1. Introduction

Solid-state lighting has been developed for a long time. Among all the solid-state lighting technologies, light-emitting diode (LED) is a research hotspot for its high efficiency, energy saving, longer lifetime and environmental protection advantages. AlGaN deep-ultraviolet (DUV) LED has attracted great attention owing to its wide applications in sterilization, air or water purification, high-density optical data storage and biochemistry devices [1]. Great progresses have been achieved in DUV LEDs recently, especially in the range of emission wavelengths shorter than 280nm [2–4]. However, the external quantum efficiency (EQE) of DUV LEDs is still much lower than that of blue LEDs. According to its definition, EQE is the product of internal quantum efficiency (IQE), injection efficiency (IE) and light extraction efficiency (LEE). While the EQE of DUV LED has been improved via significantly improved IQE and IE [1,2,5–7], low LEE is still a bottleneck for high-efficiency DUV devices [1].

The low LEE in AlGaN-based DUV LEDs has been recognized and basically understood. It is believed that the increasing contribution of transverse-magnetic (TM, polarization vector of electric field, $\widehat{e}=\widehat{z}$// c-axis) polarized light is an important reason for low LEE [8,9]. Compared with transverse-electric (TE, $\widehat{e}=\widehat{x}$ or $\widehat{y}\perp$ c-axis) polarized light, TM is more difficult to be extracted since it mainly propagates along lateral direction and undergoes strong total internal reflection (TIR) [8]. Based on these knowledge, some researchers have studied the optical polarization properties in DUV LEDs [9–11]. And these researches qualitatively explained the relationship between polarization emissions and LEE. However, propagation process will affect optical polarization and LEE. A comprehensive picture to quantitatively describe the relationship between polarization properties and LEE during the whole process of light’s production and propagation is needed. Finding how light polarization affects LEE could guide researchers exploring effective ways to enhance LEE. Furthermore, for shorter-wavelength LEDs, the extent from TM to TE by tuning valence band order is rigorously limited. In order to pursue higher possibilities to increase the efficiency of LEDs, we noticed that the angular distribution of polarized light could be changed during propagation process. And the varied angular distribution finally determines LEE [12]. Thus, modulating angular distribution of polarized light would be a feasible way to enhance LEE.

In this paper, LEE dependent on angular distribution of polarized light in [0001]-oriented AlGaN DUV LEDs is comprehensively studied. The polarization properties of light are described by s and p oscillating components. The angular distributed sources for s and p polarizations were derived by a calculation based on k⋅p perturbation method. Their propagation process was simulated by Monte Carol ray-tracing technique. The LEE and angular distributions of 277nm and 215nm LEDs with two typical different polarization properties were analyzed and angularly resolved polarized electroluminescence (EL) spectra were also measured. It is found that the intensity distributions of differently polarized light can be changed in propagation process and this determines the LEE of LEDs. By comparing an optimized 215nm LED with conventional one, we showed that intensity angular distribution of polarized light could be modulated and great amounts of light rays were extracted from top and bottom surfaces.

2. Angular distribution of polarized emission

To simulate the angular distribution of polarized light intensity, the source terms of dipole emissions in multiple quantum wells (MQWs) should be derived. TE and TM mode spontaneous emission rates ($r_{sp}^{TE}\left(\hslash \omega \right)$ and $r_{sp}^{TM}\left(\hslash \omega \right)$) of c-oriented AlGaN are calculated based on the k⋅p perturbation method [13–15]. The parameters of AlN and GaN are taken from literatures [16,17]. And the AlGaN parameters are obtained by linear combinations of the components of AlN and GaN. The calculated spontaneous emission light will emit from the active layer. When light is emitted along any direction, the measured polarized components are not sole TE and TM modes of LED emissions [18]. The polarization of recombination transitions between conduction and valence subbands can be described by two oscillating components, denoted as s and p [19]. The emitting direction and polarization vector are expressed by azimuthal angle φ and zenith angle θ shown in Fig. 1(a).The electric field of p (-cosθcosφ, -cosθsinφ, sinθ) is in the plane determined by c-axis and the emitting direction of ray, while s (sinφ, -cosφ, 0) oscillates vertically to this plane and the electric field of p. Under biaxial stress hypothesis and using hexagonal symmetry, the relations of emission rates

 

Fig. 1 (a) Sketch of coordinate system for simulation and measurement, s and p oscillating components. Angular distributions of (b) s-polarized source, (c) cos²θ p-polarized source and (d) sin²θ p-polarized source.

