The ternary Al Ga N alloys are of interest in the production of high-performance UV wavelength optoelectronic devices such as light-emitting diodes (LEDs) and photo-detectors in the UV spectral region in the range of 200 nm–365 nm according to the band gap of AlGaN.^[1,2] However, due to the large mismatch in lattice constant and thermal expansion coefficient between the epitaxial layer and substrates,^[3–5] as well as the much lower mobility of Al versus Ga (Ga–N bond energy = 2.2 eV, Al–N bond energy = 2.88 eV),^[6] AlGaN materials typically have high density defects, which act as non-radiative recombination centers. As a result, these high density defects are detrimental for device applications. Therefore, it is vital to conduct detailed structural analyses and improve crystal quality to fabricate efficient devices.

Heteroepitaxial thin films with large lattice mismatch to the substrate can be modeled by mosaic structure consisting of many small hexagonal grains,^[7–10] as illustrated in Fig. 1.^[11,12] Based on the mosaic model, the structural properties can be thoroughly analyzed by using Williamson–Hall plots calculated from XRD data, which provide information of the layers including tilt angle ( ), heterogeneous strain ( ), vertical coherence length , and lateral coherence length .^[13] Meanwhile, a reciprocal space map (RSM) of asymmetric reflections was also performed. Both the mosaic tilt and lateral coherence length can also be determined from the inclination angle of asymmetric reciprocal lattice points (RLPs).^[11] In addition, a mosaic twist can be extracted from rocking curves of asymmetric reflections in off-axis skew symmetric geometries with increasing lattice plane inclination.^[14,15] Recently, some literature discussed the above mosaic model and estimated the structural quality of III-nitrides,^[16–24] which proved the validity of this method.

Fig. 1.

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	Fig. 1. (color online) Illustration of a mosaic structure with characteristic parameters.

In contrast, transmission electron microscopy (TEM) measurements are performed in order to obtain a direct observation of structural defects. Therefore, the aim of the present paper undertakes a detailed study on the structure characteristics of AlGaN layer, including tilt angle, twist angle, heterogeneous strain, vertical coherence length, lateral coherence length, and dislocation (edge and screw dislocation densities). Furthermore, it demonstrates determining structural quality by different XRD measurement methods, which are verified by the results obtained by TEM.

Al Ga N epilayer was grown at 1100 °C on GaN template with high temperature AlN layer (HT-AlN) as the interlayer at a reactor pressure of 76 Torr (1 Torr = 1.33322 Pa) by metal organic chemical vapor deposition (MOCVD). The molar flux of trimethylgallium (TMGa), trimethylaluminum (TMAl) and ammonia (NH ) were 1.375 × 10 mol/min, 1.18 × 10 mol/min, and 1.62 × 10 mol/min, respectively. The detail of the growth procedure was described in Ref. [25]. The thickness of AlGaN layer was measured as about 0.502 μm by TEM.

The x-ray diffraction measurements were performed using high resolution x-ray diffractometer (PANalyticalX’Pert Pro MRD) equipped with a four-crystal Ge (220) mono chromator and a three reflection Ge (220) analyzer, delivering x-ray of Cu Ka line = 0.15406 nm with a resolution limit of about 12 arc sec. The cross-sectional transmission electron microscope (TEM) images were taken by FEI Tecnai G2 F20 S-TWIN working at 200 kV.

The mosaic structure of the AlGaN epilayer is evaluated by the size and the angular distribution of the mosaic blocks by Williamson–Hall (W-H) plots.^[13] Figure 2(a) shows the corresponding W-H plots of (0002), (0004), (0006) reflection planes for triple-axis ω scan of the samples. The straight lines are linear fits of the experimental data, where the FWHM is given with reciprocal lattice units, is the Bragg reflection angle and is the x-ray wavelength. From the y-intersection , the lateral correlation length is estimated to be 0.452 μm using . Since the broadening in symmetric diffractions using W-H plot is only sensitive to the pure screw-type dislocations or the screw-type component of mixed-type dislocations,^[4] the determined lateral coherence length characterizes the mosaic structure correlated with the screw-type dislocations. The tilt angle of 0.060 degree is obtained from the slope of the linear dependence. The screw-type dislocations density of 1.0 × 10 cm was obtained using Eq. (1).^[26]

Fig. 2.

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	Fig. 2. (a) Triple-axis ω scan for measuring tilt angle and lateral coherence length from W-H plot for AlGaN layers; (b) Triple-axis ω– scan for measuring heterogeneous strain and vertical coherence length of AlGaN layer from W-H plot for AlGaN layers.

