We have investigated the three-dimensional emission patterns of GaAs/AlGaAs ridge structures with a sub-wavelength-sized top-flat facet by angle-resolved photoluminescence (PL). We found that the integrated PL intensity, and hence the light-extraction efficiency, can be enhanced by about 34% just by covering the ridge surface with a thin SiO2 layer. A double-coupling effect of evanescent waves that occurs at both the semiconductor–SiO2 and SiO2–air interfaces is suggested to be responsible for the improvement, based on a finite-difference time-domain simulation of the electromagnetic field around the ridge top.
© 2014 Optical Society of America
There is much current interest in extracting light from semiconductors with efficiencies close to 100% in order to improve the energy conversion efficiency of light-emitting diodes (LEDs). However, owing to the existence of strong total internal reflection (TIR) at the semiconductor–air interface, in conventional structures with a flat light-extraction surface, only light arriving at the interface at an angle smaller than the critical angle for TIR, i.e., light contained in the so-called escape cone, is allowed to couple out to the air, and this typically accounts for only a few percent of the total emissions . A widely employed conventional technique for improving light-extraction efficiency is to redirect the totally reflected light into an escape cone through multiple reflections of light between a randomly roughened surface and a metal mirror [2–7]. However, in this case, a considerable portion of the light will be absorbed by epitaxial layers, electrodes, and metal mirrors in this multiple reflection process, thus limiting the light-extraction efficiencies to a relatively lower value, especially in materials with high refractive indices and/or low internal quantum efficiencies.
In a recent paper, we reported that the light outside the escape cone, i.e., the light that is otherwise totally reflected in a planar structure, can be extracted directly to the air with a high efficiency in a small ridge structure composed of one sub-wavelength-sized top-flat facet and two inclined sidewall facets via an evanescent-to-propagating light transformation effect . In this structure, evanescent waves are generated on the two sidewall surfaces of the ridge when light from the center of a quantum well (QW) located beneath the top-flat facet of the ridge arrives at the sidewall–air interfaces at an angle comparable to or greater than the critical angle for TIR. These evanescent waves then move slightly along the sidewall surface toward the ridge-top facet, and are efficiently transformed into light propagating in the air by coupling when they meet at the sub-wavelength-sized ridge-top facet. We further found that this effect exists for light sources located at any position on the top-flat QW, although the transformed light began to be emitted in directions that form an increasingly larger angle with respect to the surface normal of the ridge flat facet when the light source was displaced from the center to the edge of the top-flat QW [9, 10]. In this paper, we report that the evanescent wave coupling effect can be further enhanced by simply depositing a thin layer of material with a refractive index lower than that of the semiconductor material on the ridge surface.
The sample used in this work was similar to that used in . It was a single Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As QW, sandwiched between two Al-richer Al0.65Ga0.35As layers, grown on a [1–10]-oriented, 4-μm-pitched V-grooved GaAs substrate by metal-organic vapor-phase epitaxy . In this case, a ridge structure composed of one (001) flat and two (111)A sidewall facets was formed between two adjacent V-grooves. The lateral width of the (001) flat facet was about 0.6 μm, and the angle of intersection between the (001) flat and (111)A sidewall facets was about 125°. A (001) flat GaAs QW with a thickness of about 5 nm was located at a depth of about 0.9 μm below the ridge top surface. As demonstrated in our previous study, this sample showed a photoluminescence (PL) intensity (integrated, per unit (001) QW area) that was about a factor of 10 times stronger than that of a flat-surface sample, which resulted from a light-extraction efficiency greatly enhanced by the above evanescent wave coupling effect . In the present study, a thin SiO2 layer (thickness: 150–600 nm) was also deposited on the surface of the above sample by plasma-enhanced chemical vapor deposition at 380°C.
