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Abstract
Parasitic substrate mode readily appears in GaN-based laser diodes (LDs) because of insufficient optical confinement, especially for green LDs. Substrate modes affect the behavior of a LD severely, including the laser beam quality, the optical output power, the longitudinal mode stability, and the maximum modulation speed. In this article, systematic studies on the n-cladding layer (CL) design to suppress the substrate mode of GaN-based green LDs were carried out. We established a contour map to describe the relationship between the optical confinement (determined by the thickness and the refractive index) of n-CL and the substrate mode intensity by simulating the near-field pattern and the far-field pattern. We found that it was difficult to obtain the Gaussian-shape far-field pattern using AlGaN as a cladding layer due to the appearance of cracks induced by tensile strain. However, this can be realized by introducing quaternary AlInGaN as a cladding layer since refractive index and strain can be tuned separately for quaternary alloy.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nitride laser diode (LD) has been attracting significant attention of researchers for its fast-growing and extensive applications in many fields such as laser display, laser lighting, materials processing, under water communication, and data storage [1–7]. The far-field pattern is one of most important device characteristics for LD devices. The far-field pattern will not be Gaussian-shape in the direction perpendicular to the layers (vertical direction) when substrate mode appears, which is attributed to the light leaking into the substrate and then forming a standing wave in the substrate [8,9]. Mode leakage readily occurs in GaN LDs since both the AlGaN cladding layer (CL) and InGaN waveguide layer (WG) are lattice-mismatched to GaN substrate and thus their thickness and composition are limited to a critical value, which readily leads to insufficient optical confinement. Our previous work indicates that this issue becomes more severe in green GaN-based LDs since the refractive index difference between WG and CL decreases as the wavelength increases [10].
The substrate mode can be eliminated thoroughly when the effective refractive index of waveguide mode (neff) is larger than the refractive index of substrate (nsubstrate). In the case of GaN-based LDs, the value of neff depend on: i) the thickness of InGaN WG; ii) the In content of InGaN WG; iii) the Al content of AlGaN CL. Muziol et al. have demonstrated this in blue LDs by applying 140 nm In0.05GaN WG and Al0.06GaN CL [11]. As the wavelength extends to green, much higher indium composition and thicker InGaN WG is needed to insure neff > nsubstrate, which is very challenging in epitaxy because of large lattice mismatch between InN and GaN. In the case of neff < nsubstrate, substrate mode is inevitable but can be suppressed by increasing the thickness of n-CL. Strauss et al. have reported for GaN-based LDs with GaN WG and AlGaN n-CL, the thickness of n-CL (Al composition not disclosed) had to be increased from 2 µm to 3 µm to suppress substrate mode if the operating wavelength increased from 405 nm to 440 nm [12]. Unfortunately, lattice mismatch will induce tensile stress in AlGaN CL and cracking will occur when the stress reaches the critical value. Another solution to substrate mode is to introduce GaN as n-CL to eliminate its index contrast with the GaN substrate responsible for parasitic WG. However, this will lead to a great reduction of optical confinement factor of InGaN multi-quantum-wells and thus significant reduction of modal gain of LDs [13].
Currently, there are rare systematic studies, especially experimentally, about suppression of substrate mode in GaN-based green LDs. In this article, we first investigate the relationship between n-CL and substrate mode for green LDs by simulating the near-field pattern and the far-field pattern, and establish a contour map to describe the relationship between optical confinement (determined by the thickness and the refractive index) of n-CL and substrate mode intensity. We then found that it was difficult to obtain Gaussian-shape far-field pattern using AlGaN as n-CL due to the appearance of cracks induced by tensile strain. While this can be realized by introducing quaternary AlInGaN as n-CL since refractive index and strain can be tuned separately for quaternary AlInGaN, which is demonstrated experimentally in this work.
2. Simulation structures and refractive indices
To obtain optical field pattern and profile in ridge-waveguide LDs, a commercial optical simulation software named Mode Solution by Lumerical Solution Inc. was applied. Finite Difference Eigenmode (FDE) solver which can calculate the mode field profiles by solving Maxwell’s equations on a cross-sectional mesh of the waveguide was adopted in simulation. For the refractive indices of InGaN and AlGaN at the wavelength of 520 nm, we refer to several literatures and the data are illustrated in Fig. 1. We used the values illustrated by the gray line, which are in between the values reported by different authors [13–18]. For the index of AlInGaN, linear interpolation was applied:
The device structures of green LDs studied in this work are shown in Fig. 2. It is worth to note that the real thickness of GaN substrate in LD devices is about 100 µm while 8 µm was adopted in our simulation for simplicity. This thickness is enough to make sure substrate mode will show up if any.