Download Full Size | PDF

3. Results and discussion

For relatively long wavelength in DUV range such as 277nm, the calculated emission rates $r_{sp}^{TE}\left(\hslash \omega \right)$ and $r_{sp}^{TM}\left(\hslash \omega \right)$are shown in Fig. 2(a). It is clear that the light intensity of TM is much smaller than that of TE and the light source is composed of mostly s-polarized and cos²θ p-polarized components. The insets in Fig. 2(a) are the sketches of extraction cones and cross sections of s-polarized and cos²θ p-polarized angular distributions. The s-polarized light distributes isotropically and is extracted from top, bottom and lateral surfaces of LEDs, while cos²θ p-polarized light is mainly extracted from extraction cones around θ = 0° and 180°. Besides the angular distributions of light sources, light extraction is also influenced by the refraction, reflection and absorption during light propagation process. These processes can be simulated with a Monte Carlo ray-tracing method which uses Fresnel’s law [21,22]. In this simulation, light behaviors are mainly determined by refractions and reflections at the interfaces with large refractive index differences, and are further corrected by detailed differences of refractive index among AlGaN epilayers. And the simulation is performed with the consideration of absorption effects of all the epilayers. In the model, light source in MQWs is represented by a grid source layer. A set of grid points in the source layer emit s-polarized or p-polarized rays. The total intensity of all rays is distributed angularly following Eq. (1) for s-polarization and Eq. (2) for p-polarization. Figure 2(b) shows the structure of a 1.1mm*1.1mm flip chip LED. To reduce the interference of external factors, electrodes are not considered. The refractive indices and absorption coefficients of AlGaN, GaN and sapphire in the simulation are taken from Ref [21–26].

 

Fig. 2 (a) 277nm spontaneous emission rates for TE and TM modes, the inset is sketch of extraction cones and cross sections of angular distributions of s-polarized (up) and cos²θ p-polarized (down) sources and (b) the flip chip LED structure, the simulated (c) and measured (d) s-polarized and p-polarized light intensities as the functions of θ.

Download Full Size | PDF

Figure 2(c) gives the angular dependent total extracted intensities (φ = 90°, θ from 0° to 90°) for s-polarized and p-polarized light according to our simulation. Because of the square geometry, light intensities are repeated when φ changes by 90°. Although light intensities are different when φ changes within 90°, the variation trends of light intensities with θ are similar. So intensities at φ = 90° are focused to clarify the effects of source patterns [12]. To compare with the simulated results, angularly resolved polarized EL spectra via θ of 277nm AlGaN 1.1mm*1.1mm flip chip LED were measured at a current density of ~28 A/cm². In the experiment (measurement schematic is shown in Fig. 1(a)), a LED was vertically placed on the center of a rotation stage. A Glan-Taylor polarizer and an optical fiber were successively placed within 15cm away from the LED. When the LED chip rotates, the distances among LED, polarizer and optical fiber keep constant. The measured data are shown in Fig. 2(d). The simulated and measured results both reveal that the s-polarized light intensity is slightly stronger than that of p-polarized light. Both the s-polarized and p-polarized light intensities increase first and decrease afterwards with θ changing from 0° to 90°. The existences of maximum intensities are attributed to the lateral extractions. Despite of discrepancies between simulations and experiments due to the inaccuracies of parameters, the simplified model and measurement error, the angular distribution trends of simulated results are consistent with experimental ones. These results are similar to those of InGaN LEDs reported previously [12,18]. This is comprehensible because their angular distributions of light sources are both mainly contributed from TE polarized and TE cos²θ polarized light sources. However, when light wavelength shortens, TM increases and angular distribution becomes different.

For LEDs of shorter wavelength such as 215nm, the calculated spontaneous emission rates in Fig. 3(a) show that TM overtakes TE. The sin²θ p-polarized component plays an important role in the total extracted light in such LEDs. However, the LEE of sin²θ p-polarized component is much lower attributing to its emission pattern plotted in the inset of Fig. 3(a). Its angular distribution is much different from those of s-polarized and cos²θ p-polarized components as the intensity of light is weak at θ = 0° (or 180°) and strong at high slant angles around θ = 90° [27]. Such kind of intensity distributed light mainly propagates in lateral direction with a long path. It suffers more absorption and TIR than that of top and bottom surface extracted light and this hinders the extraction of light.

 

Fig. 3 (a) 215nm spontaneous emission rates for TE and TM modes, inset is sketch of extraction cones and cross section of angular distribution of sin²θ p-polarized source. (b) 0.2mm*0.2mm conventional flip chip LED structure. (c) Simulated s-polarized and p-polarized light intensities as the functions of θ in 215nm and 277nm conventional flip chip LEDs, inset in the bottom left corner is experimental data of normalized intensities in 277nm (blue triangle), 283nm (black sphere) and 210nm (red square) LEDs.

Download Full Size | PDF

To reduce the light absorption, a small size LED is proposed and simulated. Figure 3(b) presents the 0.2mm*0.2mm conventional flip chip LED structure. The angular dependent extracted intensities for s-polarized and p-polarized light rays in 215nm and 277nm 0.2mm*0.2mm conventional flip chip LEDs are shown in Fig. 3(c). The extracted light intensities of 215nm LED are lower than those of 277nm LED. Unlike results in 277nm LED, the p-polarized light intensity overtakes that of s-polarized light in 215nm LED. And the peak intensities appear at θ around 50°, which is greater than 30° in 277nm LED. This discrepancy is attributed to the angular distribution of sin²θ p-polarized light. Some experimental data gave the similar tendency with these results. In the bottom left corner of Fig. 3(c), the peak intensity (without distinguishing their polarization properties, i.e. the summation of s-polarized and p-polarized light) appeared around θ = 30° for 277nm LED in this work. Lee et al. measured the peak intensity at θ = 30° for c-plane 283nm LED [28] and Taniyasu et al. obtained the peak intensity at θ = 50° for c-plane 210nm AlN LED [27]. By summing the intensity of s-polarized and p-polarized light, our results are consistent with these data.

