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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 11 — Jun. 3, 2013
  • pp: 13492–13501
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Surface-plasmon-enhanced GaN-LED based on a multilayered M-shaped nano-grating

Haosu Zhang, Jun Zhu, Zhendong Zhu, Yuanhao Jin, Qunqing Li, and Guofan Jin  »View Author Affiliations


Optics Express, Vol. 21, Issue 11, pp. 13492-13501 (2013)
http://dx.doi.org/10.1364/OE.21.013492


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Abstract

A multilayered metallic M-shaped nano-grating is proposed to enhance the internal quantum efficiency, light extraction efficiency and surface-plasmon (SP) extraction efficiency of the gallium nitride-based light emitting diodes. This structure is fabricated by the low-cost nano-imprint lithography. The suitable grating based on quasi-symmetrical-waveguide structure has a high transmission in the visible region. The properties of SP mode and the Purcell effect in this type of LED is investigated. The experimental results demonstrate that its peak photoluminescence intensity of the proposed LED is over 10 times greater than that from a naked GaN-LED without any nanostructure.

© 2013 OSA

1. Introduction

Gallium nitride (GaN) based light emitting diodes (LEDs) have many advantages, such as energy-saving, longer lifetime and better stability and so on, compared with other light sources. Recently GaN-LEDs have attracted great interest in broad applications such as full-color display, printing, solid-state lighting and many other fields. However, if the emission efficiency can be further improved, the GaN-LED will be more widely developed. The emission efficiency or external quantum efficiency (ηext) of a LED is defined as the product of the light extraction efficiency (Cext) and the internal quantum efficiency (ηint). Due to the refractive index difference between GaN (nGaN = 2.5) and air (nair = 1), the critical angle of total internal reflection on the GaN/Air interface at which light generated in the quantum-well region can radiate out is only 23.6°, so that the Cext is less than 10% [1

1. S. Nakamura and S. F. Chichibu, Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes, (Taylor & Francis, 2000).

]. The internal quantum efficiency is determined by the radiative (krad) and non-radiative (knon-rad) recombination rates of the electron-hole pairs, and it can be obtained by the relationship of ηint = krad/(krad + knon-rad). The internal quantum efficiency at room temperature is usually only few percent, limited by the material quality, charge separation issues, dislocation density and so on [1

1. S. Nakamura and S. F. Chichibu, Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes, (Taylor & Francis, 2000).

, 2

2. B. Monemar, J. P. Bergman, G. Pozina, J. Dalfors, B. E. Sernelius, P. O. Holtz, H. Amano, and I. Akasaki, “Carrier and exciton dynamics in In0.15Ga0.85N/GaN multiple quantum well Structures,” Proc. SPIE 3624, 168–178 (1999). [CrossRef]

]. The low Cext and ηint result in that the emission efficiency in conventional GaN-LED is not high enough. Therefore, it is highly demanded to enhance the emission efficiency of GaN-LEDs.

It has been studied for decades to enhance the emission efficiency. On the one hand, some diffractive micro/nano structures such as gratings [3

3. X. S. Zhang, S. Liu, Y. Liu, X. Y. Chen, H. Lin, and X. C. Ren, “Enhancement of LED light extraction via diffraction of hexagonal lattice fabricated in ITO layer with holographic lithography and wet etching,” Phys. Lett. A 372, 2738–3740 (2008).

, 4

4. A. Drezet, F. Przybilla, E. Laux, O. Mahboub, C. Genet, T. W. Ebbesen, J. S. Bouillard, A. Zayats, I. S. Spevak, A. V. Zayats, A. Y. Nikitin, and L. Martín-Moreno, “Opening the light extraction cone of high index substrates with plasmonic gratings: Light emitting diode applications,” Appl. Phys. Lett. 95(2), 021101 (2009). [CrossRef]

], nano-texturing [5

5. T. J. Suleski and Y.-C. Chuang, “Nanotexturing in Ultraviolet Light-Emitting Diodes for Enhanced Light Extraction,” OSA/NANO (Optical Society of America, 2006) paper NWC2.

] and photonic crystals [6

6. D.-H. Kim, C.-O. Cho, Y.-G. Roh, H. Jeon, Y. S. Park, J. Cho, J. S. Im, C. Sone, Y. Park, W. J. Choi, and Q.-H. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87(20), 203508 (2005). [CrossRef]

] had been employed in LED to increase Cext. On the other hand, ηint can be improved by increasing the radiative recombination rate of the electron-hole pairs [7

7. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

9

9. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]

]. In 1998, Hecker et al. reported the enhanced spontaneous radiation in metal coated semi-conductor (GaAs) devices [10

10. N. E. Hecker, R. A. Hopfel, and N. Sawaki, “Enhanced light emission from a single quantum well located near a metal coated surface,” Physica E 2(1-4), 98–101 (1998). [CrossRef]

], where the enhancement of ηint is owing to the coupling between the surface plasmon polaritons (SPPs) and the quantum wells (QWs) [11

11. I. Gontijo, M. Borodisky, E. Yablonvitch, S. Keller, and U. K. Mishra, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]

16

16. J. Chen, N.-H. Shen, C. Cheng, Y.-X. Fan, J. P. Ding, and H.-T. Wang, “Tunable resonance in surface-plasmon-polariton enhanced spontaneous emission using a denser dielectric cladding,” Appl. Phys. Lett. 89(5), 051916 (2006). [CrossRef]

]. In such SPP-enhanced LED devices, the emission efficiency (η'ext) and internal quantum efficiency (η'int) are given by the following Eqs. (1a) and (1b), respectively [14

14. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]

].
ηext=Cextkrad+CSPPkSPPkrad+kSPP+knonrad
(1a)
ηint=krad+kSPPkrad+kSPP+knonrad=11ηintFp
(1b)
where kSPP is the coupling rate between QWs and SPP; CSPP is the SPP extraction efficiency; FP = (krad + kSPP + knon-rad)/(krad + knon-rad) is defined as the Purcell factor which quantifies the enhancement effect of internal quantum efficiency; ηint is the internal quantum efficiency in the conventional LEDs. According to the Eqs. (1a) and (1b), if η'int (or FP), Cext and CSPP increase simultaneously, the emission intensity will be improved greatly.

