GaN Semiconductor Laser Diodes on SiC and GaN ... - IEEE Xplore

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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 1, JANUARY 2007

Substrate Modes of (Al,In)GaN Semiconductor Laser Diodes on SiC and GaN Substrates Valerio Laino, Student Member, IEEE, Friedhard Roemer, Bernd Witzigmann, Member, IEEE, Christoph Lauterbach, Ulrich T. Schwarz, Christian Rumbolz, Marc O. Schillgalies, Michael Furitsch, Alfred Lell, and Volker Härle

Dedicated to Christoph Lauterbach, whose near-field measurements were a key contribution and it is tragic that he cannot see the publication of his work.

Abstract—In semiconductor laser diodes layers with high refractive index can act as parasitic waveguides and cause severe losses to the optical mode propagating in the longitudinal direction. For (Al,In)GaN laser diodes, the parasitic modes are typically caused by the SiC or GaN substrate or buffer layers, hence the name substrate modes. A set of four different experiments shows the effect of substrate modes in the near-field (the most direct evidence of substrate modes), as side lobes in far-field, oscillations of the optical gain spectra, and as dependency of threshold current on n-cladding thickness. We derive several basic properties of the substrate modes by simple estimates. For a quantitative analysis we employ a 2-D finite element electromagnetic simulation tool. We simulate periodic variations in the cavity gain spectrum that explain the measurements in terms of absolute value and oscillation amplitude. We show that it is necessary to include the refractive index dispersion in order to get the correct period of the gain oscillations. Furthermore, we use the simulations to optimize the laser diode design with respect to substrate mode losses within the constraints given, e.g., by growth conditions. Index Terms—Blue laser, gallium nitride, substrate modes.

I. INTRODUCTION EMICONDUCTOR laser diodes (LDs) often contain layers with an index of refraction which is equal to or higher than that of the effective mode index. While these layers may be necessary, e.g., as buffer layers to compensate strain, as contact layers, or as substrate, they can also act as parasitic waveguide and sustain propagating optical modes. The term “ghost modes” is sometimes used for these modes which may couple to the waveguide mode through evanescent waves in the cladding layer [1]. In the case of (Al,In)GaN LDs the standard substrates

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Manuscript received June 28, 2006; revised August 10, 2006. V. Laino is currently with EXALOS AG, CH-8952 Schlieren, Switzerland (e-mail: [email protected]) F. Roemer and B. Witzigmann are with the Integrated Systems Laboratory, Swiss Federal Institute of Technology (ETH) Zurich, CH-8092 Zurich, Switzerland. C. Lauterbach, deceased, was with the Institute of Physics, Regensburg University, D-93040 Regensburg, Germany. U. T. Schwarz is with the Institute of Physics, Regensburg University, D-93040 Regensburg, Germany (e-mail: [email protected]). C. Rumbolz, M. O. Schillgalies, M. Furitsch, A. Lell, and V. Härle are with the Osram Opto Semiconductors GmbH, D-93055 Regensburg, Germany. Color versions of Figs. 1, 2, 4, 6, 7, and 9–13 are available online at http:// ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2006.884769

are SiC, GaN, and sapphire. The first two types of substrates fall in this category. For the sapphire substrate, thick GaN buffer or epitaxial lateral overgrowth (ELOG) layers necessary for defect and strain reduction can act as parasitic waveguides. Therefore, the term substrate modes (SM) is frequently used when dealing with the (Al,In)GaN material system. Substrate modes affect the behavior of a LD severely. It has been shown that SMs influence the light intensity versus current ( – ) curves of 980-nm pump lasers, affecting the longitudinal mode stability not only around threshold but also under high driving current condition [2]. The high refractive index of the GaAs substrate is the cause of the SM. Similarly, research on quantum-dot LDs has pointed out comparable influences in these devices [3], [4]. SMs affect the maximum modulation speed in devices for telecommunication applications, increasing the attenuation and decreasing the bandwidth [5]. For (Al,In)GaN LD side lobes of the far-field [6]–[8] and oscillations in the optical gain spectra [9], [10] have been assigned to SM. There are a few eminent theoretical articles on SM in this material system [1], [11]. An alternative explanation of gain oscillations is a longitudinal sub-resonator in the LD waveguide, caused by cracks or accumulation of dislocations [12]. We were able to clearly distinguish gain oscillations caused by cracks and by SM in an earlier work [13]. However, a quantitative assignment of gain oscillations to modes bound between the few micrometer narrow waveguide and the 100- m distant rough lower surface of the substrate hasn’t been established. In this article, we show to our knowledge the first near-field intensity distribution as direct evidence of a substrate mode. This measurement is performed with a scanning near-field microscope (SNOM) on the cleaved facet of an (Al,In)GaN LD (Section III). Further experiments show the impact of the SM on far-field spectra, threshold current (both in Section IV), and optical gain spectra (Section III). Accurate gain measurements by the Hakki–Paoli method show periodic variation of the mode gain, especially for low driving currents. We attribute such oscillation to periodic modifications of the cavity loss due to variations in the portion of the waveguide mode overlapping with the substrate. In Section VI, we perform a detailed analysis of the experimental results. In addition to a discussion of the k-vectors, the solutions of the Helmholtz equation describing the 2-D optical mode distribution using a finite-element solver are used. Simulation results are then compared with experiments in terms