3. Substrate mode and n-CL design
Before we discuss substrate mode and design of n-CL, it is worth to point out that design of p-CL can also have impact on the intensity of substrate mode. According to our optical simulation (not shown here), the intensity of substrate mode can be suppressed by increasing the thickness or decreasing the composition of p-AlGaN CL because the optical field will shift away from substrate as a result. However, the thickness of p-AlGaN is also limited by the tensile strain, while decreasing Al composition of p-AlGaN will lead to increasing internal loss of LD because of insufficient optical confinement. For these reasons, typical thickness and composition for p-AlGaN CL was used in simulation, and we focus on suppressing substrate mode by designing n-CL in this article. Firstly, we simulated green LDs with n-CL of 1.25 µm thick and refractive index of n = 2.38. The optical simulation results are shown in Fig. 3. Due to neff < nsubstrate, some light leaks into thick GaN substrate and induces standing wave [shown in Figs. 3(a) and (c)] with normalized peak intensity around 2E-3. The far-field pattern and profile are shown in Figs. 3(b) and 3(d), respectively. Symmetrical lobes originating from substate mode can be found at two sides of main pattern clearly, which was also reported by other researchers [12,19]. Then, we tried to suppress the lobes in far-field profile by reducing the intensity of substrate mode. The thickness and the refractive index of n-CL are adjusted to 2.5 µm and 2.39, respectively. Figure 4 shows the simulation results. According to the near-field pattern and profile showed in Figs. 4(a) and 4(c), the substrate mode can still be observed while its peak intensity has decreased to about 6E-6. It must be mentioned that even though the refractive index of n-CL increases, the intensity of substrate mode decreases by increasing n-CL thickness. This is very important since n-AlGaN CL (typically used in LDs) with large thickness and low refractive index is hard to obtain at same time because of lattice mismatch. With the reduced intensity of substrate mode, the lobes almost disappear in the far-field profile as shown in Fig. 4(d). Only two kinks can be found in the Gaussian-shape far-field profile. These simulation results indicate there is a correlation between the intensity of substrate mode and the far-field profile. By suppressing the intensity of substrate mode to certain value, the lobes will vanish in the far-field profile.
Fig. 3. Near-field (a), far-field pattern (b) and related optical mode intensity profile (c, d) of green LDs with 1.25 µm n = 2.38 n-CL are shown. Logarithmic axes are used in (a) and (c) while linear axes in (b) and (d). The lobes caused by substrate mode are showed by arrows in (d). The number of oscillations in near-field profile depends on the thickness of substrate in simulation. Since the far-field pattern is given by Fourier transformation from the near-field profile, there are many lobes in far-field profile.
Fig. 4. Near-field (a), far-field (b) pattern and related optical mode intensity profile (c, d) of green LDs with 2.5 µm n = 2.39 n-CL. The kinks are showed by arrows in (d).
We then did further simulation for various thickness and refractive indices of n-CL. Figure 5(a) shows the far-field profiles for four cases. As can be seen, if the normalized peak intensity of substrate mode is around 3.2 E-5 or smaller, the lobes can’t be distinguished in the far-field profile. We then plot the contour map of the optical intensity of substrate mode for various thicknesses and refractive indices, as shown in Fig. 5(b). The solid line corresponds roughly to the peak intensity of 1E-6 for the substrate mode, which is the boundary for LD n-CL design with or without lobes in the far-field profile considering the tolerance of fabrication. The lower-right portion of the map corresponds to n-CL design without lobes in the far-field profiles. The dash line is the boundary for LD n-CL structures with or without cracking when AlGaN is used as n-CL based on our experimental data, as given in Fig. 6(a). As it can be seen that it is very difficult to obtain LD structure without lobes in far-field profile and without cracking in wafers simultaneously. The area marked by a circle in Fig. 5(b) shows the possible AlGaN n-CL design, but it is extremely narrow. In Fig. 5(a), we can also find the neff depends on the refractive index of n-CL while independent on the thickness of n-CL which agrees well with Ref. [11]. In order to suppress the substrate mode intensity to less than 1E-6, when Al0.043GaN n-CL with n = 2.39 is chosen, the thickness needs to be 2.5 µm. However, based on the Fig. 6(a), this thickness is approaching to the critical value for AlGaN with 4.3% Al, which means LD structure applying such thick AlGaN as n-CL is prone to cracking. Besides, LD wafers with large curvature are difficult to obtain smooth cavity facet even if cracking doesn’t appear. Therefore, AlInGaN quaternary alloy is introduced. The detail of bulk AlInGaN epitaxy and characterization will be published elsewhere. The in-plane lattice parameters are taken from Ref. [20] and linear interpolation was employed to obtain the parameters of AlInGaN. For AlInGaN, the compositions of 7.3% Al and 1.8% In can meet the requirement for optical confinement, and cracking will not appear since it is a little compressively strained as showed in Fig. 6(b).
