High resolution X-ray diffraction

HRXRD rocking curve (XRC) measurement for symmetrical GaN (002) reflections was applied to evaluate the crystal quality of GaN thin films. The FWHM of XRC for GaN (002) was plotted as shown in Fig. 4.3.6. We can observe that the FWHM is decreased as misorientation angle increases from 0^o to 0.2^o, but it increases as misorientation angle increase above 0.2^o. The FWHM of the symmetrical GaN (002) is correlated to the threading dislocations density [49]. Therefore, it is ascertained that dislocation density tends to decrease as sapphire substrate with slight misorientation angle about 0.2^o, but the crystal quality is deteriorated as misorientation angle increases above 0.2^o, which is agree with our HRTEM analysis results.

Fig. 4.3.7 shows the HRXRD ω-2θ diffraction pattern for the LEDs with misorientation of 0^o, 0.2^o, 0.35^o, and 1^o, respectively. As can be seen, the HRXRD diffraction pattern shows

one periodical structures, which can be attributed to the In0.2Ga0.8N/GaN MQWs. In addition, the third order satellite peak of the diffraction pattern for all samples can be clearly observed, suggesting that the grown structure has sharp interfaces and good periodicity between GaN barrier and InGaN well. Additionally, the inset shows the variation of MQWs interface roughness (IRN) with misorientation angle of sapphire substrate. The interface roughness value of MQWs can be obtained from the following equation [63].

⋅Λ

where n is the order of the satellite; Λ and σ/Λ are thickness of the period and IRN, respectively; ∆θM is the angle distance between adjacent satellite peaks; W0 and Wn are the FWHM of zeroth- and nth-order peaks, respectively. The results are shown in Fig. 4.3.7. From figure we can found that IRN of InGaN/GaN MQWs decreases with increasing misorientation angle of substrate, and reaches minimum which is about 1.35% for 0.2° misorientation sapphire substrate was used. Increasing the misorientation angle to 1° increases the IRN of MQWs. The previous reports indicated that the IRN of MQWs is affected by defect, microstructure and phase separation in MQWs [63]. Based on x-ray analysis, we can prove that the defect density of 0.2^o sample is lower than other samples, and can also concluded that defect density of 0.2^o sample was reduced dramatically, which are consistent with the results observed from HRTEM images.

Fig. 4.3.9 shows the RSM results for InGaN/GaN MQW LEDs grown on (a) 0°, (b) 0.2°,

(c) 0.35° and (d) 1° misorientation sapphire substrate, respectively. The diffraction pattern was obtained from the asymmetric (1015) reflection of the GaN epilayer. Compared with sample 0^o, 0.35^o and 1^o, the reciprocal lattice point (RLP) of GaN layer of 0.2^o sample is circular, indicating that the spread of RSM intensity for 0.2^o sample is narrower than that of RSM intensity for other samples. In general, the spread of diffraction intensity is related to the orientation distribution and decrease in the coherency of the scattering along the structure [64].

The asymmetrical feature for RLP of GaN indicates the out-of-plane lattice mismatch formed in GaN layer. This means that the GaN epilayer grown on 0.2° substrate has better crystallization quality. Besides, the RLP of satellite peaks can be clearly observed for 0.2^o sample and the satellite peaks up to four orders, while the reciprocal lattice point of satellite peaks became relatively weak for 0^o sample and 0.35^o sample or vanished for 1^o sample, suggesting that the InGaN/GaN MQWs of good quality were grown. Therefore, based on the above-mentioned results, the crystalline quality of 0.2^o sample is relatively good in contrast to the quality of other samples, and the noticeable improvement in the quality of GaN epilayer could be responsible for achievement of high quality InGaN/GaN MQWs.

On the other hand, the overall strain state of MQWs with respect to the GaN epilayer can be examined by RSM. S. Pereira et al. proposed the method to investigate the strain and composition distributions within wurtzite InGaN/GaN layers [50]. The information can be extracted from the elongation of broadened RLP in asymmetric x-ray reflections. The

schematic diagram illustrating the effect of strain and composition gradients in the symmetric and asymmetric RLP of InxGa1-xN is shown in Fig. 4.3.10.

The RSM pattern in the Fig. 4.3.9 represent the Qx and Qy position of GaN and MQWs satellite peaks. The distance between GaN epilayer and MQWs satellite peaks in the Qx

direction indicates the degree of lattice relaxation, εxx, and the relationship between εxx and Qx

for all samples can be described by the following equation [73]:

−1 layer and InGaN layer, respectively. Hence, the degree of lattice relaxation for 0

GaN

Qx Q_x^InGaNs

o, 0.2^o, 0.35^o

and 1^o sample is about 1.28×10^-4, 7.4×10^-5, 8×10^-5 and 3.64×10^-4, respectively. We can find that the 0.2^o sample have the smallest degree of lattice relaxation. For heteroepitaxial structure, the defect density, such as threading dislocation, V defect and so on, of MQWs will increases with increasing the lattice relaxation degree of MQWs. In other words, the InGaN/GaN MQWs of 0.2^o sample have the lowest defect density compared with other samples. This think can be proved by our AFM and HRTEM images, the dislocation density decreases as misorientation agnle increases from 0^o to 0.2^o, but it increases as misorientation angle increases above 0.2^o.

4.3.4 Raman spectroscopy

To determine the stress for the LED grown on different misorientation angle, the Raman spectroscopy was performed. In this study, we chose z(y,y)z configuration to probe Raman spectra. For this scattering configuration, the A1(LO) and the E2(high) phonon modes are observed, which correspond to the lattice vibration paralleling and perpendicularing to the c-axis [0001] direction, respectively. Fig 4.3.11 shows the Raman spectra for the InGaN/GaN MQW LEDs grown on different misorientation angle. The two clear active phonon bands are observed at around 568 cm^-1 and 735 cm^-1, corresponding to the E2(high) and A1(LO) phonon modes of GaN [51], and no InGaN relatived phonon bands are observed in the figure. The E2(high) mode is sensitive to changes in the elastic properties of the material, which is generally observed to estimate the biaxial stress in material. From inset of Fig. 4.3.12, we can observe the position of E2(high) peak shifts slightly with increasing misorientation angle. To extract the accurate position of E2(high) peak, the Lorentzian function was used to fit E2(high) mode peak, the results are shown in Fig. 4.3.12. We can observe that the Raman shift increases as misorientation angle increases from 0^o to 0.2^o, but it decreases as misorientation angle increase above 0.2^o. In general, the Raman shift as a function of the biaxial stress can be expressed as:

σ ω

ω

ω_E = _E − =C

∆ _{2 2 0} (4.3.4)

where ω_E2 and ω₀ are the Ramsn shift of E2(high) mode for strained sample and strain free

sample, respectively, C is the constant that the shift of the E2(high) with biaxial stress, and σ is the stress. The reports show that the E2(high) phonon of a strain free sample has an ω₀ of 568 cm^-1 and the shift of the E2(high) mode with biaxial stress is 4.1 cm^-1/GPa [52]. From above parameter, the calculated stress as a function of misorientation angle is shown in Fig.

4.3.13. We can observe that the compressive stress increases as misorientation angle increases from 0^o to 0.2^o, but it decreases as misorientation angle increase above 0.2^o, which is agree with previous analysis, due to lowest dislocation density in material, the LED grown on misorientation angle of 0.2^o has the smallest degree of lattice relaxation. But as misorientation angle increases above 0.2^o, the dislocation density increases, resulting in increasing of lattice relaxation degree of materials.