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LAINO et al.: SUBSTRATE MODES OF (Al,In)GaN SEMICONDUCTOR LASER DIODES

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TABLE I EPITAXIAL STRUCTURE OF THE DEVICES GROWN ON SiC SUBSTRATE. THE DEVICES ON GaN SUBSTRATE HAVE SIMILAR EPI DESIGN BUT NO BUFFER LAYER AND A n-CLADDING LAYER WITH 800 nm THICKNESS. THE REFRACTIVE INDEX IS GIVEN FOR AN EXCITATION’S WAVELENGTH OF 420 nm AND THE DISPERSION IS THE ABSOLUTE CHANGE OF REFRACTIVE INDEX AS FUNCTION OF THE WAVELENGTH

of the mode gain and near field measurements of the optical intensity. Using the model, the effect of material gain on the mode shape and the impact of the buffer layer thickness on the SM are described. This demonstrates how the simulations can be used as a tool to optimize the LD structure within the constrains given by the growth conditions.

Fig. 1. Substrate mode for a (Al,In)GaN ridge waveguide LD on bulk GaN substrate. The density plot shows the intensity distribution of the mode in the waveguide (top) and substrate from 2-D simulations. The horizontal axis is not to scale.

II. SUBSTRATE MODES The devices under investigation are edge-emitting lasers epitaxially grown by low-pressure MOVPE on SiC or on bulk GaN substrates. The devices are manufactured at OSRAM Opto Semiconductors GmbH. The epitaxial structure of the LDs is shown in Table I. In the active region, three 2-nm In Ga N quantum wells are separated by 6-nm-thick GaN barrier layers. The substrate thickness is approximately 100 m in all cases, and the contacts are realized in gold. The refractive index for all epitaxial layers given in Table I were taken from [14]–[18] for GaN compounds and from [19], [20] for SiC. Gold has a refractive index of about 1.6 for wavelengths around 400 nm [21], while for the thin insulating layer covering the ridge sidewall we assume a refractive index of 1.5 which ensures good confinement of the optical mode in the lateral direction. The LDs on bulk GaN substrate are identical to those on SiC substrate except for the missing buffer layer and the n-cladding thickness which is varied from 800 nm to 2 m. For a quantitative analysis of the impact of SM on mode gain we solve the Helmholtz equation for the given refractive index profile on a slice perpendicular to the direction of light emission. A density plot of the calculated intensity in the ridge waveguide and substrate in Fig. 1 clearly shows the waveguide mode leaking into the substrate. This fraction of the optical mode excites a propagating wave in the SiC or GaN substrate due to the high refractive index of the material. Reflection at the lower interface between substrate and metal contact results in a standing wave in the substrate. Because of the large width of the parasitic waveguide, this can sustain many propagating modes. Therefore, there are many propagation constants for modes in the active and parasitic waveguide that are able to match. This causes a strong coupling between both modes and high losses to the laser mode in the substrate. Our approach is to evaluate one single solution of the Helmholtz equation for the whole device, substrate included,

Fig. 2. Optical gain of a (Al,In)GaN LD on SiC substrate, measured with the Hakki–Paoli technique at the temperature of 300 K. Driving current is from 10 to 120 mA, in steps of 10 mA.

taking into account the effects of all layers on the optical mode distribution. Gain and losses are then determined by the spatial overlap of the optical mode with the active region and parasitic waveguide. The coupling between the waveguide mode and parasitic mode can in general be minimized by a thicker cladding layer or reduction of its refractive index. III. OPTICAL GAIN AND NEAR-FIELD MEASUREMENT OF THE OPTICAL INTENSITY Measurements of optical gain are performed using the Hakki–Paoli method [22]–[24]. We estimate an absolute error for optical gain of 5 cm and a relative error smaller than 2cm . Spectra of the modal gain are shown in Figs. 2 and 3 for LDs on SiC and bulk GaN substrate, respectively. Measured gain shows periodic oscillations in both cases. With increasing gain this spectral modulation becomes smaller. Oscillations are found in all devices grown on silicon carbide or bulk GaN substrates. On the contrary similar devices grown on sapphire substrates without using thick defect reduction layers do not

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Fig. 5. Near-field intensity distribution of the substrate oscillations. This plot corresponds to Fig. 4. The intensity was integrated in x direction.

