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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 10 — May. 12, 2008
  • pp: 6833–6845
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Spectral dynamics of 405 nm (Al,In)GaN laser diodes grown on GaN and SiC substrate

Tobias Meyer, Harald Braun, Ulrich T. Schwarz, Sönke Tautz, Marc Schillgalies, Stephan Lutgen, and Uwe Strauss  »View Author Affiliations


Optics Express, Vol. 16, Issue 10, pp. 6833-6845 (2008)
http://dx.doi.org/10.1364/OE.16.006833


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Abstract

We investigate the spectral properties of violet 405 nm (Al,In)GaN laser diodes (LDs). Depending on the substrate the LDs are grown on, the lasing spectra show significant differences. LDs grown on low dislocation GaN substrate have a broad spectrum with several longitudinal modes, while LDs grown on SiC substrate are lasing on a single longitudinal mode. With increasing current, the laser emission of LDs grown on SiC substrate jumps from one longitudinal mode to another (mode hopping), whereas GaN substrate LDs show a smooth but asymmetric mode comb. The different envelopes of these spectra can be understood by assuming a variation of the gain for each individual longitudinal mode. With a high spectral resolution setup, we measure the gain of each longitudinal mode, employing the Hakki–Paoli method. Measurements show a slightly fluctuating gain for the modes of GaN substrate LDs, but much larger fluctuations for LDs on SiC substrate. We carry out simulations of the longitudinal mode spectrum of (Al,In)GaN laser diodes using a rate equation model with nonlinear gain (self saturation, symmetric and asymmetric cross saturation) and including gain fluctuations. With a set of parameters which is largely identical for LDs on either substrate, the simulated spectra truly resemble those typical for LDs on GaN or SiC substrate.

© 2008 Optical Society of America

1. Introduction

Nitride based semiconductor laser diodes (LDs) have already found their way into today’s consumer electronics and optical storage devices. In spite of their current application, (Al,In)GaN LDs have many properties which are not yet investigated, but play an important role both for future applications and for the basic understanding of nitride based optoelectronic devices. Issues of current research focus are, among others, the extension of the accessible wavelength range towards deep UV and green [1

1. M. Kneissl, Z. Yang, M. Teepe, C. Knollenberg, O. Schmidt, P. Kiesel, N. M. Johnson, S. Schujman, and L. J. Schowalter, “Ultraviolet semiconductor laser diodes on bulk AlN,” Appl. Phys. Lett. 101, 123103 (2007).

, 2

2. T. Miyoshi, T. Yanamoto, T. Kozaki, S. Nagahama, Y. Narukawa, M. Sano, T. Yamada, and T. Mukai, “Recent status of white LEDs and nitride LDs,” Proc. SPIE 6894, 689414 (2008). [CrossRef]

], (Al,In)GaN VCSELs [3

3. T.-C. Lu, C.-C. Kao, H.-C. Kuo, G.-S. Huang, and S.-C. Wang, “CW lasing of current injection blue GaN-based vertical cavity surface emitting laser,” Appl. Phys. Lett. 92, 141102 (2008). [CrossRef]

], optical gain [4

4. 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, 7730 (2007). [CrossRef] [PubMed]

], waveguide properties [5

5. D. F. Feezell, M. C. Schmidt, R. M. Farrell, K.-C. Kim, M. Saito, K. Fujito, D. A. Cohen, J. S. Speck, S. P. Den-Baars, and S. Nakamura, “AlGaN-cladding-free nonpolar InGaN/GaN laser diodes,” Jpn. J. Appl. Phys. 46, L284 (2007). [CrossRef]

], and nonpolar and semipolar (Al,In)GaN LDs [6

6. R. M. Farrell, D. F. Feezell, M. C. Schmidt, D. A. Haeger, K. M. Kelchner, K. Iso, H. Yamada, M. Saito, K. Fujito, D. A. Cohen, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Continuous-wave operation of AlGaN-cladding-free nonpolar m-plane InGaN/GaN laser diodes,” Jpn. J. Appl. Phys.46, L761 (2007). [CrossRef]

, 7

7. K. Kojima, M. Funato, Y. Kawakami, S. Masui, S. Nagahama, and T. Mukai, “Stimulated emission at 474nm from an InGaN laser diode structure grown on a (112̄2) GaN substrate,” Appl. Phys. Lett. 91, 251107 (2007). [CrossRef]

]. While long living (Al,In)GaN LDs are on the marked, the understanding of degradation mechanisms is still an issue of current research [8

8. M. Rosetti, R. M. Smeeton, W.-S. Tan, M. Kauer, S. E. Hooper, J. Heffernan, H. Xiu, and C. J. Humphreys, “Degradation of InGaN/GaN laser diodes analyzed by microphotoluminescence and microelectroluminescence mappings,” Appl. Phys. Lett. 92, 151110 (2008). [CrossRef]

].

2. Current dependency of laser spectra

We investigate two types of 405 nm (Al,In)GaN laser diodes from OSRAM Opto Semiconductors. One of them was grown on low dislocation density GaN substrate, the other on SiC substrate. GaN substrates offer several advantages in comparison to SiC substrate, such as lower internal losses and suppression of degradation, but they are more expensive than SiC substrates. The laser diodes are standard test structures with a ridge waveguide, as described in detail e.g. in [16

16. B. Witzigmann, V. Laino, M. Luisier, F. Roemer, G. Feicht, and U. T. Schwarz, “Simulation and design of optical gain in In(Al)GaN/GaN short wavelength lasers,” Proc. SPIE 6184, 61840E (2006). [CrossRef]

].

Above threshold spectra of investigated lasers on GaN substrate show a characteristic shape, as seen in Fig. 1(a). Several longitudinal modes are lasing, some of them having a higher amplitude than the others. Figure 2 shows the current dependency of the spectrum of the GaN substrate LD. At threshold, some longitudinal modes at approximately 405.9 nm start lasing. With increasing current, the modes shift slightly to the red side of the spectrum, because the effective refractive index and the resonator length increase with temperature. Additionally, the envelope of the spectrum shifts to longer wavelengths, as the band gap and thus the transition energy of the quantum wells decrease with increasing temperature [17

17. Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34, 149 (1967). [CrossRef]

], which is affected by the injection current.

