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Probing Crystal Dislocations in a Micrometer-Thick GaN Film by Modern High-Voltage Electron Microscopy

We report on extreme penetration power of relativistic electrons in a micrometer-thick gallium nitride epitaxial film and its application to probing threading dislocations, which were introduced during crystal growth. Maximum usable thickness of the specimen was quantitatively evaluated using high-voltage transmission electron microscopy (TEM) operating at 1 MV. The width of dislocation images was used as a measure for the evaluation of usable thickness. Superior maximum usable thickness was obtained in scanning transmission electron microscopy (STEM) than in TEM mode; the results were 6.9 μm for STEM and 4.4 μm for TEM. In STEM, dislocations can be imaged with an almost constant width of 15–20 nm in a wide thickness range 1–4 μm. The latest high-voltage STEM is thus useful for observing dislocations in micrometer-thick inorganic materials.


■ INTRODUCTION
Dislocations in a semiconductor crystal, such as gallium nitride (GaN), degrade its optical and electrical properties. The key to the development of high-performance light-emitting and electronic devices is the growth of highly complete crystals with a low dislocation density. 1 To detect and characterize lattice defects in a crystalline solid, transmission electron microscopy (TEM) is a powerful technique in respect of spatial resolution compared to other methods such as X-ray topography. 2 Imaging of dislocations by TEM is based on diffraction contrast, and the procedure has been established. 3 To visualize spatial distribution of dislocations, a novel approach was examined using electron tomography, which revealed three-dimensional dislocation networks in GaN. 4 However, electron transmittance limits the maximum usable (or observable) thickness of the specimen at most ∼0.3 μm in the case of conventional 200 kV TEM (this was examined by our preliminary study). The importance of observing sufficiently thick specimens that can be regarded as bulk was proved half a century ago using high-voltage electron microscopy (HVEM); namely, solid-state phenomena such as recrystallization, phase transition, and dynamic behaviors of crystal dislocations in metal foils thinner than a critical thickness differ from those observed in the bulk alloys. 5 In the years around 1970, considerable interest was focused on investigating the maximum usable thickness using HVEM. 6−11 However, the penetration of relativistic electrons depends on imaging conditions as well as materials, 12,13 and quantitative unified views regarding the maximum usable thickness have not been obtained. As mentioned above, the history of this topic is long over 50 years; however, recent interest in crystal defects and internal structures in semiconductor devices has drawn renewed attention to visualizing microstructures in an extremely thick specimen by HVEM. 14,15 Recently, the authors reported that high-voltage (HV) scanning transmission electron microscopy (STEM) is capable of imaging dislocations in Si(110) crystals over 14 μm in thickness. 16 In principle, STEM has the benefit of being free from the effect of chromatic aberration since there is no imaging lens. Moreover, the technique is known to be less affected by the unfavorable diffraction contrast such as equalthickness contour or bend contour (the word "unfavorable" is used here in a sense that aforementioned contours prevent clear-cut visualization of crystal defects such as dislocations). 17,18 This is due to the nature of STEM imaging using a converged electron probe. HV-STEM is hence the suitable imaging technique that can reveal the microstructures of a micrometer-order thick specimen in a nanometer-scale spatial resolution as well as a multiscale field of view.
In this study, we examined quantitative assessment of the maximum usable thickness of a GaN crystal with high-density threading dislocations (TDs) using HV-STEM and HV-TEM. TDs in GaN are mostly straight lines, and hence, they are expected to act as a good marker for discriminating transmittance of electrons. We show superior usable thickness in HV-STEM than in HV-TEM, and the obtained results are discussed. Figure 1a shows a secondary electron image of a wedge-shaped GaN crystal observed in an oblique direction. An isosceles triangle cross section is suitable for the systematic investigation of the usable thickness by HVEM. Cross section of the wedgeshaped specimen is schematically shown in Figure 1b. Electrons are incident on the wedge-shaped crystal from the direction indicated by an arrow, and also from the opposite direction for comparison. Thickness of the wedge-shaped specimen changes from 0.5 to 8.3 μm. Figure 2a shows a bright-field (BF) STEM image of the wedge-shaped GaN with high-density TDs. The specimen becomes thicker from the right (0.5 μm) to the left (2.5 μm) of the image. Appearance of the specimen and the selected area electron diffraction (SAED) pattern are shown in Figure 2b,c, respectively. We subjected a specimen to a two-beam condition by exciting the 1̅ 100 reflection. TDs are seen as lines almost parallel to [0001] GaN with dark contrast in a bright background, and the dislocation images become blurred as the thickness increases. Judging from the invisibility criterion for wurtzite GaN, 19,20 these TDs in GaN are almost either a-type (threading-edge) or a+c-type (threading-mixed). Note that ctype (threading-screw) TDs were identified by exciting 0002 reflection as well, while their number was a few. Then, the specimen was turned upside down and comparable observation was made (Figure 2d−f). In Figure 2d, the specimen becomes thicker from the left (0.5 μm) to the right (2.5 μm) of the image. It was found that the same dislocations were identified both in Figure 2d,a in the area with thickness at least less than 2.5 μm. Dislocation width was not affected by the observation direction to the specimen. It should also be noted that the width of dislocation images is independent of collection semiangle of the BF-STEM detector in the range of 4−25 mrad. As the collection semiangle increases, image intensity enhances, which leads to a brighter image contrast. Figure 3 shows a composite BF-STEM image showing overall area of the wedge-shaped GaN specimen. The contrast

