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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2536–2544
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Stimulated emission in GaN-based laser diodes far below the threshold region

Ding Li, Hua Zong, Wei Yang, Liefeng Feng, Juan He, Weimin Du, Cunda Wang, Ya-Hong Xie, Zhijian Yang, Bo Shen, Guoyi Zhang, and Xiaodong Hu  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2536-2544 (2014)
http://dx.doi.org/10.1364/OE.22.002536


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Abstract

We identify that the stimulated emission of GaN laser diodes (LDs) emerges far below the traditionally recognized threshold from both optical and electrical experiments. Below the threshold, the linear-polarized stimulated emission has been the dominating part of overall emission and closely related to resonant cavity. Its intensity increases super linearly with current while that of spontaneous emission increases almost linearly. Moreover, the separation of quasi-Fermi levels of electrons and holes across the active region has already exceeded the photon emission energy, namely, realized the population-inversion.

© 2014 Optical Society of America

1. Introduction

GaN-based laser diodes (LDs) are one of the main applications in III-Nitrides materials. For decades, the researchers were striving their efforts on reducing the threshold current [1

1. S. Nakamura, “The roles of structural imperfections in ingan-based blue light-emitting diodes and laser diodes,” Science 281(5379), 956–961 (1998). [CrossRef] [PubMed]

5

5. T. Meyer, H. Braun, U. T. Schwarz, S. Tautz, M. Schillgalies, S. Lutgen, and U. Strauss, “Spectral dynamics of 405 nm (Al,In)GaN laser diodes grown on GaN and SiC substrate,” Opt. Express 16(10), 6833–6845 (2008). [CrossRef] [PubMed]

], improving the output power [6

6. O. H. Nam, K. H. Ha, H. Y. Ryu, S. N. Lee, T. H. Chang, K. K. Choi, J. K. Son, J. H. Chae, S. H. Chae, H. S. Paek, Y. J. Sung, T. Sakong, H. G. Kim, H. S. Kim, Y. H. Kim, and Y. J. Park, “High power AlInGaN-based blue-violet laser diodes,” Proc. SPIE 6133, 61330N (2006). [CrossRef]

9

9. S. Takagi, Y. Enya, T. Kyono, M. Adachi, Y. Yoshizumi, T. Sumitomo, Y. Yamanaka, T. Kumano, S. Tokuyama, K. Sumiyoshi, N. Saga, M. Ueno, K. Katayama, T. Ikegami, T. Nakamura, K. Yanashima, H. Nakajima, K. Tasai, K. Naganuma, N. Fuutagawa, Y. Takiguchi, T. Hamaguchi, and M. Ikeda, “High-power (over 100 mW) green laser diodes on semipolar {20(2)over-bar1} GaN substrates operating at wavelengths beyond 530 nm,” Appl. Phys. Express 5(8), 082102 (2012). [CrossRef]

], and expanding the wavelength range [10

10. A. Khan, “Semiconductor photonics: Laser diodes go green,” Nat. Photonics 3(8), 432–434 (2009). [CrossRef]

14

14. K. Kojima, U. T. Schwarz, M. Funato, Y. Kawakami, S. Nagahama, and T. Mukai, “Optical gain spectra for near UV to aquamarine (Al,In)GaN laser diodes,” Opt. Express 15(12), 7730–7736 (2007). [CrossRef] [PubMed]

] among other things. They focus their attentions mainly on the behavior of LDs above the threshold region. Nowadays, the life time of commercially available GaN LDs has extended over 10000 hours.

However, it is also essential to investigate the behavior of GaN-based LD below the threshold region for understanding the physical mechanisms during the generation of lasing. Some of the fundamental physical problems in LDs still deserve close attentions. The emergence of stimulated emission and the amplification of stimulated emission into lasing are undoubtedly challenging topics among them. The information hidden in the compositions, polarizations, and intensities of spectra which varies with current could provide effective clues to these topics. Unfortunately, these are rarely reported in literatures perhaps due to the lack of precise measurements under low injection with extremely weak emissions.