Fig. 1. (a) The spectrum of a LD on GaN substrate at I=1.3×I th. (b) The spectrum of a LD on SiC substrate at I=1.3×I th.

SiC substrate LDs exhibit a rather different spectrum. Figure 1(b) shows the spectrum at 1.3 times the threshold current I th, where only one single longitudinal mode is lasing. This behavior can be seen over a wide range of the injection current I. Some mA above threshold, a single longitudinal mode starts lasing (see Fig. 3). As the current increases, the laser emission jumps to another longitudinal mode with greater wavelength. This phenomenon is known as mode hopping and can result in an increase of the intensity noise. At higher currents, the emission shows several jumps to longer wavelengths, which is already known from SiC substrate LDs under pulsed operation [18

18. C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. Härle, and D. Hofstetter, “Time resolved study of laser diode characteristics during pulsed operation,” Phys. Status Solidi C 0, 2283 (2003). [CrossRef]

]. In some of the investigated SiC substrate LDs, the number of emitting modes at high currents increases, but the spectra never have such a regular envelope as GaN substrate LD spectra at comparable currents.

The jumps of the emission only occur between longitudinal modes of the same mode comb, i.e. the LD is always emitting on the same lateral and transverse mode and no other lateral or transverse modes are emitting. If other lateral or transverse modes were emitting, another mode comb with a different mode spacing would appear. We observe a second mode comb only for laser diodes with broader ridges [19

19. H. Braun, H.-M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strauß, “Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes,” J. Appl. Phys. 103, 073102 (2008). [CrossRef]

, 20

20. H. Braun, T. Meyer, D. Scholz, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strauß, “Spectral and time resolved scanning near-field microscopy of broad area 405 nm InGaN laser diode dynamics,” Phys. Status Solidi C (to be published).

].

3. Gain fluctuations

Fig. 2. The current dependency of the spectrum of a LD on GaN substrate. In this density plot color represents the intensity of the longitudinal modes (white: zero; blue: low; red: high intensity).
Fig. 3. The current dependency of the spectrum of a LD on SiC substrate. Density plot in analogy to Fig. 2.

Figures 4(a) and (b) show electroluminescence (EL) spectra belowthreshold for GaN and SiC substrate LDs, respectively. In contrast to the spectra above threshold, many longitudinal modes are visible. The spectra have an envelope which is approximately parabolic, due to the shape of the gain spectrum in the immediate vicinity of the gain maximum [21

21. B. Witzigmann, V. Laino, M. Luisier, U. T. Schwarz, G. Feicht, W. Wegscheider, K. Engl, M. Furitsch, A. Leber, A. Lell, and V. Härle, “Microscopic analysis of optical gain in InGaN/GaN quantum wells,” Appl. Phys. Lett. 88, 021104 (2006). [CrossRef]

, 22

22. U. T. Schwarz, H. Braun, K. Kojima, M. Funato, Y. Kawakami, S. Nagahama, and T. Mukai, “Investigation and comparison of optical gain spectra of (Al,In)GaN laser diodes emitting in the 375 nm to 470 nm spectral range,” Proc. SPIE 6485, 648506 (2007). [CrossRef]

]. The difference between SiC and GaN substrate LDs can be seen in these spectra below threshold, but is not as pronounced as above threshold. Figure 4(b), the SiC substrate LD spectrum, shows variations in the amplitude of the modes. They are also present in the GaN substrate spectrum, however less prominent. This leads to the assumption that gain spectra of LDs on SiC substrate fluctuate more than those for LDs on GaN substrate. These fluctuations are time independent and reproducible for individual LDs.

Fig. 4. The spectrum of a GaN substrate LD (a) and a SiC substrate LD (b) slightly below threshold. Intensities are given in arbitrary units. (c) Magnification of a single longitudinal mode from (a).

The Hakki–Paoli method provides the possibility to estimate the gain from EL spectra below threshold [9

9. B. W. Hakki and T. L. Paoli, “cw degradation at 300 K of GaAs double-heterostructure junction lasers. II. Electronic gain,” J. Appl. Phys. 44, 4113 (1973). [CrossRef]

, 10

10. B. W. Hakki and T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299 (1974). [CrossRef]

], but the narrow spacing of the longitudinal modes for (Al,In)GaN LDs request a very high spectral resolution setup [23

23. U. T. Schwarz, E. Sturm, W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, “Optical gain, carrier-induced phase shift, and linewidth enhancement factor in InGaN quantum well lasers,” Appl. Phys. Lett. 83, 4095 (2003). [CrossRef]

]. With a double Czerny–Turner monochromator operated in second order, we achieve a resolution of approximately 1.5 pm. This allows us to resolve the maxima and minima of the longitudinal mode comb with very high accuracy, which is mandatory for the Hakki–Paoli method. Figure 4(c) shows a single longitudinal mode, the maximum and minimum of this mode is clearly resolved.

As explained before, we expect higher variations in the gain spectra for SiC substrate LDs than for GaN substrate LDs. Figure 5 shows the gain spectra determined from the two EL spectra shown in Fig. 4(a) and (b), each point represents the gain of a longitudinal mode. Both the GaN substrate and SiC substrate LD gain spectra have a parabolic shape, but show slight deviations of the ideal form, herein after called gain fluctuations. These gain fluctuations exist for both the GaN and SiC substrate diodes, but it can be clearly seen that the gain fluctuations are higher for the SiC substrate diode than for the GaN substrate LD.

