1. Introduction

Group III Nitrides (e.g. AlN, GaN, InN and their alloys) are predestinated for optoelectronic applications from the long visible light range down to UV wavelengths since they cover a bandgap range from 1.6 to 6.2 eV. Nowadays, one of the most important optoelectronic applications of group III Nitrides are GaN based blue and green LEDs. High-brightness GaN based blue LEDs were first fabricated by S. Nakamura using c-oriented sapphire as substrate material and two-flow metal organic vapour phase epitaxy (MOVPE) for the epitaxial growth Reference Nakamura, Mukai and Senoh[1]. So far, best results in growth of high quality group III nitrides are achieved by MOVPE techniques. However, the growth of group III nitrides by gas source molecular beam epitaxy (GSMBE) using On Surface Cracking (OSC) of NH₃ appears also to be very promising Reference Kamp, Mayer, Pelzmann, Menzel, Kirchner, Chung, Sternschulte and Ebeling[2] Reference Kamp, Mayer, Pelzmann, Thies, Chung, Sternschulte, Marti and Ebeling[3]. Particularly in our department we have the opportunity to compare both growth techniques directly since we are equipped with a MOVPE and a GSMBE system.

The lattice mismatch between sapphire and GaN is very large (Δa/a=16 %. 6H SiC is a more suitable substrate material for the epitaxial growth of GaN (Δa/a=3.5 %). However, due to the high price and the low availability of suitable 6H SiC, most groups use the less expensive sapphire for the growth of wurtzite-type nitrides. Due to the large mismatch of the lattice constants and the thermal expansion coefficients, GaN grown on sapphire has very high defect densities.

The first step in the fabrication of optoelectronic semiconductor devices is the optimization of the grown material referring to optical, electrical and crystalline quality. In our investigations we focus on transmission electron microscopy (TEM), Rutherford backscattering spectrometry (RBS) and high resolution x-ray diffraction (XRD) to examine the crystalline quality.

2. Experimental

3. Theoretical model for x-ray analysis of threading dislocations

A model described by Ayers Reference Ayers[4] uses the x-ray linewidth broadening due to threading dislocations (TD) for calculation of their densities. Following the model of Ayers, we assume that the x-ray rocking curve peaks are Gaussian in shape and the linewidth represents a convolution of the following contributions: the intrinsic rocking curve width β ₀, the intrinsic rocking curve width for the Bartels monochromator β _d , the rocking curve broadening due to angular rotation at dislocations β_α , the broadening caused by strain surrounding dislocations β _ε, the rocking curve broadening due to crystal size β _L , and the broadening due to curvature of the crystal β _r . Thus the square of the measured rocking curve linewidth β _m is given by Reference Ayers[4]:

The intrinsic rocking curve width is calculated by Reference Warren[5]:

Where θ is the Bragg angle, θ₁ and θ₂ are the angles of the primary and the reflected x-ray beams, λ is the wavelength and F_hkl is the structure factor. The contributions β _α and β _ε are calculated by Reference Ayers[4]:

where b is the length of the burgers vector, D is the dislocation density and K_α and K _ε are introduced to simplify equations 3 and 4. Equation 4 is valid for pure screw dislocations, but the actual character of the TD will have only weak effect on strain broadening Reference Ayers[4]. Therefore equation 4 was taken for our calculations. Broadening due to crystal size β _L can often be neglected for layers thicker than 1μm Reference Ayers[4]. The broadening due to curvature β_r can be estimated by comparison of the substrate rocking curves before and after growth of a layer. For our samples the effect of broadening due to curvature yields a few arcseconds and can therefore be neglected. Thus equation 1 simplifies to:

Since β₀ can be calculated according to equation 2, β_m is the measured linewidth and β_d is constant we now introduce the adjusted linewidth β_adj to simplify the relation.

Plotting

for at least three different x-ray reflections versus tan²θ should yield a straight line. The dislocation densities can then be independently calculated from the slope as well as the intercept of that line. For internal consistency the results should be identical.

4. Results and discussion

TEM measurements of both MOVPE and GSMBE samples showed large numbers of TD perpendicular to the sapphire substrate. Additionally, large amounts of plane defects and stacking faults were observed. Figure 1 and figure 2 show a cross sectional view of a GSMBE sample and a plane view of a MOVPE one. The observed TD have pure screw and edge character with burgers vectors b in ± [0 0 0 1] directions for the screw and

for the pure edge dislocations. Also mixed TD were found with burgers vectors b in directions. Additionally, HRTEM showed regions tilted by an angle of 60° with regard to the sapphire substrate. These tilted regions are attributed to islands in the AlN buffer layer, which grow tilted to reduce the stress by the lattice mismatch (This results will be puplished elsewhere). The dislocation densities counted from the cross section TEM micrographs lie in the range among 10⁹to 10¹⁰per cm² for the GSMBE and MOVPE samples. The obtained information about the defect structure and the dislocation densities can be taken to prove if it is possible to determine quantitative values for dislocation densities in heteroepitaxially grown GaN by x-ray diffraction. For this purpose we employed the theoretical model described above. TEM micrographs of the GSMBE sample used for x-ray measurements show 3×10⁹ TD/cm² with screw and edge dislocations in the same order of magnitude and additionally large amounts of plane defects. The MOVPE sample taken for the x-ray measurements has 3.5×10⁸/cm² screw dislocations, 6×10⁹/cm²edge dislocations and no plane defects, which was also observed by TEM.