2. Experiments

The schematic of the optical measurement system was in Fig. 1.
Fig. 1 The schematic of the optical measurement setup.
The LDs were driven under DC source Keithley 2601A. And the edge emission light along the cavity from LDs became parallel through quartz convex lens. Then the parallel light propagated through the Glan prism as a polarizer, and was finally collected by Thorlabs optical power meter PM100D with an S130C sensor head as the detector and Ocean Optics S2000 as the spectrometer at the end. As shown in the upper-left, the angle between the transverse electrical (TE) mode direction and the polarization direction of the Glan prism was denoted as θ. So that the TE mode direction was defined as θ = 0° with power maximum Pmax while the output power in θ = 90° was denoted as Pmin. Its ac admittance profile was measured by an Agilent 4294A precision impendence analyzer.

3. Results and discussions

Fig. 2 (a) Dependence of the separation of the quasi-Fermi levels of electron and holes across active region Vj (solid line) and series resistance rs (dashed line) of the sample on the injected current. (b) Corresponding first (solid line) and second derivative (dashed line) of the optical output power. The two kink points of the first derivatives correspond to Ithl andIthu, respectively.
The sample under discussions was a GaN-based LD Sony SLD3132VF diode lasing at 404 nm manufactured by Sony Corp. Its electrical characterizations are accomplished using ac IV method, which were described in detail elsewhere [18

18. C. D. Wang, C. Y. Zhu, G. Y. Zhang, J. Shen, and L. Li, “Accurate electrical characterization of forward AC behavior of real semiconductor diode: giant negative capacitance and nonlinear interfacial layer,” IEEE Trans. Electron. Dev. 50(4), 1145–1148 (2003). [CrossRef]

20

20. L. F. Feng, D. Li, C. Y. Zhu, C. D. Wang, H. X. Cong, G. Y. Zhang, and W. M. Du, “Deep saturation of junction voltage at large forward current of light-emitting diodes,” J. Appl. Phys. 102(9), 094511 (2007). [CrossRef]

]. As shown in Fig. 2, Vj (solid line) of the sample temporarily dropped between 27.1 mA (the lower threshold Ithl) and 29.8 mA (the upper threshold Ithu). Then it kept increasing with current beyond. And series resistance rs (dashed line) changes accordingly. Corresponding first (solid line) and second derivatives (dashed line) of the optical output power were also plotted. The two kink points of the first derivatives corresponded to the lower threshold Ithl and the upper threshold Ithu, respectively. Similar behavior was also found in a number of commercially-available LDs, including Nichia NDV4312 and Sanyo DL-4146-301S. Above results were similar to the ones reported in [21

21. D. Li, W. Yang, L. F. Feng, P. W. Roth, J. He, W. M. Du, Z. J. Yang, C. D. Wang, G. Y. Zhang, and X. D. Hu, “Stimulated emission related anomalous change of electrical parameters at threshold in GaN-based laser diodes,” Appl. Phys. Lett. 102(12), 0123501 (2013). [CrossRef]

].

Fig. 3 The spectra collected along cavity exhibited two types of polarity. The combination (dot dash) of spectra at θ = 90° (dash) and at θ = 0° (with attenuation of cos278° about 4.3%, dot) is identical to the one recorded at θ = 78° (solid). The one with lower energy is dominate emission when injection below the threshold. (a) at 3mA and (b) at 10 mA.
We record the spectra at different polarization angles under different injection levels to clarify their origins. From spectral analysis to these recorded results, we discover that below the threshold the spectra are comprised of two parts with different polarization properties. We denote the spectra recorded when the Glan prism was set θ at 0° and 90° as Peak A (PA) and Peak B (PB), respectively. As shown in Fig. 3, PA, around 404 nm, is the main part of the overall spectra even at the injection low to 3 mA. The intensity of PA could be attenuated by rotating the angle of the Glan prism until vanished at θ = 90°. So PA exhibits highly polarized properties with polarization direction identical to the lasing TE mode. However, PB is considerable weak and only became visible when the Glan prism is far away from θ = 0°. So it is hard to identify PB’s polarization in this configuration.

