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Optical properties of individual zinc oxide microrods grown by a microwave-assisted hydrothermal method are investigated by spatially and spectrally resolved cathodoluminescence spectroscopy and imaging at liquid-helium temperature. For optimized growth conditions the strong localization of cathodoluminescence emission at the corners of the individual hexagonal ZnO microrods has been revealed. Locally distributed luminescence and fine structure of near-band-edge emission are discussed as a manifestation of whispering gallery modes of the hexagonal resonator occurring for the near band-gap luminescence in the investigated microrods.
© 2016 Optical Society of America
1. Introduction
Due to the wide direct bandgap (3.37 eV at room temperature) and large exciton binding energy (60 meV) ZnO has attracted considerable attention as a material with great application potential in optoelectronic devices, such as ultraviolet (UV) laser diodes [1], light-emitting devices [2, 3] or UV detectors [4]. The nano-structurisation leading to formation of optical resonators with the size comparable with the wavelength of emitted electromagnetic radiation allows optimization of the important parameters of the structure, like optical gain, crucial for photonic applications. Therefore, structures with various shapes and sizes are grown and investigated with the view of selecting the optimum preparation method of nanoresonators suitable for possible direct use in photonic devices. Recently, a lot of attention has been paid to the resonant cavities supporting whispering gallery modes (WGMs) based on the ZnO structures, like microdisks [5], micro/nanoneedles [6,7], nanowires [8], etc. These studies aimed at generating the enhanced luminescence emission from the structures.
A ZnO microrod growing along the hexagonal axis of its wurtzite crystal structure and with the regular hexagonal cross-section may naturally serve as a small-sized optical resonator. The light can circulate around this microcavity in hexagonal loop path due to the multiple total internal reflection (TIR) from the inner walls of the prism. Six side walls of the microstructure act as reflective mirrors and support the optical gain. In this geometry an angle of incidence is 60°, much exceeding the critical angle for ZnO (25°) corresponding to the high refractive index of ZnO of about 2.3 for the near-band-edge (NBE) emission. The light is confined inside of the ZnO microstructure and the optical losses are considerably reduced. So, the single ZnO microrod with well-defined cavity geometry can support a set of transverse cavity modes [7] which lead to enhancement of luminescence efficiency in small-scale optical resonators. However, the description of the electromagnetic field distribution in small resonators developed by Wiersig [9] beyond the ray optics theory revealed three mechanisms responsible for partial leakage of light from the hexagonal cavity: corner diffraction, boundary-wave leakage associated with the presence of evanescent waves and the pseudointegrable leakage. So, the light does not circulate forever in the microrod but is leaking partly out of the cavity at the corners. This leads to the electromagnetic field distribution patterns more complicated than simple hexagonal trace of light rays expected from the description based on TIR only.
In this work we present the results of cathodoluminescence (CL) experiments on the ZnO microrods grown by the microwave-assisted hydrothermal method described in detail in Ref. 10. In our approach, considerable shortening of the growth time and cost reduction are achieved. Simplicity and low costs relate to the fact that our method does not require vacuum, high temperature, high pressure, or harmful chemicals. Growth of the ZnO microrods can proceed on various substrates including the inexpensive ones (e.g. glass, silicon, ZnO or GaN). The size and distribution density of the microrods can be controlled by the growth conditions. The high crystal quality of the rods (confirmed by transmission electron microscopy results [10]) and their regular hexagonal shapes are important advantages for optical experiments and possible future applications. Another characteristic important for applications, the intensity ratio of NBE luminescence and green, defect-related luminescence, can be modified by a post-growth treatment. The microrods of such properties seem to be well fitted for both basic research of photonic phenomena and optoelectronic applications, provided the above-mentioned resonant effects can be effectively stimulated and observed. However, the particular preparation process may lead to particular structural modifications, defect formation or impurity incorporation modifying the optical properties of the system. So, apart from the existing extensive literature about various ZnO nanostructures, including nano- and microrods, the properties of the system grown by modified method has to be tested separately. We believe that this task is worth undertaking because the use growth method is promising for applications. Therefore in this work we explore the optical properties of individual microrods, looking for optical excitations occurring in them and for manifestation of resonant phenomena. Our aim is to demonstrate that the investigated microrods exhibit optical properties at least comparable to those of the structures grown by more time-consuming or technologically demanding methods. The present study is based on the possibility to excite the individual micro- and nanoobject with focused electron beam and recording the luminescence response with high spatial resolution in the CL experiment correlated with electron microscopy observation of the sample morphology. As a result, the CL patterns which can be ascribed to microcavity resonances are revealed for NBE emission. Occurrence of WGMs is also confirmed by presence in the CL spectra of series of features with wavelengths which can be described using the plane wave model. We also observe manifestations of the transition from the exciton gas to the electron-hole plasma (EHP) conditions in the ZnO microrod irradiated with the high energy electron beam.
