Open Access
Add to BibSonomy
Abstract
A doping optimization model towards lower loss and higher efficiency at the target operating current is investigated. This model considers the effect of doping concentration on the series resistance and the internal loss. 780 nm lasers doped with a normal doping profile (Dop_normal) and an optimized doping profile (Dop_optimize) are both designed and fabricated. After doping optimization, the power loss decreased by 17%, the output power of the lasers increased by 26% and the electro-optical conversion efficiency increased by 22%. The model provides significant theoretical guidance for the optimization of the laser doping.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
7xx-9xx nm high-power semiconductor lasers have a wide range of applications. 780 nm semiconductor lasers can be used to pump alkali metal gas lasers (DPAL) and rubidium atomic clocks in space [1,2]. 79x nm lasers are available as pump sources for kilowatt-class thulium-doped fiber lasers [3]. 808 nm lasers are widely used in material processing and medical applications [4,5]. 830 nm lasers are commonly applied in industrial printing systems [6]. 905 nm lasers have wide demand in the field of radar monitoring and autonomous driving [7]. Increasing the power conversion efficiency (PCE) of broad area semiconductor lasers is one of the major issues studied by various teams. Higher efficiency means lower power loss.
The power loss of high-power broad area lasers is mainly composed of five parts: joule heating, carrier absorption, hetero-junction band alignment, carrier leakage, and below-threshold loss [8]. Among them, the joule heating, caused by the series resistance and the carrier absorption attributed to the internal loss, occupies a large proportion of the power loss.
The series resistance and the internal loss of the lasers are both related to the doping concentration. The power losses caused by other factors are less related to the doping concentration. A higher doping concentration can reduce the series resistance, but also increase the internal loss. Therefore, it is important to choose an appropriate doping concentration to balance the series resistance and the internal loss. Crump et al. reported in their article that increasing the doping level of P-waveguide could reduce the current leakage and suppress the power saturation [9]. Ryvkin concluded that the suppression of optical losses in long-wavelength lasers at high temperatures could be achieved by highly doped n-waveguides [10]. Alin Fecior et al. found that a proper doping profile of the waveguide layer could be beneficial to increasing the PCE of the device [11]. Zhong Li et al. used a waveguide layer doping and cladding gradient doping design in the trade-off between the series resistance and the internal loss [12]. K.Yu. Telegin et al. investigated the effect of different waveguide width doping profiles on the output power of the laser. Doped broad waveguide lasers enable an increased differential quantum efficiency [13]. Tan Shao-Yang et al. used lightly doped N-type cladding layers, and step-doped P-type cladding layers to obtain a lower internal loss laser [14]. Xiong Cong et al. found that the PCE of devices with a parabolic doping profile and a linear doping profile of P-type waveguide layers was substantially improved [15]. Аvrutin et al. analyzed the nonlinear resistance and waveguide doping effects. Doping in the cladding layer had a small effect on the improvement of the laser’s series resistance at high injection currents [16].
The above groups analyzed the effect of doping on device performance, but no theoretical guidance was given for optimizing doping. Therefore, a doping optimization model, which achieves lower loss and higher efficiency, is proposed in this paper. Lasers with a normal doping profile (Dop_normal) and an optimized doping profile (Dop_optimize) are both designed and fabricated. By the doping optimization, the output power and the PCE of the laser are improved. The power loss is greatly reduced, while the vertical far-field divergence angle remains unchanged.
In this paper, recent progresses in the laser doping optimization are reviewed at the beginning. In section 2, it is specifically analyzed that how the doping concentration affects the series resistance and the internal loss of lasers, and a model is proposed to reduce loss and improve efficiency. Based on this model, an optimized doping profile is calculated for a 780 nm photonic crystal (PC) laser. In section 3, conventionally doped and optimally doped semiconductor lasers are grown and fabricated. In section 4, the measured results are shown and discussed.
