1. Introduction

AlGaN-based deep-ultraviolet (DUV) light-emitting diode (LED) has attracted much attention due to its wide range of potential applications, such as water purification, sterilization and high-density optical data storage [1,2]. However, compared to visible range LEDs, the AlGaN-based LEDs have still been limited in commercial applications because of their low external quantum efficiency (EQE), especially for the emission wavelength (λ) < 300 nm [3–9]. Improving the crystalline quality of AlGaN grown on sapphire substrate, hole concentration in p-AlGaN layer and hole injection efficiency related to the EQE are urgent problems to be solved [10,11]. Moreover, the optical polarization characteristics of AlGaN-based active layer determine the emission patterns and play an important role in the light extraction efficiency (LEE) of DUV LEDs, which makes a major contribution to EQE [12–15]. Previous investigations report that the polarization of emission light switches from transverse-electric (TE) mode (electric vector, E⊥c) to transverse-magnetic (TM) mode (E∥c) when the Al composition of AlGaN quantum wells (QWs) increases [16–20]. In contrast to TE mode, TM mode light predominantly propagates along lateral direction and undergoes strong total internal reflection (TIR), which is more difficult to extract from LEDs [21].

Generally, the anisotropic optical polarization is considered to be determined by the valence band structure of AlGaN QWs. In order to enhance the proportion of TE mode emission, many simulations and experiments have been carried out to modulate polarized sources by designing the structure of AlGaN active region [22,23]. For example, using compressive strain, narrow quantum well layers, barriers with high aluminum mole fractions or AlN-deta-GaN QW structures, dominant TE-polarized light can be obtained [18,19,24–26]. In addition to the polarized source determined by QW band structures, the propagation process is also an important factor that should not be ignored, which greatly affects the extraction behavior of polarized light from LEDs. It has been experimentally indicated that using the narrow mesa stripe structures exposing more sidewall of active region, better extraction of the sidewall-emitting TM-polarized DUV light can be obtained, leading to a remarkable enhancement in LEDs’ LEE [27]. The main reason has been considered as shorter average propagation path for the DUV photons prior to being extracted that reduces the probability of re-absorption loss [27,28]. To the best of our knowledge, however, the propagation path effect closely related to the extraction behavior of polarized light has not been clearly identified. It is necessary to investigate the relationship between anisotropic extraction behavior and propagation path, and find out how polarized sources extract from DUV LEDs.

In this paper, a systematic investigation of propagation path impact on anisotropic extraction behavior in AlGaN-based DUV LEDs is carried out by using k⋅p approximation, Monte Carol ray tracing technique and polarization-resolved photoluminescence (PL) measurements. Based on k⋅p approximation, s- and p-polarizations are derived to describe polarization properties of emitted light from active region. The propagation process of angularly distributed sources is simulated by Monte Carol ray tracing technique. We have analyzed detailed extraction behaviors of s- and p-polarized light from ~280 nm AlGaN-based LEDs with different chip sizes and their contributions to the polarization degree. It is found that the total light extraction intensities are improved with decreasing the propagation path, and the lateral surface extraction becomes dominant. Moreover, the extraction intensity of s-polarized light improves more than that of p-polarized light as the propagation path decreases, which results in a greater polarization degree. Polarization-resolved PL measurements confirm that the polarization degree of extracted light from lateral facet of the AlGaN multiple quantum well (MQW) sample can be enhanced from 1% to 17% when the average propagation path reduces by 0.6 mm. Our results enlighten that not only the properties of polarized sources but also their anisotropic extraction dependences on propagation path give great influence on the light extraction efficiency. By changing paths of light propagation, we can modulate the light extraction behaviors so as to improve the efficiency of DUV LEDs.