Optical properties of the above samples were characterized by both conventional and angle-resolved PL measurements by using a cw Ti:sapphire laser as the excitation source. A laser power of 30 mW was used in all the experiments. As in our previous study, in the PL measurement, the excitation laser wavelength (720 nm) was tuned to not excite the (111)A QW, which is much thinner (~2 nm) than the (001) flat QW  to avoid any possible carrier diffusion from the (111)A to the (001) QW . The angle-resolved PL measurement which was used to obtain three-dimensional (3D) PL emission patterns was performed by using an experimental setup shown in Fig. 1(a).An optical fiber fixed to a rotation stage was placed at a distance of about 10 cm from the sample, which was contained in a He flow cryostat. The optical fiber can be rotated with respect to the laser excitation spot on the sample surface along the θ direction shown in Fig. 1(a). The cryostat itself can be rotated around the normal direction of the sample surface (φ rotation in Fig. 1(a)). The excitation laser beam, which had a diameter of about 4 mm, was focused onto the sample surface by a lens with a focal length of 20 cm. The laser beam was oriented to form an incident angle of about 5° with respect to the surface normal direction to ensure that the laser beam would not be blocked by the holder of the optical fiber. A long-pass filter was placed in front of the monochromator to cut the scattered laser beam. At a given angular position of the cryostat (that is, a given φ angle), the optical fiber was rotated with a step size of 2° (θ angle), and the PL spectrum was recorded at each step, to thus obtain the two-dimensional (2D) emission pattern I(θ,φ) in a plane forming an angle of φ with respect to the ridge axis direction (see Fig. 1(b) for a schematic illustration). The cryostat was rotated with a step size of 5° from φ = 0° to φ = 90°. The 2D emission patterns in the φ angle range of 95°–355° were duplicated from those in the angle range of 0°–90°, which is a reasonable simplification since the ridge shape is symmetric with respect to both the directions parallel with and perpendicular to the ridge axis.
3. Results and discussion
Figure 2 shows the PL spectrum of a sample with a 150-nm-thick SiO2 layer, and compares it with that of a sample without the SiO2 layer; both spectra were measured at 15 K. We were surprised to find that the PL intensity was enhanced by about a factor of 1.75 just by the presence of the 150-nm-thick SiO2 layer on the sample surface, suggesting the possibility of further improvement to the light-extraction efficiency. A similar enhancement in PL intensity was confirmed, at least over the SiO2 thickness range of 150–600 nm.
As discussed in previous studies, the spatial distribution of the PL intensity shows a strong directionality in ridge samples with a strong evanescent wave coupling effect [8–10]. Therefore, in order to make a more accurate comparison of the PL intensities of the two samples, we must measure the emission patterns three-dimensionally and integrate the PL intensities over 2π steradians. Figures 3(a) and 3(b) display the measured 3D emission patterns of the as-grown sample and the sample covered with the 150-nm-thick SiO2 layer, respectively, whereas Fig. 3(c) compares the emission patterns of the two samples measured in planes parallel with or perpendicular to the ridge axis direction. First, for the as-grown sample, the emission pattern measured in the plane perpendicular to the ridge axis is strongly localized near the direction normal to the sample surface with a full angle (at which the PL intensity decreased to half of the intensity in the normal direction) of about 34°. This emission pattern is significantly narrower than the Lambertian pattern for a flat-surface sample, and has been explained by the strong directionality of light transformed from evanescent waves for a localized light source and localization of excitation laser intensity near the center of the top-flat QW . On the other hand, in the plane parallel to the ridge direction, the emission pattern became very broad, with several distinguishable lobes, the origins of which are not clear at this moment. Three dimensionally, the emission pattern is significantly elongated along the ridge axis direction. An Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As single QW sample with thesame well thickness as the ridge sample grown on a flat substrate was also measured as a reference for the estimation of light-extraction efficiencies, and its emission pattern was confirmed to follow the Lambertian distribution.
Next, total PL intensities were calculated by using the following equation:
Here, an average 2D emission pattern was defined for the simplicity of calculation:
The first column of Table 1 gives the calculated total PL intensities of the 3 samples, where the intensities of the ridge samples were normalized to that of the flat sample. The total PL intensity of the ridge sample covered with the SiO2 layer was about a factor of 1.78 times stronger than the ridge sample without the SiO2 layer, which is in good agreement with the PL intensity ratio of these two samples obtained from Fig. 2.