4. Possible origins of the gain fluctuations

The fluctuations of the gain of the single longitudinal modes can be either due to a different gain or loss observed by each mode, i.e. a variation of the imaginary part of the refractive index, or by a modulation of the real part of the refractive index along the waveguide. Peters and Cassidy attribute irregular longitudinal mode spectra to interference caused by scattering from randomly distributed scattering centers along the ridge [24

24. F. H. Peters and D. T. Cassidy, “Strain and scattering related spectral output of 1.3-µm InGaAsP semiconductor diode lasers,” Appl. Optics 30, 1036 (1991). [CrossRef]

]. This mechanism could also be active in (Al,In)GaN LDs, where an inhomogeneous distribution of threading dislocations may cause inhomogeneous strain and local scattering centers. For LDs on GaN and SiC substrates the defect density and therefore the strain and scattering center distribution are different. Corbett and McDonald employ this effect to force a 1.3µm Fabry–Perot LD to single mode operation by etchings slots acting as scatterers at certain positions along the ridge waveguide [25

25. B. Corbett and D. McDonald, “Single longitudinal mode ridge waveguide 1.3 µm Fabry-Perot laser by modal perturbation,” Electron. Lett. 31, 2181 (1995). [CrossRef]

, 26

26. B. Roycroft, P. Lambkin, S. Riesner, B. Corbett, and J. F. Donegan, “Transition from perturbed to coupled-cavity behavior with asymmetric spectral emission in ridge lasers emitting at 1.55µm,” IEEE Photon. Technol. Lett. 19, 58 (2007). [CrossRef]

]. The optimum position of these intentionally introduced scatterers can be determined in an perturbative inverse scattering approach [27

27. S. O’Brien, A. Amann, R. Fehse, S. Osborne, and E. P. O’Reilly, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046 (2006). [CrossRef]

]. For a few strong scatterers the LD is in the coupled cavity regime. For an (Al,In)GaN LD with a single crack in the waveguide we observed a strong periodic modulation of the longitudinal mode gain together with a side–peak in the Fourier transform of the longitudinal mode spectrum [28

28. U. T. Schwarz, W. Wegscheider, A. Lell, and V. Härle, “Nitride-based in-plane laser diodes with vertical current path,” Proc. SPIE 5365, 267 (2004). [CrossRef]

]. The small and irregular fluctuation of the gain for the present LDs (see Fig. 5) is distinctly different from that regime of one or a few strong scattering centers. Another mechanism causing a second feedback path are substrate modes. They cause a periodic modulation of the gain spectra with a much longer period of approximately 2nm in similar (Al,In)GaN laser diodes [29

29. V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. O. Schillgalies, M. Furitsch, A. Lell, and V. Härle, “Substrate Modes of (Al,In)GaN Semiconductor Laser Diodes on SiC and GaN Substrates,” IEEE J. Quantum Electron. 43, 16 (2007). [CrossRef]

]. In the present LDs the n–side cladding layer thickness was increased to suppress substrate modes [30

30. U. Strauss, C. Eichler, C. Rumbolz, A. Lell, S. Lutgen, S. Tautz, M. O. Schillgalies, and S. Brüninghoff, “Beam quality of blue InGaN lasers for projection,” Phys. Status Solidi C (to be published).

]. We cannot rule out that the roughness of the etched ridge waveguide is affected by the defect density. This could be a mechanism causing different losses and/or feedback to individual longitudinal modes, adding to the differences between LDs on SiC and GaN substrate.

Fig. 5. Gain spectra for a LD on GaN and SiC substrate, respectively. Each point is the gain of an individual longitudinal mode.

There is manifold evidence of gain fluctuations on several length scales for (Al,In)GaN LDs. Therefore we favor gain fluctuations as origin for the irregular longitudinal mode spectrum, while we cannot exclude the mechanism acting through feedback from irregularly spaced scatterers. There are several mechanisms that can cause an increase or decrease of the gain for specific longitudinal modes. Spatial fluctuations of the quantum well depth have been proposed as origin [31

31. C. Eichler, S.-S. Schad, F. Scholz, D. Hofstetter, S. Miller, A. Weimar, A. Lell, and V. Härle, “Observation of temperature-independent longitudinal-mode patterns in violet-blue InGaN-based laser diodes,” IEEE Photon. Technol. Lett. 17, 1782 (2005). [CrossRef]

]. The gain of an individual longitudinal mode is then given by the overlap of the mode intensity distribution and the gain profile along the waveguide. Therefore gain fluctuation is bound to the individual longitudinal modes and not to the wavelength. With increasing current, the temperature of the waveguide changes, leading to a change of the effective refractive index, resonator length, and wavelength shift of each longitudinal mode. However, the positions of the oscillation maxima and nodes of the longitudinal modes remain on the same locations in the waveguide, as well as the gain and loss centers. Thus every longitudinal mode experiences the same gain and loss centers across the full injection current range. This was confirmed by experiments where we measured the gain for different temperatures.

We tried unsuccessfully to estimate the number and size of the centers causing additional gain or loss from the Hakki–Paoli gain spectra. The number of points along the gain curve is given by the number of longitudinal modes and thus fixed for a given resonator length. While this discrete spectrum does not appear to be completely random, as would be the case for a large (>100) number of scatterers, the Fourier spectrum does not show distinct peaks, as expected for a few (<5) scatterers.

5. Multimode rate equation model with gain fluctuations

We use a multimode rate equation model with self– and cross–saturation for semiconductor lasers (see e.g. [11

11. G. P. Agrawal and N. K. Dutta, Semiconductor lasers, 2nd ed. (Kluwer Academic Publishers, 1993).

, 13

13. L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, Wiley series in microwave and optical engineering (Wiley, 1995).

]) as described by Yamada et al. [12

12. M. Yamada, “Advanced theory of semiconductor lasers,” in Handbook of semiconductor lasers and photonic integrated circuits, Y. Suematsu and A. R. Adams , eds. (Chapman & Hall, 1994).