In this paper, we demonstrate a type of novel multilayered M-shaped nano-gratings, which can be fabricated by low-cost nano imprint lithography (NIL) to enhance the emission efficiency of GaN-LEDs. This nano-structured LED contains a SiO2 layer of low refractive index, a Ag-film and a HfO2 layer of high refractive index coated on the patterned p-GaN layer in sequence, as shown in Fig. 1(c)
Fig. 1 Fabrication procedure of the MMG. (a) The naked or unprocessed sample. (b) The M-shaped grating formed in the p-GaN layer fabricated by NIL. (c) The finally obtained MMG structure after coating three layers. (d) SEM image of the fabricated MG sample. (e) The geometric parameters of the ‘M’ shape.
below. The metal-film is used to sustain SPPs, by which to enhance the internal quantum efficiency. The HfO2 and SiO2 layers symmetrize the distribution of the refractive indexes and make the field intensity of SPP modes appropriately distributed on both interfaces of the Ag-film, which can lead to a strong coupling between the SPP modes and the far-field radiation modes. On the one hand, when the quasi-symmetrical structure is optimized, the transmission through the multilayered metallic grating in the visible region will be very high. This results in the high Cext and high CSPP. On the other hand, the SiO2 layer may suppress the absorption loss of SPP, so that CSPP can be further improved. The M-shaped profile has three sharp points. These sharp points are beneficial for the coupling between SPPs and QWs [25

25. W.-H. Chuang, J.-Y. Wang, C. C. Yang, and Y.-W. Kiang, “Differentiating the contributions between localized surface plasmon and surface plasmon polariton on a one-dimensional metal grating in coupling with a light emitter,” Appl. Phys. Lett. 92(13), 133115 (2008). [CrossRef]

, 26

26. C.-W. Shen, J.-Y. Wang, W.-H. Chuang, H.-L. Chen, Y.-C. Lu, Y.-W. Kiang, C. C. Yang, and Y.-J. Yang, “Effective energy coupling and preservation in a surface plasmon-light emitter coupling system on a metal nanostructure,” Nanotechnology 20(13), 135202 (2009). [CrossRef] [PubMed]

]. Therefore, if the transmission of this grating is high, it may be utilized to enhance FP, Cext and CSPP of the GaN-LED simultaneously.

2. Fabrication

Figures 1(a)-1(c) demonstrate the fabrication procedure. Firstly, a naked GaN sample was prepared, which consisted of a sapphire substrate, a 800 nm thick n-GaN layer, a single 3 nm thick yellow-emitting (with the center wavelength around 510 nm) InGaN/GaN QW and a 200 nm thick p-GaN layer, as shown in Fig. 1(a). The InGaN QW was grown onto the GaN/sapphire (0001) substrates by metal-organic chemical vapor deposition. Then a M-shaped nano-grating (MG), as shown in Fig. 1(b), was patterned in p-GaN layer by NIL with bi-layered photo-resists. Briefly, a layer of ZEP 520A resist and a layer of HSQ resist were spin-coated onto the surface of the p-GaN in sequence. The NIL was operated at room temperature with a diamond stamp, which was patterned with a rectangular profile linear grating of 200 nm period and 100 nm line-width by EBL. After demolding and releasing, the residual resist of the top resist HSQ was removed by CF4 plasma reactive ion etch (RIE). Then, the ZEP was dry-etched by O2 plasma RIE to open the windows of p-GaN layer. The MG on p-GaN was formed by dry-etching with the compound plasma gases, which involving O2, Cl2, and BCl3. Afterwards, as shown in Fig. 1(c), a 30 nm SiO2 (Silica) layer, 15 nm Ag (Silver) layer for excitation of SPP and 45 nm HfO2 (Hafnium Oxide) layer were deposited or spin-coated onto the nano-patterned p-GaN layer to manufacture the multilayered M-shaped nano-grating (MMG).

Figure 1(d) shows the scanning electron microscopy (SEM) image of the MG sample. The designed geometric parameters of the ‘M’ shape, which are utilized in the fabrication, are shown in the Fig. 1(e). The period (d) is 200 nm; The depth of the deep-valley between two adjacent ‘M’ shapes (H) is about 160 nm; The apex angle of this triangular-valley (α) is about 42°; The depth of the shallow-valley in the middle of one ‘M’ shape (h) is 80 nm; Its apex angle (β) is about 51°; The two apex angles (γ) in the ‘M’ shape are both about 46.5°. These geometric parameters can be controllable by varying the fabricating conditions. In the MG, the QW is 20 nm away below the bottom of the deep-valley in the ‘M’ shape. So that the average thickness of the p-GaN layer in the MG and MMG is about 100 nm.

Under the standard fabricating conditions chosen by us, the M-shaped grating with the parameters shown in Fig. 1(e) can be conveniently and stably manufactured. In this paper, taking the ‘M’ shape shown in Fig. 1(e) for example, the simulations and application of the MMG are analyzed and discussed.

3. Numerical simulation

3.1 Calculating model

The high transmission through the top layers signifies the high light extraction efficiency and SPP extraction efficiency in top-emitting LEDs [27

27. Y. W. Kiang, J. Y. Wang, and C. C. Yang, “Numerical study on surface plasmon polariton behaviors in periodic metal-dielectric structures using a plane-wave-assisted boundary integral-equation method,” Opt. Express 15(14), 9048–9062 (2007). [CrossRef] [PubMed]

, 28

28. A. Bay, N. André, M. Sarrazin, A. Belarouci, V. Aimez, L. A. Francis, and J. P. Vigneron, “Optimal overlayer inspired by Photuris firefly improves light-extraction efficiency of existing light-emitting diodes,” Opt. Express 21(S1Suppl 1), A179–A189 (2013). [CrossRef] [PubMed]

]. The thickness of GaN layer is assumed to be semi-infinite in our calculating model. The model is shown in the Fig. 2
Fig. 2 Schematic illustration of the layered structure utilized in the simulations. The light-wave at the incident angle θ is incident from the GaN substrate with a semi-infinite thickness. The 3D coordinate is also shown here. The z-axis is perpendicular to the x-y plane.
.