Figure 1. TEM cross section of a GSMBE grown GaN sample

Figure 2. TEM plane view of a MOVPE grown sample

We measured 3 symmetric and 3 asymmetric reflections of each sample. Figure 3 and figure 4 show the plots according to equation 6 for various x-ray peaks. In both cases the symmetric and the asymmetric reflections are not on a single straight line as predicted by the model. Because of the obvious separation of the data in figure 3 and figure 4 the linear fits were separately employed on the symmetric and the asymmetric reflections for each sample. Table 1 shows the dislocation densities calculated according to the Ayers model from slopes and intercepts of these linear fits shown in figure 3 and figure 4. TEM data are given for comparison.

Figure 3. Plot according to Ayers model (GSMBE)

Figure 4. Plot according to Ayers model (MOVPE)

Figure 5. RBS of GSMBE grown GaN

Figure 6. RBS of MOVPE grown GaN

Since the calculated dislocation densities vary significantly, there is a lack of internal consistency when the Ayers model is applied. For the GSMBE sample internal consistency can just be achieved for the results belonging to the symmetrical reflections but the calculated dislocation densities are an order of magnitude lower than the results achieved by TEM. It is not yet understood clearly why the strong separation of the x-ray linewidths appears in both samples. A possible explanation comes out of the real defect structure examined by TEM, where we found stacking faults and other plane defects in addition to the TD in the GSMBE sample. Stacking faults can have a major influence on the strong separation of symmetric and asymmetric linewidths because they create crystal regions with small coherence length perpendicular to the substrate. Stacking faults and other kinds of plane defects however are not included into the Ayers model, which takes only the effect of pure TD into account.

Heying et al. reported that the symmetric (00.2) reflex is broadened by screw or mixed TD, whereas the asymmetric (10.2) reflex is broadened by all TD Reference Heying, Wu, Keller, Li, Kapolnek, Keller, DenBaars and Speck[6]. All the measured asymmetric reflections of our MOVPE sample have broader linewidth compared to the symmetric ones (figure 4). The comparison of the real defect structure gained by TEM with this x-ray results shows that the reason for the different broadening of the peaks must be the same as reported by Heying. For the MOVPE sample internal consistency that is demanded in the Ayers model is just fulfilled for the results of the asymmetric data. Here, the calculated dislocation densities correspond to the density of screw dislocations determined by TEM and not to the total amount of threading dislocations. This is contradictory to Heyings finding and to our TEM results. The specific dislocation structures in heteroepitaxial GaN can lead to anomalously low symmetric rocking curve linewidths Reference Heying, Wu, Keller, Li, Kapolnek, Keller, DenBaars and Speck[6]. For accurate determination of the dislocation densities in heteroepitaxial GaN with the Ayers model this anomalous lowering must be taken into account by modification of the used equations. With our GSMBE sample (figure 3) we observe asymmetric reflections with linewidths smaller than the symmetric ones. This is in contrast to Heyings hypothesis and reveals that the broadening can not only be explained by the ratio of the density of screw to total TD. As mentioned above we propose that plane defects (such as stacking faults) have to be considered, too.

Our x-ray results compiled in figure 3 and figure 4 clearly show that it is not sufficient to measure a single reflex for crystalline optimization. The Ayers model predicts that it should be sufficient to measure three different reflections (symmetric or asymmetric), assuming that the defect structure is determined by TD. We showed that the whole defect structure has to be considered since in GaN beside TD, plain defects are also present, giving significant differences in the defect densities determined from symmetric and asymmetric reflections.

Anyhow, the Ayers model which has proven its validity for different material systems and for GaN bulk crystals Reference Leszczynski[7], is also useful to GaN since it gives indications on the actual defect structure namely if the crystal contains only TD or if other defects are present in addition.

In addition to TEM and x-ray diffraction, RBS and ion channeling measurements were performed to investigate the crystalline perfection of the GaN layers. Figs. 5 and 6 show random RBS and [0 0 0 1] channeling spectra of the GSMBE and MOVPE samples. In the case of the MOVPE sample, the backscattering contribution of N is superimposed on the Al and O contribution of the substrate below channel 400. In the case of the GSMBE sample, the backscattering contribution of the substrate cannot be detected because of the large layer thickness. The GSMBE grown sample exhibits a channeling minimum yield of only 1.2 % indicating a very good crystalline quality. In comparison, the MOVPE sample shows a minimum yield of 3.0 % and a considerable dechanneling with increasing depth, indicating a significantly higher density of structural defects, especially near the interface to the substrate. Further planar dechanneling measurements are necessary to improve the sensitivity for TD perpendicular to the surface.

5. Conclusion

TEM investigations clearly showed the defect structure of our MOVPE and GSMBE grown GaN. Dislocation densities were estimated by TEM cross sections to be in the range between 3x10⁹ to 6x10⁹/cm². A theoretical model for quantitative calculation of dislocation densities from x-ray rocking curve linewidths was applied to the data obtained by our x-ray measurements. The results showed that the employed Ayers model must be modified for stacking faults and other plane defects to give accurate determination of TD densities. Furthermore, anomalous lowering of symmetric reflections in heteroepitaxial GaN also has to be considered when applying the Ayers model on samples with pure TD defect structure. Additionally, our rocking curve analysis showed that optimization on the crystalline quality with symmetric reflections is not sufficient. The asymmetric reflections must also be taken into account. RBS/channeling revealed astonishing low minimum yield of 1.2 % for the GSMBE grown sample (which is comparable to GaAs homoepitaxy) in spite of the high dislocation density. Further investigations in different crystal orientations have to be accomplished to gain a deeper understanding of the RBS data.