For detailed quantitative analyses, we carefully record the spectra and the light output power under different injection with respect to θ. In most cases of our measurements, the intensity of PA is much stronger than that of PB, so we provide here only the spectra recorded at 78°, where the intensities of PA and PB are comparable at this polarization configuration. It is found that the spectrum recorded at 78° is remarkably identical to the combination of spectra of the one at 90° and the one at 0° attenuated by 4.3% (cos2 78°) ([Fig. 3(a)] at 3 mA). This spectra analyses further manifest that PA with highly polarization is the principle part in the emission from a GaN LD. Similar behavior is also found at other injection below the threshold region, for example, [Fig. 3(b)] at 10 mA. When current increases, the intensity of PA increases much faster than that of PB. PA’s peak intensity is 7.4 times of PB at 3mA and climbs up to 11.4 times of PB at 10 mA.

Since PA is the main part of the emission, the polarization of PA can be further revealed by the output power as a function of θ. The polarized output power Pθ are recorded and presented here five typical angles at θ = 0°, 30°, 45°, 60°, and 90° [Fig. 4(a)].
Fig. 4 (a) Dependance of the optical power as a function of the current. The slope values of for θ = 0°, 30°, 45°, and 60° are larger than the linear increase one for θ = 90°, exhibiting the property of super-linear increase. (b) The dominate emission is linear-polarized as the power ratios Rsθ=(PθPmin)/(PmaxPmin) are almost coincident with relation Rsθ=cos2θ when Glan lens set at the angle of θ = 30°, 45° and 60° to transverse electrical mode.
The slope values of PθI for θ = 0°, 30°, 45°, and 60° in semilogarithmic coordinates are larger than the linear increase one for θ = 90°. Hence the output powers increase super-linearly with current under all angles except the one at 90°, indicating the property of stimulated emission. From above spectra analysis, the output powers recorded at 90° are totally from PB with notation Pmin. Assuming PB is isotropic (Though this assumption might be not that accurate, it does not hinder to reveal the polarization characteristics of PA considering the small fractions of PB in output.), the power ratio Rsθ=(PθPmin)/(PmaxPmin) are proposed to identify the polarization of PA. Rsθ follows with relation Rsθ=cos2θ when Glan prism set at the angle θ = 30°, 45° and 60° [Fig. 4(b)]. It evidentially proves that the principle emission PA below the threshold is linear-polarized. This linear-polarized property of PA emerges far below the threshold region and maintains till the lasing with the same direction as that of lasing light.

4. Conclusion

Acknowledgments

This work was supported by National Basic Research Program of China under Grant Nos. 2013CB328705, 2012CB619304 and 2012CB619306, the National Natural Science Foundation of China under Grant Nos. 61334005, 61076013, 51272008 and 11204209, and China Postdoctoral Science Foundation (Grant No.2013M530007). The authors acknowledge the support given by all staff at the beamline 1W1A at BSRF. We also appreciate the helpful discussions with the technical support engineers in Agilent (China) Technologies, Inc., on forward admittance and I-V measurements.

References and links

1.

S. Nakamura, “The roles of structural imperfections in ingan-based blue light-emitting diodes and laser diodes,” Science 281(5379), 956–961 (1998). [CrossRef] [PubMed]

2.

W. Yang, D. Li, N. Liu, Z. Chen, L. Wang, L. Liu, L. Li, C. Wan, W. Chen, X. Hu, and W. Du, “Improvement of hole injection and electron overflow by a tapered AlGaN electron blocking layer in InGaN-based blue laser diodes,” Appl. Phys. Lett. 100(3), 031105 (2012). [CrossRef]

3.

C. S. Kim, Y. D. Jang, D. M. Shin, J. H. Kim, D. Lee, Y. H. Choi, M. S. Noh, and K. J. Yee, “Estimation of relative defect densities in InGaN laser diodes by induced absorption of photoexcited carriers,” Opt. Express 18(26), 27136–27141 (2010). [CrossRef] [PubMed]

4.

D. Scholz, H. Braun, U. T. Schwarz, S. Brüninghoff, D. Queren, A. Lell, and U. Strauss, “Measurement and simulation of filamentation in (Al,In)GaN laser diodes,” Opt. Express 16(10), 6846–6859 (2008). [CrossRef] [PubMed]

5.

