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 (η_ext) of a LED is defined as the product of the light extraction efficiency (C_ext) and the internal quantum efficiency (η_int). Due to the refractive index difference between GaN (n_GaN = 2.5) and air (n_air = 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 C_ext is less than 10% [1]. The internal quantum efficiency is determined by the radiative (k_rad) and non-radiative (k_non-rad) recombination rates of the electron-hole pairs, and it can be obtained by the relationship of η_int = k_rad/(k_rad + k_non-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, 2]. The low C_ext and η_int 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, 4], nano-texturing [5] and photonic crystals [6] had been employed in LED to increase C_ext. On the other hand, η_int can be improved by increasing the radiative recombination rate of the electron-hole pairs [7–9]. In 1998, Hecker et al. reported the enhanced spontaneous radiation in metal coated semi-conductor (GaAs) devices [10], where the enhancement of η_int is owing to the coupling between the surface plasmon polaritons (SPPs) and the quantum wells (QWs) [11–16]. 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].

However, tireless efforts should be made to further improve the emission efficiency and reduce the fabricating cost of SPP-enhanced GaN-LED. Firstly, in the previous works, usually only one or two of the three efficiencies (η'_int, C_ext and C_SPP) were concerned. Both the light extraction efficiency and SPP extraction efficiency play an important role in the SPP-enhanced devices. The SPP extraction efficiency can also be improved by the nano/micro structures [17–19]. The metallic nano/micro structure with a high transmission can be utilized to improve C_ext and C_SPP effectively. However, in the nano/micro structure coated by a single metal-film, the asymmetrical distribution of refractive indexes around both sides of the metal-film results in low transmission through the metal-film and the destructive interference in the extraction of the SPP mode [20, 21]. It implies low C_ext and low C_SPP. This problem can be overcome by the quasi-symmetrical-waveguide structure [21]. In addition, the SPP extraction efficiency can also be promoted by inserting a dielectric layer of low refractive index between metal-film and GaN [22–24]. The optimized multilayered metallic-grating is expected to effectively promote the transmission, and hence both C_ext, C_SPP and F_P can be further improved. Secondly, some of the reported nano/micro structured LEDs were mainly fabricated by electron beam lithography (EBL) and this technology is obviously too costly for the mass production of LEDs.

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) 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 C_ext and high C_SPP. On the other hand, the SiO₂ layer may suppress the absorption loss of SPP, so that C_SPP 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, 26]. Therefore, if the transmission of this grating is high, it may be utilized to enhance F_P, C_ext and C_SPP of the GaN-LED simultaneously.

 

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.

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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, 28]. 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.

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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, t_Sili, t_Ag and t_Haf respectively. An initial set of parameters are chosen as d = 200 nm, H = 160 nm, t_Sili = 30 nm, t_Ag = 15 nm, and t_Haf = 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, 23]. 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].

Firstly the parameters d and t_Haf 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] and the results are shown in the Figs. 3(a) 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, 31]. 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, 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.

 

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.

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Then, by fixing the parameter d to be 200 nm and varying the parameter t_Haf, the TM and TE zero-order transmission spectrums for different t_Haf values are shown in the Figs. 3(c) and 3(d). For TM (TE) polarization, the integrated transmission arrives at a maximum when t_Haf = 15 (60) nm. The non-polarized integrated transmission reaches a maximum when t_Haf = 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]. 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) and 4(b) respectively. The absorption and transmission peaks signify the SPP resonance in the sub-wavelength gratings [36]. 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).

 

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.

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The commercial software “COMSOL^TM—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 (E_x) and y component of the electric field (E_y) 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 (S_avg) 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 E_x|²and |E_y|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, 35]. (2) The intensities of E_x and E_y 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 [22–24]. (3) The intensities of E_x and E_y around both sides of Ag- film are almost the same. (4) The symmetrical distributions of E_x, E_y and H_z result in the symmetrical distribution of S_avg, 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 S_avg 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, 26]. 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. 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.

 

Fig. 5 Snap shots of the calculated magnitude distribution of electric field in the x-y plane of the MMG.

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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 |E_MMG|², |E_MG|² and |E_Naked|². The great |E_MMG|²signifies the large Purcell factor in MMG [7-9, 34-35]. The order of magnitude of |E_MMG/E_Naked|² is 10. On the contrary, that of |E_MG/E_Naked|²is 1. It indicates that the internal quantum efficiency in MMG is much larger than that in MG. Although the C_extand_CSPP 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) below).

 

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.

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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 T_MMG, T_MG and T_Naked respectively. And the results T_MMG≈0.87, T_MG≈0.96 and T_Naked≈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 T_Naked /T_MMG = 0.93 and T_Naked /T_MG = 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.