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Enhancement of light emission from nanostructured In2O3 via surface plasmons

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Abstract

We report the construction of In2O3/Ag/In2O3 sandwich nanostructures and realization of effective coupling with surface plasmon (SP) modes. An enhancement of photoluminescence as large as 278-fold is achieved for the new nanostructures, while only eightfold is obtained from bilayer structures. The advancement of the nanostructures is that both the frequency of incidence photons and the in-plane wavevector of the excited SP modes along each side of the sandwiched nanometer metal layer are identical, thus the momenta mismatch between two SP modes which inevitably occurs in commonly used metal/dielectric bilayer structures is no longer a problem. The fulfillment of the cross coupling and resonance conditions of the two SP modes leads to the tremendous amplification of light emission. Such sandwich nanostructures can be readily extended to other dielectric/metal/dielectric nanomaterial combinations and identified as technologically useful for SP mediated light emitting devices.

©2010 Optical Society of America

1. Introduction

Surface plasmons (SPs) have attracted increasing attention because of their fundamental importance and extensive applications in sensing [14], surface enhanced spectrum [5], enhancing transmission [6,7], nanowaveguiding [1,4], and bright light sources in nanoscale dimensions [812]. The enhancement of internal quantum efficiency of light emitting materials and devices by SP coupling was realized with various metal/dielectric bilayer structures [1317], such as Ag/InGaN [13] and Al/ZnO [15]. However, the SP mediated emission enhancement ratios (EERs) of the bilayer structures reported hitherto were not high enough and many emission amplifications were limited to the backward direction in which light emits via a transparent substrate into the free space [12,13,16]. For example, Okamoto et al observed a 14-fold enhancement in peak photoluminescence (PL) intensity from the Ag-capped InGaN quantum wells [13]. Lei and Ong [15] and Cheng et al [14] showed twofold and threefold band edge emission enhancement from ZnO using Al and Ag cap-layers, respectively. Lai et al demonstrated a 10-fold enhancement of the near-band-edge (NBE) emission of ZnO thin films capped with an 89-nm-thick Ag layer, but negligible enhancement was observed on Au-coated ZnO films [15]. Liu et al realized 12-fold and twofold emission enhancements from ZnO films by sputtering Pt nanopatterns and Pt films onto ZnO films, respectively [17]. Clearly, the realized maximum EER for metal/dielectric bilayer structures reported hitherto was 45-fold ZnO/Ag [16]. Questions still remain on the further elevation of EER of the SP mediated light emission. It is noted the metal in a metal/dielectric bilayer structure supports two SP modes that are associated with each metal surface [1]. For a given frequency, these two modes have different in-plane wavevectors and can hardly interact. Hence, one cannot anticipate very high light emission enhancement for such metal/dielectric bilayer designs. In addition, the metal in a metal/dielectric bilayer structure is prone to suffering from surface oxidation which shall lead to the degradation of light-emitting device performance. To solve such a problem of wavevector mismatch, we propose a dielectric/metal/dielectric sandwich nanostructure model rather than a commonly used metal/dielectric bilayer structure by which strong cross coupling between the two SP modes and consequently much higher internal quantum efficiency is achieved.

Here we report on the construction of In2O3/Ag/In2O3 sandwich nanostructures and demonstration of their ultra-giant PL enhancement. In this work Ag is selected as a metal nanoparticle material because of the lowest losses of SP energy in the visible spectrum and wide utilization in the study of metal/dielectric bilayer structures [1,1316], while In2O3 is selected as the dielectric material because it is a distinctive semiconductor with a wide direct band gap (3.5-3.6 eV) [18,19], a high electron mobility (160 cm2V−1s−1) [18,20], and extensive applications in transparent electronics [2123], but In2O3 was rarely used as a robust luminescent material for light emitting device applications yet. We exhilaratingly find that, an NBE-EER as large as 278-fold is readily achieved from the In2O3/Ag/In2O3 sandwich nanostructures referring to the light emission from the bare In2O3 monolayer samples, which is the largest light emission enhancement ever reported to the authors’ knowledge. The realization of the giant enhancement of light emitting efficiency in In2O3 via SP mediation will render the feasibility to integrate its unique electrical and optical functions into a single chip. Moreover, our proposed sandwich nanostructure model can be readily extended to other dielectric/metal/dielectric material combinations and would lead to a new class of highly efficient light emitting sources.