T. Meyer, H. Braun, U. T. Schwarz, S. Tautz, M. Schillgalies, S. Lutgen, and U. Strauss, “Spectral dynamics of 405 nm (Al,In)GaN laser diodes grown on GaN and SiC substrate,” Opt. Express 16(10), 6833–6845 (2008). [CrossRef] [PubMed]

6.

O. H. Nam, K. H. Ha, H. Y. Ryu, S. N. Lee, T. H. Chang, K. K. Choi, J. K. Son, J. H. Chae, S. H. Chae, H. S. Paek, Y. J. Sung, T. Sakong, H. G. Kim, H. S. Kim, Y. H. Kim, and Y. J. Park, “High power AlInGaN-based blue-violet laser diodes,” Proc. SPIE 6133, 61330N (2006). [CrossRef]

7.

C. Sasaoka, K. Fukuda, M. Ohya, K. Shiba, M. Sumino, S. Kohmoto, K. Naniwae, M. Matsudate, E. Mizuki, I. Masumoto, R. Kobayashi, K. Kudo, T. Sasaki, and K. Nishi, “Over 1000 mW single mode operation of planar inner stripe blue-violet laser diodes,” Phys. Status Solidi A 203(7), 1824–1828 (2006). [CrossRef]

8.

S. Nakamura, “High-power InGaN-based blue laser diodes with a long lifetime,” J. Cryst. Growth 195(1-4), 242–247 (1998). [CrossRef]

9.

S. Takagi, Y. Enya, T. Kyono, M. Adachi, Y. Yoshizumi, T. Sumitomo, Y. Yamanaka, T. Kumano, S. Tokuyama, K. Sumiyoshi, N. Saga, M. Ueno, K. Katayama, T. Ikegami, T. Nakamura, K. Yanashima, H. Nakajima, K. Tasai, K. Naganuma, N. Fuutagawa, Y. Takiguchi, T. Hamaguchi, and M. Ikeda, “High-power (over 100 mW) green laser diodes on semipolar {20(2)over-bar1} GaN substrates operating at wavelengths beyond 530 nm,” Appl. Phys. Express 5(8), 082102 (2012). [CrossRef]

10.

A. Khan, “Semiconductor photonics: Laser diodes go green,” Nat. Photonics 3(8), 432–434 (2009). [CrossRef]

11.

T. Miyoshi, S. Masui, T. Okada, T. Yanamoto, T. Kozaki, S. Nagahama, and T. Mukai, “510–515 nm InGaN-Based Green Laser Diodes on c -Plane GaN Substrate,” Appl. Phys. Express 2, 062201 (2009). [CrossRef]

12.

A. Avramescu, T. Lermer, J. Müller, S. Tautz, D. Queren, S. Lutgen, and U. Strauß, “InGaN laser diodes with 50 mW output power emitting at 515 nm,” Appl. Phys. Lett. 95(7), 071103 (2009). [CrossRef]

13.

Y. Yamashita, M. Kuwabara, K. Torii, and H. Yoshida, “A 340-nm-band ultraviolet laser diode composed of GaN well layers,” Opt. Express 21(3), 3133–3137 (2013). [CrossRef] [PubMed]

14.

K. Kojima, U. T. Schwarz, M. Funato, Y. Kawakami, S. Nagahama, and T. Mukai, “Optical gain spectra for near UV to aquamarine (Al,In)GaN laser diodes,” Opt. Express 15(12), 7730–7736 (2007). [CrossRef] [PubMed]

15.

S. L. Chuang, “Physics of Optoelectronic Devices,” in Physics of Optoelectronic Devices (Wiley-Intescience Publication, New York, 1995), pp. 399.

16.

P. Barnes and T. Paoli, “Derivative measurements of the current-voltage characteristics of double-heterostructure injection lasers,” IEEE J. Quantum Electron. 12(10), 633–639 (1976). [CrossRef]

17.