Fig. 3. Optical gain of a (Al,In)GaN LD on bulk GaN substrate, measured with the Hakki–Paoli technique at the temperature of 300 K. Driving currents are 40, 120, and 240 mA.

Fig. 4. Near-field intensity distribution (density plot) of the substrate oscillations measured on the cleaved substrate below the facet of a 3.5-m-wide ridge LD. The center of the waveguide is 10 m to the left of the field.

show this feature. This is to be expected, because the refractive index of sapphire is lower than that of (Al)GaN and therefore the waveguide mode is evanescent in the sapphire substrate. For 16 LDs on SiC substrate with a single mode waveguide the oscillation period is in the range of 11–14 meV independent of the ridge width. Five LDs on bulk GaN substrate show periods in the same range. From the different refractive indexes and GaN one would exof SiC pect different oscillation periods. It is counter-intuitive that the period of the oscillations in the gain spectra is similar for both substrates. We will later show, that dispersion can explain this fact. For a direct observation of the SM a scanning near-field microscope (SNOM) is employed to measure the intensity distribution on the cleaved LD facet and substrate below the facet (see Fig. 4). For the near-field measurement the LD is driven with 500-ns-long pulses. During each pulse, the SM shift by three periods of the mode pattern. This is likely due to heating of the waveguide during the pulse and therefore a changing effective refractive index. As the LD is electrically driven, we measure the optical intensity of the laser mode. More details about the SNOM setup and measurements of the near-field mode dynamics are described elsewhere [25]–[27]. In Fig. 4, the waveguide mode is located to the left of the m. The peak intensity of the mode is much figure at higher than the average intensity of the mode in the substrate. To omit saturation of the detector only the latter was measured. The substrate mode is clearly visible with a decreasing intensity

Fig. 6. Far-field intensity distributions of LDs on GaN substrate. The three measurements are from LDs with different n-cladding layer thickness of 0.8, 1.5, and 2.0 m. Negative angles point towards the substrate.

from the laser waveguide deeper into the substrate. In addition, a slight curvature of the mode below the waveguide can be observed, which is a signature of the lateral diffraction of the substrate mode. The oscillations of the near-field intensity are shown again in Fig. 5, integrated over direction. From this scan we measure the period 1.0 m of the intensity oscillation. The wavelength perpendicular to the substrate causing a standing wave m. The beating pattern of this period is might be the signature of two interfering SM. The lower surface is rough and coated by sputtering of a metal contact. It might be surprising that a clear standing wave is built up between the waveguide and the rough lower surface of the substrate. Yet the . At very low anangle of incidence is very small gles of incidence (nearly) all surfaces reflect mirror-like. Also diffraction plays a minor role, as shown in detail from the 2-D simulations in Section V. IV. FAR-FIELD DISTRIBUTION AND THRESHOLD IMPROVEMENT The far-field of (Al,In)GaN LDs on bulk GaN substrates exhibit narrow side lobes which can be assigned to SM [6]. In contrast (Al,In)GaN LDs on SiC substrate do not show those side lobes even if optical gain spectra indicate the presence of strong substrate oscillations. The far-field intensity angle distribution for three LDs on bulk GaN substrate is shown in Fig. 6 as a func0.8, 1.5 , and 2.0 m. tion of the n-cladding thickness For the LD with 0.8- m n-cladding a large percentage of the far-field intensity concentrates into a narrow side lobe at . For the LD with 1.5- m n-cladding the side lobe gets weaker and splits into two peaks at and .


Fig. 7. Optical power as function of current (PI) curves for three LDs with with different n-cladding layer thickness of 0.5, 1.5, and 2.0 m and otherwise identical specifications.