2. Experimental details
As mentioned above the ZnO microrods are obtained by a microwave-assisted hydrothermal method. Growth of the ZnO microrods proceeds in the aqueous solution on commercial c-plane, non-intentionally doped GaN template acquired from Saint Gobain Lumilog. The lattice constant misfit between ZnO and GaN is about 1.8%. The reaction mixture contains deionized water, zinc acetate dihydrate and sodium hydroxide (used as pH regulator) from Sigma-Aldrich Co. Zinc acetate as a zinc precursor was used previously by other groups for nanorod growth [11, 12], however, in contrast to our method, other phases of zinc (Zn(OH)2 and ZnO(OH)2-) were employed. In our approach, a more reactive Zn(OH)+ phase is used. Thus dynamic chemical reaction proceeds instead of a slow crystalization process from saturated solution. The growth rate of the ZnO microrods is therefore extremely high. Uniformity of heating of the solution is very important in our method, wherefore a microwave-assisted version of a hydrothermal reactor is exploited.
The optimum pH value of the reaction solution is 7 and the zinc ion concentration is 0.13 mol/dm3. The growth is carried out in 2–3 minutes at a temperature of 70°C and under atmospheric pressure.
The morphology and size of the so-obtained ZnO microrods are observed by scanning electron microscope (SEM) Hitachi SU-70 using secondary electron detector. Light emission properties of the ZnO microrods are investigated by CL spectroscopy and imaging. CL measurements are performed with SEM equipped with the Gatan Mono CL3 system. The results are acquired at a temperature of 5 K, the accelerating voltage ranges from 5 to 15 kV and the beam current ranges from 2.4 to 14 nA. Such conditions, in particular low beam current settings, allow us to avoid noticeable system modifications during the experiments. Two main reasons for such changes could be defect creation and/or substantial temperature rise due to electron irradiation. Measurements repeated several times for the same microrod have not revealed changes neither in the shape of the CL spectra nor in the spectral feature positions. Therefore, we assume that the structure modifications created by the electron beam, if any, do not influence the luminescent properties of the investigated systems, within the sensitivity limits of the method. We also believe that stable temperature conditions are achieved during our experiments. Since the measured energy positions of characteristic luminescence peaks correspond well to those reported in literature [13] for similar systems and temperatures, we assume that the deviation of the real temperature of the sample surface from that measured at the sample holder during the experiment is negligible and does not influence the conclusions of the reported study.
3. Results and discussion
3.1 An observation of WGM resonances from the ZnO microrods grown by hydrothermal method using CL spectroscopy and imaging
Figures 1(a) and 1(b) show the as-grown ZnO microrods. The well-defined hexagonal shape and vertical alignment of the microstructures is clearly visible. Smooth edge facets of the microrods are expected to support WGM propagation. The diameters of the microrods range from about 500 nm to 2.3 µm. The monochromatic CL maps of the two typical, individual ZnO microrods are shown in Fig. 2(a) and 2(b). The NBE emission intensity is not distributed homogeneously across the microrod, but is locally concentrated near the hexagonal boundary, especially at the six corners of the hexagon. In accordance with Wiersig’s simulations [9], the observed spatial localization of emission intensity can be ascribed to the transverse resonant modes in the hexagonal resonator.
Fig. 1 (a) Top and (b) side-view SEM images of ZnO microrods taken with secondary electron detector at 15 kV. The well-defined hexagonal symmetry is clearly seen.