T. Paoli and P. Barnes, “Saturation of the junction voltage in stripe-geometry (AlGa)As double-heterostructure junction lasers,” Appl. Phys. Lett. 28(12), 714 (1976). [CrossRef]

18.

C. D. Wang, C. Y. Zhu, G. Y. Zhang, J. Shen, and L. Li, “Accurate electrical characterization of forward AC behavior of real semiconductor diode: giant negative capacitance and nonlinear interfacial layer,” IEEE Trans. Electron. Dev. 50(4), 1145–1148 (2003). [CrossRef]

19.

L. F. Feng, D. Li, C. Y. Zhu, C. D. Wang, H. X. Cong, X. S. Xie, and C. Z. Lu, “Simultaneous sudden changes of electrical behavior at the threshold in laser diodes,” J. Appl. Phys. 102(6), 063102 (2007). [CrossRef]

20.

L. F. Feng, D. Li, C. Y. Zhu, C. D. Wang, H. X. Cong, G. Y. Zhang, and W. M. Du, “Deep saturation of junction voltage at large forward current of light-emitting diodes,” J. Appl. Phys. 102(9), 094511 (2007). [CrossRef]

21.

D. Li, W. Yang, L. F. Feng, P. W. Roth, J. He, W. M. Du, Z. J. Yang, C. D. Wang, G. Y. Zhang, and X. D. Hu, “Stimulated emission related anomalous change of electrical parameters at threshold in GaN-based laser diodes,” Appl. Phys. Lett. 102(12), 0123501 (2013). [CrossRef]

22.

E. Feltin, A. Castiglia, G. Cosendey, L. Sulmoni, J. F. Carlin, N. Grandjean, M. Rossetti, J. Dorsaz, V. Laino, M. Duelk, and C. Velez, “Broadband blue superluminescent light-emitting diodes based on GaN,” Appl. Phys. Lett. 95(8), 081107 (2009). [CrossRef]

23.

K. Holc, Ł. Marona, R. Czernecki, M. Boćkowski, T. Suski, S. Najda, and P. Perlin, “Temperature dependence of superluminescence in InGaN-based superluminescent light emitting diode structures,” J. Appl. Phys. 108(1), 013110 (2010). [CrossRef]

24.

S. Ling, T. Lu, S. Chang, J. Chen, H. Kuo, and S. Wang, “Low efficiency droop in blue-green m-plane InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 96(23), 231101 (2010). [CrossRef]

25.

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26.

K. C. Kim, M. C. Schmidt, H. Sato, F. Wu, N. Fellows, M. Saito, K. Fujito, J. S. Speck, S. Nakamura, and S. P. DenBaars, “Improved electroluminescence on nonpolar m-plane InGaN/GaN quantum wells LEDs,” Phys. Status Solidi-Rapid Res. Lett. 1, 125 (2007).

27.

S. E. Brinkley, Y. D. Lin, A. Chakraborty, N. Pfaff, D. Cohen, J. S. Speck, S. Nakamura, and S. P. DenBaars, “Polarized spontaneous emission from blue-green m-plane GaN-based light emitting diodes,” Appl. Phys. Lett. 98(1), 011110 (2011). [CrossRef]

28.

O. Brandt, P. Misra, T. Flissikowski, and H. T. Grahn, “Excitation polarization anisotropy of the spontaneous emission from an M-plane GaN film: Competition between hole relaxation and exciton recombination,” Phys. Rev. B 87(16), 165308 (2013). [CrossRef]

29.

T. Flissikowski, K. Omae, P. Misra, O. Brandt, and H. T. Grahn, “Ultrafast behavior of the polarization filtering in anisotropically strained M-plane GaN films: A time-resolved pump-probe spectroscopy study,” Phys. Rev. B 74(8), 085323 (2006). [CrossRef]

30.

N. F. Gardner, J. C. Kim, J. J. Wierer, Y. C. Shen, and M. R. Krames, “Polarization anisotropy in the electroluminescence of m-plane InGaN-GaN multiple-quantum-well light-emitting diodes,” Appl. Phys. Lett. 86(11), 111101 (2005). [CrossRef]

31.