, 40

40. M. Ahmed, M. Yamada, and M. Saito, “Numerical modeling of intensity and phase noise in semiconductor lasers,” IEEE J. Quantum Electron. 37, 1600 (2001). [CrossRef]

, 41

41. M. Ahmed, M. Yamada, and S. Abdulrahmann, “A multimode simulation model of mode-competition low-frequency noise in semiconductor lasers,” Fluctuation and Noise Letters 1, L163 (2001). [CrossRef]

, 42

42. M. Ahmed and M. Yamada, “Influence of instantaneous mode competition on the dynamics of semiconductor lasers,” IEEE J. Quantum Electron. 38, 682 (2002). [CrossRef]

]. In this model, we include gain fluctuations and other modifications.

The dynamics is described in the rate equations for the electron number N and the photon numbers Sp for the longitudinal modes p.

dNdt=ηinjIinjqeNτspg~pSp
(1)
dSpdt=(g~pg~th)Sp+βpNτr
(2)

The current injected into the laser diode is denoted as I inj, q e is the elementary charge. η inj describes the injection efficiency into the quantum wells, as not all electrons and holes will recombine in the wells. τ s is the spontaneous carrier lifetime, which is given by τ -1 s=τ -1 r+τ -1 nr, where τ r and τ nr are the time constant belonging to the radiative and nonradiative recombination, respectively.

Every longitudinal mode is denoted with a mode number p=0,±1,±2,… and has the wavelength λp. The central mode with p=0, i.e. the mode where the laser emission is highest when reaching laser threshold, has the wavelength λ 0, modes with p>0 lie on the long-wavelength side of the spectrum. th is the threshold gain and is given by

g~th=cvacngr[αint12Lln(1R1R2)].
(3)

c vac stands for the speed of light in vacuum and n gr is the group refractive index of the waveguide. α int are the internal losses of the waveguide, L is the length of the resonator, R 1 and R 2 are the mirror reflectivities.

g~p=ζpApBSpqp(Dpq+Hpq)Sq
(4)

Ap=aΓV[NNgbV(λpλg)2]
(5)
B=92πcvacε0ngr2h¯λ0(ΓτinV)2aRcv2(NNs)
(6)
Dpq=43B(2πcvacτinλp2)2(λpλq)2+1
(7)
Hpq3λp28πcvac(aΓV)2α(NNg)λqλp
(8)

Here, a is the slope coefficient characterizing the linear gain and was measured for the discussed LDs by the Hakki–Paoli method. Γ is the confinement factor into the quantum wells. Ng denotes the transparency electron number and is given by

Ng=ηinjIinjqeτsVaΓg~th.
(9)

V is the volume of the quantum wells. The parameter b describing the dispersion of the gain was derived from the curvature at gain maximum of measured gain spectra. In summary, the linear gain coefficient Ap describes the linear dependence of the gain on the carrier number N and the spectral shape of the gain as a parabola around the gain maximum located at λg.

The other gain coefficients contain the vacuum permittivity ε 0, the intraband relaxation time τ in, the dipole moment of the quantum wells Rcv, the antiguiding or Henry factor α, and the carrier number N s characterizing the saturation coefficient B.

The saturation coefficients play an important role for the shape of the laser spectrum. B leads to a saturation of the gain at high photon numbers and is caused by spectral hole burning. Dpq is called the symmetrical cross–saturation coefficient and influences modes q on the higher and shorter wavelength side of the mode p in the same manner. In contrast, the asymmetrical cross–saturation coefficient Hpq enhances the gain on the longerwavelength side and suppresses the modes on the shorter wavelength side. Thus, it leads to an asymmetrical envelope of the spectrum.

The rate equation for the photon numbers include the spontaneous emission factor βp, which characterizes the fraction of spontaneously generated light that is coupled into the longitudinal mode p [11

11. G. P. Agrawal and N. K. Dutta, Semiconductor lasers, 2nd ed. (Kluwer Academic Publishers, 1993).

, 13

13. L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, Wiley series in microwave and optical engineering (Wiley, 1995).

]. We take into account the Lorentzian shape of the spontaneous emission.

βp=KenΓλp44π2nref2ngrVδλsp(λpλsp)2+δλsp2
(10)

K en is a numerical factor that depends on the waveguiding of the laser (i.e. ridge waveguide or gain guided LD), n ref is the refractive index of the waveguide, δλ sp is the half–width at half–maximum of the spontaneous emission and λ sp is the wavelength of the peak of the spontaneous emission.

Additionally, the shift of both the peak gain and the longitudinal modes has to be considered. Without a current dependent shift, the spectrum would remain nearly unchanged over a wide range of the injection current. As approximation, the shift of the longitudinal modes can be regarded linearly with the injection current I inj:

λp=λ0,th+pΔλ+dλpdIinj(IinjIth)
(11)

λ 0,th is the wavelength of the maximum laser emission at the threshold current I th. Δλ is the mode spacing and g/dI inj is a constant factor given by the current dependent shift of the modes which is estimated from longitudinal mode spectra above threshold. Similarly, the shift of the peak gain is given by

λg=λ0,th+dλgdIinj(IinjIth).
(12)

The constant factor g/dI inj leads to the shift of the peak gain and thus the spectrum’s envelope with increasing current.

A factor yet unmentioned is the gain fluctuations factor ζp. It is included in both the rate equations for electrons and for photons and modifies the linear gain coefficient Ap. For our simulations, we use a gain fluctuations factor given by

ζp=1+δζ·rp
(13)

where rp is a random number given by the standard normal distribution. ζp is a random number which increases or decreases the linear gain Ap independently for every longitudinal mode and is not affected by the injection current. High values for the amplitude δζ lead to large gain fluctuations and a value of δζ=0 would produce a smooth gain spectrum without any fluctuations.