In this model, the period, the groove depth (peak-to-valley), the thicknesses of the SiO2 layer, the Ag layer and the HfO2 layer are denoted by d, H, tSili, tAg and tHaf respectively. An initial set of parameters are chosen as d = 200 nm, H = 160 nm, tSili = 30 nm, tAg = 15 nm, and tHaf = 50 nm. This period makes the grating to be sub-wavelength structure to enhance the zero-order transmission. The 30 nm thick SiO2 layer improves the SPP extraction efficiency effectively, and it does not reduce the Purcell Factor too sharply [22

22. Y.-C. Lu, Y.-S. Chen, F.-J. Tsai, J.-Y. Wang, C.-H. Lin, C.-Y. Chen, Y.-W. Kiang, and C. C. Yang, “Improving emission enhancement in surface plasmon coupling with an InGaN/GaN quantum well by inserting a dielectric layer of low refractive index between metal and semiconductor,” Appl. Phys. Lett. 94(23), 233113 (2009). [CrossRef]

, 23

23. K.-C. Shen, C.-H. Liao, Z.-Y. Yu, J.-Y. Wang, C.-H. Lin, Y.-W. Kiang, and C. C. Yang, “Effects of the intermediate SiO2 layer on polarized output of a light-emitting diode with Surface plasmon coupling,” J. Appl. Phys. 108(11), 113101 (2010). [CrossRef]

]. The 15 nm silver-film is selected to keep the transmission of this metallic grating to be high enough. The thickness of HfO2 layer is roughly equal to the SPP field penetration-depth in HfO2. This thickness makes the distribution of the refractive indices in the MMG to be quasi-symmetry [27

27. Y. W. Kiang, J. Y. Wang, and C. C. Yang, “Numerical study on surface plasmon polariton behaviors in periodic metal-dielectric structures using a plane-wave-assisted boundary integral-equation method,” Opt. Express 15(14), 9048–9062 (2007). [CrossRef] [PubMed]

].

Firstly the parameters d and tHaf will be adjusted to promote the transmission in the visible region. Then, the properties of the SPP mode in the adjusted MMG are investigated and the Purcell effect is qualitatively analyzed.

3.2 Adjustments of the period and thickness of HfO2 layer

The transmission through the cover layers depends on the incident angle and the wavelength of the light generated from the QW. Here, we optimize the zero-order transmission versus wavelength at a fixed incident angle (θ = 0°) when the grating is in classical mounting. In other words, a plane light-wave is normally incident from the GaN substrate.

Keeping the other parameters as the given ones, the transverse magnetic (TM) and transverse electric (TE) zero-order transmissions versus wavelength for different periods are calculated. For TM and TE waves, the vectors of electric field are in the x-y plane and toward the ± z axis respectively. The 3D coordinate is shown in Fig. 2. As mentioned in the last of section 2, the ‘M’ shape is assumed to be similar when the period changes. So that the parameters H/d (depth-to-period ratio), h/d, α, β and γ are fixed to be 0.8, 0.4, 42°, 51° and 46.5°, as shown in Fig. 1(e). The transmissions are rigorously simulated by the C-method [29

29. L. F. Li, A User’s Guide to DELTA©(Version 1.4): A Computer Program for Modeling Planar, One-dimensionally Periodic, Multilayer-coated, Diffraction Gratings (Tsinghua University, Copyright 1993–2009

] and the results are shown in the Figs. 3(a)
Fig. 3 (a) The transmission versus wavelength for different periods. The polarization is TM. (b) The TE transmission versus wavelength for different periods. (c) The TM transmission versus wavelength for different thicknesses of the HfO2 layer in MMG. The TM transmissions of the MG and naked samples are also shown. (d) The TE transmission versus wavelength for different thicknesses of the HfO2 layer in MMG. The TE transmissions of the MG and naked samples are also shown.
and 3(b). The C-method was originally developed by Chandezon et. al. to study the optical properties of the multilayer-coated deep-groove metallic gratings [30

30. J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72(7), 839–846 (1982). [CrossRef]

, 31

31. J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11(4), 235–241 (1980). [CrossRef]

]. The refractive indices of GaN and SiO2 are set to be 2.5 and 1.5. The refractive indices of Ag and HfO2 are from the experimental data [32

32. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

, 33]. The wavelength range of the full width at half maximum of the photoluminescence spectra (shown in Fig. 6(b) below) is from 480 to 540 nm. For the adjustments of the parameters, the transmission integrated over the wavelength range 480-540 nm is considered. The discretization step of the parameter d is set to be 10 nm in the calculations. And the varying range of this parameter is from 20 to 500 nm. According to the calculations, the non-polarized integrated transmission in MMG reaches a maximum when the parameter d is 200 nm. The three curves are chosen to be shown in Figs. 3(a) and 3(b). And the period is adjusted to be 200 nm.

Then, by fixing the parameter d to be 200 nm and varying the parameter tHaf, the TM and TE zero-order transmission spectrums for different tHaf values are shown in the Figs. 3(c) and 3(d). For TM (TE) polarization, the integrated transmission arrives at a maximum when tHaf = 15 (60) nm. The non-polarized integrated transmission reaches a maximum when tHaf = 45 nm. So that the optimum thickness is determined to be 45 nm (as the cyan curves shown in the Figs. 3(c) and 3(d)). Many SPP modes or other TM and TE guided-modes supported by this MMG are excited by the visible light-waves generated from the QW region. And these modes can be coupled to far-field-radiated modes efficiently [21

21. S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12(16), 3673–3685 (2004). [CrossRef] [PubMed]

]. These lead to the high transmission in the adjusted MMG. The khaki curves in the Figs. 3(c) and 3(d) manifest the high transmission of the MG.