H. Masui, H. Yamada, K. Iso, S. Nakamura, and S. P. DenBaars, “Optical polarization characteristics of m-oriented InGaN/GaN light-emitting diodes with various indium compositions in single-quantum-well structure,” J. Phys. D Appl. Phys. 41(22), 225104 (2008). [CrossRef]

OCIS Codes
(140.2020) Lasers and laser optics : Diode lasers
(140.3430) Lasers and laser optics : Laser theory
(140.5960) Lasers and laser optics : Semiconductor lasers
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: December 2, 2013
Revised Manuscript: January 17, 2014
Manuscript Accepted: January 19, 2014
Published: January 29, 2014

Citation
Ding Li, Hua Zong, Wei Yang, Liefeng Feng, Juan He, Weimin Du, Cunda Wang, Ya-Hong Xie, Zhijian Yang, Bo Shen, Guoyi Zhang, and Xiaodong Hu, "Stimulated emission in GaN-based laser diodes far below the threshold region," Opt. Express 22, 2536-2544 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2536


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References

  1. S. Nakamura, “The roles of structural imperfections in ingan-based blue light-emitting diodes and laser diodes,” Science 281(5379), 956–961 (1998). [CrossRef] [PubMed]
  2. W. Yang, D. Li, N. Liu, Z. Chen, L. Wang, L. Liu, L. Li, C. Wan, W. Chen, X. Hu, W. Du, “Improvement of hole injection and electron overflow by a tapered AlGaN electron blocking layer in InGaN-based blue laser diodes,” Appl. Phys. Lett. 100(3), 031105 (2012). [CrossRef]
  3. C. S. Kim, Y. D. Jang, D. M. Shin, J. H. Kim, D. Lee, Y. H. Choi, M. S. Noh, K. J. Yee, “Estimation of relative defect densities in InGaN laser diodes by induced absorption of photoexcited carriers,” Opt. Express 18(26), 27136–27141 (2010). [CrossRef] [PubMed]
  4. D. Scholz, H. Braun, U. T. Schwarz, S. Brüninghoff, D. Queren, A. Lell, U. Strauss, “Measurement and simulation of filamentation in (Al,In)GaN laser diodes,” Opt. Express 16(10), 6846–6859 (2008). [CrossRef] [PubMed]
  5. T. Meyer, H. Braun, U. T. Schwarz, S. Tautz, M. Schillgalies, S. Lutgen, U. Strauss, “Spectral dynamics of 405 nm (Al,In)GaN laser diodes grown on GaN and SiC substrate,” Opt. Express 16(10), 6833–6845 (2008). [CrossRef] [PubMed]
  6. O. H. Nam, K. H. Ha, H. Y. Ryu, S. N. Lee, T. H. Chang, K. K. Choi, J. K. Son, J. H. Chae, S. H. Chae, H. S. Paek, Y. J. Sung, T. Sakong, H. G. Kim, H. S. Kim, Y. H. Kim, Y. J. Park, “High power AlInGaN-based blue-violet laser diodes,” Proc. SPIE 6133, 61330N (2006). [CrossRef]
  7. C. Sasaoka, K. Fukuda, M. Ohya, K. Shiba, M. Sumino, S. Kohmoto, K. Naniwae, M. Matsudate, E. Mizuki, I. Masumoto, R. Kobayashi, K. Kudo, T. Sasaki, K. Nishi, “Over 1000 mW single mode operation of planar inner stripe blue-violet laser diodes,” Phys. Status Solidi A 203(7), 1824–1828 (2006). [CrossRef]
  8. S. Nakamura, “High-power InGaN-based blue laser diodes with a long lifetime,” J. Cryst. Growth 195(1-4), 242–247 (1998). [CrossRef]
  9. S. Takagi, Y. Enya, T. Kyono, M. Adachi, Y. Yoshizumi, T. Sumitomo, Y. Yamanaka, T. Kumano, S. Tokuyama, K. Sumiyoshi, N. Saga, M. Ueno, K. Katayama, T. Ikegami, T. Nakamura, K. Yanashima, H. Nakajima, K. Tasai, K. Naganuma, N. Fuutagawa, Y. Takiguchi, T. Hamaguchi, M. Ikeda, “High-power (over 100 mW) green laser diodes on semipolar {20(2)over-bar1} GaN substrates operating at wavelengths beyond 530 nm,” Appl. Phys. Express 5(8), 082102 (2012). [CrossRef]