2. Theoretical designs
The series resistance and the internal loss are two important parameters that affect the power loss of the laser. The series resistance Rs of the laser can be calculated by using the following expression.
where h is the overall thickness of the epitaxial layer, q is the electron charge, µ(y) is the majority carrier mobility of each layer in the epitaxial direction, D(y) is the doping concentration of each layer in the epitaxial direction (the doping concentration is considered as the carrier concentration), W is the strip width of the semiconductor laser, and L is the cavity length of the semiconductor laser.The carrier mobility µ(y) is calculated by the model [17]
The internal loss αi of the laser can be calculated by the following expression [18]
The carrier absorption cross-section coefficient is not a constant. It can be obtained from the equation [19]
The epitaxial structure of the lasers at 7xx nm-9xx nm is mainly made of AlGaAs materials except for the quantum wells and barriers. The refractive index of AlGaAs is very little affected by the doping concentration. Therefore, when the material component and the thickness of each layer in the epitaxial direction are determined, the Helmholtz equation is solved by Python software using uniform grid dissection and dichotomous algorithm. Thus, the optical field distribution Ij(y) in the epitaxial direction can be obtained.
The joule heat function due to series resistance at a certain current is
where I is the operating current.The power loss due to the carrier absorption can be written as [8]
The power loss due to heterojunction energy band alignment can be written as [8]
where V0 is the overall built-in voltage, VF is the voltage corresponding to the quasi-Fermi energy level difference in the laser stimulated state.The power loss caused by carrier leakage can be written as [8]
where ηi is the internal injection efficiency.The power loss caused by the below-threshold loss can be written as [8]
where Ith is the threshold current.Therefore, the total power loss can be written as the following equation
From the above Eq. (1)-Eq. (6), it can be seen that the doping concentration strongly affects the carrier mobility, the absorption cross-section coefficient, and thus the series resistance, the internal loss, the power loss, and the PCE of the laser.From Eq. (7)-Eq. (10), the power loss caused by heterojunction energy band alignment, carrier leakage and below-threshold can be considered as a constant independent of the doping concentration for a given operating current. If the total power loss is minimized, a suitable doping concentration is used to minimize the power loss caused by joule heating and carrier absorption. Although it is difficult to analytically calculate the doping curve function that minimizes the total power loss, the doping distribution can be more easily solved by the numerical analysis method. The epitaxial structure is segmented along the vertical direction, so the total power loss caused by series resistance and carrier absorption is equal to the sum of the power loss due to these two factors at each node.
PR + opt is a monotonically increasing function of the epitaxial thickness. The minimum value of the power loss PR + opt is the sum of the minimum power loss pR + opt (j) at each node. It is easier to be solved for the doping concentration that achieves the minimum power loss pR + opt (j) at each node.
To ensure the stability of the fundamental mode at high powers, a 780 nm laser based on a longitudinal PC structure is designed.
GaAsP quantum well and AlGaAs quantum barriers are used in the active region of the laser to prevent carrier leakage. The ternary compound AlGaAs is used for the rest epitaxial layers to ensure the growth quality of the interface between adjacent layers. The epitaxial structure takes an asymmetric design. The waveguide layer on the P side is referred to as the upper waveguide layer, and the waveguide layer on the N side is referred to as the lower waveguide layer. The thickness of the upper waveguide layer is less than that of the lower waveguide to reduce the internal loss. The P-contact layer is grown with a higher doping concentration to achieve a good ohmic contact. The P-cladding layer is grown with AlGaAs material with a higher Al content, compared to the N-cladding layer, to prevent the increase of the internal loss due to the optical field leakage into the P-contact layer. PC lasers have shown excellent performances in mode modulations and beam quality improvements. PC lasers can effectively extend the near-field to reduce the vertical far-field divergence angle [20–23]. Therefore, the PC structure is also adopted in this design. Two pairs of PC layers with the periodically varying refractive index are placed in the N-doping side of the epitaxy. Each pair of PC layers consists of a high refractive index layer and a low refractive index layer. The epitaxial structure is segmented according to a grid with an accuracy of 1 nm. The resulting refractive index distribution in the epitaxial direction and the profiles of the fundamental mode (mode 0) and higher order modes (modes 1, 2, 3, 4) are calculated as shown in Fig. 1(a). From Fig. 1(a), it can be shown that the optical field of the fundamental mode is localized in the core region, while the high-order modes extend to the PC-layers. Therefore, the fundamental mode has a large confinement factor than that of the higher-order modes so that the PC laser can operate stable in the fundamental mode even at high currents. Figure 1(b) is the calculated vertical far-field distribution corresponding to the fundamental mode with a full width at half maximum (FWHM) of the divergence angle of 27°.