A splitting of the far-field corresponds to a beating pattern in the near-field as observed in Fig. 5. For the LD with 2.0- m n-cladding the side lobe vanishes almost completely and the LD lases from a single transverse mode. In principle, the side lobes should be symmetric, because there is a downward and an upward traveling wave in the substrate. It is because of the damping in the substrate (and gain in the waveguide on the other side) that the upward traveling wave is much weaker and symmetry in the far-field is broken. Fig. 7 shows the impact of the cladding thickness variation on the threshold current for lasers with different cladding thickness, and otherwise identical specifications. As expected, decreases with increasing n-cladding thickness. The decrease of by more than a factor of 2 from the 800-nm n-cladding to the 2.0- m n-cladding clearly demonstrates the large contribution of the SM to the waveguide loss. V. SIMULATION MODEL In order to interpret the experimental results shown so far, a detailed analysis with the aid of simulation is done in the following. In this section, the simulation model is described briefly. The complex vectorial Helmholtz equation is solved using a finite element (FE) method. The simulation domain is a 2-D cross section of the waveguide, terminated with Dirichlet boundary conditions outside of the metallic material at the top and bottom, and perfectly matched layers (PML), as absorbing boundary conditions, at the remaining boundaries. The complex notation of the refractive index allows to define optical gain and loss for each region in the FE description, including the metallic regions [28], [29]. The solutions of the Helmholtz equation consist of complex eigenvalues composed of an effective mode index as real part and the waveguide loss as imaginary part [30]. The corresponding eigenvector gives the vectorial electric field spatial distribution (see Fig. 1). Therefore, both the optical near-field measurements as well as the oscillations in the Hakki–Paoli spectra (effective cavity losses) can be analyzed with this simulation technique. The 2-D simulations are carried out as follows. Due to the high refractive index of the substrates, the waveguide mode is not the one with the highest effective index in both devices. To

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identify the correct solution, a two step approach is used: First, we simulate a model without substrate, where the waveguide mode is the one with the highest effective index. In this case the waveguide mode can be found giving as first guess for the effective mode index the index of refraction of the quantum well regions. Then, the computed effective mode index is used as first guess for the a second model that includes the substrate. In general, both the eigenvalue and the eigenvector are function of the excitation’s wavelength. In contrast to 1-D simulations, the approach taken here includes diffraction losses. In 1-D models, all the energy coupled from the lasing cavity to the substrate reaches the bottom metallization perpendicularly to the metallic interface. Most of this energy is reflected back and gives rise to a standing wave. In a realistic setting, only a small fraction of this energy is directed back to the lasing cavity, the energy corresponding to the direction perpendicular to the metal contact and this is well described by the 2-D model. The rest of the energy is reflected towards the side of the lasing cavity and is absorbed into the substrate. Therefore, a 1-D model overestimates the amplitude of the standing wave in the substrate. VI. ANALYSIS OF EXPERIMENTAL RESULTS A. Near Field and Far Field In order to gain insight into the measured results, the configuration of the propagation vector in the case of SM is given first. The basic geometry of the -vectors and refractive index model is plotted in Fig. 8. A substrate mode is present when the parallel wavevector component of the waveguide is equal to the parallel component of the substrate mode. The waveguide can be rep. The substrate has resented by an effective refractive index for GaN and a refractive index for SiC. One could use more accurate numbers here, depending on wavelength and temperature, but this is not necessary for the current analysis. In the substrate the k-vector is given by the vacuum waveand the refractive index of the substrate. The analysis length is done for GaN substrate case as example (1) The vector parallel to the waveguide is given by the effective of the mode refractive index on one hand and by the angle propagating in the substrate on the other hand (2) and the

vector perpendicular to the waveguide is (3)

The angle of the substrate mode outside, i.e., the angle far-field side lobe is given by Snells’ law

of the

(4)

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Fig. 8. Schematic picture of k-vectors in waveguide and substrate for (a) bulk GaN and (b) SiC substrate. The figure is not to scale.

These relations can be used for estimating the side lobes in the measured far-field in Fig. 6. For the LDs on GaN substrate and the angle of the far-field side lobe is between . According to (4) the corresponding internal angles and , and the effective reare between fractive index of the waveguide mode is between and (2). The larger number corresponds to the are in the smaller angle and vice versa. These values of range of bound modes (according to the waveguide simulations) and their variation indicate a variation in the ridge waveguide parameters. Next, the near-field data are evaluated for the GaN substrate case. Starting with the period of the near-field oscillations m, (3) gives an internal angle , which results in . The effective refractive index is an external angle . From this calculation, the external angle is much smaller than the angle extracted from the far-field measurement. A reason for this could be a strong variation of the waveguiding properties given by structural details, as already indicated from the far-field measurements on different laser samples. Due to the complexity of the near-field measurement setup, we do not have any statistical data of near-field patterns for different LDs. The 2-D simulation model shows a periodic interference pattern in the substrate (see Fig. 1), very similar to what can be found in measurements (see Fig. 4). An oscillation period of about 1 m can be extracted from this pattern. The far-field , lobe calculated with this period results in an angle which is in good agreement to the farfield measurements. On the other hand, the near-field experiment gives an oscillation period which is two times the modeled one. As discussed earlier, this might be due to the variation of the waveguide properties. Similarly to the substrate, in the epitaxial region the waveguide and p-contact layers have an index of refraction larger than the effective mode index. However, no periodic pattern is present here according to simulations. This happens because the thickness of such layer is smaller than the minimum thickness (about 1000 nm) suitable to fit one full lobe of a standing wave. Similar conclusions have been drawn in terms of “ghost modes” by Osinski and coworkers [1], [31]. For the SiC substrate the effective refractive index of the laser waveguide is assumed to be the identical to the one in the bulk GaN substrate, because the de-

sign of the active region and waveguide is nominally unchanged. From (3) and (1), the internal angle in the substrate is