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Article of each image was adjusted locally to show the dislocations clearly. The specimen becomes thicker from the right (0.5 μm) to the left (8.3 μm) of the image. Dislocation density was on the order of 10 12 m −2 and was almost constant, regardless of the thickness, while apparent areal number density of TDs gradually increased as the thickness increased. On the basis of the analysis of areal number density of TDs, we found that overlapping of TDs in the observation direction is negligible, and hence, it little affects evaluation of the width of dislocation images. Dislocation images become blurred as the thickness increases. A notable feature is that it is possible to judge whether TDs exist even in the thick region with thickness around 7 μm. This is the direct evidence that 1 MeV electrons can transmit a 7 μm thick GaN crystal. More quantitative evaluation of the usable thickness is shown in Figure 6. Figure 4 shows a composite BF-TEM image showing overall area of the wedge-shaped GaN, corresponding to the STEM images shown in Figure 3. Dislocation images are almost invisible at thickness around 5 μm, indicating the superior usable thickness in STEM (i.e., Figure 3) than in TEM (i.e., Figure 4). Namely, usable thickness depends on the imaging mode, converged beam, or parallel beam, while the electron energy is the same in both cases (1 MeV). Figure 5a,b compare BF-STEM and BF-TEM images of the same area with thickness of 0.8−2.2 μm. As can be seen, same dislocations are imaged in STEM and TEM modes, and this tendency was observed in the thickness range up to 4 μm. Thus, reciprocity of BF-STEM and BF-TEM can be confirmed qualitatively. Note that the dislocation image contrast in STEM is slightly sharper than that obtained in TEM. We found that annular dark-field (ADF) STEM at 1 MV was not useful for imaging dislocations in a thick specimen in respect of low detection efficiency due to weak intensity of an ADF-STEM signal. Namely, sufficient signal strength is mandatory for imaging microstructures in a micrometer-order thick specimen.
To quantitatively evaluate usable thickness, we measured width of dislocation images as a function of the specimen thickness. The width is defined as full width at half-maximum of the image intensity profile measured perpendicular to a dislocation line. Figure 6 shows the thickness dependence of the width of dislocation images measured from the STEM and TEM images. To avoid ambiguity regarding the visibility of dislocations, we introduced a criterion for the evaluation of usable thickness: theoretical dislocation width ξ hkl /π (ξ hkl stands for the extinction distance of the hkl reflection excited for imaging) 21 was employed as the criterion. Dashed line indicates the criterion ξ 1̅ 100 /π = 28.2 nm (ξ 1̅ 100 = 88.6 nm at 1 MV for GaN), and we judged that data points below this line are "observable". As seen, width of dislocation images increases as the thickness increases. The obtained maximum usable thickness is 6.9 μm for BF-STEM and 4.4 μm for BF-TEM operating at 1 MV.

■ DISCUSSION
Focusing on the results of STEM, in the thickness range between 1 and 4 μm, we found that the width of dislocation