Ropars et al. also observe fluctuations of the gain and an asymmetric envelope of the longitudinal mode spectrum of (Al,In)GaN LDs [43

43. G. Ropars, A. Le Floch, and G. P. Agrawal, “Spectral and spatial dynamics in InGaN blue-violet lasers,” Appl. Phys. Lett. 89, 241128 (2006). [CrossRef]

]. They used gain guided LDs and explained the asymmetric envelope in terms of defocussing which was supported by far-field measurements. As we observe a similar asymmetric envelope for our index guided LDs, where defocussing should play a minor role, we are the opinion that symmetric and asymmetric cross saturation are the origin of the observed asymmetry. The ridge widths of our index guided LDs are between 1.5 µm and 2.5 µm which is narrow enough to guarantee lateral ground mode operation.

6. Simulation of (Al,In)GaN laser spectra with gain fluctuations

We use the multimode rate equation model with gain fluctuations to simulate the current dependency of the spectra of LDs. The parameters used for these simulations are given in tables 1 and 2.

Figure 6 shows a simulated spectrum with GaN substrate parameters. Compared with the measured spectrum (see Fig. 2), the simulation looks quite similar: The longitudinal modes of the simulated spectrum shift to the long wavelength side as well as the envelope of the spectrum, which is due to Eq. 11 and 12. Furthermore, the increasing current broadens the envelope of the spectrum slightly. Without gain fluctuations (i.e. δζ=0), the envelope of the spectrum would have a smooth, slightly asymmetric shape. Here, we use a value for the gain fluctuations of δζ=5×10-4

4. 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, 7730 (2007). [CrossRef] [PubMed]

to describe the gain fluctuations. With this value, the simulated spectra are in

Table 1. Common parameters for GaN and SiC substrate LDs

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In summary, the gain fluctuations of the SiC substrate LD are significantly higher than the

Table 2. Parameters for GaN and SiC substrate LDs, respectively

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Fig. 6. The simulated current dependency of the spectrum of a LD on GaN substrate. Density plot in analogy to Fig. 2.
Fig. 7. The simulated current dependency of the spectrum of a LD on SiC substrate. Density plot in analogy to Fig. 2.

7. Conclusion

We measured above threshold spectra of 405 nm (Al,In)GaN laser diodes grown on SiC and GaN substrates, respectively. While the GaN substrate LD shows a broad spectrum with several longitudinal modes, the SiC substrate LD is lasing on single longitudinal modes with jumps of the laser emission with increasing current. This implies differences in the gain spectra between the LDs, which are demonstrated by high resolution Hakki–Paoli gain measurements, where the SiC substrate LD shows a gain spectrum with larger modeȓtoȓmode fluctuations than the GaN substrate LD.

Furthermore, we provide a parameter set for (Al,In)GaN based laser diodes which can be used with the multimode rate equation model and other types of simulations. In particular the symmetric and asymmetric cross saturation parameters are determined. This allows to describe the asymmetric longitudinal mode spectrum for (Al,In)GaN LDs on GaN substrate. The majority of commercial (Al,In)GaN LDs are grown on GaN substrate, so that the parameter set should provide valuable input for advanced simulations of (Al,In)GaN LDs for various applications ranging from single mode over fast modulation to high output power operation.

References and links

1.

M. Kneissl, Z. Yang, M. Teepe, C. Knollenberg, O. Schmidt, P. Kiesel, N. M. Johnson, S. Schujman, and L. J. Schowalter, “Ultraviolet semiconductor laser diodes on bulk AlN,” Appl. Phys. Lett. 101, 123103 (2007).

2.

T. Miyoshi, T. Yanamoto, T. Kozaki, S. Nagahama, Y. Narukawa, M. Sano, T. Yamada, and T. Mukai, “Recent status of white LEDs and nitride LDs,” Proc. SPIE 6894, 689414 (2008). [CrossRef]

3.

T.-C. Lu, C.-C. Kao, H.-C. Kuo, G.-S. Huang, and S.-C. Wang, “CW lasing of current injection blue GaN-based vertical cavity surface emitting laser,” Appl. Phys. Lett. 92, 141102 (2008). [CrossRef]

4.

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, 7730 (2007). [CrossRef] [PubMed]

5.

D. F. Feezell, M. C. Schmidt, R. M. Farrell, K.-C. Kim, M. Saito, K. Fujito, D. A. Cohen, J. S. Speck, S. P. Den-Baars, and S. Nakamura, “AlGaN-cladding-free nonpolar InGaN/GaN laser diodes,” Jpn. J. Appl. Phys. 46, L284 (2007). [CrossRef]

6.

R. M. Farrell, D. F. Feezell, M. C. Schmidt, D. A. Haeger, K. M. Kelchner, K. Iso, H. Yamada, M. Saito, K. Fujito, D. A. Cohen, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Continuous-wave operation of AlGaN-cladding-free nonpolar m-plane InGaN/GaN laser diodes,” Jpn. J. Appl. Phys.46, L761 (2007). [CrossRef]

7.

K. Kojima, M. Funato, Y. Kawakami, S. Masui, S. Nagahama, and T. Mukai, “Stimulated emission at 474nm from an InGaN laser diode structure grown on a (112̄2) GaN substrate,” Appl. Phys. Lett. 91, 251107 (2007). [CrossRef]

8.

M. Rosetti, R. M. Smeeton, W.-S. Tan, M. Kauer, S. E. Hooper, J. Heffernan, H. Xiu, and C. J. Humphreys, “Degradation of InGaN/GaN laser diodes analyzed by microphotoluminescence and microelectroluminescence mappings,” Appl. Phys. Lett. 92, 151110 (2008). [CrossRef]

9.

B. W. Hakki and T. L. Paoli, “cw degradation at 300 K of GaAs double-heterostructure junction lasers. II. Electronic gain,” J. Appl. Phys. 44, 4113 (1973). [CrossRef]

10.

B. W. Hakki and T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299 (1974). [CrossRef]

11.

G. P. Agrawal and N. K. Dutta, Semiconductor lasers, 2nd ed. (Kluwer Academic Publishers, 1993).

12.

M. Yamada, “Advanced theory of semiconductor lasers,” in Handbook of semiconductor lasers and photonic integrated circuits, Y. Suematsu and A. R. Adams , eds. (Chapman & Hall, 1994).