Fig. 1. (a) Calculated refractive index profile and mode profiles of epitaxial structures. (b) Calculated vertical far-field divergence angles.
Conventional doping profile architectures usually adopt the heavy doping in cladding layers and the light doping in waveguide layers. In this way, the internal loss and the series resistance are balanced. As illustrated by the blue solid line in Fig. 2, both the N-cladding layer and the P-cladding layer possess a higher doping concentration of 2E18 cm-3. Compared to electrons, holes have a higher absorption cross-section coefficient. In order to reduce the internal loss of the P-side layer, the upper waveguide layer is not doped. A constant doping concentration of 1E17 cm-3 is used for the lower waveguide layer and PC-layers. To achieve a good ohmic contact, the P-contact layer is doped with a concentration of more than 1E19 cm-3.
Fig. 2. Refractive index profile of the epitaxial structure (black line), calculated fundamental mode optical field distribution (red line), normal doping distribution (blue solid line) and calculated optimized doping distribution (blue dotted line).
The blue dotted line in Fig. 2 represents the calcuated optimized doping profile. The specific calculation method is as follows. According to the optical field intensity distribution, the confinement factor corresponding to each node can be calculated. The heavy doping is used where the node's optical confinement factor is less than 1E-7, so the impact on the corresponding internal loss is small and the series resistance is also effectively reduced. When the optical confinement factor of the node is greater than 1E-7, the doping concentration of each node can be solved numerically except for the active region which is not doped. The selected range of the doping concentration for each node of the P-side region is from 5E16 cm-3 to 1E19 cm-3. The range of the doping concentration selected for each node of the N-side region is from 5E16 cm-3 to 2E18 cm-3. When an operating current I and an average power in the cavity P0 are given, it is easy to solve the doping concentration that achieves the minimum power loss at that node according to Eq. (11). Since the precision of the discretization of the epitaxy is small enough, when the doping concentration of each node is determined, the doping profile of the overall epitaxy is also given. Based on the above method, the optimized doping curve is calculated and shown in Fig. 2 by the blue dotted line.
High injection currents can cause severe thermal effects, which become more pronounced at short wavelengths. In order to reduce the effect of temperature on the series resistance and internal losses, the target operating current of the device is chosen to be 5A. The electrical properties of the above two structured lasers with a 2 mm cavity length and a 200 µm stripe width at 5 A are calculated according to Eqs. (1), (3) and (10). The calculation results are shown in Fig. 3. The black and red lines represent the Dop_normal and Dop_optimize structures, respectively. The colored areas in Fig. 3 correspond to the P-contact, P-cladding, Upper waveguide, Lower waveguide, PC-Layers, N-cladding, and Buffer layers in Fig. 2. Figure 3(a) shows the integral value of the series resistance in the vertical direction. The series resistances of the Dop_normal and Dop_optimize structures are 28 mΩ and 30 mΩ, respectively. There is a slight increase in the series resistance of the Dop_optimize structure due to the slightly lower doping concentration in the P-side region than that of the Dop_normal structure. Figure 3(b) illustrates the integral value of the internal loss in the vertical direction. The internal losses of the Dop_normal and Dop_optimize structures are 1.2 cm-1 and 0.9 cm-1, respectively. Similarly, the internal loss of the Dop_optimize structure is significantly reduced due to the lower doping concentration in the P-side region than that of the Dop_normal structure. Figure 3(c) plots the integral value of the power loss in the vertical direction. Under ideal conditions, the internal quantum efficiency is set to 100%, the Fermi level difference is the emitted photon energy, the threshold current is set to 1A, and the built-in voltage minus the Fermi level difference is set to 0.03 V. According to Eqs. (7)–(9), the power loss caused by band alignment, carrier leakage, and threshold are calculated to be 0.15W, 0W and 1.59W, respectively. The total power loss of the Dop_normal and Dop_optimize structures are 4.8 W and 4.2 W, respectively. The calculation results show that the power loss of the laser based on the doping-optimized model structure is significantly lower than that of the normal design.