2. Experiment

For the fabrication of In2O3/Ag/In2O3 sandwich nanostructures on Si(100) substrates, both of In2O3 layers on and under the Ag nanometer layer were grown by rf magnetron sputtering using an In2O3 ceramic target (purity 99.99%) as a source material, while the Ag layer was deposited by thermal evaporation using silver dots (purity 99.99%) as the evaporating material. An SAJS-450 sputter-coater and an SAZF-450 evaporator (Shenyang Tengao Vacuum Technology Co.) were used for the deposition of In2O3 and Ag thin films, respectively. A fixed thickness of 50 nm was designed for all In2O3 layers, while a variable thickness of the Ag layer (9, 15, 21 and 30 nm) was adopted to evaluate the influence of the metal-layer thickness on the SP mediated emission enhancement. During In2O3 sputtering or Ag evaporation, the substrate was set at room temperature and the sample holder was kept rotating to assure an isotropic distribution in the thickness for each layer of the sandwich nanostructures. Sputtering was performed in a pure Ar (99.999%) ambient while evaporation was carried out under a vacuum condition (prior to sputtering or evaporating a base pressure of 10−4 Pa was attained in the respective growth chamber). The flow rate of Ar gas and the power of rf were set to be 20 sccm and 100 W, respectively, which induced a sustained sputtering pressure of 3 Pa and a growth rate of 6 nm/min. The growth rate was monitored using a crystal oscillator. To clarify the effect of the In2O3 cap-layer in the In2O3/Ag/In2O3 sandwich nanostructures on the enhancement of PL intensity, PL measurements for a bare In2O3 monolayer and the Ag/In2O3 bilayer structures were firstly carried out. Then we deposited an In2O3 cap-layer onto each of the Ag/In2O3 bilayer samples to form the In2O3/Ag/In2O3 sandwich nanostructures and repeated PL measurements. Schematic images of the three structures and PL measurement configurations are illustrated in Fig. 1 .

 figure: Fig. 1

Fig. 1 Schematic images of three structures on Si substrates, the layer thicknesses, as well as the excitation and PL signal collection configurations are illustrated:(a) an In2O3 monolayer sample, (b) a Ag /In2O3 bilayer sample, (c) an In2O3/Ag/In2O3 sandwich nanostructure sample.

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A HITACHI S4800 field emission scanning electron microscope (FESEM) was employed to characterize the in-plane morphologies and the cross sections of the In2O3 monolayer, Ag/In2O3 bilayer and In2O3/Ag/In2O3 sandwich nanostructures. PL measurements were carried out on an FLS920 fluorophotometer using a xenon lamp as the excitation source in which a 300 nm excitation line and an incidence angle of 45° were selected. The power of the excitation for PL measurements was kept same (5 mW) when comparing the PL intensities from all the samples so that a direct EER comparison can be made among the three structures. By employing a 341 nm optical filter, PL signals were detected using a Red PMT equipped spectrometer (Acton SP2500i) from the top side geometry of the samples.

3. Results and discussion

Figure 2 shows typical top view FESEM images for an In2O3 (50 nm) monolayer sample and a Ag(21 nm)/In2O3(50 nm) bilayer sample grown on Si substrates. Figure 2(a) is a surface morphology of the In2O3 monolayer sample and the inset displays a high resolution image. Obviously, the surface of In2O3 monolayer sample is reasonably smooth and uniform. However, as shown in Fig. 2(b), when covered with a 21 nm Ag layer the Ag(21 nm)/In2O3(50 nm) bilayer sample becomes much rougher. AFM measurement (not shown) demonstrated a typical root mean square (RMS) roughness of about 3 and 10 nm for the In2O3 monolayer sample and the Ag(21 nm)/In2O3(50 nm) bilayer sample, respectively.

 figure: Fig. 2

Fig. 2 The top view FESEM images: (a) an In2O3(50 nm) monolayer sample and (b) a Ag(21 nm)/In2O3(50 nm) bilayer sample. The inset in the image (a) is an amplified view of the In2O3(50 nm) monolayer sample.