13.

L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, Wiley series in microwave and optical engineering (Wiley, 1995).

14.

M. Yamada and Y. Suematsu, “Analysis of gain suppression in undoped injection lasers,” J. Appl. Phys. 52, 2653 (1981). [CrossRef]

15.

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semidonductor lasers,” J. Appl. Phys. 66, 81 (1989). [CrossRef]

16.

B. Witzigmann, V. Laino, M. Luisier, F. Roemer, G. Feicht, and U. T. Schwarz, “Simulation and design of optical gain in In(Al)GaN/GaN short wavelength lasers,” Proc. SPIE 6184, 61840E (2006). [CrossRef]

17.

Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34, 149 (1967). [CrossRef]

18.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. Härle, and D. Hofstetter, “Time resolved study of laser diode characteristics during pulsed operation,” Phys. Status Solidi C 0, 2283 (2003). [CrossRef]

19.

H. Braun, H.-M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strauß, “Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes,” J. Appl. Phys. 103, 073102 (2008). [CrossRef]

20.

H. Braun, T. Meyer, D. Scholz, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strauß, “Spectral and time resolved scanning near-field microscopy of broad area 405 nm InGaN laser diode dynamics,” Phys. Status Solidi C (to be published).

21.

B. Witzigmann, V. Laino, M. Luisier, U. T. Schwarz, G. Feicht, W. Wegscheider, K. Engl, M. Furitsch, A. Leber, A. Lell, and V. Härle, “Microscopic analysis of optical gain in InGaN/GaN quantum wells,” Appl. Phys. Lett. 88, 021104 (2006). [CrossRef]

22.

U. T. Schwarz, H. Braun, K. Kojima, M. Funato, Y. Kawakami, S. Nagahama, and T. Mukai, “Investigation and comparison of optical gain spectra of (Al,In)GaN laser diodes emitting in the 375 nm to 470 nm spectral range,” Proc. SPIE 6485, 648506 (2007). [CrossRef]

23.

U. T. Schwarz, E. Sturm, W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, “Optical gain, carrier-induced phase shift, and linewidth enhancement factor in InGaN quantum well lasers,” Appl. Phys. Lett. 83, 4095 (2003). [CrossRef]

24.

F. H. Peters and D. T. Cassidy, “Strain and scattering related spectral output of 1.3-µm InGaAsP semiconductor diode lasers,” Appl. Optics 30, 1036 (1991). [CrossRef]

25.

B. Corbett and D. McDonald, “Single longitudinal mode ridge waveguide 1.3 µm Fabry-Perot laser by modal perturbation,” Electron. Lett. 31, 2181 (1995). [CrossRef]

26.

B. Roycroft, P. Lambkin, S. Riesner, B. Corbett, and J. F. Donegan, “Transition from perturbed to coupled-cavity behavior with asymmetric spectral emission in ridge lasers emitting at 1.55µm,” IEEE Photon. Technol. Lett. 19, 58 (2007). [CrossRef]

27.

S. O’Brien, A. Amann, R. Fehse, S. Osborne, and E. P. O’Reilly, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046 (2006). [CrossRef]

28.

U. T. Schwarz, W. Wegscheider, A. Lell, and V. Härle, “Nitride-based in-plane laser diodes with vertical current path,” Proc. SPIE 5365, 267 (2004). [CrossRef]

29.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. O. Schillgalies, M. Furitsch, A. Lell, and V. Härle, “Substrate Modes of (Al,In)GaN Semiconductor Laser Diodes on SiC and GaN Substrates,” IEEE J. Quantum Electron. 43, 16 (2007). [CrossRef]

30.

U. Strauss, C. Eichler, C. Rumbolz, A. Lell, S. Lutgen, S. Tautz, M. O. Schillgalies, and S. Brüninghoff, “Beam quality of blue InGaN lasers for projection,” Phys. Status Solidi C (to be published).

31.

C. Eichler, S.-S. Schad, F. Scholz, D. Hofstetter, S. Miller, A. Weimar, A. Lell, and V. Härle, “Observation of temperature-independent longitudinal-mode patterns in violet-blue InGaN-based laser diodes,” IEEE Photon. Technol. Lett. 17, 1782 (2005). [CrossRef]

32.

N. K. van der Laak, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “Role of gross well-width fluctuations in bright, green-emitting single InGaN/GaN quantum well structures,” Appl. Phys. Lett. 90, 121911 (2007). [CrossRef]

33.

U. Strauß, S. Brüninghoff, M. Schillgalies, C. Vierheilig, N. Gmeinwieser, V. Kümmler, G. Brüderl, S. Lutgen, A. Avramescu, D. Dini, C. Eichler, A. Lell, and U. T. Schwarz. “True blue InGaN laser for pico size projectors,” Proc. SPIE 6894, 689417 (2008). [CrossRef]

34.

R. A. Oliver, M. J. Kappers, C. J. Humphreys, and G. A. D. Briggs, “Growth modes in heteroepitaxy of InGaN on GaN,” J. Appl. Phys. 97, 013707 (2005). [CrossRef]

35.

H. Sato, T. Sugahara, Y. Naoi, and S. Sakai, “Compositional inhomogeneity of InGaN grown on sapphire and bulk GaN substrates by metalorganic chemical vapor deposition,” Jpn. J. Appl. Phys. 37, 2013 (1998). [CrossRef]

36.

K. Akita, T. Kyono, Y. Yoshizumi, H. Kitabayashi, and K. Katayama, “Improvements of external quantum efficiency of InGaN-based blue light-emitting diodes at high current density using GaN substrates,” J. Appl. Phys. 101, 033104 (2007). [CrossRef]

37.

N. Duxbury, U. Bangert, P. Dawson, E. J. Thrush, W. Van der Stricht, K. Jacobs, and I. Moerman, “Indium segregation in InGaN quantum-well structures,” Appl. Phys. Lett. 76, 1600 (2000). [CrossRef]

38.