2. Theoretical model

To investigate the effect of propagation path on the extraction behavior of polarized light, we first derive the angular distribution of polarized sources in QWs. Based on k⋅p perturbation method [29–31], TE- and TM-polarized spontaneous emission rates ($r_{sp}^{TE}(\hslash \omega )$and$r_{sp}^{TM}(\hslash \omega )$) of c-oriented AlGaN MQWs can be calculated. The AlGaN related parameters are taken from linear combinations of AlN and GaN components in [32]. It is noted that the light ray along a particular direction includes both TE and TM modes. Therefore we use s and p oscillating components to describe the optical polarization of propagated light [33,34], the direction of which is illustrated by azimuthal angle φ and zenith angle θ shown in Fig. 1(a). The electric field of the s-component (-sinφ, cosφ, 0) is perpendicular to the plane determined by the emitting direction of the ray and the c-axis, while p-component (-cosθcosφ, -cosθsinφ, sinθ) oscillates in this plane and vertically to the electric field of s. In particular, when $\theta =90°$, s- and p-components just correspond to the TE and TM modes, respectively. Under hexagonal symmetry and biaxial stress hypothesis, the relation of spontaneous emission rates can be expressed as [34],

 

Fig. 1 (a) Schematic diagrams of coordinate system in simulation and measurement. The two oscillating components (s and p) are illustrated. Angular distributions of (b) s-polarized, (c) cos²θ p-polarized and (d) sin²θ p-polarized sources.

Download Full Size | PDF

It is clearly found that the spontaneous emission’s spatially angular dependence separates from the energy dependence. Thus there are three kinds of polarized sources with different angular distributions, named as s-polarized, cos²θ p-polarized and sin²θ p-polarized sources, which are shown in Figs. 1(b)-1(d). Moreover, the contributions of these angularly distributed sources are determined by the energy dependences $r_{sp}^{TE}(\hslash \omega )$ and $r_{sp}^{TM}(\hslash \omega )$.

When the polarized sources from active region including s and p oscillating components are obtained, the propagation path impact on light extraction behavior for the AlGaN-based DUV LEDs can be further analyzed by Monte Carol ray tracing technique. The light extraction process including refraction, reflection and absorption, which affects the final angularly polarized intensity, is considered in tracing a million of light rays based on Fresnel’s law [35,36]. In the simulation model of the LED structure, MQWs are regarded as a source layer composed of a set of grid points emitting s- or p-polarized rays. The refractive indices of AlGaN, AlN and sapphire are set as 2.6, 2.2 and 1.8, respectively [36–38]. Moreover, the absorption coefficients of MQW and n-AlGaN layer are assumed to be 1000 and 10 cm⁻¹, respectively [39].

3. Results and discussion

The simulated model is simplified typical ~280 nm AlGaN DUV LED structure shown in Fig. 2(a). The p-GaN contact layer is not included here to eliminate its absorption and highlight the effect of propagation path. In order to investigate the propagation path impact on anisotropic extraction behavior, we select two chips of different sizes (0.1 mm × 0.1 mm and 1 mm × 1 mm) for simulation. Based on k⋅p method, we obtain $r_{sp}^{TE}(\hslash \omega )\gg r_{sp}^{TM}(\hslash \omega )$ in ~280 nm AlGaN QWs [34], i.e., the contribution of sin²θ p-polarized source is much smaller and can be neglected in this system. Hence, in the following simulation, only s-polarized and cos²θ p-polarized sources are considered.

 

Fig. 2 (a) Simplified LED structure and the two chips of different sizes (1 mm × 1 mm and 0.1 mm × 0.1 mm). (b) Simulated total light extraction intensity for s- and p-polarizations as a function of θ. S- and p-polarized extraction intensities from top surface, lateral surface and bottom surface for 1 mm × 1 mm (c) and 0.1 mm × 0.1 mm (d) chips in simulation.

Download Full Size | PDF

The angular-dependent total light extraction intensities ($\phi =90°$, θ from 0$°$ to 180$°$) for s- and p-polarizations from all sides of the LEDs with different chip sizes are shown in Fig. 2(b). The light sources used in the simulations for the 1 mm × 1 mm and 0.1 mm × 0.1 mm chips are the combination of s-polarized and cos²θ p-polarized sources. Here we assume that both intensities and numbers of isolated sources are the same in these two chips, and the spacing of dot-shaped light rays is different. The extracted intensities at $\phi =90°$ are just given here because light intensities are repeated when φ changes by 90$°$ for the symmetry of square geometry and the variation trends of light intensities with θ are similar when φ changes within 90$°$. The thick sapphire substrate (80 μm in thickness) with large lateral area favors light extraction. Also, the refractive index of sapphire (1.8) is smaller than that of AlGaN (2.6) resulting in less internal reflection. As a result, there is more light extracted from the sapphire side ($\theta >90°$) than the AlGaN side ($\theta <90°$). As shown in Fig. 2(b), for the smaller chip of 0.1 mm × 0.1 mm, the s-polarized extraction intensities are obviously greater than that of 1 mm × 1 mm size. However, the p-polarized intensities for the two chips with different sizes are similar, especially at $\theta =90°$. This will contribute to a greater polarization degree ($\rho$) defined as $\rho =(s-p)/(s+p)$ for smaller chip.

