δn is negligible due to more robust MSs, much smaller shift (~0.05 eV) was observed, leaving only the effects due to cavity, excitons trapped to surface defects, and many-body effects. It is thus shown that the porous property is one of the reasons causing the UV peak shift.

Table 1. Δn for different resonator diameters.

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It is noted that even though the MRI model works well for the prediction of WGM behavior in visible range, it still has limitation in UV. At high l values for certain sizes, KR values still deviate from the UR line. This problem could be fixed by including the exciton-polariton effect in a future work [31].

4. Conclusions

In summary, we have presented a relation between size, inner structure and WGM behavior in ZnO MSs grown by hydrothermal synthesis. The possible mechanisms, including cavity effect and porous structure inside MSs, for the peak shift of UV emission are revealed. The PL spectra also suggest that our MSs might be composed by polycrystalline and graphite-like ZnO. Furthermore, the universal relation for the parameter KR for MSs of various sizes is found after taking into account the refractive index correction in the MRI model. Our study is important for understanding the effects of refractive index and intrinsic structural properties on WGMs, which are often underestimated. In order to predict WGMs in UV range more precisely, the dispersion due to exciton-polariton effect needs to be considered [31].