Fig. 2 (a) and (b) Monochromatic CL maps of two individual ZnO microrods taken at 370 nm at 15 kV and 14 nA. Spatial localization of luminescence intensity near the hexagonal boundary and at corners is visible.
An alternative explanation of appearance of such inhomogenous CL emission pattern could be particular distribution of defects in some microrods. However, CL enables selective recording of the luminescence signal at certain wavelengths and thus visualizing the spatial distribution of particular recombination centres, like excitonic states or defect-related features. In our case, both the CL spectrum (Fig. 3) and the CL monochromatic map taken at 560 nm (the inset in Fig. 3) exhibit a lack of defect-related emission. The main peak of NBE emission at 3.35 eV (370 nm) originates from neutral donor bound exciton recombination [13]. The comparison of the shape of this spectral feature for microrods exhibiting or not the discussed CL pattern does not show any change which can be ascribed to the appearance of new centres of exciton bonding or recombination. Further argument supporting our interpretation is the presence of substructure described by the WGM model simultaneously with the CL pattern of Fig. 2. The strong defect-related luminescence appears in particular for small microrods grown for pH much higher than optimum. Both the inhomogeneous CL pattern and WGM-related substructure disappear for such microrods, consistent with the interpretation that poor quality microrods do not support optical resonance phenomena.
Fig. 3 CL spectrum recorded from the ZnO microrods ensemble using diffraction grating with dispersion of 10.8 nm/mm at 5 K, 15 kV and 14 nA. The main peak is located at 370 nm (3.35 eV). The inset is the top-view monochromatic CL map of the individual ZnO microrod taken at 560 nm. The lack of defect-related emission is seen in both the Cl map and the CL spectrum.
To investigate the NBE luminescence in more detail, CL spectra using a diffraction grating with dispersion of 2.7 nm/mm are recorded. Figure 4 shows the CL spectrum collected for the spot of the high energy electron beam located in the middle of the ZnO microrod with a diameter of 2.24 µm. The multi-peak structure of NBE emission occurs. To define the peak positions in the spectrum we use the inverted second derivative method. The resonance peaks are marked by arrows.
Fig. 4 CL spectrum recorded with the single point in the middle of the individual ZnO microrod excited by the electron beam. Multi-peak structure is visible. Arrows indicate the resonant wavelengths.
Longitudinal optical (LO) phonon replicas occur in the ZnO bulk crystals with the separation of 71–73 meV [13]. The phonon properties of our ZnO microrods are the same as in the case of the ZnO bulk crystals due to the large dimensions of the microrods. The values of the energy spacing seen in the CL spectrum (Fig. 4) are considerably smaller than the LO phonon energy in ZnO. This indicates that the observed multi-peak structure cannot be ascribed to the vibronic states.
In order to demonstrate that the ZnO microrods support the WGM propagation, analysis of mode spacing is carried out using a simple plane wave model. The mode spacing is given by:
where λ is the resonant wavelength, L – the optical path length, n – the refractive index, – the Sellmeier’s first order dispersion relation [14]. The Sellmeier’s equation for the refraction index n of ZnO is taken from Ref. 15. The refractive index n shows a spectral dependence, so spacing between modes changes as a function of the wavelength (energy) [16].In the calculation, the experimental resonant wavelengths λ from the CL spectrum (Fig. 4) are defined by using the inverted second derivative method. Each resonant wavelength λ corresponds to the refractive index n according to the dispersion relation described in Ref. 15. The optical path during one complete circulation of the light inside the microcavity L has in the hexagonal cavity a length of 6Ri, where Ri is the radius of the incircle of the hexagon and is related to the diameter D of the microrod by the geometric relation Ri = √3D/4 [17]. The calculated spacing for the ZnO microrod with the diameter of 2.24 µm is in the range from 46 meV on the high energy side to 68 meV on the low energy side of the CL spectrum (Δλ = 5.1–7.7 nm), which is approximately two times bigger than the experimentally observed spacing, which ranged from 18 to 45 meV (Δλ = 2–5 nm).