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Figure 3 shows typical top view and cross-sectional FESEM images for two In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructure samples. After capping an In2O3(50 nm) layer onto each of the bilayer samples to form the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures, the surface morphology changes greatly and presents the structures of large quantity islands with horizontal dimensions in hundreds nanometers as shown in Fig. 3(a)3(d). It is found that with increasing the Ag thickness from 15 to 21 nm, some islands merge into large ones and the island density becomes smaller, as shown in Fig. 3(a) and 3(c). The cross section views of the sandwich nanostructures display the islands are in shape of oval-shaped pebbles with vertical dimensions in the range of 50 ~100 nm. It is known the In2O3 thin films are very hard and robust. Considering the facts that the islands are large in horizontal dimensions (100~500 nm) and relatively thin in vertical dimensions (50~100 nm) and the morphology evolution shown in Fig. 2 and 3 is closely correlated, we can conclude the metallic Ag layers are largely sandwiched by the bottom and top In2O3 thin films. The quasi-periodically distributed islands (or a roughened surface) would act as an effectual Prague grating and enhance the power of light extraction via scattering.

 figure: Fig. 3

Fig. 3 The top view and cross-sectional FESEM images for the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures: (a) and (b) for the In2O3(50 nm)/Ag(15 nm)/In2O3(50 nm) sample; (c) and (d) for the In2O3(50 nm)/Ag(21 nm)/In2O3(50 nm) sample.

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Figure 4(a) shows the room temperature PL spectra of the Ag/In2O3(50 nm) bilayer structures with different thickness of the Ag layer. For comparison, the spectrum of the bare In2O3(50 nm) monolayer sample is also plotted in the figure. The inset in Fig. 4(a) shows the single PL spectrum of the bare In2O3(50 nm) monolayer sample. An ultraviolet emission peak centered at 362 nm (photon energy of 3.425 eV) dominates the PL spectrum. Similar PL spectra were previously reported for In2O3 nanowires and In2O3 nanoparticles [24,25]. The origin of the PL peak at 362 nm can be ascribed to the NBE emission from the In2O3 monolayer in terms of the nanoparticles’ characteristics as being shown in the inset of Fig. 2(a). It is noted from the inset in Fig. 4(a) that the oxygen-vacancy related deep-level defect emissions that are commonly located in the blue-green region (from ~467 to ~548 nm) [26,27], are very weak.

 figure: Fig. 4

Fig. 4 (a) Photoluminescence spectra of the Ag/In2O3(50 nm) bilayer samples with different thicknesses of Ag layers. The spectrum of the bare In2O3 monolayer is plotted for comparison. The inset in (a) individually shows the PL spectrum of the bare In2O3(50 nm) monolayer sample. (b) The dependence of the NBE-EER for the Ag/In2O3(50 nm) bilayer structures on the thickness of Ag layers, with the definition I(Ag/In2O3)/I(In2O3).

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Figure 4(b) exhibits the dependence of NBE-EER for the bilayer structures on the thickness of the Ag layers, with the NBE emission intensity of the bare In2O3(50 nm) monolayer sample as a reference. One can find two dominant characteristics from Fig. 4(a) and 4(b). Firstly, the PL intensities of the Ag/In2O3 bilayer structures are evidently enhanced compared with that of the In2O3 monolayer sample. A peak NBE-EER of eightfold is revealed at the Ag layer thickness of 21 nm, while either decreasing or increasing the Ag layer thickness leads to the fall of the NBE-EER. Similar dependence of NBE-EER on the thickness of metal layers was also observed and interpreted previously in other metal/dielectric material combinations, such as the Ag/ZnO bilayer films [16] and the ZnO nanorod materials covered with gold nanoparticles [28]. The NBE emission enhancement of the Ag/In2O3(50 nm) bilayer structures can be attributed to the coupling between the NBE emission of the In2O3 material and the SPs at the Ag/In2O3 interface. The resonance energy of the SPs at the in-plane of the Ag/In2O3 interface can be calculated according to the dispersion relation [1],