3.3 Analysis of the SPP mode

The TM-polarized absorptions and −1st order transmissions versus incident angle at 490 nm, 510 nm and 530 nm wavelengths are shown in the Fig. 4(a)
Fig. 4 (a) The absorption versus incident angle at 490 nm, 510 nm and 530 nm wavelengths. The peak labeled by ‘SPP’ indicates the SPP resonance at 510 nm wavelength. The resonance angle is about 40°. (b) The −1st order transmission versus incidence angle at 490 nm, 510 nm and 530 nm wavelengths. The peak labeled by ‘SPP’ signifies the SPP resonance at 510 nm wavelength. (c) Distribution of the x component of the electric field (Ex) at SPP resonance of 510 nm wavelength. The bottom of the whole simulation region represents the QW. (d) Distribution of the y component of the electric field (Ey) at SPP resonance of 510 nm wavelength. (e) Distribution of the time-average Poynting vector at the SPP resonance of 510 nm wavelength.
and 4(b) respectively. The absorption and transmission peaks signify the SPP resonance in the sub-wavelength gratings [36

36. J. Yoon, S. H. Song, and J.-H. Kim, “Extraction efficiency of highly confined surface plasmon-polaritons to far-field radiation: an upper limit,” Opt. Express 16(2), 1269–1279 (2008). [CrossRef] [PubMed]

]. In Figs. 4(a) and 4(b), one SPP resonance at 510 nm wavelength is observed. Its resonance angle is about 40°. For diverse wavelengths, the resonance angles are different. It verifies that the anomalies of absorption and transmission curves can be attributed to the guided-mode such as SPP in the MMG. Although the Ag-film is only 15 nm thick and the sizes of the sharp tips or corners in MMG are large, the SPP can be excited by QW and propagate in the HfO2, Ag and SiO2 layers (as shown in Figs. 4(c) and 4(d) below).

The commercial software “COMSOLTM—RF Module” based on the finite element method (FEM) is applied to calculate the near-field distributions of SPP. The TM-polarized light-wave with a normalized amplitude of magnetic field is assumed to be generated at the QW region. The distributions of x component of the electric field (Ex) and y component of the electric field (Ey) at the SPP resonance of 510 nm wavelength are illustrated in Figs. 4(c) and 4(d) respectively. The distribution of the time-average Poynting vector (Savg) at the SPP resonance is shown in the Fig. 4(e). The bottom of the simulation domain represents the QW.

These properties of SPP mode are observed in Figs. 4(c)-4(e). (1) The average Ex|2and |Ey|2 intensities in the QW region are enhanced by about 150 and 100 times respectively, with the assistance of the MMG. This is beneficial for enhancing the internal quantum efficiency [34

34. J. S. Biteen, L. A. Sweatlock, H. Mertens, N. S. Lewis, A. Polman, and H. A. Atwater, “Plasmon-enhanced photoluminescence of silicon quantum dots: simulation and experiment,” J. Phys. Chem. C 111(36), 13372–13377 (2007). [CrossRef]

, 35

35. J. Henson, E. Dimakis, J. DiMaria, R. Li, S. Minissale, L. Dal Negro, T. D. Moustakas, and R. Paiella, “Enhanced near-green light emission from InGaN quantum wells by use of tunable plasmonic resonances in silver nanoparticle arrays,” Opt. Express 18(20), 21322–21329 (2010). [CrossRef] [PubMed]

]. (2) The intensities of Ex and Ey in the SiO2 layer are relatively high. The localization of electromagnetic field in the dielectric layer implies low absorption loss and high extraction efficiency of the SPP mode [22

22. Y.-C. Lu, Y.-S. Chen, F.-J. Tsai, J.-Y. Wang, C.-H. Lin, C.-Y. Chen, Y.-W. Kiang, and C. C. Yang, “Improving emission enhancement in surface plasmon coupling with an InGaN/GaN quantum well by inserting a dielectric layer of low refractive index between metal and semiconductor,” Appl. Phys. Lett. 94(23), 233113 (2009). [CrossRef]

24

24. K.-C. Shen, C.-Y. Chen, C.-H. Liao, T.-Y. Tang, and C. C. Yang, “Enhancement of polarized light-emitting diode through surface plasmon coupling generated on a metal grating ,” OSA/ACP (Optical Society of America, 2009). Paper TuN5.

]. (3) The intensities of Ex and Ey around both sides of Ag- film are almost the same. (4) The symmetrical distributions of Ex, Ey and Hz result in the symmetrical distribution of Savg, which is beneficial for promoting the transmission. Based on the C-method, the −1st order transmission at the SPP resonance of 510 nm wavelength in the MMG is 0.096 (as shown in Fig. 4(b)). For comparison, the MG coated by a single 15 nm Ag-film is investigated. Its −1st order transmission at the SPP resonance is 0.063 (not shown here). The symmetrical distribution of Savg around both sides of the Ag-film, as shown in Fig. 4(e), explains the relatively high transmission of MMG. In the Fig. 4(e), we can observe that the incoming and the outgoing waves are coupled with the SPP mode via the high intensity regions around both sides of the Ag-film. This coupling implies that the SPP mode of low absorption loss is important for transferring the energy through the cover layers.

It is noted that the SPP resonance angle (about 40°) in MMG is larger than the critical angle (about 23.6°) of total internal reflection. It implies that the light of large incident angle can be extracted via SPP. In the naked sample, when the incident angle is greater than 23.6°, the light cannot be extracted.

