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Local Strain and Crystalline Defects in GaN/AlGaN/GaN(0001) Heterostructures Induced by Compositionally Graded AlGaN Buried Layers Hryhorii V. Stanchu, Andrian V. Kuchuk, Yuriy I. Mazur, Chen Li, Petro M. Lytvyn, Martin Schmidbauer, Yurii Maidaniuk, Mourad Benamara, Morgan E. Ware, Zhiming M. Wang, and Gregory J. Salamo Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b01267 • Publication Date (Web): 07 Dec 2018 Downloaded from http://pubs.acs.org on December 11, 2018

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Crystal Growth & Design

Local Strain and Crystalline Defects in GaN/AlGaN/GaN(0001) Heterostructures Induced by Compositionally Graded AlGaN Buried Layers Hryhorii V. Stanchua,b, Andrian V. Kuchukb,*, Yuriy I. Mazurb, Chen Lib, Petro M. Lytvyna,b,c, Martin Schmidbauerd, Yurii Maidaniukb, Mourad Benamarab, Morgan E. Wareb, Zhiming M. Wanga,*, Gregory J. Salamob aInstitute

of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China

bInstitute

for Nanoscience & Engineering, University of Arkansas, W. Dickson 731, Fayetteville, Arkansas 72701, United States

cV.

Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Pr. Nauky 41, 03680 Kyiv, Ukraine dLeibniz-Institute

for Crystal Growth, Max-Born-Str. 2, D-12489 Berlin, Germany

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ABSTRACT: Plastic strain relaxation in epitaxial layers is one of the crucial factors that limit the performance of III-nitride-based heterostructures. In this work, we report on strain relaxation and crystalline defects in heterostructures consisting of compositionally graded AlGaN epitaxial layers tensile-strained between a GaN-buffer and a GaN-cap. We demonstrate the effects of Al concentration and the shape of the concentration-depth profile in the buried graded layers on the accumulated elastic strain energy and how this influences the critical thickness for crack generation or fracture. It is shown that this fracture leads to the formation of partially relaxed regions with their degree of strain relaxation directly related to the density of cracks. Nevertheless, even though the in-plane coherency between the AlGaN layer and the GaN-buffer is broken, the in-plane coherency within the AlGaN layer is preserved for all regions. Furthermore, the tensile strain released in the buried graded AlGaN layers is consistent with compressive strain induced in the GaN-cap layers. Finally, the localized stress and the densities of threading dislocations are correlated with the features of the resulting fractured heterostructures. These results are important towards the control of complex plastic strain relaxation and further facilitate the growth of high quality compositionally graded AlGaN-based devices. KEYWORDS: AlGaN; epitaxy, graded layers; strain relaxation; X-ray diffraction; cracks. 1. INTRODUCTION III-nitride semiconductors have attracted considerable attention as promising materials for a variety of optoelectronic devices 1. In particular, compositionally graded AlGaN has unique properties with numerous practical applications. For example, the so-called polarization doping technique demonstrated for [0001]-oriented graded AlGaN layers facilitates p-type doping instead of using the very high ionization energy (0.63 eV) Mg-acceptor 2. By simply reversing the grading 2 ACS Paragon Plus Environment

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(i.e. from GaN to AlxGa1-xN or from AlxGa1-xN to GaN), three-dimensional electron (3DEG) or hole (3DHG) gases, respectively, can be obtained without the need of intentional impurities. Alternatively, it has been found that this polarization field can greatly enhance the efficiency of traditional dopants such as Mg in order to achieve very high carrier concentrations 3. The advantage of this technique has been demonstrated through the fabrication of such devices as deep-UV light emitting diodes