Another issue that must also be considered for a precise comparison of PL intensities among different samples is the strong non-uniformity of the distribution of excitation laser intensity inside the ridge samples, which has been discussed in . To examine this issue, we simulated the laser intensity distribution in different samples by using the finite-difference time-domain (FDTD) method. In the simulation, a plane-wave light source was used to irradiate samples at an incident angle of 5 degrees from a distance of 1 μm from the sample surface (at the center of the sample). Though, strictly speaking, a focused laser beam is not a plane wave, we believe that this assumption is acceptable as a rough approximation in ourcase since the laser beam was only focused very weakly (beam diameter: 4 mm, focal length: 20 cm). Figures 4(a) and 4(b) show the distribution of the time-averaged magnitude of the Poynting vector, i.e., the laser intensity, for the ridge samples with and without the SiO2 layer, respectively. One can see that laser energy is strongly localized at the center of the ridge top facet at the position of the QW in the lateral direction , and this localization is more pronounced in the sample with the thin SiO2 layer compared to the sample without the SiO2 layer. Next, we calculated the excitation laser intensity per unit area at the QW position by integrating the time-averaged magnitude of the Poynting vector over the lateral length of the top-flat QW and dividing the value by the width of the top-flat QW (0.6 μm); these values are also summarized in Table 1. The excitation laser intensity of the ridge sample with the SiO2 layer is about a factor of 1.33 times stronger than the sample without the SiO2 layer. After accounting for the difference in excitation intensities between these two samples, we estimated that covering the surface with the thin SiO2 layer enhanced the light-extraction efficiency of the ridge sample by about 34%. We finally estimated the light-extraction efficiencies of ridge samples by using the PL intensities calibrated by using the laser excitation intensity (column 3 of Table 1) of the ridge samples and the surface occupation ratio of the top-flat QW (0.6/4 = 15%). Here, the extraction efficiency of the flat-surface sample was calculated by using the formula (1-cos(θc))/2, where θc = sin−1(1/n) is the critical angle for TIR with n being the refractive index of Al0.3Ga0.7As (n = 3.37 at 15 K and 757 nm) [12, 13]. Fresnel reflection loss at the semiconductor-air interface was neglected for simplicity. The light-extraction efficiency of the ridge samples with and without the SiO2 layer was estimated to be about 25.5% ( = (1.71/0.15) × 2.24%) and 19.1% ( = (1.28/0.15) × 2.24%), respectively. We would like to point out that these values should represent the lower limit of the real extraction efficiency since the plane-wave approximation used in the simulation of the laser excitation distribution would over-estimate the laser intensity in ridge samples as compared with that in the flat-surface sample.
The mechanism for the enhancement in light-extraction efficiency in the presence of the SiO2 layer was investigated by means of a FDTD simulation of the electromagnetic field intensity in the ridge samples. Figures 5(a) and 5(c) present the simulated electric field intensity distribution in the as-grown ridge sample and the ridge sample covered with the 150-nm-thick SiO2 layer, while Figs. 5(b) and 5(d) show the time-averaged magnitude of the Poynting vector of the two samples. Here, an electric dipole oriented perpendicular to the ridge axis direction located at the center of the (001) QW was used as the point light source. The cross-sectional profile of the SiO2 layer was traced from a scanning electron microscopy image. A refractive index of 1.45 was used for the SiO2 layer. From Figs. 5(a) and 5(b), one can clearly confirm the existence of the evanescent field on the sidewall surface and the existence of energy flow along the ridge surface toward the ridge top, indicating theevanescent-to-propagating light transformation effect. By comparing Figs. 5(b) and 5(d), it is clear that the intensity of the propagating light was significantly enhanced in the sample with the 150-nm-thick SiO2 layer as compared with the as-grown sample. From a careful examination of the electric field intensity image in Fig. 5(c), we found that, in contrast to the as-grown sample, where evanescent waves were generated only at the AlGaAs–air interface, the sample with the SiO2 layer showed the generation of evanescent waves at both the AlGaAs–SiO2 and SiO2–air interfaces. The evanescent waves generated at both the interfaces were able to couple with each other at the ridge-top facet, resulting in a more efficient transformation of evanescent waves into propagating light. For a more quantitative comparison, we calculated the magnitude of the Poynting vector (integrated over the same lateral length as Fig. 5) at a position of 2 μm from the surface of the ridge-top facet for electric dipoles oriented both along and perpendicular to the ridge axis direction. The result showed a 29% improvement in the emission intensity (average value for the two kinds of dipoles) of the sample with the SiO2 layer compared to the as-grown sample. Considering the over-simplified single-point-source model used in the FDTD simulation and the uncertainty in estimating the excitation laser intensity as discussed before, we believe that the FDTD simulation result is in reasonable agreement with the PL experimental result (~34%).