(5) This is larger than the angle of total reflection at the interface of SiC and air. This is the reason why no far-field side lobe is being observed in the case of a SiC substrate. One has to keep in mind that an absence of those side lobes does not imply an absence of losses due to SM. A strong modulation of the gain spectrum indicates the presence of such losses, which is discussed in the following section. B. Cavity Losses In addition to the direct optical field measurement, SM can cause oscillations in the spectral dependence of the cavity losses. Figs. 2 and 3 clearly show these oscillations at low drive currents in the measurements. In this section, these oscillations are analyzed with the aid of the FE simulation. A vertical cut through the center of the mode is shown in Fig. 9. For increasing photon energy, nodes and antinodes of the standing wave in the substrate are located at the interface substrate–n-cladding. At the bottom of the substrate, the electromagnetic wave always shows a node localized at the metal–substrate interface due to the high optical loss associated with the contact. As a consequence, the amount of energy that is transferred to the substrate is a function of the excitation’s wavelength and so is the total cavity loss, as found in measurements. Therefore, the oscillations in the optical gain spectra can be attributed to the wavelength depending on the coupling between the two resonators given by the epitaxial waveguide and the substrate. This coupling alters the overlap of the optical mode with the different regions and causes variation in the waveguide loss. First the focus is on the device grown on SiC substrate. The epitaxial structure is described in Table I. To correctly evaluate the spectral evolution of the mode profile, we include the refractive index wavelength dispersion of the different layers using a linear relationship, which is a suitable approximation considering the small wavelength range under investigation. We set 10 nm for SiC [19], [20] to calibrate a value of 0.5


Fig. 9. Simulation result for the near-field optical intensity for the device with SiC substrate. The higher photon energy corresponds to a peak in the round-trip gain, while the other photon energy corresponds to the off resonance condition.

the oscillations period of the gain spectrum. Dispersion coefficients for the epitaxial layers are equal to the ones used for the device grown on GaN substrate and are given afterwards. From the simulations, we find a material loss of 120 cm for the p-doped layers [33] and of 15 cm for the n-doped layers [34] to match the oscillation amplitude of the experiment. The optical loss of the SiC substrate has been measured to be 5 cm . The optical absorption of Gold is set to 3 10 cm in agreement with [21]. For the insulating layer covering the ridge sidewalls we use an optical absorption of 15 cm although simulations suggest that this value does not significantly affect simulation results. With these numbers, our model correctly describes the peak spacing, the absolute value of the cavity loss and the oscillation amplitude of the optical gain spectrum at low drive currents, as shown in Fig. 10. Above transparency, the oscillations in the measured gain spectra disappear, and gain becomes a smooth function of energy. This can be explained by the FE simulation. In the model, optical gain is taken into account as imaginary part of the refractive index [30]. Increasing gain in the active region, the real part of the index is affected as well due to the Kramers–Kronig relations. As a consequence, the mode shifts slightly towards the p-side of the waveguide with increasing material gain. This decreases the fraction of the waveguide mode overlapping with the substrate substantially and reduces the oscillation amplitude of the cavity loss as shown in Fig. 11. There is however no noticeable impact on the total cavity loss, as it is mainly caused by the highly absorptive p-doped waveguide region. Next the focus goes to the device grown on GaN substrate. We use an optical loss of 45 cm for the p-type layers and a loss of 3 cm for the n-type layers, while the optical loss of the substrate is set to 9 cm . Despite the epitaxial structure of this device is nominally identical to the previous device, the doping profile has been optimized as well as the manufacturing process, resulting in a different loss for the epitaxial layers. Also in this case, we need to include the refractive index wavelength dispersion in our model. Without dispersion, the modulation period of the calculated gain spectrum would

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Fig. 10. Comparison between measured (large symbols) and simulated (small symbols) oscillation in mode gain for the device grown on SiC. For measurements, driving current is 10 mA and temperature is 300 K. The contribution given by mirror loss has already been subtracted. Active region gain is set to zero in the simulations.