4–6,

lasers

7,8,

p-n junctions

9–11,

and metal-oxide-semiconductor heterostructure

field-effect transistors 12. Recently, non-alloyed ohmic contacts with record low resistance were reported for GaN-based transistors with a graded AlGaN heterojunction 13. The -shaped profile of Al concentration eliminates the abrupt heterojunction band offsets and provides direct contact to the 2DEG channel. This creates the possibility of having ultra-low resistance non-alloyed ohmic contacts for wide gap materials without barrier recess or regrowth processes. In addition, as demonstrated in 14 GaN/AlGaN/GaN double heterojunction structures (DHS) with graded AlGaN display better conductivity for smaller reverse bias than for forward bias voltages (reverse rectifying behavior), which is opposite to p–n junction rectifying characteristics. This makes it possible to realize novel GaN-based heterojunction transistors. Regardless of the substrate type, the 2.4% in-plane lattice misfit between the c-oriented GaN and AlN leads to the accumulation of elastic strain energy in graded AlGaN. The amount of the elastic energy stored in the AlGaN layers strongly depends on the substrate (lattice misfit compressive or tensile strain energy), layer thickness and depth profile of the Al composition. The stress-state in graded AlGaN epitaxial layers as a function of these parameters is important to control since the accumulated elastic strain energy is partially released by the formation of defects (dislocations, cracks, etc.). Moreover, in most of the above described devices the graded AlGaN layers are buried in the GaN-matrix, and the lattice and thermal misfits at the bottom and top 3 ACS Paragon Plus Environment


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interfaces play a significant role in strain relaxation of the entire GaN/AlGaN/GaN system. Thus, the design of the heterostructures strongly influences mechanism of their strain relaxation which is crucial for polarization doping since the structural quality strongly affects the magnitude and type of conductivity of the AlGaN layer 15. Additional to threading dislocations (TDs), networks of cracks were shown to form in non-graded AlxGa1-xN layers on GaN (0001) substrate for Al mole fractions as low as x ≈ 0.1 and layer thicknesses less than 100 nm

16–18;

however, the critical

thickness and the strain relaxation mechanisms are not studied in detail for AlGaN layers with graded compositions. Nevertheless, the graded AlGaN layers have also successfully been used as strain transition buffer layers for dislocation filtering and for growing crack-free GaN on Si(111) substrates 19. The gradient of composition in the AlGaN layer leads to a large compressive stress in the overgrown GaN layer due to the gradual change of the lattice parameters and the thermal expansion coefficient from the AlN seed layer grown on Si(111) to the GaN layer. It has been shown

20

that dislocations are more prone to bend and relax the compressive stresses when the

dislocation lines intersect a smooth surface; however, this is followed by cracking of the graded AlGaN layer on Si. An improvement of the crystal quality of N-polar GaN layers with a pseudomorphicaly grown graded AlGaN interlayer on GaN(0001) was reported in Ref. 21. It was shown, that the insertion of the AlGaN interlayer causes both inclination and annihilation of TDs under tensile strain as opposed to the well-known compressive strain inclination and annihilation reaction

22.

These controversial results additionally indicate that the study of the mechanism of

strain relaxation in graded AlGaN layers involved in different types of heterostructures is in need. In the present study, we employ different configurations of graded AlGaN layers inserted in the GaN-matrix to investigate the mechanism of strain relaxation in the GaN/AlGaN/GaN(0001) heterostructures. We study the effects of Al concentration and the shape of concentration-depth 4 ACS Paragon Plus Environment

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profile on the critical thickness for crack generation and on the structural quality of the GaN/AlGaN/GaN(0001) heterostructures. 2. EXPERIMENT The samples were grown in a Veeco Gen-II plasma-assisted MBE system on GaN template substrates from KYMA Technologies which consist of ~5 μm thick [0001] oriented GaN grown on AlN/Al2O3 by hydride vapor phase epitaxy (HVPE). The substrates were first heat cleaned at 820 °C for 1 h in order to remove any residual surface contaminations. Then, for all samples a ~ 350 nm thick Ga-polar undoped GaN-buffer layer was grown under gallium-rich conditions at a substrate temperature of ~790 °C. Under the same conditions, a ~1200 nm thick GaN layer was grown for sample S0 (reference sample). Linearly changing the temperature of the Al effusion cell, 0 𝑇𝐴𝑙, a ~370 nm thick compositionally graded AlxGa1-xN layer was grown for samples S26 0 , S26, and 26 42 S42 0 . For sample S0 (S0 ), a -shaped Al concentration profile was formed with the maximum x of

