Investigation of the optical properties of a deep-ultraviolet LED with an Al nanograting structure

Yi Li; Mei Ge; Mei Ge; Meiyu Wang; Xinglong Guo; Youhua Zhu

doi:10.1364/OE.474702

1. Introduction

Since the beginning of this century, AlGaN-based light-emitting diodes (LEDs) as deep ultraviolet (DUV) light sources have received great attention due to their potential applications [1–3]. With the efforts of many scientific researchers, great progress has also been made in the research of AlGaN based DUV LEDs. For example, it has been reported that the recorded external quantum efficiency (EQE) of AlGaN based LEDs emitting near 275 nm exceeds 20% [4]. By using electron beam pumping method to improve the carrier injection efficiency, the light output power of DUV LED at 260 nm can reach 2.2W [5]. However, the luminous efficiency of commercial devices in the deep UV range is still very low [1]. So far, the development of deep UV LED still faces many challenges, such as the material quality of AlGaN alloy, the p-type doping of high aluminum AlGaN, the absorption of nontransparent p-type GaN contact layer and the strong quantum confinement Stark effect [5].

One of the alternative solutions to improve the performance of DUV LED devices is to use the coupling of surface plasmon (SP) and quantum well (QW). Through this coupling process, the dipole energy in the quantum well can be rapidly transferred to the SP mode. Thus, the radiation recombination rate of the radiating dipole can be significantly increased [6–8]. In addition, the localized surface plasmon at the interface of nanostructured metal and dielectric material can be scattered into photons, which can increase the light extraction efficiency (LEE) of LEDs [9]. In recent years, there are many reports about SP coupled deep UV LEDs in the literature. For example, He et al. reported that the internal quantum efficiency (IQE) and LEE of the SP coupled QW structure were improved by 1.3 times and 13%, respectively, compared with the bare QW structure [10]. Lee et al. also reported the IQE of DUV LED with Al nanoparticles is enhanced by 57.7% [9]. However, there are few reports to quantitatively calculate the radiation recombination rate and LEE of SP coupled DUV LEDs theoretically.

In this paper, the enhancement of radiation recombination rate and LEE of deep UV LED with Al nanograting structure is calculated by the three-dimensional (3D) finite-difference time-domain (FDTD) simulation. First, the Purcell factor of the control structure and the grating structure are simulated by using the dipole as the light source. Combined with the spontaneous emission (SE) spectrum of TE/TM polarization calculated by k-p method, the corresponding increased radiation recombination rate is shown. Then, the transmittance of the emitted light at different exit angles was simulated using the plane wave as the light source. The light extraction efficiency was obtained by using the calculated enhanced radiation recombination rate and transmittance. The calculated results show that compared with the control structure, the peak intensity of TE and TM polarized radiation recombination rate is increased by 33.3% and 22.0%, respectively, and the LEE is increased by 41.4%.

2. Theoretical model

As shown in Fig. 1(a), the simulated LED structure is composed of sapphire, 820nm AlN, 2.5μm n-Al_0.64Ga_0.36N, 3-period 2.5nm-Al_0.35Ga_0.65N/12.5nm-Al_0.5Ga_0.5N quantum wells and 175nm p-Al_0.5Ga_0.5N. The Al grating structure is deposited on the etched p-AlGaN layer. The grating period, the groove depth, the duty cycle and the inclined angle (α) for the Al nanograting structure are set as 600nm, 155nm, 0.5 and 80° respectively. The optical properties are investigated by using the FDTD simulation. For Al_xGa_1-xN alloys, the dielectric constant (ε=ε₁+ i*ε₂) as shown in Figs. 1(b) and 1(c) is obtained by using model dielectric function (MDF) [11]. Note that the absorption of the Al_0.35Ga_0.65N well layer is ignored, so the imaginary part (ε₂) of its dielectric function is set to 0. The dielectric constant of other materials such as sapphire adopts the parameters provided by FDTD Solutions software. First, using the electric dipole as an incident light source, the Purcell factor (F_P) is calculated by 3D FDTD simulation. The simulated size is set to be 1.8μm × 1.8μm × 1.8μm for the X, Y and Z directions. The boundary conditions for all boundaries are set as the perfectly matched layer (PML). The polarized dipole light source is placed in the quantum well layer close to the p-type layer. Thus, the dipole is 21.25nm away from the grating groove. The Purcell factor can be obtained by F_P= P/P₀. P is the dipole radiation power, measured by a box of power monitors around the dipole source. P₀ is the power radiated by dipole in homogeneous material. Note that the calculated dipole radiation power is the average power of the dipole at three different positions under the grating.