Fig. 3. Calculated integral values of (a) series resistance, (b) internal loss, and (c) power loss versus the vertical position at 5 A. The black and red lines indicate the calculated results for the Dop_normal and Dop_optimize structures, respectively.
3. Growth and fabrication
The above epitaxial structures are grown on GaAs substrates by the metal organic chemical vapor deposition (MOCVD) technology. The doping concentration distributions of two epitaxial structures are measured by the CVP21 diffusion concentration profiler provided by WEP, Germany. A two-step lithography process is adopted to process the grown epitaxial wafer. The first lithography forms the ridge area of the laser, and the wet etching is performed on both sides of the ridge area. SiO2 is deposited on the etched area to suppress the lateral diffusion of carriers. The second lithography forms the current injection window. Afterwards, the P-side is metallized with Ti/Pt/Au material to form a low resistivity ohmic contact [24]. The substrate is thinned to 120 µm by grinding and polishing to reduce the laser’s heat dissipation path. The N-side is metalized with AuGeNi/Au material, which facilitates the creation of a thin n-type highly doped layer on the GaAs surface [25]. Epitaxial wafers are cleaved into 2 mm, 2.5 mm, 3 mm, and 4 mm bars, used to characterize the internal loss. The front and rear cavity facets of the laser bar are coated with anti-reflectivity (AR) films and high-reflectivity (HR) films, based on SiO2/TiO2 materials, respectively. The AR film has 5% reflectivity at 780 nm and the HR film has 95% reflectivity at 780 nm, as shown in Fig. 4. The coated bar is cleaved into a single emitter with the cavity length of 2 mm and the stripe width of 200 µm. The single chip is packaged on an AlN heat sink with P-epi-down. Finally, the PCE-power-voltage-current curves and the vertical far-field distribution of the laser under continuous wave (CW) conditions are measured by Raybow Opto's COS tester. The measurement temperature is stabilized at 25°C by a thermoelectric cooler with cooling water flowing below.
Fig. 4. Reflection spectrum of the coated films. The black and red lines indicate the high reflectivity (HR) film and anti-reflectivity (AR) film, respectively.
4. Results and discussions
Figure 5 illustrates the grown doping concentrations of the two designed structures. Based on the measured results, the grown doping concentration curve basically conforms to the expected design. The larger error areas are in the cladding layers where the doping concentration has less effect on the series resistance and internal loss.
Fig. 5. Doping concentration profiles of (a) Dop_normal and (b) Dop_optimize structures. The red balls and black solid lines indicate the grown and designed doping concentration, respectively.
Figure 6 shows the measured PCE-power-voltage-current curves of the coated Dop_normal and Dop_optimize lasers with the cavity length of 2 mm and the stripe width of 200 µm. The inset shows the spectrum of the laser tested at 5 A. Figure 7 shows the spectrums of the lasers tested at 5A for both structures. The peak wavelengths of the Dop_normal laser and the Dop_optimize laser are 780.1 nm and 780.4 nm, respectively, and the FWHM of the spectra are 1.5 nm and 1.3 nm, respectively. It can be clearly seen from the graph that the output power and PCE of the Dop_optimize laser are significantly higher than those of the Dop_normal laser. After doping optimization, there is a slight increase in the laser resistance and the threshold current remains nearly unchanged. The relevant electrical characteristics are summarized in Table 1.
Fig. 6. Measured PCE-power-voltage-current curves of lasers with a cavity length of 2 mm and a stripe length of 200 µm under the CW operation at 25°C. The hollow circles represent Dop_normal lasers and the solid spheres represent Dop_optimize lasers.
Fig. 7. Measured spectra of lasers at 5 A. The black line represents Dop_normal lasers and the red line represents Dop_optimize lasers.