0.26 (0.42), by ramping 𝑇𝐴𝑙 from 957 to 1016 °C (1039.5 °C) over 50 min and then back down to 957 °C over another 50 min with no pause in the middle. For sample S026 a -shaped profile was formed with a maximum x of 0.26 by decreasing 𝑇𝐴𝑙 from 1016 to 957 °C over 50 min and then increased again to 1016 °C over another 50 min with no intermediate pause. The temperature of the Al effusion cell was ramped in accordance with calibrations performed earlier 23. Finally, the AlGaN layers were covered with a ~370 nm thick Ga-polar GaN-cap layer grown under galliumrich conditions and a substrate temperature of 787 °C. The samples design including the depth profiles of the Al concentrations is shown in Fig. 1.



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Figure 1. Schematic illustration of the samples design. High-resolution X-ray diffraction (HRXRD), grazing incidence X-ray diffraction (GIXD), atomic-force microscopy (AFM), transmission electron microscopy (TEM), photoluminescence (PL) spectroscopy, optical microscopy, scanning electron microscopy (SEM), and wet etching were used for sample characterization. The HRXRD measurements were performed using a Philips X’pert MRD system. The X-rays were generated in a 1.6 kW tube with a standard four-bounce Ge(220) monochromator and a vertical line focus selecting the Cu Kα1 radiation (λ = 0.15406 nm) and detected through a three bounce (022) channel cut Ge analyzer crystal. The GIXD measurements were carried out using a Bruker D8 Discover system. An L-shaped Montel optic is applied to collimate the X-ray beam to about 0.07° (250 arcsec) in both vertical and horizontal directions. A three-bounce channel cut Ge analyzer crystal is used to measure the scattering angle 2θ. The angle of incidence of the X-ray beam with respect to the sample surface is chosen slightly 6 ACS Paragon Plus Environment

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above the critical angle of total external reflection which is given by αc = 0.33° for GaN. AFM measurements were performed using a NanoScope IIIa Dimension 3000TM scanning probe microscope operating in tapping mode. Silicon tips of 10 nm nominal apex radius were used to map the surface at large and small scales. Cross-sectional TEM studies were conducted in an FEI Titan 80-300 TEM equipped with a Schottky FEG operated at 300 kV. SEM measurements were performed using the ZEISS EVO 50XVP scanning electron microscope operated in secondary electrons detection mode. The optical properties were studied through photoluminescence (PL) measurements at a temperature of 10 K using the 532 nm line of a frequency doubled Nd-YAG laser which was further doubled by Coherent MBD 266 module to reach an excitation wavelength of 266 nm (4.66 eV). The laser beam was focused to a ∼200 μm diameter spot at the sample. The PL signal from the sample was dispersed by a 0.32 m monochromator and detected by a liquid nitrogen cooled Si photodiode detector array. 3. RESULTS AND DISCUSSION 3.1. Al-depth profile and strain state in the graded AlGaN layers. The reciprocal space map (RSM) of an asymmetrical reflection provides the in- and out-of-plane lattice parameters of the crystal lattice. Shown in Fig. 2 are the RSMs measured around the GaN 1124 and 1104 reflections in order to investigate the epitaxial relationship between the GaN-buffer, the graded AlGaN layer, 0 42 and the GaN-cap of samples S26 0 , S26, and S0 . For all samples, a strong diffraction peak is observed

at the position of bulk GaN with a vertical streak extending above it, which are associated with the GaN-buffer and the AlGaN layer, respectively. The locations of the streaks from the AlGaN layers are compared with the positions of pseudomorphically strained (𝑎𝐴𝑙𝐺𝑎𝑁 = 𝑎𝐺𝑎𝑁) and fully relaxed 7 ACS Paragon Plus Environment