Based on the above analyses, it is known that the LEE strongly depends on angular distribution of polarized light in emitting and propagation processes. For DUV LEDs, extraction of sin²θ p-polarized light at high slant angles should be of crucial significance to LEE. As an example to illustrate the effect of modulating angular distribution on LEE in DUV LEDs, a novel design of 215nm AlGaN LED chip is given in Fig. 4(a). With the similar structure in conventional LED, the designed LED is special with a p-(AlN)₅/(GaN)₁ superlattice contact layer [29] replacing p-GaN to minimize light absorption. And the surface and backside of sapphire substrate are cone patterned. The absorption coefficient of p-(AlN)₅/(GaN)₁ is assumed to be 1000cm⁻¹ [2]. The dimensions of sapphire pattern of diameter, height and interval are 3μm, 1.2μm and 1μm, respectively. The selection of these dimensions considers fill factor, slant angle and ray tracing limit [30–32]. It is shown that the extracted light intensities in the designed LED are much stronger than those of conventional LED in Fig. 4(b). The total LEE is 60.7%, which is 5.1 times higher than the value in conventional LEDs.

 

Fig. 4 (a) The designed 215nm LED structure, and (b) simulated s-polarized and p-polarized light intensities as the functions of θ.

Download Full Size | PDF

To reveal the reason of the increases of light intensities, the angular dependent extracted intensities from s-polarized, cos²θ p-polarized and sin²θ p-polarized light in 215nm LEDs with conventional and designed structures are simulated and plotted in Fig. 5. In conventional LED, the extracted s-polarized and cos²θ p-polarized light with small slant angles are similar to each other, while s-polarized light is larger than cos²θ p-polarized light at high slant angles. Different with the above two components, the sin²θ p-polarized light mainly distributes at high slant angles and its extraction intensity is much small.

 

Fig. 5 Angular dependent extracted intensities from s-polarized, cos²θ p- polarized and sin²θ p-polarized light in 215nm conventional LED ((a), (b) and (c)) and designed LED ((d), (e) and (f)).

Download Full Size | PDF

From conventional LED to the designed one, the extracted light intensities from these three kinds of polarized light change differently. To be specific, the extracted s-polarized light is stronger than that of cos²θ p-polarized light and it is noteworthy that the extracted sin²θ p-polarized light increases significantly. This is because the light rays distributed at high slant angles are randomized into the angle region of extraction cones by the patterns on sapphire substrate. Thus, light can be extracted within a shorter path. Meanwhile, the design of p-(AlN)₅/(GaN)₁ for reducing absorption helps more light enter into extraction cones. For polarized light with different angular distributions, the improvements are different. For sin²θ p-polarized component, it is largely distributed at high slant angles and hence the improvement is the most remarkable, while the enhancement of cos²θ p-polarized light is the least which corresponds to the least distribution at high slant angles. And the increase of s-polarized light is between the results of the above two components. Among the simulated results, the maximum enhancements of light intensities are the 27 and 16.5 times higher than extracted sin²θ p-polarized light from top and bottom surfaces, respectively. This is because large amounts of light rays distributed at high slant angles are refracted or reflected into extraction cone with low slant angles. This enhances the extracted light from top and bottom surfaces. Simulation results for LEDs with different dimensions of patterns along with a reflector below p-AlGaN superlattice contact layer are accordant with the conclusions of this work in tendency change. Although there might be some errors in this work resulting from wave characteristics of light and LEDs with nano-patterns are beyond the limitation of this simulation method, it can be predicted that the design with structures changing angular distribution of polarized light in semipolar, nonpolar plane, and micron LEDs should also benefit the enhancement of LEE.

4. Conclusion

In this paper, a comprehensive study is done to understand the effects of angular distribution on LEE in AlGaN DUV LEDs. A united picture is presented to describe polarized light’s emission and propagation processes. It is clear that the electron-hole recombinations in AlGaN MQWs produce three kinds of angularly distributed light sources named as s-polarized, cos²θ p-polarized and sin²θ p-polarized light sources. For the DUV LEDs with wavelength as short as 215nm, sin²θ p-polarized light becomes more important than that in 277nm LEDs. However, the LEE of sin²θ p-polarized light is much lower attributing to its intensity distribution. We found that the intensity distributions of differently polarized light can be changed in propagation process and determines the LEE of LEDs. By intentionally changing the angular distribution of polarized light, the LEE is enhanced noticeably. Among the magnifications of extractions, sin²θ p-polarized light is the largest and its enhancement is greatly contributed by the extraction from top and bottom surfaces. In conclusion, it is proven that modulating angular distribution of polarized light should be an effective way to realize high-efficiency DUV LEDs.