However, the resonant modes emitted from the hexagonal microcavity have transverse electric (TE, ) and transverse magnetic (TM, ∥ ) character. Theory indicates that both of the resonance modes (TE and TM) can exist simultaneously in the cavity [17]. The resonance energies can also be estimated with use of a model based on TIR. The resonance in the cavity happens when the total phase shift along the optical path during one complete circulation is 2π multiplied by an integer. Only entire wave trains can perform multiple circulations and generate standing waves. In the hexagonal microcavity the constructive interference condition is expressed by:
where D is the diameter of the hexagonal cavity, λ – the light wavelength, n(λ) – the refractive index, N – the interference order, β = 1/n for TM or β = n for TE modes [18].Equation (2) enables us to calculate the discrete resonant wavelengths fulfilling the resonance conditions in respect to the cavity size. The term (λ/n(λ))N is related to the wavelength in matter. As mentioned above, the integer N describes the interference order of the resonance or the mode number. The second term of the right side of Eq. (2) containing β concerns the phase shift due to the TIR.
For the microrod diameter of 2.24 µm, the wavelength values taken from the CL spectrum and the refraction index n calculated from the dispersion relation described in Ref. 15, the resonance condition of Eq. (2) can be fulfilled for the mode numbers NTE = 30–34 and NTM = 30–35 (Fig. 5). For this configuration of TE and TM modes an acceptable correspondence between model prediction and the experimental results can be achieved (Table 1).
Fig. 5 (a) The TE and TM modes labeled with the mode numbers in the dispersion curve and (b) CL spectrum of the ZnO microrod with the diameter of 2.24 µm.
Table 1. The resonant wavelengths for TE-WGMs and TM-WGMs. Reasonable agreement between the experimental and calculated resonant wavelengths can be observed.
The experimental wavelength values vary from 362 to 401 nm. Each wavelength value corresponds to the refractive index n according to the dispersion function taken from Ref. 15. The mode numbers N are deduced in accordance with Eq. (2) (Fig. 5). Then the resonant wavelengths corresponding to the integer numbers N are found out. The results are presented and compared with the experimentally observed data in Table 1. The experimental resonant wavelengths match with calculated values acceptably good.
In order to ascribe the observed phenomena to the presence of WGMs a microrod size-dependent investigation is performed. Numerical analysis of mode spacing using the plane wave model is carried out. Figure 6(a) presents the CL spectrum of the ZnO microrod with the diameter of 1.49 µm. Lines point out the resonant mode peaks. The observed mode spacing is in the range from 3 to 7 nm, while the calculated mode spacing ranges from 7.4 to 11.9 nm, which is around two times bigger than the experimental value. In this case, similarly to the previous results (Fig. 5), both the TE and TM resonance modes occur. The maximum intensity appears at 369 nm. This position satisfies the WGM resonance occurrence requirements (Eq. (2)) for the mode number NTE = 21. In the case of the other resonant modes, the diameter and the wavelengths fulfill the constructive interference condition for the mode numbers NTE = 18–22 and NTM = 18–23 (Fig. 6(a)). However, the low intensity of the resonant modes can lead to increased errors in the peak positions. For the ZnO microrod with the diameter of 532 nm, the multi-peak structure of the NBE emission does not appear (Fig. 6(b)).
Fig. 6 (a) CL spectrum of the ZnO microrod with the diameter of 1.49 µm. Lines indicate the resonant wavelengths. (b) CL spectrum of the ZnO microrod with the diameter of 532 nm.
The presented results of CL study of three microrods with diameters of 2.24 μm, 1.49 μm and 532 nm (Fig. 5, 6(a) and 6(b)) confirm the effect of cavity size on the resonance modes. The structure of resonance modes becomes clearer as the diameter of the microrod increases. With the diameter increasing the resonance peaks on the CL are more discernible and more intensive. This is due to the smaller optical loss in the larger cavity. In our case, the multi-peak structure on the CL is evident for the largest microrod with the diameter of 2.24 μm.