Table 1. Measured electrical characteristics of Dop_normal and Dop_optimize lasersa
The series resistances of the Dop_normal and Dop_optimize lasers are 26 mΩ and 31 mΩ, respectively. After doping optimization, the series resistance increases by 19%. The measured results are in general agreement with the results calculated in Fig. 3(a). For the Dop_optimize laser, it can be found in Fig. 5 that the doping concentration in both the P-cladding layer and the upper waveguide layer is lower than that of the Dop_normal laser. Lower doping concentrations inevitably increase the series resistance. The internal losses of Dop_normal and Dop_optimize are 1.06 cm-1 and 0.68 cm-1, respectively, tested by the variable cavity length method. Figure 5 shows that the doping concentration of the growth is lower than the designed doping concentration, which is also the cause of the test results being slightly lower than the calculated results in Fig. 3(b). The threshold currents of the above two structures are 0.98 A and 0.94 A, respectively. The optical confinement factor Γ strongly determines the threshold current. The doping concentration has a small effect on the optical field distribution of the laser, so the variation of Γ is not significant after the optimization. From the power-current curves, the slope efficiencies of two structures are 1.01 W/A, and 1.22 W/A, respectively. At the operating current of 5 A, the output power of the Dop_normal and Dop_optimize lasers are 3.9 W and 4.9 W, respectively, which means the output power increases by 26% after the optimization. The thermal effect of the laser at an injection current of 5 A is less obvious. The output power of the laser is mainly related to the internal loss. The internal loss of the Dop_optimize is significantly lower than that of the Dop_normal, so the output power of the Dop_optimize is higher than that of the Dop_normal. In addition, the doping concentration of the upper waveguide layer of the Dop_optimize structure is higher than that of Dop_normal, which contributes to the reduction of carrier leakage [9]. This is another cause of the significant increase in power after optimized doping.
The PCE of the Dop_optimize laser is 55% at 5 A, which is 22% higher than that of the Dop_normal laser. The power loss of the Dop_optimize laser is 4.0 W, which is 17% lower than that of the Dop_normal laser. The measured results are essentially the same as the calculated results. The test results demonstrate that the power loss of the laser is significantly reduced and the PCE is substantially improved with the doping optimization. The optimized doping model achieves an effective balance between the series resistance and the internal loss.
Figure 8 depicts the vertical far-field distribution of the Dop_normal and Dop_optimze lasers at 5 A. The FWHM of the vertical far-field divergence angles of two structures are 27° and 26°, respectively. The measured results are consistent with the calculated results in Fig. 1(b). The vertical far-field is a Fourier transformation of its near-field (optical field). The far field is essentially the same for both structures, which indicates that the doping concentration has a relatively small effect on their near fields and confirms again that it is feasible to ignore the effect of doping concentration on the refractive index in the calculation of the optical field distribution.
Fig. 8. Measured vertical far-field divergence angles of lasers at 5 A. The black line represents Dop_normal lasers and the red line represents Dop_optimize lasers.
5. Conclusions
In summary, a doping design model is proposed to reduce the power loss and improve the PCE of 780 nm photonic crystal broad area lasers. The model considers the effect of the doping concentration on the mobility and the absorption cross-section coefficient. Compared with conventional doping lasers, the power loss of the laser, based on the optimized doping model, is reduced by 17%, the output power of the laser is increased by 26% and the PCE is increased by 22% under the same current. In addition, the effect of the doping concentration on vertical far-field distributions of lasers is relatively small. The performance of the device is substantially improved only at the cost of a 19% increase in the series resistance. This design idea is not only applicable to semiconductor lasers, but also has greater guidance for improving the efficiency of solar cells and increasing the quantum yield of nonlinear semiconductor materials [26–29].
Funding
Key Technology Research and Development Program of Shandong (2022CXGC020104, 2023ZLYS03); Key-Area Research and Development Program of Guangdong Province (2020B090922003).
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.
