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The photoluminescence properties of a ZnO nanobelt are investigated. Both the band-edge emission and the green-yellow emission bands have a series of eigenmodes. The theoretical results demonstrate that in the band-edge emission region the photoluminescence modes are determined by the polariton modes. In the green-yellow band there is no coupling between the photons and excitons and the photoluminescence modes are determined by the transverse Fabry-Perot modes. The photoluminescence spectra at different spots confirm that the Fabry-Perot modes are determined by the transverse size. Furthermore, the fitting results show in the waveband in the ultraviolet and visible band the quality-factor Q of the cavity is decreased from 280 to 70 with the increase of the wavelength.
©2009 Optical Society of America
1. Introduction
Semiconductor microcavities have fascinated many researchers in the last decade as they not only precisely control the optical modes, but also allow precise control of the light-matter interaction [1–3]. The one-dimensional microcavities consisting of quantum wells surrounded by Bragg reflectors have been fabricated to investigate the coupling between excitons and optical modes [4]. It has been shown that the strong photon-exciton coupling leads to the formation of a new kind of quasiparticle, i.e., the exciton polariton [5]. Nanowires of the II-VI semiconductor compounds, such as CdS [6], ZnO [7], and the III-V compound GaN [8] are currently attracting strong interest due to their intriguing optical properties. Single nanowires are a new type of microcavities and have become a focus of the cavity physics. For instance, the single wires show lasing under optical excitation with the resonator cavities composed from the single nanowires [9]. If the transverse size of the micro cavities composed of the two reflectors is comparable to the wavelength, the micro cavities become three dimensional (3D) micro cavities. In the 3D micro cavities there are many new phenomena to be investigated. Up to now, the investigated waveband in the micro cavities is limited to the band-edge emission region. For example, in the micro cavities composed of ZnO nanowire [10,11] the investigated waveband is 3.05~3.35 eV and 1.32~1.37 eV in the micro cavities composed of GaAs/InGaAs quantum wells [4], respectively, both are in the band-edge emission region. As the analyzed wavebands are very narrow, the cavities have a single quality-factor Q. However, there is no reported result for the nanocavities within a wide optical waveband. It should be pointed out that, up to now, only the longitudinal modes are studied both for the nanowire cavities and for the quantum well cavities. There is no result about the transverse mode of the ZnO nano cavity even in the 3D micro cavities [12].
As it is well known that the luminescence of ZnO has two emission bands [13]: One is the band-edge emission band as mentioned above and another one is the green-yellow band, extending from 2.9 eV to 1.65 eV. This band almost covers the whole visible band. The mechanism of the green-yellow band is very complex and several different mechanisms have been proposed. It is generally attributed to the transitions from a shallow donor to a deep acceptor with an ionization energy of about 0.4 eV. The deep acceptor is tentatively assigned to a VZn (Zn vacancy)-related complex [14,15]. The donor-related emission is also an important luminescence mechanism. Among the donorlike native defects, oxygen vacancies (VO) with the (2+/0) transition level at ~1.0 eV below the bottom of the conduction band are expected to be the dominant defects in the ZnO samples [16]. The wide emission band in the ultraviolet and visible band makes it possible to investigate the micro cavities in a wide waveband. The nanobelt is an important form of ZnO nano structure, which has a definite structure size and can be solved by the simple mathematical method. Therefore, studies on the ZnO nanobelt in the whole luminescence band can provide much important information about the micro cavities. In this work, the photoluminescence modes covering the ultraviolet and visible band are observed in a single ZnO nanobelt. The origin of the eigenmodes is also investigated in details.
2. Experiments details
The nanobelt sample was synthesized on a silicon substrate by a vapor-phase transport method at a temperature of 700°C under the atmospheric pressure. Figure 1 presents the scanning electron micrograph (SEM) image of the local part in the nanobelt. The nanobelt dimensions were determined by the SEM with a size of 85.4×12.3×0.218 µm. As the thickness of the structure is several hundred nanometers, the structure is a typical nanobelt. The nanobelt is not a complete ideal structure. At one end of the namobelt the lateral size increases by about tenhundredth. The spectroscopic experiments were carried out in a confocal micro-photoluminescence (PL) system. The single nanobelt lying on the substrate was homogeneously excited with a cw He-Cd laser at a wavelength of 325 nm. To keep the thermal stabilization, the substrate was on a metal holder. The energy of excitation (3.82 eV) was considerably above the exciton resonances (3.31~3.35 eV). The luminescence was analyzed with a Horiba Jobin Yvon spectrophotometer and a semiconductor refrigerator cooled (down to −70°C) CCD. To Investigate the photoluminescence properties at different spots of the nanobelt, in addition to the central part (spot A) of the nanobelt, the emission at spot B and C in the nanobelt were also investigated. Spot B is about 10 µm from spot A in the longitudinal direction and has almost the same lateral size. Spot C is near the end of the nanobelt, where the lateral size is about 13.5 µm.