One can see in Figs. 5, 6(a) and 6(b) that the main maxima are blueshifted when the diameter of the microstructure decreases. The corresponding WGMs also shift toward higher energies. The effect of cavity size on the overall resonant system can be described in terms of the simple plane wave model. The maximum intensities appear at the positions satisfying the resonance occurrence, where the wavelengths and the diameter fulfill the constructive interference conditions of Eq. (2). According to Eq. (2), for given mode number, the maxima shift toward shorter wavelength with the diameter and the optical path length decreasing. As expected for WGMs, with the diameter decreasing the resonance peaks on the CL are less discernible, less intensive and have sparser mode spacing (Fig. 6(a)). In the case of the smallest ZnO microrod (D = 532 nm) (Fig. 6(b)) the multi-peak structure does not occur. This effect is caused by the larger optical loss in the smaller cavity. Besides, the simple plane wave model, a ray-tracing approach can be used to approximate conditions for optical resonance in the dielectric cavity only if their size is markedly bigger than the wavelength. When the cavity size is close to or smaller than the wavelength, WGM resonance cannot be analyzed using a simple ray optics model.
3.2 Transition from spontaneous towards stimulated emission
The intense high energy electron beam in the CL experiment together with reduced optical losses due to the presence of WGMs can induce so high an excitation of the electronic system in the individual ZnO microrod that the transition from the exciton gas conditions to the electron-hole plasma may appear. In the case of high density of nonequilibrium carriers, when the distance between particles is close to the exciton Bohr radius, the excitons become destabilized as a consequence of screening of the Coulomb interaction. Indeed, the analysis of the optical properties of the ZnO microrods as a function of excitation power shows that such transition may occur in the investigated system. Figure 7(a) and 7(b) demonstrate that with increasing excitation power, a new band appears on the low energy side of the main peak. This new band can be attributed to the EHP emission. The critical excitation power to make the EHP transition start, although the transition is gradual, ranges between 54 and 80 μW. The new band appears under the excitation power of 80 μW. Under 54 μW the band does not occur yet. The formation of the EHP and many-body interactions leads to a renormalization of the band gap and to a spectral red-shift of the main emission with increasing excitation power. One can see in Fig. 7(a) and 7(b) that the low energy onset of the spectrum shifts towards lower energies and the width of the band increases with increasing concentration of the electron-hole pairs, as expected for the EHP emission [16, 19]. One can also see that with increasing excitation power the peaks on NBE emission band become sharper and better resolved, as expected for WGMs [20].
Fig. 7 (a) CL spectra obtained when the whole ZnO microrod with diameter of 2.24 μm is scanned by electron beam at excitation power 12 µW (black), 54 µW (red), 80 µW (blue), 121 µW (cyan), 210 µW (magenta) and (b) the enlarged spectra of the region where the new band on the low energy side of the main peak appears. Red-shift and the increasing width of the emission band with increasing excitation power occur.
With increase of the excitation power the whole emission band is broadened, more peaks are discernible in the longer-wavelength region and the strongest peak shifts towards lower energies. These phenomena are typical for the EHP effect. The increase of excitation power up to 210 μW still does not lead to any manifestations of lasing phenomena in the structure. We observe resonance phenomena in the regime of spontaneous emission, similar to that reported, for example in Ref. 5 or 21 for markedly bigger microrods synthesized by some other technique or for nanonails.
4. Summary
ZnO microrod resonators with hexagonal prism shape grown by ultra-fast microwave-assisted hydrothermal method are investigated by CL spectroscopy and imaging. The dependence of light emission properties on the dimensions of the microstructures and thus also on growth conditions is an important advantage and allows easy modification of the optical properties of the microrods by changes of the growth conditions.
The optical resonance phenomena are demonstrated. The monochromatic CL maps show that NBE emission is enhanced and highly localized near the boundaries and corners of the ZnO microrod. The model analysis of the electromagnetic wave propagation in the microcavity and the size-dependent investigation confirm that the multi-peak structure of the UV emission band can be interpreted as manifestations of WGMs.
Changes in the ZnO microrod luminescence are observed as a function of the excitation power, which can be ascribed to the transition from the exciton gas to EHP conditions. The spectral red-shift and increasing width of the emission band with increasing excitation power indicate occurrence of the EHP.
In summary, the results of this study prove that the microrods grown by our fast variant of hydrothermal method support efficient luminescence and related resonant phenomena, needed for future optoelectronic applications. Consequently, further studies of such microrods aimed directly at device fabrication, are fully justified.
Funding
This work was supported by the Polish National Science Centre (NCN) Grant No. DEC-2012/07/B/ST5/02484.
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