Besides the SPP, the localized-SPP (LSPP) also plays a important role in the coupling between the nanostructures and the dipole in QW [25

25. W.-H. Chuang, J.-Y. Wang, C. C. Yang, and Y.-W. Kiang, “Differentiating the contributions between localized surface plasmon and surface plasmon polariton on a one-dimensional metal grating in coupling with a light emitter,” Appl. Phys. Lett. 92(13), 133115 (2008). [CrossRef]

, 26

26. C.-W. Shen, J.-Y. Wang, W.-H. Chuang, H.-L. Chen, Y.-C. Lu, Y.-W. Kiang, C. C. Yang, and Y.-J. Yang, “Effective energy coupling and preservation in a surface plasmon-light emitter coupling system on a metal nanostructure,” Nanotechnology 20(13), 135202 (2009). [CrossRef] [PubMed]

]. However, based on the calculations of the software DELTA, the resonance wavelength of LSPP in our MMG structure is determined to be about 750 nm. This wavelength is out of the emission range 450-600 nm of the LED. So that only the SPP takes effects in the coupling between the MMG and QW.

3.4 Analysis of the Purcell effect

The enhancement of internal quantum efficiency in MMG comes from the scattering and diffraction of the electric field from a dipole. For the qualitative analysis of Purcell effect in MMG, the 3D numerical simulation based on the single dipole source are performed by COMSOL. The size in the x-z plane of this model is 1800 × 1800 nm2. It makes the relative electric field on the front, back, left and right sides of the simulation region low enough. And hence the simulation precision is improved. By placing the perfect mirror at four sides of the structure, we can mimic light which is propagating indefinitely. To represent the QW in MMG, a randomly polarized dipole emitting at 510 nm wavelength is placed at the middle of the QW.

The calculated magnitude distribution of electric field in the x-y plane is shown in Fig. 5
Fig. 5 Snap shots of the calculated magnitude distribution of electric field in the x-y plane of the MMG.
. In this figure, one can observe these characteristics. (1) The electric fields near all the sharp points of the MMG, especially the corners in the ‘M’ shape above the dipole, are relatively high. (2) For the ‘M’ shape above the dipole, the electric field in the SiO2 and HfO2 layers near the shallow and deep valleys are large. It indirectly verifies that the two dielectric layers indeed transfer the electromagnetic energy through the cover layers. (3) The wavelike distribution of electric field in or around the Ag-film is high. It implies that the 15 nm Ag-film indeed plays the important role in the coupling between MMG and QW.

The same models about the MG and Naked sample can also be established. For the MMG, MG and Naked models, the average electric field-intensities in the hemispheroid of 20 nm in radius dimension centered at the dipole position are denoted by |EMMG|2, |EMG|2 and |ENaked|2. The great |EMMG|2signifies the large Purcell factor in MMG [7

7. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

-9

9. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]

, 34

34. J. S. Biteen, L. A. Sweatlock, H. Mertens, N. S. Lewis, A. Polman, and H. A. Atwater, “Plasmon-enhanced photoluminescence of silicon quantum dots: simulation and experiment,” J. Phys. Chem. C 111(36), 13372–13377 (2007). [CrossRef]

-35

35. J. Henson, E. Dimakis, J. DiMaria, R. Li, S. Minissale, L. Dal Negro, T. D. Moustakas, and R. Paiella, “Enhanced near-green light emission from InGaN quantum wells by use of tunable plasmonic resonances in silver nanoparticle arrays,” Opt. Express 18(20), 21322–21329 (2010). [CrossRef] [PubMed]

]. The order of magnitude of |EMMG/ENaked|2 is 10. On the contrary, that of |EMG/ENaked|2is 1. It indicates that the internal quantum efficiency in MMG is much larger than that in MG. Although the CextandCSPP in MG are slightly higher than those in MMG, the emission intensity from the MMG is higher than that form the MG (as shown in Fig. 6(b)
Fig. 6 (a) The excitation/emission configuration of PL measurement. The excitation laser was normally incident upon the sample from the top side (HfO2 side). (b) The top-emitting PL intensities of the naked, MG and MMG samples respectively. The PL peak intensity of naked sample was normalized to 1. The dotted lines represent the modified PL intensities, considering the pumping efficiency. They are fairer to be compared with the naked sample than the un-modified ones.
below).

4. Experiment and discussion

For the cw PL measurements, the samples were pumped at normal incidence using light from a He-Cd laser. And the samples were kept at room temperature. The laser provided about 15 mW of TE-polarized output power at 325 nm. The laser beam was penetrated through an attenuator and then focused onto the sample from the top side (HfO2 side) using a 40 × UV objective lens. The diameter of the focused spot was approximately 5 μm. The PL signals were collected using the same objective lens, and then analyzed using a spectrometer (Horiba Jobin Yvon). The excitation/emission configuration of Photoluminescence (PL) measurement is shown in the Fig. 6(a). The experimental results are shown in the Fig. 6(b). Every intensity curve is the average value of 10 measurements of different LED cells.

In Fig. 6(b), 11.9 and 5.0 times enhancements in peak PL intensity of the MMG and MG samples are observed. The transmission of the MMG sample is slightly lower than that of MG sample, as shown in the Figs. 3(c) and 3(d). The high PL intensity of the MMG sample verifies the coupling between the QW and silver-film is obvious and the internal quantum efficiency is effectively enhanced.

Although the excitation power is identity (about 15 mW) in the measurements, the pumping efficiencies of these three samples are different. The pumping efficiency is roughly proportional to T, where T is the total transmission of excitation laser through the layers/layer above the QW. These transmissions of MMG, MG and naked samples are denoted by TMMG, TMG and TNaked respectively. And the results TMMG≈0.87, TMG≈0.96 and TNaked≈0.81 are obtained by 3D numerical simulations based on COMSOL. For fairer comparisons with the naked sample, the PL intensities of the MMG and MG samples in Fig. 6(b) are multiplied by the factors TNaked /TMMG = 0.93 and TNaked /TMG = 0.84 respectively. These modified intensities (as shown by dotted lines in Fig. 6(b)) are fairer to describe the performances of these samples. The modified intensities reveal that the peak PL intensities from MMG and MG are increased by about 11.0 and 4.3 times, compared with the naked sample.

