Nondestructive visualization of threading dislocations in GaN by micro raman mapping

Threading dislocations (TDs) in a HVPE-grown c-plane (0001) GaN single crystal were analyzed by micro Raman spectroscopy mapping. The mapping image exhibited the pairs of higher and lower wavenumber regions of E 2 H peak shift of GaN, which corresponded to the compressive and tensile strains due to TDs. By comparing X-ray topography and etch pit images, the contrasts are considered as the edge component of TDs. By analyzing the existing 290 TDs in 80 × 80 μm2, the directions of the contrast were mainly dominant toward 〈 10 1 ¯ 0 〉 . A few brighter contrasts toward 〈 11 2 ¯ 0 〉 were also observed. These TDs are affiliated with Burgers vectors b = a / 3 〈 11 2 ¯ 0 〉 , and b = a 〈 0 1 ¯ 10 〉 , respectively. Judging from experimental and simulated result, it is confirmed that the contrast in the Raman mapping image of the b = a 〈 0 1 ¯ 10 〉 has a larger magnitude than the b = a / 3 〈 11 2 ¯ 0 〉 .


Introduction
Wide band-gap semiconductors, silicon carbide (SiC) and gallium nitride (GaN), have attracted considerable attention as next-generation power semiconductor materials because of high-temperature operation owing to its large band-gap and low intrinsic carrier density. SiC-based power device has started mass production with 150 mm wafers. Although state of the arts hydride vapor-phase epitaxy (HVPE)-grown freestanding GaN substrates have become commercially available, the size is only 50 mm and their dislocation densities are still on the order of 10 6 cm −2 . [1][2][3][4] These GaN substrates contain threading dislocations (TDs), those of which are composed of threading screw dislocations (TSDs), threading edge dislocations (TEDs), and threading mixed dislocations (TMDs). The TSDs, TEDs, and TMDs have dislocations propagating to the c-axis with Burgers vectors of b = c 0001 , á ñ a 3 1120 , á ñ / and c a 0001 3 1120 , á ñ + á ñ / respectively. It is important to characterize the TDs in GaN crystals because the device performance would be affected by existence of the TDs. [5][6][7][8][9][10][11][12] Several evaluation methods for TDs in GaN crystals are proposed, such as chemical etching, [13][14][15][16] transmission electron microscopy (TEM), [17][18][19] X-ray topography, 20) cathodoluminescence (CL), 16,21) and photoluminescence (PL). 22) Among them, the chemical etching of GaN bulk crystals is commonly used: however, classification of the dislocations is relatively difficult because the shape of the etch pits depends on the etching conditions and crystal manufacturing methods. 15,16) TEM can determine the Burgers vector of dislocations: [17][18][19] however, the sample must be thinned into a thickness of several 100 nm, which requires time and destructive process. The X-ray topography is usually used as a nondestructive characterization method for determination of the direction of the Burgers vector of TMDs and TSDs in GaN crystals: 20) however, a synchrotron radiation facility is required to obtain clear contrast images. CL mapping measurements can identify the location of dislocations:, 16,21) however, they must be performed under vacuum conditions. The three-dimensional imaging of TDs in GaN films was recently visualized by two-photon excitation PL without any destructive preparations. 22) We proposed the micro Raman spectroscopy mapping as a nondestructive characterization method for evaluation of TDs in GaN. 23,24) In the commercially available GaN freestanding substrates, the densities and types of the TDs would vary between wafer venders. It is unrealistic to determine the direction and magnitude of Burgers vectors for all TDs by TEM. By analyzing the Raman mapping of the E H 2 peak shift within 0.1 cm −1 range, the density, direction, and magnitude of the edge component of the TDs were determined. 24) In this study, we analyzed the direction of the E H 2 peak shift from Raman spectroscopy mapping images for 290 TDs. By comparing computer simulation, we found that almost all TDs were composed Burgers vectors of b a 3 1120 , = á ñ / a few TDs were composed of b a 0110 .

Experimental
A HVPE-grown c-plane GaN substrate, produced by Nanowin, was used as the evaluation sample. The thickness and density of the TDs were 350 μm and ∼10 5 cm −2 , respectively. Raman scattering spectroscopy measurements were performed at RT using an in-Via Raman system (RENISHAW). 23,24) To increase the wavenumber resolution, the 532 nm laser intensity was maximized ∼150 mW and the grating width of 3000 gl mm −1 was selected. An objective lens with a magnification of 100 times and a high numerical aperture of 0.85 were used. The theoretical minimum spot size and excitation power density were estimated to be 0.76 μm and 33 MW cm −2 , respectively. The laser was focused at 1.0 μm depth from the surface and the depth range of focus was calculated as ± 0.86 μm. The irradiation time and integration number were 0.2 s and 1, respectively.
A step width of 0.3 μm was applied to increase the spatial resolution. The wavenumber resolution at the detector was estimated to be 0.8 cm −1 . For data analysis, the Raman software WiRE 3.4 (made by RENISHAW) was used. X-ray topography was conducted at the beam line of BL8S2 in Aichi Synchrotron Optical Center. The diffracted X-rays were imaged on a nuclear dry plate. In X-ray topography, the diffraction planes of g 0006 = was used. The penetration depth of the g 0006 = was estimated to be t 15.78 m.
The etch pit formation of GaN substrate was chemically etched by a KOH in the Ni crucible at 500°C for 15 min. After the etching, the surface of GaN were observed by optical microscope.
The simulation of Raman mapping is based on the theory of elasticity. 25) The strain field ( i e ) around the TD in the GaN crystals is calculated by using the elastic compliance constant (S ij ) and the stress field  26) Additionally, the lattice constants a 0.319 = nm and c 0.519 nm = were adopted. 27) Fig. 1 ) were used. 28) By this conversion, the distribution of the peak shifts was calculated. The Raman mapping image was created by calculating the peak shift at each point with a 0.3 μm step. The detailed simulation procedure will be reported in a separate paper.