Fig. 1. Schematic diagram (a) of the SP-coupled LED with Al nanograting structure, the real part ε₁ (b) and imaginary part ε₂ (c) of the dielectric constants for Al_xGa_1-xN alloys, and (d) TE/TM polarized spontaneous emission spectra.

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Using the obtained Purcell factor, the enhanced radiation recombination rates of the three polarization directions can be calculated by the following formula:

(1)$$\left\{ {\begin{array}{c} {{r_{T{E_1}}}(\hbar \omega ) = F_P^x \times r_{sp}^{TE}}\\ {{r_{T{E_2}}}(\hbar \omega ) = F_P^y \times r_{sp}^{TE}}\\ {{r_{TM}}(\hbar \omega ) = F_P^z \times r_{sp}^{TM}} \end{array}} \right.$$

Here, $F_P^x$, $F_P^y$ and $F_P^z$ are Purcell factors of X, Y, and Z polarization directions, respectively. $r_{sp}^{TE}$ and $r_{sp}^{TM}$ are the TE- and TM-polarized spontaneous emission rates, which is calculated by the k-p perturbation method [12]. Figure 1(d) shows the calculated TE/TM polarized spontaneous emission spectra. Then, the SE rates of the s- and p- polarized light can be written as [13]:

(2)$$\left\{ {\begin{array}{c} {s - polarization:r_{sp}^s(\hbar \omega ) = {r_{T{E_1}}}(\hbar \omega ){{\cos }^2}\varphi + {r_{T{E_2}}}(\hbar \omega ){{\sin }^2}\varphi ,}\\ {p - polarization:r_{sp}^p(\hbar \omega ) = r_{sp}^s(\hbar \omega ){{\cos }^2}\theta + {r_{TM}}(\hbar \omega ){{\sin }^2}\theta .} \end{array}} \right.$$

Next, in order to investigate the light extraction efficiency of LED, the transmittance (T^s/p(θ, φ)) of s- and p- polarized light in different emission directions is calculated by 3D FDTD simulation [14]. The size of the simulation range is 0.6μm × 1nm × 8.44μm for the X, Y and Z directions. Here, the source shape adopts the plane wave, whose propagation direction is determined by azimuth angle φ and zenith angle θ. The zenith angle θ refers to the angle between the Z-axis and the plane wave propagation direction. The plane wave source is placed in the quantum well layer close to the p-type layer. For the four lateral boundaries on the YZ and XZ planes, Bloch boundary conditions are adopted. For both top and bottom boundaries on the XY planes, PML boundary conditions are used. Note that the thickness of sapphire is assumed to be 3μm. Then, A power monitor is set under the sapphire to measure the transmittance (T^s/p(θ, φ)).

In combination with the transmittance (T^s/p(θ, φ)) and the SE rates of the s- and p-components ($r_{sp}^s$, $r_{sp}^p$) described above, angle dependent (R^s/p(θ, φ)) and wavelength dependent (R^s/p(λ)) output spectral lines can be expressed as:

(3)$$\left\{ {\begin{array}{c} {{R^{s/p}}(\theta ,\varphi ) = \int {r_{sp}^{s/p}(\hbar \omega )} \times {T^{s/p}}(\theta ,\varphi )d\hbar \omega \textrm{ }}\\ {{R^{s/p}}(\lambda ) = 4\int_0^{\pi /2} {d\varphi \int_0^\pi {r_{sp}^{s/p}(\hbar \omega ) \times {T^{s/p}}(\theta ,\varphi )\sin \theta d\theta } } \textrm{ }} \end{array}} \right.$$

The wavelength dependent light extraction efficiency of the s- and p-components is defined as:

(4)$${L^{s/p}}(\lambda ) = \frac{{{R^{s/p}}(\lambda )}}{{{R_0}^{s/p}(\lambda )}}$$

where ${R_0}^{s/p}(\lambda )$ is the value of ${R^{s/p}}(\lambda )$ when T^s/p(θ, φ) is 1. The total LEE is calculated by the following formula:

(5)$$LEE = \frac{{\int {({R^s} + {R^p})d\hbar \omega } }}{{\int {({R_0}^s + {R_0}^p)d\hbar \omega } }}$$

3. Results and discussion

Figure 2 shows the Purcell factor and the enhanced radiation recombination rate for the grating structure and plane structure. It should be noted that the plane structure refers to a structure in which only the Al layer is covered on the p-AlGaN layer. The inset in Fig. 2(a) is the structural diagram of FDTD simulation. Where, A, B, and C are three different positions where the dipole is placed. The presented Purcell factor in Fig. 2(a) is the average of the Purcell values obtained when the dipole is at these three different positions. TE₁ and TE₂ polarization denotes that the electric field direction of the dipole is parallel to the X-axis and the Y-axis, respectively. Compared with the plane structure, the Purcell factor of the grating structure is significantly improved. This can be attributed to the improvement of radiation recombination rate caused by SP-QW coupling [15]. In addition, for the grating structure, the Purcell factor of TE polarization is slightly higher than that of TM polarization near the peak wavelength (λ=278nm), while that of plane structure is just the opposite. It should be noted that the difference in the Purcell factor of TE/TM polarization is related to the dipole position for the grating structure. As the dipole is located at point A, the Purcell factor of TM polarization is larger than that of TE polarization near the peak wavelength, which is similar to the result of the plane Al/AlGaN structure in Ref. [15]. As the dipole is at point B, the Purcell factor of TM polarization is smaller as compared to that of TE polarization. Using the Purcell factor obtained, the calculated ${r_{T{E_1}}}$ and ${r_{T{E_2}}}$ are almost the same due to the small Purcell factor difference. Note that the small Purcell factor difference for X and Y polarized dipoles can be attributed to the local characteristics of SP-QW coupling. As compared with the plane structure, the peak intensities of ${r_{T{E_1}}}( \textrm{or }{r_{TE2}})$ and ${r_{TM}}$ of the grating structure are increased by 33.3% and 22.0%, respectively. Since the radiation recombination rate of the TE polarization component increases more than that of the TM polarization component, the emitted light can be extracted more easily.

Fig. 2. The Purcell factor (a, c) and the enhanced radiation recombination rate (b, d) for the grating structure and plane structure. The inset in Fig. 2(a) is the structural diagram of FDTD simulation. Where, A, B, and C are three different positions where the dipole is placed.

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Figure 3 shows the transmittance (T^s/p(θ, φ)) of s- and p- polarized light with different zenith angle θ. For the grating structure, φ is set to 0 and 90 degrees, i.e., corresponding to XZ plane and YZ plane. For the plane structure, we only calculate the case where φ is equal to 0 because of its symmetry. As can be clearly seen from the figure, due to the difference in the refractive index of AlN/Sapphire/air, the θ range of light propagating to the outside is limited to about 22 degrees, regardless of whether the light is emitted forward (θ<90°) or backward (90°<θ<180°). Nevertheless, as shown in Figs. 3(a) and 3(b), for the grating structure, the emitted light with 24°<θ<156° in the XZ plane can still partially escape to the outside, especially for the s-polarized light. The reason why the emitted light with 24°<θ<156° can be extracted can be attributed to the scattering of the grating structure changing the propagation direction of the emitted light. It is also observed that when the propagation direction of the emitted light is in the YZ plane, the extraction behavior of the grating structure is similar to that of the plane structure. It should be noted that due to the interference in the sapphire layer, the transmission intensity will change periodically with the change of sapphire thickness, especially for normal incidence. There will be some differences between the transmittances of the structure with 3μm sapphire thickness used in the calculation and the actual structure. However, the interference in the sapphire layer has the same effect on the plane structure and the grating structure, so the comparison results of the two structures should not be affected.

Fig. 3. The transmittance (T^s/p(θ, φ)) of s- and p- polarized light with different zenith angle θ for the grating structure (a-d) and plane structure (e-f).