References
1. G. A. Pitz and M. D. Anderson, “Recent advances in optically pumped alkali lasers,” Appl. Phys. Rev. 4(4), 041101 (2017). [CrossRef]
2. J. Keaveney, W. J. Hamlyn, C. S. Adams, and I. G. Hughes, “A single-mode external cavity diode laser using an intra-cavity atomic Faraday filter with short-term linewidth <400 kHz and long-term stability of <1 MHz,” Rev. Sci. Instrum. 87(9), 095111 (2016). [CrossRef]
3. P. F. Moulton, G. A. Rines, E. V. Slobodtchikov, K. F. Wall, G. Frith, B. Samson, and A. L. G. Carter, “Tm-Doped Fiber Lasers: Fundamentals and Power Scaling,” IEEE J. Select. Topics Quantum Electron. 15(1), 85–92 (2009). [CrossRef]
4. F. Bachmann, “Industrial applications of high power diode lasers in materials processing,” Appl. Surf. Sci. 208-209, 125–136 (2003). [CrossRef]
5. Y. Gu, J. Niu, J. Yang, and H. Xu, “Application of laser in the medical field,” Chinese Optics 16(2), 283–295 (2023). [CrossRef]
6. L. Chen, G. Yang, and Y. Liu, “Development of Semiconductor Lasers,” Chin. J. Laser 47(5), 0500001 (2020). [CrossRef]
7. Y. Li and J. Ibanez-Guzman, “Lidar for Autonomous Driving: The Principles, Challenges, and Trends for Automotive Lidar and Perception Systems,” IEEE Signal Process. Mag. 37(4), 50–61 (2020). [CrossRef]
8. M. Kanskar, T. Earles, T. Goodnough, E. Stiers, D. Botez, and L. J. Mawst, “High-power conversion efficiency Al-free diode lasers for pumping high-power solid-state laser systems,” Proc. SPIE 5738, 47–56 (2005). [CrossRef]
9. H. Wenzel, P. Crump, A. Pietrzak, X. Wang, G. Erbert, and G. Tränkle, “Theoretical and experimental investigations of the limits to the maximum output power of laser diodes,” New J. Phys. 12(8), 085007 (2010). [CrossRef]
10. B. S. Ryvkin, E. A. Avrutin, and J. T. Kostamovaara, “Optical loss suppression in long-wavelength semiconductor lasers at elevated temperatures by high doping of the n -waveguide,” Semicond. Sci. Technol. 33(10), 105010 (2018). [CrossRef]
11. A. Fecioru, N. Boohan, J. Justice, A. Gocalinska, E. Pelucchi, M. A. Gubbins, M. B. Mooney, and B. Corbett, “AlGaAs ridge laser with 33% wall-plug efficiency at 100 °C based on a design of experiments approach,” Semicond. Sci. Technol. 31(4), 045002 (2016). [CrossRef]
12. Y. Man, L. Zhong, X. Ma, and S. Liu, “975 nm Semiconductor Lasers with Ultra-Low Internal Optical Loss,” Acta Opt. Sin. 40(19), 1914001 (2020). [CrossRef]
13. K. Y. Telegin, M. A. Ladugin, A. Y. Andreev, I. V. Yarotskaya, N. A. Volkov, A. A. Padalitsa, A. V. Lobintsov, A. N. Aparnikov, S. M. Sapozhnikov, and A. A. Marmalyuk, “The influence of waveguide doping on the output characteristics of AlGaAs/GaAs lasers,” Quantum Electron. 50(5), 489–492 (2020). [CrossRef]
14. S. Tan, T. Zhai, R. Zhang, D. Lu, W. Wang, and C. Ji, “Graded doping low internal loss 1060-nm InGaAs/AlGaAs quantum well semiconductor lasers,” Chinese Phys. B 24(6), 064211 (2015). [CrossRef]
15. C. Xiong, F. Chong, J. Wang, G. Wang, L. Han, S. Liu, and X. Ma, “Doping Profile Optimization and Design of Waveguide Layer for Laser Diode with High Conversion Efficiency,” Semiconductor Optoelectronics 31(1), 16–19 (2010).