  10. A. Khan, “Semiconductor photonics: Laser diodes go green,” Nat. Photonics 3(8), 432–434 (2009). [CrossRef]
  11. T. Miyoshi, S. Masui, T. Okada, T. Yanamoto, T. Kozaki, S. Nagahama, T. Mukai, “510–515 nm InGaN-Based Green Laser Diodes on c -Plane GaN Substrate,” Appl. Phys. Express 2, 062201 (2009). [CrossRef]
  12. A. Avramescu, T. Lermer, J. Müller, S. Tautz, D. Queren, S. Lutgen, U. Strauß, “InGaN laser diodes with 50 mW output power emitting at 515 nm,” Appl. Phys. Lett. 95(7), 071103 (2009). [CrossRef]
  13. Y. Yamashita, M. Kuwabara, K. Torii, H. Yoshida, “A 340-nm-band ultraviolet laser diode composed of GaN well layers,” Opt. Express 21(3), 3133–3137 (2013). [CrossRef] [PubMed]
  14. K. Kojima, U. T. Schwarz, M. Funato, Y. Kawakami, S. Nagahama, T. Mukai, “Optical gain spectra for near UV to aquamarine (Al,In)GaN laser diodes,” Opt. Express 15(12), 7730–7736 (2007). [CrossRef] [PubMed]
  15. S. L. Chuang, “Physics of Optoelectronic Devices,” in Physics of Optoelectronic Devices (Wiley-Intescience Publication, New York, 1995), pp. 399.
  16. P. Barnes, T. Paoli, “Derivative measurements of the current-voltage characteristics of double-heterostructure injection lasers,” IEEE J. Quantum Electron. 12(10), 633–639 (1976). [CrossRef]
  17. T. Paoli, P. Barnes, “Saturation of the junction voltage in stripe-geometry (AlGa)As double-heterostructure junction lasers,” Appl. Phys. Lett. 28(12), 714 (1976). [CrossRef]
  18. C. D. Wang, C. Y. Zhu, G. Y. Zhang, J. Shen, L. Li, “Accurate electrical characterization of forward AC behavior of real semiconductor diode: giant negative capacitance and nonlinear interfacial layer,” IEEE Trans. Electron. Dev. 50(4), 1145–1148 (2003). [CrossRef]
  19. L. F. Feng, D. Li, C. Y. Zhu, C. D. Wang, H. X. Cong, X. S. Xie, C. Z. Lu, “Simultaneous sudden changes of electrical behavior at the threshold in laser diodes,” J. Appl. Phys. 102(6), 063102 (2007). [CrossRef]
  20. L. F. Feng, D. Li, C. Y. Zhu, C. D. Wang, H. X. Cong, G. Y. Zhang, W. M. Du, “Deep saturation of junction voltage at large forward current of light-emitting diodes,” J. Appl. Phys. 102(9), 094511 (2007). [CrossRef]
  21. D. Li, W. Yang, L. F. Feng, P. W. Roth, J. He, W. M. Du, Z. J. Yang, C. D. Wang, G. Y. Zhang, X. D. Hu, “Stimulated emission related anomalous change of electrical parameters at threshold in GaN-based laser diodes,” Appl. Phys. Lett. 102(12), 0123501 (2013). [CrossRef]
  22. E. Feltin, A. Castiglia, G. Cosendey, L. Sulmoni, J. F. Carlin, N. Grandjean, M. Rossetti, J. Dorsaz, V. Laino, M. Duelk, C. Velez, “Broadband blue superluminescent light-emitting diodes based on GaN,” Appl. Phys. Lett. 95(8), 081107 (2009). [CrossRef]
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  24. S. Ling, T. Lu, S. Chang, J. Chen, H. Kuo, S. Wang, “Low efficiency droop in blue-green m-plane InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 96(23), 231101 (2010). [CrossRef]
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