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(𝑎𝐴𝑙𝐺𝑎𝑁 = 𝑎0(x)) AlxGa1-xN alloys (vertical and inclined black dashed lines, respectively), which for an ℎ𝑘𝑖𝑙 reflection were plotted by calculating the (𝑄 ∥ , 𝑄 ⊥ ) coordinates pairs according to Eq. 1–3 24: 𝜀∥ =

𝜀⊥ =

𝑎𝐴𝑙𝐺𝑎𝑁 ― 𝑎0(x) 𝑎0(x)

𝑐𝐴𝑙𝐺𝑎𝑁 ― 𝑐0(x) 𝑐0(x)

𝑄 ∥ 2 + 𝑄 ⊥ 2 = 2𝜋

(1)

𝐶13(x) = ―2 𝜀 𝐶33(x) ∥

(2)

4ℎ2 + ℎ𝑘 + 𝑘2 𝑙2 + 3 𝑎2𝐴𝑙𝐺𝑎𝑁 𝑐2𝐴𝑙𝐺𝑎𝑁

(3)

where, 𝜀 ∥ and 𝜀 ⊥ are the in- and out-of-plane strain; 𝑎𝐴𝑙𝐺𝑎𝑁 and 𝑐𝐴𝑙𝐺𝑎𝑁 are the strained in- and out-of-plane lattice parameters in the AlGaN layers; 𝑄 ∥ and 𝑄 ⊥ are the RSM’s coordinates; and x is the Al concentration. The values for 𝑎0(x), 𝑐0(x), 𝐶13(x), and 𝐶33(x), which are the lattice and elastic constants of fully relaxed AlxGa1-xN alloys, are determined by a linear interpolation between those of bulk GaN (𝑎𝐺𝑎𝑁 = 0.31893 nm, 𝑐𝐺𝑎𝑁 = 0.51851 nm, 𝐶13 = 103 GPa, 𝐶33 = 405 GPa) and bulk AlN (𝑎𝐴𝑙𝑁 = 0.3113 nm, 𝑐𝐴𝑙𝑁 = 0.49816 nm, 𝐶13 = 108 GPa, 𝐶33 = 373 GPa) 25. For all samples, the vertical orientation of the AlGaN streak on the RSM confirms the preserved in-plane coherency along the c-axis of the crystal lattice of the AlGaN layer; however, a slight shift or extension of the streak towards the relaxation line indicates that there is some broken inplane coherency between the AlGaN layer and the crystal lattice of the GaN-buffer layer. Moreover, since the coherent relaxation (𝑎𝐴𝑙𝐺𝑎𝑁 = 𝑐𝑜𝑛𝑠𝑡) of the AlGaN layer would result in a shift of the streak in its entirety, we suggest that any broadening or extension of the streak in the 𝑄 ∥ direction towards the relaxation line indicates that laterally within the AlGaN layer there are 8 ACS Paragon Plus Environment

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regions with different in-plane lattice parameters, thus with different degrees of strain relaxation. The expansion of the AlGaN peak toward the larger 𝑄 ∥ increases with increasing Al concentration in the AlGaN layer and is highest for sample S42 0 (Figs. 2c and 2f).