A. Hangleiter, F. Hitzel, C. Netzel, D. Fuhrmann, U. Rossow, G. Ade, and P. Hinze, “Suppression of nonradiative recombination by V-shaped pits in GaInN/GaN quantum wells produces a large increase in the light emission efficiency,” Phys. Rev. Lett. 95 , 127, 402 (2005).

39.

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1-xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76, 155322 (2007). [CrossRef]

40.

M. Ahmed, M. Yamada, and M. Saito, “Numerical modeling of intensity and phase noise in semiconductor lasers,” IEEE J. Quantum Electron. 37, 1600 (2001). [CrossRef]

41.

M. Ahmed, M. Yamada, and S. Abdulrahmann, “A multimode simulation model of mode-competition low-frequency noise in semiconductor lasers,” Fluctuation and Noise Letters 1, L163 (2001). [CrossRef]

42.

M. Ahmed and M. Yamada, “Influence of instantaneous mode competition on the dynamics of semiconductor lasers,” IEEE J. Quantum Electron. 38, 682 (2002). [CrossRef]

43.

G. Ropars, A. Le Floch, and G. P. Agrawal, “Spectral and spatial dynamics in InGaN blue-violet lasers,” Appl. Phys. Lett. 89, 241128 (2006). [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

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: March 10, 2008
Revised Manuscript: April 21, 2008
Manuscript Accepted: April 21, 2008
Published: April 28, 2008

Citation
Tobias Meyer, Harald Braun, Ulrich T. Schwarz, Sönke Tautz, Marc Schillgalies, Stephan Lutgen, and Uwe Strauss, "Spectral dynamics of 405 nm (Al,In)GaN laser diodes grown on GaN and SiC substrate," Opt. Express 16, 6833-6845 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-6833