Although it is difficult to calculate and measure efficiencies in LEDs separately, the high PL intensity of the MMG sample demonstrates all these efficiencies have been enhanced.

5. Conclusion

In this paper, a type of highly-efficient GaN-LED based on the MMG is proposed. By the numerical simulation, the parameters in the MMG are adjusted to improve the emission efficiency. The experiments have proofed that the theory analyses in this paper are valid and effective. The peak PL intensity from the MMG is increased by about 11 times, compared with the naked sample. Here, three advantages of the M-shaped gratings contribute to the highly efficient GaN-LEDs. (i) The transmission of MMG in the visible region is very high. (ii) The sharp points in the “M” shape are beneficial for the coupling between QWs and SPP. (iii) It is convenient to fabricate. And the tunable geometric parameters of “M” shape can be easily controlled by the NIL to adjust the diffraction behaviors of the gratings. In conclusion, this structure is easy to fabricate by the low-cost NIL and practical for the LED devices.

References and links

1.

S. Nakamura and S. F. Chichibu, Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes, (Taylor & Francis, 2000).

2.

B. Monemar, J. P. Bergman, G. Pozina, J. Dalfors, B. E. Sernelius, P. O. Holtz, H. Amano, and I. Akasaki, “Carrier and exciton dynamics in In0.15Ga0.85N/GaN multiple quantum well Structures,” Proc. SPIE 3624, 168–178 (1999). [CrossRef]

3.

X. S. Zhang, S. Liu, Y. Liu, X. Y. Chen, H. Lin, and X. C. Ren, “Enhancement of LED light extraction via diffraction of hexagonal lattice fabricated in ITO layer with holographic lithography and wet etching,” Phys. Lett. A 372, 2738–3740 (2008).

4.

A. Drezet, F. Przybilla, E. Laux, O. Mahboub, C. Genet, T. W. Ebbesen, J. S. Bouillard, A. Zayats, I. S. Spevak, A. V. Zayats, A. Y. Nikitin, and L. Martín-Moreno, “Opening the light extraction cone of high index substrates with plasmonic gratings: Light emitting diode applications,” Appl. Phys. Lett. 95(2), 021101 (2009). [CrossRef]

5.

T. J. Suleski and Y.-C. Chuang, “Nanotexturing in Ultraviolet Light-Emitting Diodes for Enhanced Light Extraction,” OSA/NANO (Optical Society of America, 2006) paper NWC2.

6.

D.-H. Kim, C.-O. Cho, Y.-G. Roh, H. Jeon, Y. S. Park, J. Cho, J. S. Im, C. Sone, Y. Park, W. J. Choi, and Q.-H. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87(20), 203508 (2005). [CrossRef]

7.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

8.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, Vol. XXXVII, I. Prigogine and S. A. Rice, eds. (Wiley, 1978), pp. 1–66.

9.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]

10.

N. E. Hecker, R. A. Hopfel, and N. Sawaki, “Enhanced light emission from a single quantum well located near a metal coated surface,” Physica E 2(1-4), 98–101 (1998). [CrossRef]

11.

I. Gontijo, M. Borodisky, E. Yablonvitch, S. Keller, and U. K. Mishra, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]

12.

A. Neogi, C.-W. Lee, H. O. Everitt, T. Kuroda, A. Tackeuchi, and E. Yablonvitch, “Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling,” Phys. Rev. B 66(15), 153305 (2002). [CrossRef]

13.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005). [CrossRef]

14.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]

15.

R. Paiella, “Tunable surface plasmons in coupled metallo-dielectric multiple layers for light-emission efficiency enhancement,” Appl. Phys. Lett. 87(11), 111104 (2005). [CrossRef]

16.

J. Chen, N.-H. Shen, C. Cheng, Y.-X. Fan, J. P. Ding, and H.-T. Wang, “Tunable resonance in surface-plasmon-polariton enhanced spontaneous emission using a denser dielectric cladding,” Appl. Phys. Lett. 89(5), 051916 (2006). [CrossRef]

17.

J. Morland, A. Adams, and P. K. Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25(4), 2297–2300 (1982). [CrossRef]

18.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77(21), 3340–3342 (2000). [CrossRef]

19.

D.-M. Yeh, C.-F. Huang, C.-Y. Chen, Y.-C. Lu, and C. C. Yang, “Surface plasmon coupling effect in an InGaN/GaN single-quantum-well light-emitting diode,” Appl. Phys. Lett. 91(17), 171103 (2007). [CrossRef]

20.

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on thin-slab metal gratings,” Phys. Rev. B 67(23), 235404 (2003). [CrossRef]

21.

S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12(16), 3673–3685 (2004). [CrossRef] [PubMed]

22.

Y.-C. Lu, Y.-S. Chen, F.-J. Tsai, J.-Y. Wang, C.-H. Lin, C.-Y. Chen, Y.-W. Kiang, and C. C. Yang, “Improving emission enhancement in surface plasmon coupling with an InGaN/GaN quantum well by inserting a dielectric layer of low refractive index between metal and semiconductor,” Appl. Phys. Lett. 94(23), 233113 (2009). [CrossRef]

23.

K.-C. Shen, C.-H. Liao, Z.-Y. Yu, J.-Y. Wang, C.-H. Lin, Y.-W. Kiang, and C. C. Yang, “Effects of the intermediate SiO2 layer on polarized output of a light-emitting diode with Surface plasmon coupling,” J. Appl. Phys. 108(11), 113101 (2010). [CrossRef]

24.

K.-C. Shen, C.-Y. Chen, C.-H. Liao, T.-Y. Tang, and C. C. Yang, “Enhancement of polarized light-emitting diode through surface plasmon coupling generated on a metal grating ,” OSA/ACP (Optical Society of America, 2009). Paper TuN5.

25.