To further analyze the light extraction behavior, we calculate the light extraction intensity from top surface, lateral surface and bottom surface for 1 mm × 1 mm and 0.1 mm × 0.1 mm chips as given in Figs. 2(c) and 2(d), respectively. It can be seen that the intensities of s- and p-polarized light from the top and bottom surfaces are similar for the LEDs with different chip sizes. As to the lateral surface, however, a substantial increase of the s-polarized light is revealed when the chip size becomes smaller and the extracted light from lateral surface gradually becomes dominant. Therefore, the enhancement of total s-polarized intensity is attributed to more extracted light for s-polarization from lateral surface of the LED with smaller chip size. It is obvious that as the chip size of LED increases, the average propagation path of light becomes longer. All the aforementioned simulation results clearly indicate that the propagation path greatly affects the extraction behavior of s- and p-polarized light, which is an important factor related to the extraction efficiency. It is found that the total light extraction intensity of s-polarized component improves more than that of p-polarized component as the propagation path decreases, leading to greater polarization degree.

In order to elucidate the origin of different extraction behaviors for s- and p-polarized sources, we further investigate the extraction behavior of light with different emission angles. Figure 3(a) shows the sketch map based on simulation results for the extraction path of four light rays with typical emission angles ($l_1, l_2$,$l_3$ and $l_4$). The $l_1$ and $l_4$ represent the rays in the extraction cone which can easily extract from top or bottom surface. The light ray $l_2$, which undergoes strong TIR, should be more difficult to extract with increasing the chip size. For $l_3$ in the lateral extraction cone, the proportion of extracted light becomes smaller due to the absorption loss caused by longer propagation path. We have simulated light extraction efficiency as a function of the emission angle (θ_E) for 0.1 mm × 0.1 mm and 1 mm × 1 mm chips by using Monte Carol ray tracing technique in Fig. 3(b). This method is only applicable when the geometric dimensions of LEDs are much larger than the emission wavelength. The light rays of sources are all in a particular direction when the θ_E is determined. It is demonstrated that the critical angle of total reflection here is about 23°. As a result, there is high and same extraction efficiency for two chips with different sizes when the emission angle ${\theta }_E<23°$ or ${\theta }_E>157°$. It is only the light with the emission angle from 23° to 157° ($23°<{\theta }_E<157°$) whose extraction efficiency strongly relies on the propagation path. As the propagation path decreases, the extraction efficiency shows an obvious enhancement. Such propagation-path-sensitive light can be simply represented as the shadow part in the profile of s-polarized and cos²θ p-polarized sources shown in Fig. 3(c). For the s-polarized source with isotropic spherical-shaped distribution, the propagation-path-sensitive light is much more than that for cos²θ p-polarized source. Therefore, when the average in-plane propagation path decreases, the total extraction intensity of s-polarized light improves more than that of p-polarized light, which results in a greater polarization degree.

 

Fig. 3 (a) Sketch for the extraction path of four typical light rays with different emission angles ($l_1, l_2$, $l_3$ and $l_4$). (b) The simulated extraction efficiency as a function of the emission angle (θ_E) for 0.1 mm × 0.1 mm and 1 mm × 1 mm chips, respectively. (c) The propagation-path-sensitive light is represented as the shadow part in the profile of s-polarized and cos²θ p-polarized sources.