Fig. 11. Simulated variation of oscillations amplitude and mode gain with increasing active region gain for the device grown on SiC substrate.

be a factor of two smaller than the measured one. The different refractive indexes and dispersion values of SiC and GaN is the cause for the similar period of the gain modulation in both devices. We set a refractive index dispersion of 1.30 10 nm for GaN and InGaN and a value of 1.13 10 nm for AlGaN. With these values, our model correctly describes the spacing between two peaks, the absolute value of the cavity loss and the oscillations amplitude of the optical gain spectrum, as shown in Fig. 12. The effective mode index results in 2.48 for photon energies around 3 eV, in good agreement to the measurements. In order to reduce the mode coupling into the substrate, devices with increased n-cladding thickness on a GaN substrate were manufactured. The GaN-based device discussed so far has an n-cladding thickness of 0.8 m. Results of the electrical characterization are shown in Fig. 7 and are compared to simulations in Fig. 13. In particular, we observe a drop of the threshold current from about 200 mA for a buffer thickness of 0.8 m, to about 100 mA for a buffer thickness of 1.5 m, corresponding to a factor of 2. Simulations suggest a drop of the cavity losses from about 60 to 37 cm , corresponding to a factor of 1.6 for the same change in buffer layer thickness. An approximation

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Fig. 12. Comparison between measured (large symbols) and simulated (small symbols) oscillation in mode gain for the device grown on GaN. For measurements, driving current is 10 mA and temperature is 300 K. The contribution given by mirror loss has already been subtracted. Active region gain is set to zero in the simulations.

Fig. 13. Comparison between the change in measured threshold current and simulated waveguide loss with respect to buffer layer thickness for devices grown on GaN substrate. Active region gain is set to zero in the simulations.

of the gain versus threshold current relationship can be done as follows. In [35] an estimation of threshold current resulted in Shockley–Read–Hall recombination being the dominant recombination term below threshold. Hence, the current versus carrier density relationship in the QW is almost linear in this regime. As a consequence, the relationship optical gain-carrier density is almost linear for low pumping levels as well. Threshold current scales almost linearly with optical loss, which is in agreement to the curve shown in Fig. 13. In addition the threshold current and the mode gain saturate for buffer layer thickness above 1.5 m in both measurements and simulations, indicating a correct description of the optical loss mechanism by the model. Although the threshold current is reduced by increasing the buffer thickness, the differential quantum efficiency remains almost constant in Fig. 7. This is a consequence of the internal losses dominating the total optical losses. In order to give a quantitative explanation for this, further investigations on the impact of the SM on the photon escape rate of the laser are necessary. VII. CONCLUSIONS An in-depth study of SMs combining four experimental methods with 2-D simulations is presented. The SM are ob-

served in the optical gain spectrum as oscillations. The SM can be measured directly in the near-field intensity distribution on the substrate surface just below the cleaved facet in the device grown on GaN. The far-field of the LDs shows a characteristic side lobe caused by the SM. This side lobe is asymmetric, which we attribute to losses in the substrate. With increasing thickness of the n-cladding the substrate mode and thus the side lobe vanishes. The same effect can be observed as a decreasing threshold current with increasing n-cladding thickness. We provide an estimate of the SM properties in the LD based on simple electromagnetic considerations. The far-field angle is given by the effective refractive index of the waveguide mode and the refractive index of the substrate. For typical values of the effective mode index, the substrate mode is totally reflected at the interface between substrate and air in the case of the SiC substrate, in agreement with the fact that no side lobe has been observed in this case. For a detailed analysis of the coupling between the lasing cavity and the substrate a 2-D finite element simulation tool is used. Using the calibrated model the oscillations in the cavity loss spectrum can be attributed to changes in the mode shape with excitation wavelength. The lasing mode focuses at the location of the active region when the optical gain increases, affecting the fraction of the mode that overlaps with the substrate. This is due to the Kramer-Kroning relations and determines the decrease in oscillation amplitude with increasing driving current, as observed in measurements. We simulate the periodic variation of the cavity loss as function of the photon energy. The results match the measurements in terms of the oscillation period, absolute value and amplitude of the cavity loss variation. Refractive index dispersion of the epitaxial layers is found to be a pertinent effect. Finally, the 2-D simulations are used to optimize the LD design. Specifically, the buffer and n-cladding layer thicknesses for LDs in SiC and GaN substrates are varied. The impact on the amplitude of the gain modulation, cavity loss, and threshold current is evaluated. It follows that coupling between lasing cavity and substrate can be minimized growing a thick buffer layer with low refractive index between the substrate and the optical cavity. REFERENCES [1] G. A. Smolyakov, P. G. Eliseev, and M. Osinski, “Effects of resonant mode coupling on optical characteristics of InGaN–GaN–AlGaN lasers,” IEEE J. Quantum Electron., vol. 41, no. 4, pp. 517–522, Apr. 2005. [2] H. Horie, N. Arai, Y. Yamamoto, and S. Nagao, “Longitudinal-mode characteristics of weakly index-guided buried-stripe type 980-nm laser diodes with and without substrate-mode-induced phenomena,” IEEE J. Quantum Electron., vol. 36, no. 12, pp. 1454–1461, Dec. 2000. [3] D. Bhattacharyya, E. A. Avrutin, A. C. Bryce, J. H. Marsh, D. Bimberg, F. Heinrichsdorff, V. M. Ustinov, S. V. Zaitsev, N. N. Ledentsov, P. S. Kopev, Z. I. Alferov, A. I. Onischenko, and E. P. O’Reilly, “Spectral and dynamic properties of InAs-GaAs self-organized quantum-dot lasers,” IEEE J. Sel. Topics Quantum Electron., vol. 5, no. 3, pp. 648–657, May/Jun. 1999. [4] P. M. Smowton, E. J. Johnston, S. V. Dewar, P. J. Hulyer, H. D. Summers, A. Patane, A. Polimeni, and M. Henini, “Spectral analysis of InGaAs/GaAs quantum-dot lasers,” Appl. Phys. Lett., vol. 75, pp. 2169–2171, 1999. [5] K. Goverdhanam, “Effect of substrate modes in 40 Gbit traveling wave Limo3 modulators,” in Proc. IEEE MTT-S Dig., 2002, pp. 1285–1288.