16. E. A. Avrutin and B. S. Ryvkin, “eq,” Proc. IEEE, 10–11 (2013).
17. M. Sotoodeh, A. H. Khalid, and A. A. Rezazadeh, “Empirical low-field mobility model for III–V compounds applicable in device simulation codes,” J. Appl. Phys. 87(6), 2890–2900 (2000). [CrossRef]
18. T. Kaul, G. Erbert, A. Klehr, A. Maasdorf, D. Martin, and P. Crump, “Impact of Carrier Nonpinning Effect on Thermal Power Saturation in GaAs-Based High Power Diode Lasers,” IEEE J. Sel. Top. Quantum Electron. 25(6), 1–10 (2019). [CrossRef]
19. K. A. Bulashevich, V. F. Mymrin, S. Y. Karpov, D. M. Demidov, and A. L. Ter-Martirosyan, “Effect of free-carrier absorption on performance of 808 nm AlGaAs-based high-power laser diodes,” Semicond. Sci. Technol. 22(5), 502–510 (2007). [CrossRef]
20. Z. Chen, A. Qi, X. Zhou, H. Qu, J. Chen, Y. Jia, and W. Zheng, “High Power and Narrow Vertical Divergence Laser Diodes With Photonic Crystal Structure,” IEEE Photonics Technol. Lett. 33(8), 399–402 (2021). [CrossRef]
21. L. Wang, A. Qi, X. Zhou, T. Fu, C. Xu, R. Han, H. Qu, and W. Zheng, “High Power Conversion Efficiency Narrow Divergence Angle Photonic Crystal Laser Diodes,” IEEE Photonics J. 14(6), 1–20 (2022). [CrossRef]
22. X. Zhou, X. Ma, H. Qu, A. Qi, Z. Chen, Y. Wang, and W. Zheng, “Extremely high-brightness tapered photonic crystal diode laser with narrow-emitting aperture,” Appl. Phys. Express 12(9), 094004 (2019). [CrossRef]
23. Z. Chen, H. Qu, X. Ma, A. Qi, X. Zhou, Y. Wang, and W. Zheng, “High-Brightness Low-Divergence Tapered Lasers with a Narrow Taper Angle,” Chinese Phys. Lett. 36(8), 084201 (2019). [CrossRef]
24. L. Zhou, W. Lanford, A. T. Ping, I. Adesida, J. W. Yang, and A. Khan, “Low resistance Ti/Pt/Au ohmic contacts to p -type GaN,” Appl. Phys. Lett. 76(23), 3451–3453 (2000). [CrossRef]
25. S. Tahamtan, A. Goodarzi, S. P. Abbasi, A. Hodaei, M. S. Zabihi, and J. Sabbaghzadeh, “Investigation on the effect of annealing process parameters on AuGeNi ohmic contact to n-GaAs using microstructural characteristics,” Microelectron. Reliab. 51(8), 1330–1336 (2011). [CrossRef]
26. C. L. M. Hofmann, E. H. Eriksen, S. Fischer, B. S. Richards, P. Balling, and J. C. Goldschmidt, “Enhanced upconversion in one-dimensional photonic crystals: a simulation-based assessment within realistic material and fabrication constraints,” Opt. Express 26(6), 7537 (2018). [CrossRef]
27. S. Dottermusch, A. Quintilla, G. Gomard, A. Roslizar, V. R. Voggu, B. A. Simonsen, J. S. Park, D. R. Pernik, B. A. Korgel, U. W. Paetzold, and B. S. Richards, “Infiltrated photonic crystals for light-trapping in CuInSe_2 nanocrystal-based solar cells,” Opt. Express 25(12), A502 (2017). [CrossRef]
28. N. D. Gupta, V. Janyani, and M. Mathew, “Light trapping in p-i-n superlattice based InGaN/GaN solar cells using photonic crystal,” Opt. Quantum Electron. 48(11), 502 (2016). [CrossRef]
29. J. Marques-Hueso, R. Peretti, R. Abargues, B. S. Richards, C. Seassal, and J. P. Martínez-Pastor, “Photonic Crystal-Driven Spectral Concentration for Upconversion Photovoltaics,” Adv. Opt. Mater. 3(4), 568–574 (2015). [CrossRef]