3. Results and discussion
Figure 2 shows the photoluminescence spectra at spot A of the single ZnO nanobelt. As a common ZnO nanostructure, the photoluminescence includes two parts: One is the band edge emission and another is the green-yellow band originating from the defect states. As shown in Fig. 2(b) the band edge photoluminescence, which is observed from 3.35 eV (close to the electronic band gap) extending to below 3.0 eV, includes three emission parts. The main emission peak is located at 3.269 eV, while there are a broadened peak at 3.203 eV with a long energy tail and a weak high-energy peak at 3.300 eV. The three emission peaks are commonly considered as the recombination of the excitons A, B and C. The noticeable characteristics are the series of peaks observed from 3.24 eV extending to below 3.07 eV, while it is nearly invisible in the range where the luminescence intensity varies rapidly. The peak spacing is about 4.5 meV at 3.24 eV, and it gradually increase to about 11 meV at 3.07 eV. As shown in Fig. 2(c) the green-yellow band emission also has a series of peaks from the 2.85 eV to 1.78 eV, which almost covers the whole visible band. Even in the weakest photoluminescence region between the band edge emission and green-yellow band emission there are obvious peaks as shown in the inset of Fig. 2(c). Just like the band edge emission, the emission peaks are not obvious in the range where the luminescence intensity varies rapidly from 2.49 to 2.57 eV. In the visible band the peak spacing also changes with the variation of the photon energy. The peak spacing is about 13 meV at 2.90 eV, and gradually increases to about 22 meV at 1.82 eV. About 20 modes are observed in the band-edge emission band, and about 60 modes are observed in the green-yellow band. To our knowledge, it is the first observation that so many photoluminescence modes are found in the wide waveband covering the ultraviolet and visible band.
The emission spectra were systematically investigated under variation of the excitation intensity. The typical results are presented in Fig. 3. Just as the general reported results, the band edge emission is less than the green-yellow band under low excitation intensity, while the band edge emission is far larger than the green-yellow band for high excitation intensity. The band-edge emission is very weak with the excitation intensity of 2.1×103 W/cm2, and there is an obvious threshold excitation intensity. Another noticeable phenomenon is the emission peak located at 3.30 eV, which is more strong for the low excitation intensity of 2.1×104 W/cm2, while it is weaker for the higher excitation intensity. Figure 3 demonstrates that the mode location does not have any change both for the green-yellow band emission and for the band-edge emission. In addition, the number of modes and the shape of each mode also have no change. These phenomena imply that the modes do not depend on the excitation intensity. Since the structure parameters of the nanobelt will not change with the increase of the excitation intensity, the experimental results presented in Fig. 3 strongly support the conclusion that the structure size is a determination factor for the modes. It is well known that the location of the band-edge emission depends on the energy gap of the ZnO semiconductor. The same location of the band-edge emission in Fig. 3 confirms that the sample temperature does not change for different excitation intensities, otherwise the band-gap will change for different excitation intensities.
Fig. 2. Photoluminescence spectra at spot A of the ZnO nanobelt with an excitation intensity of 2.1×105 W/cm2. (a) Whole photoluminescence spectrum. (b) Band-edge photoluminescence.
Fig. 3. Photoluminescence spectra at spot A of ZnO nanobelt with a excitation intensity of 2.1×105 (cyan), 1.1×105 (black), 5.4×104 (red), 2.1×104 (green), and 2.1×103 W/cm2 (blue), respectively (a) Whole photoluminescence spectra. (b) Band-edge photoluminescence. (c) Green-yellow band photoluminescence.
The properties of the eigenmodes in the nanobelt are the key problem of this paper. The Fabry-Perot modes in the cavity are the possible mode origin. As the size of the nanobelt is 85.4×12.3×0.218 µm, the corresponding Fabry-Perot mode spacing in these directions is 2.92 meV, 20.2 meV and 1.14 eV, respectively. Among these values, the transverse mode spacing 20.2 meV is the only possible one, which coincides with the experimental results in the green-yellow band in general. However, in the ultraviolet band, there is a distinct difference between the fitting results of the Fabry-Perot mode and the experimental data, which means that the photoluminescence modes in the nanobelt cavity are not determined only by the Fabry-Perot effects. In the band-edge emission region, the coupling between the photon and excitons cannot be neglected, and the polariton in the cavity becomes an important determination factor for the optical modes.