W.-H. Chuang, J.-Y. Wang, C. C. Yang, and Y.-W. Kiang, “Differentiating the contributions between localized surface plasmon and surface plasmon polariton on a one-dimensional metal grating in coupling with a light emitter,” Appl. Phys. Lett. 92(13), 133115 (2008). [CrossRef]

26.

C.-W. Shen, J.-Y. Wang, W.-H. Chuang, H.-L. Chen, Y.-C. Lu, Y.-W. Kiang, C. C. Yang, and Y.-J. Yang, “Effective energy coupling and preservation in a surface plasmon-light emitter coupling system on a metal nanostructure,” Nanotechnology 20(13), 135202 (2009). [CrossRef] [PubMed]

27.

Y. W. Kiang, J. Y. Wang, and C. C. Yang, “Numerical study on surface plasmon polariton behaviors in periodic metal-dielectric structures using a plane-wave-assisted boundary integral-equation method,” Opt. Express 15(14), 9048–9062 (2007). [CrossRef] [PubMed]

28.

A. Bay, N. André, M. Sarrazin, A. Belarouci, V. Aimez, L. A. Francis, and J. P. Vigneron, “Optimal overlayer inspired by Photuris firefly improves light-extraction efficiency of existing light-emitting diodes,” Opt. Express 21(S1Suppl 1), A179–A189 (2013). [CrossRef] [PubMed]

29.

L. F. Li, A User’s Guide to DELTA©(Version 1.4): A Computer Program for Modeling Planar, One-dimensionally Periodic, Multilayer-coated, Diffraction Gratings (Tsinghua University, Copyright 1993–2009

30.

J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72(7), 839–846 (1982). [CrossRef]

31.

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11(4), 235–241 (1980). [CrossRef]

32.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

33.

http://refractiveindex.info/?group=CRYSTALS&material=HfO2

34.

J. S. Biteen, L. A. Sweatlock, H. Mertens, N. S. Lewis, A. Polman, and H. A. Atwater, “Plasmon-enhanced photoluminescence of silicon quantum dots: simulation and experiment,” J. Phys. Chem. C 111(36), 13372–13377 (2007). [CrossRef]

35.

J. Henson, E. Dimakis, J. DiMaria, R. Li, S. Minissale, L. Dal Negro, T. D. Moustakas, and R. Paiella, “Enhanced near-green light emission from InGaN quantum wells by use of tunable plasmonic resonances in silver nanoparticle arrays,” Opt. Express 18(20), 21322–21329 (2010). [CrossRef] [PubMed]

36.

J. Yoon, S. H. Song, and J.-H. Kim, “Extraction efficiency of highly confined surface plasmon-polaritons to far-field radiation: an upper limit,” Opt. Express 16(2), 1269–1279 (2008). [CrossRef] [PubMed]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(230.3670) Optical devices : Light-emitting diodes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(250.5230) Optoelectronics : Photoluminescence

ToC Category:
Optical Devices

History
Original Manuscript: February 25, 2013
Revised Manuscript: April 27, 2013
Manuscript Accepted: May 20, 2013
Published: May 29, 2013

Citation
Haosu Zhang, Jun Zhu, Zhendong Zhu, Yuanhao Jin, Qunqing Li, and Guofan Jin, "Surface-plasmon-enhanced GaN-LED based on a multilayered M-shaped nano-grating," Opt. Express 21, 13492-13501 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-11-13492