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Combined with the $r_{sp}^{s/p}$ and T^s/p(θ, φ), the θ dependent output spectrum R^s/p(θ, φ) of s- and p-components is calculated, as shown in Figs. 4(a)–4(c). φ is set as 0° and 90°, corresponding to the XZ plane and the YZ plane, respectively. For the grating structure, the output intensity of the emitted light is significantly higher than that of the plane structure. The emitted light with 24°<θ<156° in the XZ plane can also be partially emitted to the outside. In addition, the output intensity of s-polarization component is higher than that of p-polarization component in the θ range. However, the R^s/p(θ, φ=90°) of the emitted light with 24°<θ<156° in the YZ plane is almost zero, similar to that of the plane structure. By making φ in formula (3) equal to 0° (or 90°), it can be calculated that the total LEE of the emitted light in the XZ plane (YZ plane) is 3.2% (1.93%). In the calculation of LEE, the lateral surface extraction and packaging are not considered. For plane structure, the calculated LEE is 1.81%, which is close to the extraction efficiency of the emitted light in the YZ plane. That is, the LED with grating structure has a significant influence only on the extraction behavior of the emitted light in the XZ plane. Figure 4(d) shows the total output intensity R(λ) of the emitted light for both structure. The total output intensity is calculated by summing the output intensities R^s/p(λ) of the s- and p-polarized components. It should be noted that in order to save the calculation time, in formula 3, only two points of 0 and 90 degrees are taken for the integration of φ. From this figure, it can be observed that the peak intensity of the LED with grating structure is increased by 70.3% compared with the plane structure. The total LEE calculated according to formula (5) is 2.56% for the grating structure.

Fig. 4. The θ dependent output spectrum of s- and p-components for the grating structure (a-b) and plane structure (c), (d) the total output intensity R(λ) of the emitted light for both structures.

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Although the light extraction efficiency of the grating structure is 41.4% higher than that of the plane structure, its absolute value is still small. The smaller LEE can be partly attributed to the internal total reflection caused by the larger refractive index difference of the AlN (n(278nm) = 2.37)/sapphire (n(278nm) = 1.83)/air. Figure 5 shows the transmittance (T^s/p(θ, φ)) of s- and p- polarized light reaching sapphire and air at λ=278nm for the grating structure. From the figure, we can intuitively observe that the s-/p-polarized light reaching sapphire is much larger than that reaching air. According to formula (4), the extraction efficiency of s-/p-polarized light reaching sapphire at 278nm is L^s(λ=278nm) = 10.74% and L^p(λ=278nm) = 10.4%, respectively, while the extraction efficiency reaching air is L^s(λ=278nm) = 3.32% and L^p(λ=278nm)= 2.83%. That is, if all the light reaching the sapphire can be extracted, the average extraction efficiency at 278nm can be increased by up to 2.46 times. Therefore, the bottom roughening or patterning of the sapphire substrate can significantly improve the LEE of the deep UV LED [16]. In addition, since the imaginary part of the dielectric constant of AlGaN used in this work is large, the absorption of deep ultraviolet light by AlGaN is significant, which leads to low extraction efficiency.

Fig. 5. The transmittance (T^s/p(θ, φ)) of s- and p- polarized light reaching sapphire and air at λ=278 nm for the grating structure. The propagation direction of the emitted light lies in the XZ plane (a) and the YZ plane (b).

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4. Conclusion

In summary, the optical properties of AlGaN-based LED with Al nanograting structure are investigated by 3D FDTD simulation. Compared with the control structure with Al plane, the peak intensity of TE/TM polarization radiation recombination rate of the grating structure is increased by 33.3% and 22.0% respectively due to the increase of Purcell factor. The increase in radiation recombination rate can be attributed to the SP-QW coupling. Without considering the lateral surface extraction and packaging, the LEE of the emitted light propagating in the XZ plane and the YZ plane is calculated to be 3.2% and 1.93%, respectively, while the LEE of the control structure is 1.81%. Although the total LEE of the grating structure is 41.4% higher than that of the control structure, its absolute value is still small. The smaller extraction efficiency can be partly attributed to the internal total reflection due to the larger refractive index difference of AlN/sapphire/air. The calculation results show that if all the light reaching sapphire can be extracted, the average extraction efficiency at 278nm can be increased by 2.46 times.

Funding

National Natural Science Foundation of China (61874168, 62004109, 62074086); Jiangsu Provincial Double-Innovation Doctor Program; Development of antibacterial multifunctional PVC facing new material technology (21ZH626); Jiangsu Province I-U-R Cooperation Project (BY2019114)

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Investigation of the optical properties of a deep-ultraviolet LED with an Al nanograting structure

Abstract

1. Introduction

2. Theoretical model

3. Results and discussion

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (5)

Equations (5)

Optics Express