For determination of the heterogeneous strain and vertical correlation length, FWHM is plotted against for each reflection and again fitted by a straight line as shown in Fig. 2(b). From the y-intersection , the vertical correlation length (0.767 μm) can be obtained using , which is close to the thickness of AlGaN film. The strain value is calculated to be 6.5 × 10 from these symmetric reflections.

The reciprocal space map of Al Ga N diffraction can be also used to calculate the lateral correlation length and tilt. Figure 3 shows the reciprocal space map taken from asymmetric reflection, where and are the reciprocal space coordinates, which are parallel and perpendicular to the surface normal, respectively.

Fig. 3.

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	Fig. 3. Reciprocal space map of Al Ga N . The straight line is used for measuring the FWHMs of the overall ellipse.

Using the trigonometry relationships, the lateral correlation length can be obtained by Eqs. (2)–(4)

The lateral coherence length of AlGaN epilayer was calculated to be 0.048 μm from the RSM measurements, while the tilt angle (0.464 degree) obtained by RSM is much larger than the result (0.060 degree) obtained by W-H plot previously described. Since the orientation of the RSM is sensitive to tilt and lateral coherence length using a dynamic diffraction model developed by Holy et al.,^[10] an extraction of both and from RSM of reflection is not feasible. The results indicated that the tilt angle obtained by W-H plots and the calculated from RSM are close to TEM observation.

As to determining the twist angle in the mosaic structure of Al Ga N film, the twist angle is measured in off-axis skew symmetric rocking curves of , , , , , and symmetric planes. The theory of rigid body rotations can be taken into account for the fitting by Eqs.(6) and (7).^[14]

As is shown in Fig. 4, the fitting of data points is utilized to extrapolate FWHMs of asymmetric planes versus inclination angles, and the twist can be extracted by an extrapolation to φ = 90°. In this case, the result of the twist angle is about 0.392 degree.

Fig. 4.

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	Fig. 4. Measured FWHMs of off-axis skew-symmetric (except (0002) plane) plotted against surface-to-plane angle.

Accordingly, the dislocation density of AlGaN film was calculated from the following Eq. (8).^[26]

If dislocations are piled up in small grain boundaries to release strain, the density of edge-type dislocations can be obtained by Eq. (9).^[27]

Thus the density of edge-type dislocation of Al Ga N is 1.8×10 cm . The above calculated results are given in Table 1.

Table 1.

Table 1.

Table 1. Summary of the structural parameters of the Al Ga N film obtained by HRXRD and TEM. . Parameter Value Method Lateral correlation length /μm 0.452 W-H plot 0.048 RSM 0.407 TEM (average distance of screw-typed dislocation) 0.052 TEM (average distance of edge-typed dislocation) Vertical correlation length m 0.767 W-H plot 0.502 TEM Tilt angle /(°)} 0.060 W-H plot 0.464 RSM Twist angle /(°) 0.392 Srikant model[14] Heterogeneous strain parallel 6.5×10 W-H plot Screw dislocation density /cm 1.0 ×10 W-H plot 2.0×10 TEM 6.0×10 RSM Edge dislocation density /cm 1.3 ×10 [Eq. (8)] 1.8×10 [Eq. (9)] 2.8 ×10 TEM

Table 1. Summary of the structural parameters of the Al Ga N film obtained by HRXRD and TEM. .

TEM analysis is a direct method to characterize defect properties of thin film. Figure 5 shows the cross-sectional TEM images of the sample. The screw-type and edge-type dislocations can be observed under Burgers vectors [0002] and , respectively. Based on counts of threading dislocations, the screw-type and edge-type dislocation densities of the sample are 2.0×10 cm and 2.8×10 cm , respectively. From cross-sectional TEM images, the lateral correlation length caused by edge-type dislocation is 0.052 μm, and the average distance between screw-type dislocations is 0.407 μm for Al Ga N film, which agrees with the XRD results.

Fig. 5.

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	Fig. 5. Cross-sectional TEM images of Al Ga N layer: (a) burger vector of [0002]; (b) burger vector of .

The mosaic characteristics of Al Ga N epitaxial layer have been studied by XRD analysis and TEM observation. The structural features including heterogeneous strain, correlation lengths, tilt, twist, and dislocation densities have been determined by means of Williamson–Hall plots and the theory of rigid body rotations from HRXRD. The RSM is also performed for investigation of the AlGaN epilayer to estimate tilt and lateral correlation lengths. The result shows that the lateral correlation lengths obtained by W-H plot and RSM agree with the results obtained by cross-sectional TEM with Burgers vectors [0002] and , respectively. The vertical coherence length of the AlGaN epilayer is consistent with the thickness of AlGaN layer. Furthermore, the screw-type and edge-type dislocation densities obtained from HRXRD are in good agreement with the results observed from TEM, which proves accuracy of evaluation for the dislocation density using the mosaic model.