It is well known that a SiO2 layer can significantly suppress the Fresnel reflection if its thickness is close to λ/4nS, with λ and nS being the emission wavelength and the refractive index of the SiO2 layer, respectively. This anti-reflection effect could also give rise to enhancement of the light-extraction efficiency. The question then arises: is the enhancement in light-extraction efficiency in the sample with the SiO2 layer observed in this work simply due to the anti-reflection effect of the SiO2 layer? To investigate this issue, we calculated the SiO2 thickness dependence of the light-extraction efficiency by using the same calculation procedure as that used in Fig. 5, and the results are shown in Fig. 6.In the calculation, a cross-sectional profile for the SiO2 layer same as that used in Fig. 5 was assumed. In Fig. 6, for a given SiO2 layer thickness (at the top-flat facet) of d, the calculated emission intensity I(d) was converted into light-extraction efficiency ηext-ridge(d) by using the following formula14]. Incidence angle dependence of the Fresnel reflection was ignored for simplicity. As expected, the extraction efficiency of the flat-surface sample just showed periodic oscillation between the efficiency of the sample without the SiO2 layer (~1.5%) and that of the sample with a SiO2 thickness of λ/4nS ≈129nm (~2.1%). On the contrary, the extraction efficiency of the ridge sample showed very different SiO2 thickness dependence from that of the flat-surface sample. The light-extraction efficiency increases almost monotonously from the efficiency of the sample without the SiO2 layer (19.1%) up to a maximum value of about 28% at a SiO2 thickness of about 390nm with increasing the thickness of the SiO2 layer. A weak periodic undulation with peak and valley appearing at approximately the same position as the flat-surface sample was observed, and is attributed to the anti-reflection effect of the SiO2 layer. It is important to note that the extraction efficiency at the λ/2nS thickness position doesn’t drop back to the value of the sample without the SiO2 layer, but is rather slightly higher than the efficiency at the λ/4nS position. This result clearly indicates the evanescent wave coupling effect is the primary reason responsible for the large enhancement in light-extraction efficiency in samples covered with the SiO2 layer, and the conventional anti-reflection effect of a SiO2 layer only has a minor influence on the light-extraction efficiency.It clearly follows from the above discussion that this effect is not limited to SiO2, but rather applies to any material with a refractive index lower than that of the semiconductors. Of particular interest are transparent conductive materials, such as ITO and ZnO, which are widely used as current spreading layers in LEDs. Furthermore, by using multiple layers with refractive indexes successively decreasing from that of the semiconductor to that of air, one can expect to generate evanescent waves at more than two interfaces and thus even higher light-extraction efficiencies.
In conclusion, we have measured the 3D emission patterns of a QW located underneath the sub-wavelength-sized top-flat facet of GaAs/AlGaAs ridge structures by means of angle-resolved PL measurement at 15 K. We demonstrated an enhancement of the integrated PL intensity by about 34% just by covering the ridge surface with a thin SiO2 layer, resulting in the same amount of improvement in the light-extraction efficiency. Based on a comparison with a flat-surface reference sample, the light-extraction efficiencies of the ridge sample with and without a 150-nm-thick SiO2 layer were estimated to be at least 25.5 and 19.1%, which are respectively about 11.4 and 8.5 times higher than the flat-surface sample. A double coupling effect of evanescent waves occurring at both the AlGaAs–SiO2 and SiO2–air interfaces is believed to be the mechanism for the enhancement of light-extraction efficiencies. It is confirmed by a theoretical study on the SiO2 thickness dependence of the emission intensity that the conventional anti-reflection effect of a SiO2 layer only has a minor influence on the light-extraction efficiency.
The authors would like to thank A. Enderlin and M. Ravaro for useful discussions. Part of this work was financially supported by a Grant-in-Aid for Scientific Research B (No. 21360016) from the Japan Society for the Promotion of Science.
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