Band gap properties of 2D square lattice photonic crystal composed of rectangular cells

Abstract

In this paper, the photonic band gap (PBG) properties of two dimensional (2D) square lattice photonic crystal structures composed of rectangular cells were studied. The effect of refractive index, rectangles length and the ratio of width to length of the rectangles on the PBG properties of the structure with different configurations was investigated. It is found that the density of gaps in both modes (transverse electric (TE) and transverse magnetic (TM)) is high for structure composed of rectangular dielectric rods in air, while the density of the gaps is very low for structure composed of rectangular air pores in dielectric material.

Keywords

photonic crystal (PhC) / band gap / refractive index

1 Introduction

Surface-enhanced fluorescence (SEF) is known for more than a few decades [1]. A metallic particle near a fluorophore can influence both its excitation and emission, eventually leading to significantly enhanced spectral properties [2-5]. The enhancement is suggested to occur via a coupling interaction of the fluorophore and the electric field around the metal particle, which can be induced by incident light or by the excited fluorophore [6-10]. This effect can bring an increase in the quantum yield and improve the efficiency of light absorption [11-13].

Recently, research on the enhanced fluorescence properties of lanthanide ions such as Pr³⁺ and Nd³⁺ [14-17] in low dimensional semiconductors has attracted much interest because of their potential application in optoelectronic devices.

The photoluminescence (PL) properties of lanthanide ions have been investigated for decades [18-20]. An attractive feature of luminescent lanthanide ions is their line-like emission, which results in a high color purity of the emitted light. Actually lanthanide ions have been considered the most important optical activators for luminescent devices.

Emission of light from lanthanide ions is a fundamentally important process with a continuously expanding range of applications in contemporary electronic devices. However, the photon absorption cross section of some trivalent Ln³⁺ ions (Pr³⁺, Nd³⁺, etc) is very small due to the dipole-forbidden nature of the intra^-4f transitions and, thus, the intensity of the PL is relatively low. In order to overcome the small absorption cross section, coupling Ln3+ ions with metal nanoparticles was a valuable strategy.

Metal nanoparticles were ready to agglomerate during their application [21]. To overcome the limitation, in the paper, the Cu/Si nanomaterials were employed in investigating the SEF process of Ln³⁺ (Ln= Pr, Nd, Ho, and Er). It showed that the emission of intrinsically fluorescent Ln³⁺ could be significantly enhanced by Cu/Si nanostructure, which had a greater enhancement than the unsupported Cu nanoparticles. Furthermore the preliminary explanation of excellent SEF based on Cu/Si nanostructure was proposed.

2 Experiment

2.1 Materials

Pr₆O₁₁, Nd₂O₃, Ho₂O₃, Er₂O₃ and CuSO₄·5H₂O were purchased from Alfa Aesar Co. Pr₆O₁₁, Nd₂O₃, Ho₂O₃ and Er₂O₃ powders were dissolved in concentrated nitric acid to make a 0.1 M stock solution. CuSO₄ was prepared to 5.0×10^-3 M with doubly distilled water.

Other reagents were of analytical grade without further purification. Doubly distilled water was used throughout.

2.2 Synthesis of silicon nanowires (SiNWs) and modification with Cu nanoparticles

The SiNWs were prepared via a simple thermal evaporation of SiO powder using the oxide-assisted growth method developed by us [22]. The as-synthesized SiNWs (0.008 g) were etched with 5 mL 5% HF aqueous solution for 1 min to get rid of their outer oxide layer, rinsed with distilled water, and then immersed in 15 mL 1×10^-3 M CuSO₄ aqueous solution. Then the yellow SiNWs gradually turned black, which indicated that they were modified with Cu nanoparticles. The total amount of copper on the surface was determined to be 75 µg. Then the Cu/Si nanomaterials were dispersed in 2 mL distilled water under the violent ultrasonic irradiation.

2.3 Synthesis of unsupported Cu nanoparticles

Unsupported Cu nanoparticles were prepared by reducing CuSO₄ solution directly to Cu nanoparticles with the method reported before [23].

2.4 Characterization

The as-prepared products were characterized by X-ray diffraction (XRD), which was carried out on a Philips X’pert PRO MPD diffractometer with Cu Kα radiation (λ = 0.15406 nm). A scanning rate of 0.05^o·s^-1 was applied to record the pattern in the 2θ range of 25°-80°. The morphology of the SiNWs was characterized by scanning electron microscopy (SEM, FEI Co., model Quanta-200) with an energy dispersive X-ray (EDS) spectrum. Fluorescence spectra were measured with a Fluoromax-4 spectrofluorimeter.

3 Results and discussion

3.1 Synthesis and modification of SiNWs

The SEM image in Fig. 1 reveals that the sample takes the shape of a wire, which is smooth and uniform with length up to several micrometers. The elemental analysis of SiNWs shows no peaks of other elements except Si and O, indicating a high purity of the products.

Fig.1 SEM image and EDS (insert) of SiNWs

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Figure 2(a) shows the XRD pattern of the as-prepared SiNWs, and all diffraction peaks can be indexed as the cubic phase of Si. The cell parameter is calculated to be a = 0.5435±0.0054 nm, which is in agreement with the value of face-centered cubic silicon a = 0.5430 nm (Joint Committee of Powder Diffraction Standards, JCPDS card No. 27-1402). The XRD pattern of SiNW-supported Cu nanoparticles is shown in Fig. 2(b). No other characteristic peaks are observed except Cu and Si. The XRD pattern demonstrates that the SiNWs have been modified with Cu nanoparticles. The calculated cell parameter of Cu is a = 0.3616±0.0003 nm, which is in agreement with the reported value, a = 0.3615 nm (JCPDS card No. 04-0836).