Fig. 4. The mode energy of the confined photon versus the transverse wave vector in the nanobelt. This figure also shows comparison between theoretical and experimental modes. (a) From 3.30 eV to 2.80 eV. (b) From 2.80 eV to 1.82 eV. In the luminescence spectrum 10 modes are not observed between 3.06 eV and 2.94 eV, and 3 modes cannot be determined between 2.41 eV and 2.36 eV.
If the polariton effect is taken into account, the dispersion of photon confined in the nanobelt can be expressed as [10,17]
with the background dielectric constant ε ∞, the speed of light in vacuum c, the oscillator strength fj, which can be expressed by the transverse (ω j,T) and longitudinal (ωj,L) frequencies (fi=ω 2 j,L-ω 2 j,T), a prefactor Ωj as defined in ref 17. The resonant frequencies (for A, B, C excitons) were taken as for a macroscopic ZnO crystal. If the frequency ω is far from the exciton energy, the term in Eq. (1) can be ignored, and no coupling occurs between the photon and the excitons. Otherwise, the term cannot be ignored, and there is a coupling between the photon and the excitons. As it has been pointed out, the coupling will lead to the formation of the quasi-particle of polariton. The parameter kt=mtπ/t is the wavevector perpendicular to the nanobelt, in which t is the thickness of the nanobelt, and the integer mt=1 as the frequency in this paper is larger than the cutoff frequency in this direction. The parameter kT=mTπ/T is the transverse wavevector of the nanobelt, in which T is the transverse size of the nanobelt. The parameter kL=mLπ/L is the longitudinal wavevector in the nanobelt, in which L is the length of the nanobelt.
Fig. 5. Fitting of the photoluminescence spectra with the Lorentzians at the waveband of 3.19, 2.84 and 2.26 eV. The quality factor Q at 3.193 eV (arrow C), 2.841 eV (arrow B) and 2.259 eV (arrow A) is 280, 135 and 77, respectively. The spectra were some parts of the spectrum in Fig. 1.
It has been pointed out that the experimental photoluminescence modes in the visible band are related with the transverse Fabry-Perot modes. It is reasonable to believe that in the band-edge region the polariton mode in this micro cavity is also affected by the transverse modes. The fitting parameters are as in the literature reported by B. Gil et al [18]. Figure 4 presents the simulated mode dispersion between the frequency ω and the transverse wavevector kT for the lower polariton branch (LPB) based on Eq. (1). In fact, the coupling term in Eq. (1) has no any effect for the energy far from the exciton energy in the visible range, where the luminescence modes only correspond to the Fabry-Perot modes. The dispersion curve can be divided into two parts. One is the non-coupling region in the visible band, where there is a good linear relation between the frequency ω and the wavevector kT. Another one is the coupling region in the band-edge emission band, where there is a strong coupling between photon and excitons. For the simulation results there are 97 modes between 1.826 eV and 3.256 eV, among which about 80 modes are located in the non-coupling region and about 17 modes are located in the coupling region. In the high energy region the deviation between theoretical and experimental modes is about 15 meV. In the ultraviolet region the simulated mode spacing varies from 4.5 to 14 meV, and in the visible region the mode spacing is 14 to 16 meV, which is in approximate agreement with the experimental values and requires further investigation in the future. The mode spacing provides clear evidence that the modes observed in the emission spectra are the transverse modes of the nanobelt. As the possible longitudinal mode spacing is far less than the experimental mode spacing, the longitudinal mode of the nanobelt can be excluded. It has been reported that the polariton modes depend on the excitation intensity [10]. However, the experimental results in this work demonstrate that there is no relation between the photoluminescence eigenmodes and the excitation intensity. In fact, if the exciton energy does not change with the increase of the excitation intensity, the polariton mode does not have any change as Eq. (1). The above experimental results confirm that for the excitation intensity of 2.1×104~2.1×105 W/cm2, the polariton modes and exciton energy do not change.
It has been reported that the eigenmode is observed at the end of nanowire [10]. In the emission measurement of the nanobelt, the transverse modes can be observed in the central part of the nanobelt sample. This phenomenon can be explained as follows. In fact, in the longitudinal direction, if the wavevector k points perpendicular to the facet, k is sufficiently large for outcoupling of the polaritons, which is similar as at the end facets of the nanobelt. Meanwhile, the light is detected outside the nanobelt due to the scattering between polaritons or between photons and phonons.