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References

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  2. T. Miyoshi, T. Yanamoto, T. Kozaki, S. Nagahama, Y. Narukawa, M. Sano, T. Yamada, and T. Mukai, "Recent status of white LEDs and nitride LDs," Proc. SPIE 6894, 689414 (2008). [CrossRef]
  3. T.-C. Lu, C.-C. Kao, H.-C. Kuo, G.-S. Huang, and S.-C. Wang, "CW lasing of current injection blue GaN-based vertical cavity surface emitting laser," Appl. Phys. Lett. 92, 141102 (2008). [CrossRef]
  4. 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, 7730 (2007). [CrossRef] [PubMed]
  5. D. F. Feezell, M. C. Schmidt, R. M. Farrell, K.-C. Kim, M. Saito, K. Fujito, D. A. Cohen, J. S. Speck, S. P. Den-Baars, and S. Nakamura, "AlGaN-cladding-free nonpolar InGaN/GaN laser diodes," Jpn. J. Appl. Phys. 46, L284 (2007). [CrossRef]
  6. R. M. Farrell, D. F. Feezell, M. C. Schmidt, D. A. Haeger, K.M. Kelchner, K. Iso, H. Yamada, M. Saito, K. Fujito, D. A. Cohen, J. S. Speck, S. P. DenBaars, and S. Nakamura, "Continuous-wave operation of AlGaN-cladding-free nonpolar m-plane InGaN/GaN laser diodes," Jpn. J. Appl. Phys. 46, L761 (2007). [CrossRef]
  7. K. Kojima, M. Funato, Y. Kawakami, S. Masui, S. Nagahama, and T. Mukai, "Stimulated emission at 474nm from an InGaN laser diode structure grown on a (11¯22) GaN substrate," Appl. Phys. Lett. 91, 251107 (2007). [CrossRef]
  8. M. Rosetti, R. M. Smeeton, W.-S. Tan, M. Kauer, S. E. Hooper, J. Heffernan, H. Xiu, and C. J. Humphreys, "Degradation of InGaN/GaN laser diodes analyzed by micro-photoluminescence and micro-electroluminescence mappings," Appl. Phys. Lett. 92, 151110 (2008). [CrossRef]
  9. B. W. Hakki and T. L. Paoli, "cw degradation at 300 K of GaAs double-heterostructure junction lasers. II. Electronic gain," J. Appl. Phys. 44, 4113 (1973). [CrossRef]
  10. B. W. Hakki and T. L. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," J. Appl. Phys. 46, 1299 (1974). [CrossRef]
  11. G. P. Agrawal and N. K. Dutta, Semiconductor lasers, 2nd ed. (Kluwer Academic Publishers, 1993).
  12. M. Yamada, "Advanced theory of semiconductor lasers," in Handbook of semiconductor lasers and photonic integrated circuits, Y. Suematsu and A. R. Adams, eds. (Chapman & Hall, 1994).
  13. L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, Wiley series in microwave and optical engineering (Wiley, 1995).
  14. M. Yamada and Y. Suematsu, "Analysis of gain suppression in undoped injection lasers," J. Appl. Phys. 52, 2653 (1981). [CrossRef]
  15. M. Yamada, "Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers," J. Appl. Phys. 66, 81 (1989). [CrossRef]
  16. B. Witzigmann, V. Laino, M. Luisier, F. Roemer, G. Feicht, and U. T. Schwarz, "Simulation and design of optical gain in In(Al)GaN/GaN short wavelength lasers," Proc. SPIE 6184, 61840E (2006). [CrossRef]
  17. Y. P. Varshni, "Temperature dependence of the energy gap in semiconductors," Physica 34, 149 (1967). [CrossRef]
  18. C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. Härle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003). [CrossRef]
  19. H. Braun, H.-M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008). [CrossRef]
  20. H. Braun, T. Meyer, D. Scholz, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Spectral and time resolved scanning near-field microscopy of broad area 405 nm InGaN laser diode dynamics,"Phys. Status Solidi C (to be published).
  21. B. Witzigmann, V. Laino, M. Luisier, U. T. Schwarz, G. Feicht, W. Wegscheider, K. Engl, M. Furitsch, A. Leber, A. Lell, and V. Härle, "Microscopic analysis of optical gain in InGaN/GaN quantum wells," Appl. Phys. Lett. 88, 021104 (2006). [CrossRef]
  22. U. T. Schwarz, H. Braun, K. Kojima, M. Funato, Y. Kawakami, S. Nagahama, and T. Mukai, "Investigation and comparison of optical gain spectra of (Al,In)GaN laser diodes emitting in the 375 nm to 470 nm spectral range," Proc. SPIE 6485, 648506 (2007). [CrossRef]
  23. U. T. Schwarz, E. Sturm, W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Optical gain, carrier-induced phase shift, and linewidth enhancement factor in InGaN quantum well lasers," Appl. Phys. Lett. 83, 4095 (2003). [CrossRef]
  24. F. H. Peters and D. T. Cassidy, "Strain and scattering related spectral output of 1.3-?m InGaAsP semiconductor diode lasers," Appl. Optics 30, 1036 (1991). [CrossRef]
  25. B. Corbett and D. McDonald, "Single longitudinal mode ridge waveguide 1.3�??m Fabry-Perot laser by modal perturbation," Electron. Lett. 31, 2181 (1995). [CrossRef]
  26. B. Roycroft, P. Lambkin, S. Riesner, B. Corbett, and J. F. Donegan, "Transition from perturbed to coupled-cavity behavior with asymmetric spectral emission in ridge lasers emitting at 1.55?m," IEEE Photon. Technol. Lett. 19, 58 (2007). [CrossRef]
  27. S. O�??Brien, A. Amann, R. Fehse, S. Osborne, and E. P. O�??Reilly, "Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach," J. Opt. Soc. Am. B 23, 1046 (2006). [CrossRef]
  28. U. T. Schwarz, W. Wegscheider, A. Lell, and V. Härle, "Nitride-based in-plane laser diodes with vertical current path," Proc. SPIE 5365, 267 (2004) [CrossRef]
  29. V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. O. Schillgalies, M. Furitsch, A. Lell, and V. H¨arle, "Substrate Modes of (Al,In)GaN Semiconductor Laser Diodes on SiC and GaN Substrates," IEEE J. Quantum Electron. 43, 16 (2007) [CrossRef]
  30. U. Strauss, C. Eichler, C. Rumbolz, A. Lell, S. Lutgen, S. Tautz, M. O. Schillgalies, and S. Brüninghoff, "Beam quality of blue InGaN lasers for projection," Phys. Status Solidi C (to be published).
  31. C. Eichler, S.-S. Schad, F. Scholz, D. Hofstetter, S. Miller, A. Weimar, A. Lell, and V. Härle, "Observation of temperature-independent longitudinal-mode patterns in violet-blue InGaN-based laser diodes," IEEE Photon. Technol. Lett. 17, 1782 (2005). [CrossRef]
  32. N. K. van der Laak, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, "Role of gross well-width fluctuations in bright, green-emitting single InGaN/GaN quantum well structures," Appl. Phys. Lett. 90, 121911 (2007). [CrossRef]
  33. U. Strau�?, S. Brüninghoff, M. Schillgalies, C. Vierheilig, N. Gmeinwieser, V. Kümmler, G. Brüderl, S. Lutgen, A. Avramescu, D. Dini, C. Eichler, A. Lell, and U. T. Schwarz. "True blue InGaN laser for pico size projectors," Proc. SPIE 6894, 689417 (2008). [CrossRef]
  34. R. A. Oliver, M. J. Kappers, C. J. Humphreys, and G. A. D. Briggs, "Growth modes in heteroepitaxy of InGaN on GaN," J. Appl. Phys. 97, 013707 (2005). [CrossRef]
  35. H. Sato, T. Sugahara, Y. Naoi, and S. Sakai, "Compositional inhomogeneity of InGaN grown on sapphire and bulk GaN substrates by metalorganic chemical vapor deposition," Jpn. J. Appl. Phys. 37, 2013 (1998). [CrossRef]
  36. K. Akita, T. Kyono, Y. Yoshizumi, H. Kitabayashi, and K. Katayama, "Improvements of external quantum efficiency of InGaN-based blue light-emitting diodes at high current density using GaN substrates," J. Appl. Phys. 101, 033104 (2007). [CrossRef]
  37. N. Duxbury, U. Bangert, P. Dawson, E. J. Thrush, W. Van der Stricht, K. Jacobs, and I. Moerman, "Indium segregation in InGaN quantum-well structures," Appl. Phys. Lett. 76, 1600 (2000). [CrossRef]
  38. A. Hangleiter, F. Hitzel, C. Netzel, D. Fuhrmann, U. Rossow, G. Ade, and P. Hinze, "Suppression of non-radiative recombination by V-shaped pits in GaInN/GaN quantum wells produces a large increase in the light emission efficiency," Phys. Rev. Lett. 95, 127, 402 (2005).
  39. C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, "Emission and recombination characteristics of Ga1�??xInxN/GaN quantum well structures with nonradiative recombination suppression by V- shaped pits," Phys. Rev. B 76, 155322 (2007). [CrossRef]
  40. M. Ahmed, M. Yamada, and M. Saito, "Numerical modeling of intensity and phase noise in semiconductor lasers," IEEE J. Quantum Electron. 37, 1600 (2001). [CrossRef]
  41. M. Ahmed, M. Yamada, and S. Abdulrahmann, "A multimode simulation model of mode-competition low-frequency noise in semiconductor lasers," Fluctuation and Noise Letters 1, L163 (2001). [CrossRef]
  42. M. Ahmed and M. Yamada, "Influence of instantaneous mode competition on the dynamics of semiconductor lasers," IEEE J. Quantum Electron. 38, 682 (2002). [CrossRef]
  43. G. Ropars, A. Le Floch, and G. P. Agrawal, "Spectral and spatial dynamics in InGaN blue-violet lasers," Appl. Phys. Lett. 89, 241128 (2006). [CrossRef]

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