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[28] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics Book, Wiley series in pure and applied optics. [29] H. Wenzel, “Designing high-power single-frequency lasers, invited paper numerical simulation of semiconductor optoelectronic devices,” in Proc. IEEE/LEOS 3rd Int. Conf. 2003, pp. 31–34. [30] M. Streiff, A. Witzig, and W. Fichtner, “Computing optical modes for VCSEL device simulation,” in Proc. Inst. Elect. Eng. Optoelectron., 2002, pp. 166–173. [31] P. G. Eliseev, G. A. Smolyakov, and M. Osinski, “Ghost modes and resonant effects in AlGaN–InGaN–GaN lasers,” IEEE J. Sel. Topics Quantum Electron., vol. 5, no. 3, pp. 771–779, May/Jun. 1999. [32] X. W. Sun, S. F. Yu, C. X. Xu, C. Yuen, B. J. Chen, and S. Li, “Room-temperature ultraviolet lasing from zinc oxide microtubes,” Jpn. J. Appl. Phys., vol. 42, no. 10B, pp. L1229–L1231, 2003. [33] W. Goetz, N. M. Johnson, J. Walker, D. P. Bour, and R. A. Street, “Activation of acceptors in Mg-doped GaN grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett., vol. 68, no. 5, pp. 667–669, 1996. [34] W. Goetz, N. M. Johnson, C. Chen, H. Liu, C. Kuo, and W. Imler, “Activation energies of Si donors in GaN,” Appl. Phys. Lett., vol. 68, no. 22, pp. 3144–3146, 1996. [35] 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, vol. 6184, Apr. 2006, 61840E. [36] V. A. Karpina, V. I. Lazorenko, C. V. Lashkarev, V. D. Dobrowolski, L. I. Kopylova, V. A. Baturin, S. A. Pustovoytov, A. J. Karpenko, S. A. Eremin, P. M. Lytvyn, V. P. Ovsyannikov, and E. A. Mazurenko, “Zinc oxide analogue of GaN with new perspective possibilities,” Cryst. Res. Technol., vol. 39, no. 11, pp. 980–992, 2004. [37] I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, “Investigations of the spectral characteristics of 980-nm InGaAs–GaAs–AlGaAs lasers,” IEEE J. Quantum Electron., vol. 33, no. 10, pp. 1801–1809, 1997. [38] U. T. Schwarz, E. Sturm, W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, “Excitonic signature in gain and carrier induced change of refractive index spectra of (In,Al)GaN quantum well lasers,” Appl. Phys. Lett., vol. 85, no. 9, pp. 1475–1477, 2004. [39] Z. K. Tang, G. K. L. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett., vol. 72, no. 25, pp. 3270–3272, 1998. [40] U. T. Schwarz, W. Wegscheider, A. Lell, and V. Härle, “Nitride-based in-plane diodes with vertical current path,” Proc. SPIE, vol. 5365, pp. 267–277, May 2004.

Valerio Laino (S’05) received the M.S. degree (cum laude) in electrical engineering at the University of Modena, Modena, Italy, in 2002 for work on characterization and explanation of snap-back and current collapse phenomena in HFET transistors for microwave applications. In October 2002, he joined the Integrated Systems Laboratory at the Swiss Federal Institute of Technology (ETH) Zurich, Switzerland, where he received the Ph.D. degree for work on the microscopic simulation of optoelectronic devices. He is currently working for EXALOS AG, Switzerland. His research interests are in the field of microscopic modeling and characterization of semiconductor devices, in particular visible LASERs, and their applications.