Results and discussion
3.1. Comparing etch pit, X-ray topography, and Raman mapping images Figure 2(a) shows an etch pit image of the GaN single crystal (100 × 100 μm 2 ). Two different contrasts (black and white hexagonal shape) are clearly observed. The black ones have the densities of 2.6 × 10 5 cm −2 and are considered as the TDs. In contrast, the white ones are not related to the TDs since there is no core from depth profile (not shown). In our etching condition, it is difficult to classify TDs into TEDs, TSDs, and TMDs. Figure 2(b) shows an X-ray topography image along the g 0006 = diffraction at the same location. It should be noted that the X-ray topography was measured before etch pit formation. In the X-ray topography image along the g 0006, = the TSDs and TMDs are observed as bright dot-like contrast. The TEDs cannot be observed in the g 0006 = diffraction due to g b 0. = · In the Raman mapping contrast image of the E H 2 peak shift in Fig. 2(c), the white (higher wavenumber) and the black (lower wavenumber) regions are clearly observed. It is noteworthy that the wavenumber resolution at the detector is estimated to be 0.8 cm −1 , change in E H 2 peak shift within 0.1 cm −1 range is detected. We insist very slight peak shift can be discussed by peak fitting using Voigt function. When an isotropic compressive strain is applied to the GaN crystal, the E H 2 peak is shifted to the higher wavenumbers and a tensile strain results in the lower wavenumbers. 28) Therefore, it is considered that compressive strain and tensile strain are present as a pair at a place where contrast appears, which can be addressed as the TEDs and TMDs. As already reported, the TSDs do not affect the E H 2 peak shift. This is because the shear strain, which is described as TSDs, has less influence on the E H 2 peak shift. 29) Comparing the contrast spot in Figs. 2(b) and 2(c), the TEDs and TMDs are classified as red arrows and green arrows, respectively. The density of the TEDs and TMDs are then counted as 1.0 × 10 5 cm −2 and 1.3 × 10 5 cm −2 , respectively. The density of the TSD is estimated to be less than 1.0 × 10 4 cm −2 because there is no TSDs in the 100 × 100 μm 2 scan area. Figure 3(a) shows a typical Raman mapping image of the E H 2 peak shift of 80 × 80 μm 2 . Here, the direction from the white (higher wavenumber) to the black (lower wavenumber) regions is indicated by the white dotted arrow. As seen in Fig. 3(b)   respectively. It is clearly seen the directions from the higher wavenumber region to the lower wavenumber region are found to be in the 90°rotation from the Burgers vectors. The directions of the contrast by simulation agree with experimental result. Therefore, the direction of the edge component of the TD can be identified by analyzing the Raman mapping image.

The magnitude of the edge-component Burgers vector in GaN crystal
In order to discuss the magnitude of Burgers vector of TDs, the E H 2 peak shift of the TD-A and TD-B were compared.   [  and ±0.04 cm −1 , respectively. Although the shapes of the line profiles are consistent with the experimental results as in Fig. 5(c), the maximum E H 2 peak shifts in the simulation results are larger than that in the experimental results. We suspect that the laser irradiation region in the experimental setup was wider than that in the simulation model. In this situation, the maximum E H 2 peak shift is emphasized near the TD in the simulation model, because only a large distortion is considered near the TD. These results indicate that the direction and magnitude of the Burgers vector can be identified according to the contrast image of Raman mapping.

Conclusions
We analyzed TDs in a HVPE-grown c-plane (0001) GaN single crystal by micro Raman spectroscopy mapping. The mapping image exhibited the pairs of higher and lower wavenumber regions of E H 2 peak shift of GaN, which corresponded to the compressive and tensile strains due to TDs. The location of contrast spots of the E H 2 peak shift from Raman mapping image agreed with that of the etch pit image. The location and the density of the TED and TMD were classified by comparing the X-ray topography image along the g 0006.
= By comparing X-ray topography and etch pit images, the contrasts are considered as the edge component of TDs. By analyzing the existing 290 TDs in 80 × 80 μm 2 , the directions of the contrast were mainly dominant toward 1010 . á ñ A few brighter contrasts toward 1120 á ñ were also observed. These TDs are affiliated with Burgers vectors of b a 3 1120 , = á ñ / and b a 0110 , = á ñ respectively. Judging from the experimental and simulated result, it is confirmed that the contrast in Raman mapping image of b a 0110 = á ñ has a larger magnitude than the b a 3 1120 . = á ñ /