kSP=(ωc)εdεmεd+εm
where ksp is the in-plane wavevector of a SP mode, εd and εm are the dielectric constants of the In2O3 and Ag films, c is the velocity of light and ω is the energy of incident photons. By using the Eq. (1) and the dielectric constants of In2O3 and Ag cited from [21] and [29] respectively, the resonance energy of the SPs at the Ag/In2O3 interface is determined to be 2.930 eV that is close to the photon energy of the NBE emission of In2O3 (3.425 eV). The resonance energy of the SPs could be modulated to lie within the NBE emission band of the semiconductor by changing the thickness and surface roughness of the metal layer (i.e., by tailoring the size and shape of Ag nanoparticles).. Secondly, it is also found that, besides the enhancement of the NBE emission, two broad bands centered at ~467 (2.655 eV) and ~548 nm (2.263 eV) become pronounced for the Ag/In2O3 bilayer samples, as is seen in Fig. 4(a). These emission bands were ascribed to the oxygen-vacancy related deep-level defect emissions [26,27], which is also close to the SP resonance energy of Ag/In2O3 structures and may couple with the SPs. It is believed that two factors are responsible for the enhancement of the deep-level defect emissions, one is the energy coupling with the SPs and the other is the more prominent light scattering on the surface of the Ag/In2O3 bilayer samples since the coverage of a Ag layer on In2O3 turns the surface rougher which is favorable to the light escape from the nanostructures.

From Fig. 4(b) one finds that the maximal NBE-EER for the Ag/In2O3 bilayer structures is only eightfold, which is a typical result compared with that reported in the literatures [14,15,17]. The small EER values for the Ag/In2O3 bilayer structures can be attributed to the fact that the Ag layer in a Ag/In2O3 bilayer structure supports two different SP modes, one supports Ag/In2O3 while the other supports Air/In2O3. For a given frequency, these two modes have different in-plane wavevectors (momenta) and do not interact. To realize a strong cross coupling between the two SP modes and a resultant higher internal quantum efficiency, we capped an In2O3(50 nm) layer onto each of the above Ag/In2O3(50 nm) bilayer structures and constructed the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures.

Shown in Fig. 5(a) are the PL spectra of the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures with different Ag layer thicknesses. Again the spectrum of the bare In2O3 monolayer sample is shown for comparison. The interesting finding in Fig. 5(a) is that the sandwich nanostructures demonstrate much stronger PL intensities than that of corresponding Ag/In2O3(50 nm) bilayer structures shown in Fig. 4(a) and the maximal EER corresponds to the Ag layer thickness of 21 nm as well. Figure 5(b) plots the dependence of the In2O3 NBE-EERs for the sandwich nanostructures on the thicknesses of the Ag layers, again with the NBE PL intensity of the bare In2O3(50 nm) monolayer sample as the reference. An ultra-giant EER of 278-fold realized here is the largest value of the SP mediated EERs so far as the authors know. The realization of such ultra-giant NBE-EER can essentially be attributed to the cross coupling mechanism and the complete or partial coherence enhancement effect of the two SP modes in each side of the Ag layer owing to their identical natures both in frequency and in wavevector. Further, by comparing Fig. 5(a) with Fig. 4(a) it is interestingly found that the relative intensities of oxygen-vacancy defect related emission bands are greatly suppressed for the sandwich nanostructures. For instance, it is elicited from Fig. 4(a) and Fig. 5(a) that the peak intensity ratios between the NBE emission and the defect emission at 470 nm, INBE/I470 nm, are 3.5 and 5.6 for the Ag(21 nm)/In2O3(50 nm) bilayer structure and the In2O3(50 nm)/Ag(21 nm)/In2O3(50 nm) sandwich structure, respectively. However, the SEM observation of Fig. 3 shows the surfaces of the sandwich nanostructures are much rougher than that of the Ag/In2O3 bilayer structures which should bring on a more prominent surface scattering effect for the sandwich nanostructures than the bilayer structures. Therefore we deduce that there exists a competing process between the enhancements of the NBE emission and the defect state related emissions since the photon energies of the deep-level defect emissions are also close to the SP resonance energy of the Ag/In2O3 interface and the emissions from the defects are enhanced via the SP mediation as well.

 figure: Fig. 5

Fig. 5 (a) Photoluminescence spectra of the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures with different thicknesses of Ag layers. The spectrum of the bare In2O3 is also plotted for comparison. (b) The dependence of the NBE-EER for the sandwich nanostructures on the thickness of Ag layers, with the definitionI(In2O3/Ag/In2O3)/I(In2O3).