Fig.2 XRD patterns of (a) SiNWs; (b) Cu/Si nanostructure

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3.2 Enhancement fluorescence experiment of Cu/Si nanostructure

In Fig. 3, the Ln³⁺ (Ln= Pr, Nd, Ho, and Er) displayed weak fluorescence emission at the peaks of 595 nm, 604 nm, 640 nm of Pr³⁺, 592 nm of Nd³⁺ upon excitation at 470, and 550 nm of Ho³⁺, 533 nm of Er³⁺ upon excitation at 430 nm, which were attributed to be the 4f inter-level ¹I₆ →³F₃ (595 nm), ¹D₂→³H₄ (604 nm) and ³P₀→³F₂ (640 nm) of Pr³⁺, ²F_7/2 →²P_1/2 (592 nm) of Nd³⁺, ⁵G₂→⁵I₅ (550 nm) of Ho³⁺ and ⁴S_3/2→⁴I1_5/2 (533 nm) transitions of Er³⁺.

Fig.3 Fluorescence spectra of Ln3+ free of Cu/Si nanomaterials. (a) Different concentrations of Pr3+; (b) 0.05 M Nd3+; (c) 0.05 M Ho3+; (d) 0.05 M Er3+

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Figures 4(a), (c), and (e), show the fluorescence spectra of Pr³⁺ at the different concentrations with the increment of Cu/Si amount (50 μL each time). As can be seen, the fluorescence intensity increases gradually with the addition of Cu/Si nanomaterials. After that, the intensity keeps steady with further growth of the Cu/Si. In addition, the enhancement decreased (from 167-fold to 12-fold at 640 nm and 30-fold to 9-fold at 604 nm) when Pr³⁺ concentration changed from 0.01 to 0.05 M. Moreover, the peak at 604 nm dominated gradually and finally resulted in the mergence of the peak about 595 nm.

To make a comparison, unsupported Cu nanoparticles were used. It can be observed from Figs. 4(b), (d), and (f) that the fluorescence intensity of Pr³⁺ was also enhanced with the addition of the unsupported Cu nanoparticles. The enhancement was about 59-fold to 8-fold at 640 nm and 9-fold to 6-fold at 604 nm, respectively. The fluorescence emission increased to the maximum and then keeps steady, which was in agreement with the Cu/Si nanostructure. However, the enhancement factor was smaller than that caused by Cu/Si nanostructure.

Fig.4 Fluorescence spectra of different Pr3+ concentrations as adding of (a), (c), (e) Cu/Si nanomaterials, and (b), (d), (f) unsupported Cu nanoparticles

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Figures 5(a), 6(a), and 7(a) show the fluorescence spectra of other Ln³⁺ at the concentration of 0.05 M (Ln=Nd, Ho, and Er) in the presence of Cu/Si nanomaterials. An enhancement factor of 127-fold for Nd³⁺, 59-fold for Ho³⁺ and 52-fold for Er³⁺ could be obtained. However, in Figs. 5(b), 6(b) and 7(b), the enhancement was only about 45-fold, 25-fold and 21-fold for Nd³⁺, Ho³⁺ and Er³⁺ respectively when unsupported Cu nanoparticles were employed.

The above results indicated that the enhancement of Cu/Si nanostructure is better than that of the unsupported Cu nanoparticles, which drew our interest.

One explanation might result from the overlap of enhanced local fields. The essential difference between these nanomaterials is that Cu/Si nanostructure has silicon carrier, The excellent SEF feature of Cu/Si nanostructure might be attributed to the unique fearures of H-SiNWs (SiNWs after HF-treatment) in anchoring metal NPs (e.g., Au, Ag, Pd, Cu) firmly and in a dispersed fashion on SiNWs surfaces [24,25]. The Cu/Si nanostructure is kept from congregating and growing larger because the small Cu nanoparticles are fixed by the SiNWs and the interparticle overlap might lead to larger field enhancement factors [26].

Fig.5 Fluorescence spectra of Nd3+ as adding of different nanoparticles. (a) Cu/Si nanomaterials;(b) unsupported Cu nanoparticles

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Fig.6 Fluorescence spectra of the Ho3+ as adding of different nanoparticles. (a) Cu/Si nanomaterials; (b) unsupported Cu nanoparticles

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Fig.7 Fluorescence spectra of Er3+ as adding of different nanoparticles. (a) Cu/Si nanomaterials; (b) unsupported Cu nanoparticles

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The unsupported Cu nanoparticles also have SEF feature. However, they are apt to agglomerate and may gradually grow large during the SEF process. Large particles might meet stronger steric hindrances in the couplings, whereas Cu nanoparticles immobilized on the SiNWs are kept from growing large; and the distances among the particles were close enough to favor the enhanced fields’ overlapping, which caused great SEF effect.

4 Conclusions

In conclusion, the Cu/Si nanostructure was prepared using SiNWs as a carrier, which has the advantage of easy surface modification with various metals. The as-fabricated Cu/Si nanostructure was comparatively stable and was able to prevent Cu nanoparticles from aggregating, and thus enhanced the fluorescence of Ln³⁺ dramatically. The enhancement of Cu/Si nanomaterials are larger than that on unsupported Cu nanoparticles. This result might be attributed to the large local plasmons oscillation resulted from the interparticle overlap on the SiNWs. This easy fabrication of Cu/Si nanostructure with excellent properties enables itself to find wider applications.

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