Fig. 5. (a) far-field profile of green LDs with different n-CL. Those four far-field profiles are corresponding to points shown in Fig. (b). (b) The contour map of the optical intensity of substrate mode as the function of thickness and refractive index of n-CL. The dash line is the boundary of wafer w/wo cracking when growing AlGaN. The solid line is the rough boundary for LD n-CL design with or without lobes in the far-field profile. The area marked by circle shows the possible AlGaN n-CL design which is extremely narrow.
Fig. 6. (a) The critical thickness of AlGaN vs composition. Serious cracking means there are more than 4 cracks in the wafer by microscope while light cracking means 1∼4 cracks. The blue dot is corresponding to designed AlGaN n-CL without lobes (b) Designed 2.5 µm Al0.073In0.018GaN n-CL to suppress substrate mode. The black line shows composition of AlInGaN when the refractive index is fixed at 2.39 while red line shows corresponding strain. As the designed strain is slightly compressive, cracking can be avoided even the AlInGaN n-CL is as thick as 2.5 µm.
4. Substrate mode suppressed green LDs
In order to confirm our theoretical analysis, two GaN-based green LDs with 1.25 µm Al0.07GaN or 2.5 µm Al0.08In0.0123GaN as the n-CL, respectively, were fabricated. Details of green LD growth and processing can be found in our previous paper [21]. The compositions of AlInGaN was 8% Al and 1.23% In measured by quantitative second ion mass spectroscopy (SIMS) as shown in Fig. 7(a). The aluminum composition is a little bit higher than designed while indium composition is lower. Therefore, the strain is tensile stress leading to concave wafer as showed in Fig. 7(b). However, compared with AlGaN n-CL, AlInGaN n-CL shows much smaller curvature increment as the thickness increases, which results into that the curvature of LD wafer with AlInGaN n-CL is much smaller even at the thickness of 2.5 µm. The far-field profiles of these two LDs were measured and are shown in Fig. 8. In the case of LD with 2.5 µm AlInGaN n-CL, no any side lobes can be observed in the far-field profile and the profile shows relatively good Gaussian-shape which agrees well with our simulation. In contrast, the LDs with 1.25 µm AlGaN showed serious oscillation near the peak position induced by substrate mode. The lobes mainly appear on one side in the measured far-field profile, which is different with the simulated one. The reason is that finite thickness is used for substrate in the simulation [9].
Fig. 7. (a) Quantitative SIMS result of green LD with 2.5 µm AlInGaN n-CL. (b) The in-situ curvature of wafer when growing n-CL of LDs depends on thickness.
Fig. 8. Far-field optical profiles of green LDs with 1.25 µm Al0.07GaN n-CL (a) and 2.5 µm Al0.08In0.0123GaN n-CL (b). the shadow area indicated by green color is the simulated far-field profile while red line shows the measured one. The inset pictures are patterns taken by camera and oscillations induced by substrate mode can be clearly seen in (b).
5. Conclusion
In summary, we had conducted systematic studies on the n-CL design to suppress substrate mode of GaN-based green LDs. We first investigate the relationship between n-CL and substrate mode for green LDs by simulating the near-field and far-field pattern, and establish a contour map to describe the relationship between optical confinement (determined by the thickness and the refractive index) of n-CL and substrate mode intensity. We then find that it is difficult to obtain Gaussian-shape far-field pattern using AlGaN as cladding layer due to the appearance of cracks induced by tensile strain. While this can be realized by introducing quaternary AlInGaN as cladding layer since refractive index and strain can be tuned separately for quaternary AlInGaN.
Funding
National Key Research and Development Program of China (2016YFB0401803, 2017YFB0405000, 2017YFE0131500); National Natural Science Foundation of China (61574160, 61704184, 61804164, 61834008); Natural Science Foundation of Jiangsu Province (BK20180254); China Postdoctoral Science Foundation (2018M630619).
Acknowledgements
We appreciate the technical support from Nano Fabrication Facility, Platform for Characterization and Test, and Nano-X of SINANO, CAS.
Disclosures
The authors declare no conflicts of interest
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