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Article images shows weak thickness dependence and the values are distributed around 15−20 nm. This result may be related to the depth of focus of STEM. Let us consider a STEM probe with the convergence semiangle α and depth of focus Δz. Assuming the smallest converged STEM probe (approximately 1 nm at 1 MV in the present experimental setup), a depth of focus as short as 110 nm is derived using the following equation where λ denotes the wavelength of incident electrons. 22,23 However, same dislocations were observed irrespective of the beam incidence direction to the wedge-shaped specimen with the thickness less than 2.5 μm, which is 23 times longer than the short depth of focus estimated above (Figure 2). This result suggests that Δz defined by the eq 1 no longer serves as an indicator of the usable thickness. By contrast, assuming an object with a lateral length d, the extended depth of focus can be approximated as follows 16,22 When d is equal to the width of dislocation image and by assigning the values of d = 20 nm and α = 3.75 mrad, Δz ext = 5.3 μm is obtained. Namely, if we accept the blurring of the dislocation images at most 20 nm, a specimen with thickness up to approximately 5 μm can be imaged in focus using 1 MV STEM. This is a simple geometrical consideration but in good agreement with the experimental result shown above.
As the thickness increases more than 4 μm, the distribution of the width of dislocation images spreads rapidly ( Figure 6). This is presumed to be due to possible lateral spread of the STEM probe (δ) proportional to t 3/2 (t denotes thickness of the specimen). 24 The solid curve shown in Figure 6 represents the fitted curve expressed as follows t 14 110 3/2 δ = + As can be seen, beam broadening well represents the distribution of the data points for STEM. Transmitted (T) and diffracted beam intensities (R) for 1 MV TEM were calculated by solving the Darwin−Howie− Whelan equations under a two-beam condition including absorption. 3 The T and R are expressed as follows 18 Ä  where s is the excitation error, ξ 0 is the extinction distance of the forward scattering, ξ g is the extinction distance of the diffracted beam, ξ 0 ′ and ξ g ′ are attenuation terms of ξ 0 and ξ g due to absorption, and t is the thickness that electrons propagate, with abbreviations μ 0 = 2π/ξ 0 ′, μ g = 2π/ξ g ′, and w = sξ g . Figure 7a shows calculated thickness dependence of the T and R, assuming ξ g = 88.6 nm (for g = 1̅ 100 GaN at 1 MV), ξ g / ξ g ′ = 0.10, ξ 0 ′ = ξ g ′, and w = 0.40. Under these conditions, T reproduces the experimental result, i.e., T = 0.05 at t = 4.4 μm (=50ξ g ). Note that we assumed a criterion that the minimum of 5% of the transmitted beam should remain, and below which the image contrast is invisible. Intensity oscillations for both T and R are due to the equal-thickness fringes. Figure 7b shows the parameter w dependence of T calculated for t = 6ξ g , 12ξ g , and 50ξ g at 1 MV. The peak position shifts toward w > 0, especially for t = 6ξ g and 12ξ g . This represents the well-known fact that, for BF-TEM imaging in a two-beam condition, the best transmission can be obtained when s is slightly positive. 3 As the thickness increases, the peak position of the T shifts toward w = 0 and the peak height reduces. The calculation revealed that, to obtain the best transmission, fine adjustment of the parameter s, as possible as one can, is effective, depending on the specimen thickness. However, it should be noted that it is practically difficult to see diffracted beams when specimen thickness becomes fairly thick (e.g., t = 50ξ g ).
In this study, superior usable thickness in STEM to that in TEM was found, as shown in Figure 6. The similar tendency was obtained in our previous study on Si(110) wedge-shaped crystals, 16 where the effect of the spatial distribution of dislocations was not considered explicitly. By contrast, distribution of TDs in GaN can be regarded as statistically homogeneous; the results shown in Figure 6 are not affected by the spatial distribution of TDs.

Article
In TEM observation, chromatic aberration arising from the postspecimen lens seriously degrades the resolution when observing a thick specimen. However, as already mentioned in the Introduction section, STEM requires no imaging lens for electrons transmitted through a specimen. Therefore, STEM is practically free from the effect of chromatic aberration, which may cause the superior usable thickness. From the viewpoint of chromatic aberration, the use of an energy filter (EF), which is based on electron energy-loss spectroscopy and hence inelastic scattering electrons can be either removed or selected, is also an effective solution. Using an EFTEM operating at 1.25 MV, Sadamatsu et al. reported a unique imaging technique incorporating inelastic scattering electrons; dislocations in a thick Si(001) over 10 μm have been imaged where zero-loss signal was absent. 25 Note that the maximum usable thickness of a wedge-shaped Si(110) crystal was 14.7 μm for 1 MV STEM. 16 Currently, HV-STEM and HV-EFTEM are useful methods for imaging microstructures in an extremely thick specimen, and a direct comparison between these two techniques regarding merits and demerits has not been examined yet, which will be clarified by investigations in the future.

■ CONCLUSIONS
We have studied the maximum usable thickness of the wedgeshaped GaN crystal in 1 MV STEM and 1 MV TEM using the width of dislocation images as a criterion for the quantitative evaluation. Superior usable thickness in STEM to that in TEM mode was demonstrated; the obtained results were 6.9 μm for STEM and 4.4 μm for TEM. In STEM mode, same dislocations were identified, regardless of the beam incidence direction to the wedge-shaped specimen when the thickness is less than 2.5 μm. Reciprocity of BF-STEM and BF-TEM was confirmed qualitatively as the same dislocations were imaged in STEM and TEM modes in the thickness range up to 4 μm. Intensity simulation reproduced the extreme penetration power of 1 MeV electrons. Fine adjustment of the excitation error is effective to obtain the best transmission. ■ EXPERIMENTAL PROCEDURES TEM Specimen Preparation. To quantitatively evaluate the usable thickness by HV-STEM, we studied a heteroepitaxial GaN film grown on α-Al 2 O 3 (0001). Wedge-shaped specimens were fabricated from the GaN film using a focused ion beam system. The specimen shapes were characterized using a scanning electron microscope (SEM) operating at 10 kV.
Characterization. Dislocations in a GaN film were observed using a JEOL JEM-1000EES operating at 1 MV equipped with a LaB 6 cathode. We subjected a specimen to a two-beam condition by exciting the 1̅ 100 or 11̅ 00 reflection of wurtzite GaN. BF-TEM images were obtained using a 20 μm objective aperture with a semiangle of 2.8 mrad, and they were recorded using a 2k × 2k charge-coupled device camera (Gatan Orius SC200D) with an exposure time of 1−180 s. In the BF-STEM imaging, the beam convergence was set to a semiangle of 3.75 mrad using a 50 μm condenser aperture and the outer collection angle on the BF detector was set to 4−25 mrad. STEM images 1k × 1k in size were acquired with a dwell time of 256−1365 μs/pixel, depending on the specimen thickness.