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References

  1. S. Nakamura and S. F. Chichibu, Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes, (Taylor & Francis, 2000).
  2. B.  Monemar, J. P.  Bergman, G.  Pozina, J.  Dalfors, B. E.  Sernelius, P. O.  Holtz, H.  Amano, I.  Akasaki, “Carrier and exciton dynamics in In0.15Ga0.85N/GaN multiple quantum well Structures,” Proc. SPIE 3624, 168–178 (1999). [CrossRef]
  3. X. S.  Zhang, S.  Liu, Y.  Liu, X. Y.  Chen, H.  Lin, X. C.  Ren, “Enhancement of LED light extraction via diffraction of hexagonal lattice fabricated in ITO layer with holographic lithography and wet etching,” Phys. Lett. A 372, 2738–3740 (2008).
  4. A.  Drezet, F.  Przybilla, E.  Laux, O.  Mahboub, C.  Genet, T. W.  Ebbesen, J. S.  Bouillard, A.  Zayats, I. S.  Spevak, A. V.  Zayats, A. Y.  Nikitin, L.  Martín-Moreno, “Opening the light extraction cone of high index substrates with plasmonic gratings: Light emitting diode applications,” Appl. Phys. Lett. 95(2), 021101 (2009). [CrossRef]
  5. T. J. Suleski and Y.-C. Chuang, “Nanotexturing in Ultraviolet Light-Emitting Diodes for Enhanced Light Extraction,” OSA/NANO (Optical Society of America, 2006) paper NWC2.
  6. D.-H.  Kim, C.-O.  Cho, Y.-G.  Roh, H.  Jeon, Y. S.  Park, J.  Cho, J. S.  Im, C.  Sone, Y.  Park, W. J.  Choi, Q.-H.  Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87(20), 203508 (2005). [CrossRef]
  7. E. M.  Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  8. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, Vol. XXXVII, I. Prigogine and S. A. Rice, eds. (Wiley, 1978), pp. 1–66.
  9. G. W.  Ford W. H.  Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]
  10. N. E.  Hecker, R. A.  Hopfel, N.  Sawaki, “Enhanced light emission from a single quantum well located near a metal coated surface,” Physica E 2(1-4), 98–101 (1998). [CrossRef]
  11. I.  Gontijo, M.  Borodisky, E.  Yablonvitch, S.  Keller, U. K.  Mishra, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]
  12. A.  Neogi, C.-W.  Lee, H. O.  Everitt, T.  Kuroda, A.  Tackeuchi, E.  Yablonvitch, “Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling,” Phys. Rev. B 66(15), 153305 (2002). [CrossRef]
  13. K.  Okamoto, I.  Niki, A.  Scherer, Y.  Narukawa, T.  Mukai, Y.  Kawakami, “Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005). [CrossRef]
  14. K.  Okamoto, I.  Niki, A.  Shvartser, Y.  Narukawa, T.  Mukai, A.  Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]
  15. R.  Paiella, “Tunable surface plasmons in coupled metallo-dielectric multiple layers for light-emission efficiency enhancement,” Appl. Phys. Lett. 87(11), 111104 (2005). [CrossRef]
  16. J.  Chen, N.-H.  Shen, C.  Cheng, Y.-X.  Fan, J. P.  Ding, H.-T.  Wang, “Tunable resonance in surface-plasmon-polariton enhanced spontaneous emission using a denser dielectric cladding,” Appl. Phys. Lett. 89(5), 051916 (2006). [CrossRef]
  17. J.  Morland, A.  Adams, P. K.  Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25(4), 2297–2300 (1982). [CrossRef]
  18. J. M.  Lupton, B. J.  Matterson, I. D. W.  Samuel, M. J.  Jory, W. L.  Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77(21), 3340–3342 (2000). [CrossRef]
  19. D.-M.  Yeh, C.-F.  Huang, C.-Y.  Chen, Y.-C.  Lu, C. C.  Yang, “Surface plasmon coupling effect in an InGaN/GaN single-quantum-well light-emitting diode,” Appl. Phys. Lett. 91(17), 171103 (2007). [CrossRef]
  20. I. R.  Hooper J. R.  Sambles, “Surface plasmon polaritons on thin-slab metal gratings,” Phys. Rev. B 67(23), 235404 (2003). [CrossRef]
  21. S.  Wedge W. L.  Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12(16), 3673–3685 (2004). [CrossRef] [PubMed]
  22. Y.-C.  Lu, Y.-S.  Chen, F.-J.  Tsai, J.-Y.  Wang, C.-H.  Lin, C.-Y.  Chen, Y.-W.  Kiang, C. C.  Yang, “Improving emission enhancement in surface plasmon coupling with an InGaN/GaN quantum well by inserting a dielectric layer of low refractive index between metal and semiconductor,” Appl. Phys. Lett. 94(23), 233113 (2009). [CrossRef]
  23. K.-C.  Shen, C.-H.  Liao, Z.-Y.  Yu, J.-Y.  Wang, C.-H.  Lin, Y.-W.  Kiang, C. C.  Yang, “Effects of the intermediate SiO2 layer on polarized output of a light-emitting diode with Surface plasmon coupling,” J. Appl. Phys. 108(11), 113101 (2010). [CrossRef]
  24. K.-C.  Shen, C.-Y.  Chen, C.-H.  Liao, T.-Y.  Tang, C. C.  Yang, “Enhancement of polarized light-emitting diode through surface plasmon coupling generated on a metal grating,” OSA/ACP (Optical Society of America, 2009). Paper TuN5.
  25. W.-H.  Chuang, J.-Y.  Wang, C. C.  Yang, Y.-W.  Kiang, “Differentiating the contributions between localized surface plasmon and surface plasmon polariton on a one-dimensional metal grating in coupling with a light emitter,” Appl. Phys. Lett. 92(13), 133115 (2008). [CrossRef]
  26. C.-W.  Shen, J.-Y.  Wang, W.-H.  Chuang, H.-L.  Chen, Y.-C.  Lu, Y.-W.  Kiang, C. C.  Yang, Y.-J.  Yang, “Effective energy coupling and preservation in a surface plasmon-light emitter coupling system on a metal nanostructure,” Nanotechnology 20(13), 135202 (2009). [CrossRef] [PubMed]
  27. Y. W.  Kiang, J. Y.  Wang, C. C.  Yang, “Numerical study on surface plasmon polariton behaviors in periodic metal-dielectric structures using a plane-wave-assisted boundary integral-equation method,” Opt. Express 15(14), 9048–9062 (2007). [CrossRef] [PubMed]
  28. A.  Bay, N.  André, M.  Sarrazin, A.  Belarouci, V.  Aimez, L. A.  Francis, J. P.  Vigneron, “Optimal overlayer inspired by Photuris firefly improves light-extraction efficiency of existing light-emitting diodes,” Opt. Express 21(S1Suppl 1), A179–A189 (2013). [CrossRef] [PubMed]
  29. L. F. Li, A User’s Guide to DELTA©(Version 1.4): A Computer Program for Modeling Planar, One-dimensionally Periodic, Multilayer-coated, Diffraction Gratings (Tsinghua University, Copyright 1993–2009
  30. J.  Chandezon, M. T.  Dupuis, G.  Cornet, D.  Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72(7), 839–846 (1982). [CrossRef]
  31. J.  Chandezon, D.  Maystre, G.  Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11(4), 235–241 (1980). [CrossRef]
  32. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).
  33. http://refractiveindex.info/?group=CRYSTALS&material=HfO2
  34. J. S.  Biteen, L. A.  Sweatlock, H.  Mertens, N. S.  Lewis, A.  Polman, H. A.  Atwater, “Plasmon-enhanced photoluminescence of silicon quantum dots: simulation and experiment,” J. Phys. Chem. C 111(36), 13372–13377 (2007). [CrossRef]
  35. J.  Henson, E.  Dimakis, J.  DiMaria, R.  Li, S.  Minissale, L.  Dal Negro, T. D.  Moustakas, R.  Paiella, “Enhanced near-green light emission from InGaN quantum wells by use of tunable plasmonic resonances in silver nanoparticle arrays,” Opt. Express 18(20), 21322–21329 (2010). [CrossRef] [PubMed]
  36. J.  Yoon, S. H.  Song, J.-H.  Kim, “Extraction efficiency of highly confined surface plasmon-polaritons to far-field radiation: an upper limit,” Opt. Express 16(2), 1269–1279 (2008). [CrossRef] [PubMed]

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