Download Full Size | PDF

To directly investigate the effect of propagation path in experiment, we adopt polarization-resolved PL setup as shown in Fig. 4. Such configuration is able to not only control the same emission area but also obtain the variation of the propagation path simply by changing the distance of the laser spot center from the edge of the sample. The optical polarization characteristics of the fabricated AlGaN MQW sample with the same structure as the simulated one are measured. The MQWs are grown on sapphire substrates with 3 × 2″ close-coupled-showerhead (CCS) Aixtron metal organic chemical vapor deposition (MOCVD) system. Deposition begins with a 2.2 μm thick AlN layer, followed by a 20 period AlN/AlGaN superlattice layer and a 2 μm thick Si-doped Al_0.55Ga_0.45N layer. The Si doping concentration is 2 × 10¹⁸ cm⁻³ for the n-AlGaN film. Next, 10 period MQWs are grown consisting of well and barrier layers of Al_0.37Ga_0.63N and Al_0.55Ga_0.45N, respectively. The width of each quantum barrier is 10 nm and quantum well is 2.3 nm. Finally, the structure is completed with a 25 nm thick Al_0.55Ga_0.45N cap layer. PL measurements are performed using a 4th harmonic of Q-switched YAG:Nd laser with λ = 266 nm. The polarization degree is measured by excitation on the top surface of the c-plane wafer and detection from the lateral facet ($\theta =90°$), where s- and p-polarized light just correspond respectively to the TE- and TM-polarizations. The size of the sample is 6 mm × 6 mm, and the diameter of the laser spot is 0.3 mm. As the laser spot center moves away from the sample edge, the propagation path becomes longer, and then the effect of propagation path can be evaluated by the change of polarization properties. We have measured the polarization degree with a distance interval of 0.1 mm by moving laser spot on the surface of sample.

 

Fig. 4 Schematic diagram of the polarization-resolved PL measurement setup. The observed TE- and TM-polarized light from lateral facet ($\theta =90°$) just correspond respectively to the s- and p-polarizations obtained in the simulation results.

Download Full Size | PDF

The PL results and corresponding polarization degree as a function of the average in-plane propagation path ($\overline{x}$) are shown in Fig. 5(a). Insets are TE- and TM-polarized PL spectra for $\overline{x}=0.15\text{mm}$ and $\overline{x}=0.75\text{mm}$, respectively. Both TE- and TM-polarized PL intensities show an improvement with decreasing the propagation path. As the in-plane propagation path increases, the polarization degree of light extraction from lateral facet is gradually reduced. It is worthwhile to note that the degree of polarization is enhanced from 1% to 17% when $\overline{x}$ reduces by 0.6 mm. Our experimental results directly confirm the anisotropic extraction dependence of polarized light on propagation path. On the other hand, the total light extraction intensities of s- and p-polarizations at $\theta =90°$ for a series of chips with different sizes are simulated. The calculated degree of polarization is summarized in Fig. 5(b). The polarization degree becomes larger with decreasing the propagation path because the extraction intensity of s-polarized light improves more than that of p-polarized light. There is a negative correlation between the polarization degree and in-plane propagation path, which exhibits great agreement with the experimental results. It is suggested that the light extraction intensity can be significantly improved by modulating the anisotropic extraction behavior of polarized light through the variation of propagation path.

 

Fig. 5 Measured (a) and simulated (b) polarization degree of extracted light from lateral facet of the AlGaN MQW sample as a function of the average in-plane propagation path ($\overline{x}$). Insets are TE- and TM-polarized PL spectra for $\overline{x}=0.15\text{mm}$ and $\overline{x}=0.75\text{mm}$, respectively.

Download Full Size | PDF

4. Conclusion

In summary, the anisotropic dependence of light extraction behavior on propagation path in AlGaN-based DUV LEDs has been investigated by simulations as well as polarization-resolved PL measurements. Based on k⋅p approximation and Monte Carol ray tracing technique, we find there are two kinds of polarized sources with different angular distributions (s-polarized and cos²θ p-polarized sources) in ~280 nm AlGaN-based LEDs. The propagation path is an important factor related to the extraction behavior of polarized light. As the propagation path decreases, the total light extraction intensities are improved, and the lateral surface extraction gradually becomes dominant. Moreover, the extraction intensity of s-polarized light improves more than that of p-polarized light with decreasing the propagation path, leading to a greater polarization degree. The polarization degree of extracted light from lateral facet of the AlGaN MQW sample can be enhanced from 1% to 17% when the average propagation path reduces by 0.6 mm. Our results are helpful to modulate the anisotropic extraction behavior of polarized sources, which provides a new way to design high efficiency AlGaN-based DUV LEDs.