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To explore the mechanisms of the observed ultra-giant enhancement of light emission from the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures, we also deduce the EER spectra for both of the bilayer and the sandwich nanostructures from Figs. 4(a) and 5(a), respectively. The deduced EER spectra are illustrated in Figs. 6(a) and 6(b). It can be clearly distinguished that the b labeled bands in Fig. 6(b) dominate the EER spectra for the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures while the a labeled bands in Fig. 6(a) dominate the EER spectra for the Ag/In2O3 bilayer structures. The a bands, with the peak position shift of (470 ~473 nm) in Fig. 6(a) and with the shift of (464 ~467 nm) in Fig. 6(b) respectively, are ascribed to the origin of oxygen-vacancy associated deep-level defects and the enhancement via energy coupling with the SP modes. However, the b bands in the Figs. 6(a) and 6(b) obviously deviate from the NBE emission peak of In2O3 (362 nm). The b bands (395~399 nm) shown in Figs. 6(b) for the sandwich nanostructures are evidently closer to the NBE emission peak of In2O3 (362 nm) than that for the bilayer structures (413~416 nm) shown in Figs. 6(a). The difference between the two b bands in the two structures is as large as about 17nm. This observation indicates the SP resonance energy at the Ag/In2O3 interfaces for the sandwich nanostructures matches better to the photon energy of the NBE emission than that of the bilayer structures, considering the modulation effect arisen from the changes of Ag layer thickness and surface roughness of the sandwich nanostructures. By comparing Fig. 6(b) with Fig. 5(a) where the NBE emissions of In2O3 (~362 nm) dominate all the PL spectra, it is found the EER of the NBE emission for the sandwich nanostructures does not reach its maximum. It implies that the NBE-EER of In2O3 could be further elevated as long as the band-gap energy of In2O3 is tailored via doping engineering and/or the SP resonance energy is further tuned by changing the Ag layer thickness and the surface roughness.

 figure: Fig. 6

Fig. 6 (a) and (b) are the EER spectra of the Ag/In2O3(50 nm) and In2O3(50 nm)/Ag/In2O3(50 nm) samples derived from Figs. 4(a) and 5(a), using the definitionI(Ag/In2O3)/I(In2O3) and I(In2O3/Ag/In2O3)/I(In2O3), respectively. (c) and (d) show the peak intensities and the corresponding peak positions of the b labeled EER bands from spectra (a) and (b), respectively.

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Figures 6(c) and 6(d) numerically exhibit the peak intensities and the corresponding peak positions of the b bands in the EER spectra for the bilayer and sandwich nanostructures. It is found in Fig. 6(d) that the peak intensities of the b bands turn stronger along with small blue shifts of their peak positions and the EER comes to the maximum value for the sandwich nanostructure when the Ag layer thickness is 21 nm. The peak intensity dependence of the b labeled EER bands on the blue shift of their peak positions in the EER spectra again reflects their SP mediation nature and upholds the conclusion that there exist competition between the NBE emission and the oxygen-vacancy defect related emission enhancements. The synthesis of In2O3/Ag/In2O3 sandwich nanostructures facilitates the NBE emission enhancement and simultaneously suppresses the defect emission enhancement more efficiently than that of the bilayer structures. The calculated resonance energy of the SP modes for the Ag/In2O3 bilayer structures is 2.930 eV (423nm). However, the reality shown in Fig. 6(d) is that in the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures the resonance energy of the SP modes is evidently tuned to the higher energies (3.139 ~3.108 eV) by the modulation effect of the variation of Ag layer thickness and surface roughness. The higher resonance energy the SP modes reaches, the closer to the photon energy of the NBE emission (3.425 eV) it is and simultaneously the farther away from the deep-level defect emission energies of In2O3, therefore the higher coupling efficiency of the NBE emission with the SP modes can be realized while the deep-level defect emissions is suppressed in the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures.

