Laser diode arrays on laterally patterned substrates
In spite of the growing popularity of semipolar and non-polar substrate orientations, most of the III-nitride optoelectronic devices are still grown on polar c-plane GaN templates or free-standing GaN substrates. The predominant growth technique is metal organic vapor phase epitaxy (MOVPE). In the case of MOVPE, good morphology and chemical uniformity of AlInGaN layers are obtained only in the step-flow growth mode, on vicinal surfaces. On such vicinal surfaces we can distinguish atomic steps, separated by atomically flat terraces. By the vicinal angle S, we understand the angle between the GaN c-plane and its real surface, also termed as off-cut, off-orientation, miscut, off-axis, or misor- ientation angle. Let h be the atomic step height and w the atomic terrace width. Then we have tan S = h/w. Good morphology of epitaxial layers can be obtained only for S in a certain range, which for GaN grown by MOVPE is between 0.3 and about 1°.
For 0 < S < 0.2° the step-flow growth mode with parallel and well-ordered atomic steps by MOVPE is not possible because of the lack of an effective and well-determined source of atomic steps. During growth on exact-oriented substrates the atomic steps tend to flow around the dislocations which are always present, at surface densities of 104-107 cm~3 for free-standing GaN, and 108-109 cm~3 for GaN templates on foreign substrates. As a result, for MOVPE layers grown on exact oriented substrates the density and direction of atomic steps become random. For S > 0.2° the density and direction of the atomic steps are uniform.
For GaN/sapphire and GaN/SiC templates used mostly for light-emitting diode and transistor fabrication, the vicinal angle of the GaN epilayer is determined by the miscut angle of the foreign substrate.
In the case of free-standing GaN (made by HVPE, HNPS or ammonothermal methods) used for the production of laser diodes, the desired vicinal angle is realized by polishing the substrate to high precision. Polishing causes, however, a significant loss of the material. This becomes an issue in view of the increasing size of free-standing GaN substrates and their still high price. Starting from exact c-plane-oriented 2-inch GaN wafer it requires as much as 440 pm (51.2 mm x tan(0.5 degree)) of material per side to be polished off to reach 0.5 degree miscut. Therefore, a 300-pm thick 0.5-degree miscut GaN substrate requires initially at least a 1200-pm thick GaN crystal, which accounts for a 25% yield only.
For the step flow growth mode, at a given vertical growth rate, v, we can define the lateral velocity of the atomic steps, s:
According to eq. (2.10), the surface atomic steps during epitaxial growth move faster for smaller S. It is well known that for increasing S, the amount of indium incorporated into InGaN layers grown by MOVPE in the step-flow mode, at fixed pressure, temperature, and In precursor flow, decreases (Tachibana et al., 2008; Keller et al., 2008; Leszczynski et al., 2011). This effect is shown in Fig. 2.35.
Although all experimental results obtained so far confirm the effect described above, they are focused on how indium content depends on S, without paying attention to whether the substrate miscut was chosen towards the a or m axis. This issue certainly requires more study, but the first results show that indium content is not sensitive to the azimuth of substrate miscut; see Fig. 2.35(b).
Fig. 2.35. Influence of substrate vicinal angle on photoluminescence wavelength from InGaN: (a) PL wavelength of an InGaN layer grown on patterned GaN/sapphire substrate, and its indium content measured by X-ray diffraction for different substrate vicinal angles. Solid lines are guides to the eye. (b) Room-temperature PL wavelength of a InGaN/GaN MQW structure grown on substrates with different vicinal angles.
The precise control of the quantum-well chemical composition is the key factor in the fabrication of all InGaN-based optoelectronic devices. The band gap and hence the emitted wavelength depends on indium content of QWs, and therefore in the planar light-emitting diodes and laser diodes technology it is very important that the vicinal angle is uniformly constant across the substrate.
Concerning the physics of different indium incorporations on differently angled surfaces, there are two models present in the literature:
i) Indium is incorporated on the atomic terraces at a constant rate and is not incorporated on the atomic steps (Krysko et al., 2007). For larger 5, according to Nakamura and Chichibu (2000), we have a higher density of atomic steps (narrower terraces) and therefore less indium. In this model the indium content should not depend on v for a substrate of a given 5.
ii) Indium incorporation depends on s, because to avoid thermal desorption the indium adatom has to be quickly surrounded by the neighboring gallium adatoms (Keller et al., 2008). In this model, the indium incorporation should increase for smaller 5 and constant v and also increase for larger v and constant 5.
Based on Leszczynski et al. (2011), for a 50-nm InGaN layer grown on an homogeneous GaN substrates at 820° C and reactor pressure of 300 mbar at v = 0.7 A/s, the indium content increased from 8% to 13% for 5 decreasing from 1.8 to 0.3°. For the same growth temperature and pressure, and 5 = 1° the indium content increased from 7% to 12% for v increasing from 0.35 to 1.0 A/s.
Therefore, it should be concluded that for the step-flow growth mode of InGaN by MOVPE, model ii) is more likely.