Fig. 6. The comparison of the luminescence spectra at spots A (green), B (red) and C (black) with the same measurement condition as in Fig. 2. (a) Whole photoluminescence spectra. (b) Band-edge photoluminescence. (c) Green-yellow band photoluminescence. In the inset of (c) there are 10 periods between the arrow P and Q for the black spectrum or between the arrow P’ and Q’ for the red spectrum.
Figure 5 displays the fitting results in the ultraviolet and visible band. The results approve that these spectra can be fitted to the sums of Lorentzians, where each Lorentzian represents an individual luminescence peak. The main results of the Lorentzians fitting are the properties of the resonator cavity. The full width at half maximum (FWHM) of the Lorentzins for different modes is also different. The FWHM of the mode is 11.4 meV at 3.193 eV, 21.0 meV at 2.841 eV, and 29.3 meV at 2.259 eV, respectively. Therefore the quality-factor Q of the cavity is different in the whole emission region. In the band-edge region, the Q of the cavity is 280 for the mode of 3.193 eV as shown by arrow C in Fig. 5(a). In the visible band, the Q of the cavity is 77 for the mode of 2.259 eV as shown by arrow A in Fig. 5(c). Between the band-edge emission and the green-yellow band emission, the Q of the cavity is 135 for the mode of 2.841 eV as shown by arrow B in Fig. 5(b). In general, the mode-width increases with the increase of wavelength, while the Q of the cavity decreases with the increase of the wavelength. The reported photoluminescence eigenmodes are only in the narrow emission band, therefore the property of the nano resonator is obtained only in this narrow waveband [10]. To our best knowledge, this is the first report about the optical micro cavities in so wide waveband covering the ultraviolet and whole visible band.
Figure 6 presents the photoluminescence spectra at different parts of the nanobelt. As shown in Fig. 6(a) the photoluminescence spectra at different spots are similar in general. In the band-edge emission region, the photoluminescence spectra at spot B and C also have some vibration modes in the low-energy side of the exciton peaks. The vibration period is also similar with spot A. However, the number of the vibration modes is much less than that of spot A. In the visible region, there is some difference between three spots for the defect-related emission. For spot A the defect-related emission peak is located at 2.39 eV, while it is located at 2.35 eV for spot B and C. It is shown in Fig. 6(c) that the vibration modes of spot B and C are more obvious than spot A in the visible region. The luminescence modes for spot A and B are almost completely consistent. The inset of Fig. 6(c) presents the corresponding relation in the energy range from 2.24 to 2.46 eV for spot A and B. The vibration modes for spot B and C are similar, however, there is some difference for the mode spacing. As shown in the inset of Fig. 6(c), the mode spacing at spot C is less than that at spot B for about 10%, which agrees with the lateral size difference for spot B and C very well. The similar lateral size leads to the similar mode spacing for spot A and B, although the yellow-green peak locations for spot A and B are different. The different lateral size leads to different mode spacing for spot B and C, although the yellow-green peak locations for spot B and C are similar. The mode spacing for spot A, B and C is the direct evidence that in the yellow-green band the luminescence modes are determined by the lateral size of the nanobelt.
4. Conclusion
In conclusion, the photoluminescence spectra of ZnO nanobelt are investigated in this work. For the band-edge emission band, about 20 modes are observed from 3.24 eV to 3.07 eV. For the green-yellow band, about 60 modes are observed from 2.85 eV to 1.78 eV. The results demonstrate that the photoluminescence modes do not depend on the excitation intensities. The mode spacing demonstrates that the photoluminescence modes do not only relate to the transverse Fabry-Perot modes but also depend on the polariton effect. The theoretical results imply that in the whole emission band there are two regions: the band-edge emission region with the strong photon-excitons coupling and the green-yellow band emission region without coupling. The fitting results show that the quality-factor Q of the nanobelt cavity is large at low wavelength, and it decreases with the increase of the wavelength. The photoluminescence spectra at different spots confirm that the Fabry-Perot modes are determined by the transverse size of the nanobelt.
Acknowledgments
This work was supported by the Jiangsu Provincial Key Lab of ASIC Design under grant number JSICK0401, Natural Science Foundation of China (60576059), Chinese National Key Basic Research Special Found (2006CB921700, 2007CB924902), and Shanghai Leading Academic Discipline Project (B411).
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