4. Conclusion

In summary, we have shown that by constructing the In2O3/Ag/In2O3 sandwich nanostructures, an ultra-giant NBE-EER of 278-fold that is about 35 times of magnitude larger than that of the Ag/In2O3 bilayer structures, is readily achieved. The mechanism for such ultra-giant emission enhancement is that both the frequency of incidence photons and the in-plane wavevector of the SP modes along each side of the sandwiched Ag layer are identical. The fulfillment of the cross coupling and resonance conditions of the two SP modes leads to the tremendous amplification of light emission. The formation of In2O3/Ag/In2O3 sandwich nanostructures also allows the SP resonance modes at the Ag/In2O3 interfaces move to higher energy and becomes more adjacent to the NBE emission energy of In2O3 than that of the Ag/In2O3 bilayer structures, which facilitates the enhancement of NBE emission and simultaneously suppresses the deep-level defect emissions of In2O3. The proposed dielectric/metal/dielectric sandwich nanostructure model has a variety of advantages over the commonly adopted metal/dielectric bilayer nanostructures. For example, the sandwiched metal layers can now be effectively protected and are no longer suffered from degradation due to surface oxidation which is extremely important to improve the performance and prolong the lifetime of the SP mediated light emitting devices. Moreover, the presented sandwich nanostructures can be extended to other metal-dielectric material combinations and could play an important role in the fabrication of highly efficient SP mediated light emitting devices.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 10974174, 50472058 and 91021020), National Basic research Program of China under Grant No. 2011CB925603 and the Natural Science Foundation of Zhejiang Province, China (No. Y4080171 and Z6100117).

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Figures (6)

Fig. 1
Fig. 1 Schematic images of three structures on Si substrates, the layer thicknesses, as well as the excitation and PL signal collection configurations are illustrated:(a) an In2O3 monolayer sample, (b) a Ag /In2O3 bilayer sample, (c) an In2O3/Ag/In2O3 sandwich nanostructure sample.
Fig. 2
Fig. 2 The top view FESEM images: (a) an In2O3(50 nm) monolayer sample and (b) a Ag(21 nm)/In2O3(50 nm) bilayer sample. The inset in the image (a) is an amplified view of the In2O3(50 nm) monolayer sample.
Fig. 3
Fig. 3 The top view and cross-sectional FESEM images for the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures: (a) and (b) for the In2O3(50 nm)/Ag(15 nm)/In2O3(50 nm) sample; (c) and (d) for the In2O3(50 nm)/Ag(21 nm)/In2O3(50 nm) sample.
Fig. 4
Fig. 4 (a) Photoluminescence spectra of the Ag/In2O3(50 nm) bilayer samples with different thicknesses of Ag layers. The spectrum of the bare In2O3 monolayer is plotted for comparison. The inset in (a) individually shows the PL spectrum of the bare In2O3(50 nm) monolayer sample. (b) The dependence of the NBE-EER for the Ag/In2O3(50 nm) bilayer structures on the thickness of Ag layers, with the definition I ( A g / I n 2 O 3 ) / I ( I n 2 O 3 ) .
Fig. 5
Fig. 5 (a) Photoluminescence spectra of the In2O3(50 nm)/Ag/In2O3(50 nm) sandwich nanostructures with different thicknesses of Ag layers. The spectrum of the bare In2O3 is also plotted for comparison. (b) The dependence of the NBE-EER for the sandwich nanostructures on the thickness of Ag layers, with the definition I ( I n 2 O 3 / A g / I n 2 O 3 ) / I ( I n 2 O 3 ) .
Fig. 6
Fig. 6 (a) and (b) are the EER spectra of the Ag/In2O3(50 nm) and In2O3(50 nm)/Ag/In2O3(50 nm) samples derived from Figs. 4(a) and 5(a), using the definition I ( A g / I n 2 O 3 ) / I ( I n 2 O 3 ) and I ( I n 2 O 3 / A g / I n 2 O 3 ) / I ( I n 2 O 3 ) , respectively. (c) and (d) show the peak intensities and the corresponding peak positions of the b labeled EER bands from spectra (a) and (b), respectively.

Equations (1)

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k S P = ( ω c ) ε d ε m ε d + ε m
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