Friedhard Roemer received the diploma degree in electrical engineering from the University of Karlsruhe, Karlsruhe, Germany, in 1996 and the Ph.D. degree in electrical engineering from the University of Kassel, Kassel, Germany, in 2005. From 1997 to 1999, he was with Alcatel AG, Stuttgart, Germany. In 2000, he joined the Institute for Microstructure Technology and Analytics at the University of Kassel. Since 2005, he has been with the Integrated Systems Laboratory at the Swiss Federal Institute of Technology (ETH) Zurich, Switzerland, working on the numerical simulation of optoelectronic devices.

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Bernd Witzigmann (M’03) received the Ph.D. degree (hons.) in technical sciences from the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland. In 2000, he joined Bell Laboratories, Murray Hill, NJ, as a Member of Technical Staff. In October 2001, he joined the Optical Access and Transport Division, Agere Systems, Alhambra, CA. Since 2004, he has been an Assistant Professor at ETH Zurich, Switzerland. His research interests focus on computational optoelectronics, process and device design of semiconductor photonic devices, microwave components, and electromagnetics modeling for nanophotonics. Dr. Witzigmann is a member of the IEEE LEOS.

Christoph Lauterbach was born 1980 in Guben, Germany. He was working towards a diploma degree in physics in 2006 when he was involved in a fatal car accident. His interests were in near-field spectroscopy and blue laser diode dynamics.

Ulrich T. Schwarz was born in Munich, Germany, in 1965. He received the diploma degree in experimental physics in 1993 and the Ph.D. degree in physical science in 1997, both from the Regensburg University, Regensburg, Germany. In 2004, he concluded his “Habilitation” and since then joined the faculty as assistant professor (“Privatdozent”). Awarded by the Alexander von Humboldt foundation with a Feodor Lynen scholarship he spent two postdoctorial years (1997–1999) at Cornell University, Ithaca, NY, with research on intrinsically localized modes. For several months in 2001 he joined the group of Prof. R. Grober at Yale University, New Haven, CT. Currently, he is visiting Kyoto University, Kyoto, Japan, with an invited fellowhip (long-term) awarded by the Japanese Society for the Promotion of Science.

Christian Rumbolz received the diploma degree in physics from the University of Stuttgart, Stuttgart, Germany, for work on investigating the behavior of swift heavy ion beams on thin metal layers deposited on Si-wafers. Since 2004, he has been working toward the Ph.D. degree at OSRAM Opto Semiconductors GmbH, Regensburg, Germany, on the field of InGaN-laser chip technology. The main topic of his work is the mode behavior and mode control of blue-violet laser diodes.

Marc O. Schillgalies received the M.S. degree in physics from the University of Leipzig, Leipzig, Germany, in 2004, for work on photo-reflectance mesurements of ZnO structures, and the M.S. gegree in optical engineering at the University of Arizona, Tucson, in 2005, for work on processing and characterization of VECSELs. In October 2005, he joined Osram Opto Semiconductors GmbH, Regensburg, Germany, to pursue the Ph.D. degree in the eptitaxy of In(Al)GaN laser devices.

Michael Furitsch was born in January 1976 in Tettnang, Germany. He received the Dipl.-Ing. degree in electrical engineering from the University of Ulm, Ulm, Germany, in 2002. In 2003, he joined the company OSRAM Opto Semiconductors GmbH, Regensburg, Germany, to pursue the Ph.D. degree, where he is analyzing the degradation mechanisms of (Al–In)GaN-based laser diodes.

Alfred Lell received the Diploma degree in physics from the University of Regensburg, Regensburg, Germany, in 1986. He is currently Project Leader of the blue-violet InGaN-Laser project at OSRAM Opto Semiconductors GmbH, Regensburg, Germany.

Volker Härle received the M.S. degree in physics from University of Massachusetts, in 1988, and the diploma degree in physics and Ph.D degree from the University of Stuttgart, Stuttgart, Germany, in 1990 and 1994, respectively. His dissertation was on the physics of strained GaInAs–InP-structures resulting in optical modulators, amplifiers and lasers using low-pressure MOVPE as growth method. He joined France Telecom, Paris/Bagneux, France, in 1991. In 1994, he started with the MOVPE growth of GaInN-structures and GaInN-devices as a Postdoctoral Researcher at Stuttgart University and joined Siemens in 1996 as a Process Engineer for GaInN-MOVPE growth. In 1997, he took over the responsibility of all MOVPE research and development including AlGaInP and GaInN at Siemens and in 1999, he became Head of GaInN-R&D. Today he is heading all nitride R&D at OSRAM-OS including MOVPE production as a Senior Director of R&D. Major achievements where the development of ATONand ThinGaN-Technology, as well as the first European CW blue laser.