0 42 Figure 2. The 1104 and 1124 RSMs (log scale intensity) of samples S26 0 (a, d), S26 (b, e), and S0

(c, f) and the profiles of in-plane lattice parameter (g, h, and i, respectively) which are extracted by cross sectioning the RSMs through the positions of fully relaxed and biaxially strained GaN (green curve) and Al0.2Ga0.8N (red curve). The dashed vertical and inclined lines on the RSMs are calculated for the fully strained and fully relaxed AlxGa1-xN alloy, respectively. 9 ACS Paragon Plus Environment


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The GaN-cap layer adopts the in-plane lattice parameter of the AlGaN layer immediately underneath it, which results in compressive strain due to the partial relaxation of that AlGaN layer causing a shifted GaN Bragg peak distinct from the substrate Bragg peak. Explicit evidence of the preserved in-plane coherence between the GaN-cap and the AlGaN layers is observed by comparing the profiles of the in-plane lattice parameter (Figs. 2g–i), which are extracted by crosssectioning the RSMs along their 𝑄 ∥ axis through the positions of the fully relaxed GaN (green line) and AlxGa1-xN (red lines). The 𝑄 ⊥ coordinates of the green and red lines are calculated according to Eq. 1–3, neglecting the influence of the tilt and shearing on the position in Q-space. The red curves in Figs. 2g–i correspond to cross-sections along the red lines in Figs. 2a–f, and the green curves correspond to cross-sections along the green lines. The green extracted profile for sample S42 0 exhibits a shoulder towards the smaller in-plane lattice constant side which must be from the GaN-cap layer. The positions of the peaks on the profiles extracted from the AlGaN layer coincide with those on the profile from GaN, which indicates on the in-plane coherency between the AlGaN layer and GaN-cap. In addition, the coincidence of the peaks positions on the profiles extracted from the 1124 and 1104 RSMs confirms the isotropy of biaxial strain in the GaN-cap and graded AlGaN layers. According with the position of the shoulder, the GaN-cap in sample S42 0 is under a compressive in-plane strain of about 4.4 × 10−3 resulting from the partial relaxation of the AlGaN layer. The magnitude of tensile strain in the AlGaN layer varies according to the Al concentration and increases up to about 5.7 × 10−3 as the Al concentration increase to x = 0.42 0 (Fig. 1). For samples S26 0 and S26, the cross-sections in Figs. 2g and 2h, respectively, exhibit very

small, nearly vanishing shoulders which makes it difficult to evaluate their positions and to determine the strain state of the GaN-cap.


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More details on the distribution of strain along the depth of the AlGaN layers can be extracted by simulating the 2𝜃/𝜔 scans for these samples across a symmetrical reflection which covers the full range of composition from GaN to AlN, thus can cover the entire graded structure. For all samples, the 2𝜃/𝜔 scans were measured for the 0002 reflection and are shown in Figs. 3a–c. The peak of the GaN-buffer layer is seen on each spectrum at 2𝜃 ≈ 34.57°. For sample S42 0 , an additional GaN peak is observed at 2𝜃 ≈ 34.5° and is associated with the compressively strained GaN-cap layer. The peaks from the AlGaN graded layers begin to appear to the right side of the GaN peak and extend toward larger 2𝜃. Well-defined oscillations due to the AlGaN layers are clearly seen on the measured scans of all samples. The oscillations arise from coherent superposition of scattered X-ray waves within the crystal volume 23,26 and reflect the good quality 0 of the AlGaN layer. However, it is obvious that the oscillations for samples S26 0 (Fig. 3a) and S26

(Fig. 3b) are much sharper in comparison with the relatively poor oscillations from the AlGaN layer of sample S42 0 (Fig. 3c). This indicates the loss of coherency in the AlGaN layer, which can be compared with the observed large 𝑄 ∥ extension of the AlGaN peak on the 1124 RSM (Fig. 2c). These 0002 2𝜃/𝜔 scans from the graded layers were simulated based on the approach described by Kuchuk et al.

23.

The simulation was applied for the following multilayer

heterostructure: (1) GaN-buffer layer, (2) graded AlGaN layer, and (3) GaN-cap layer. First, the 0002 2𝜃/𝜔 scans (green) were calculated (Figs. 3a–c) by fitting the profiles of Al concentrations, and assuming that the layers are pseudomorphically strained to the GaN substrate. For all samples, this results in well-defined thickness oscillations from the AlGaN layers. The obtained Al profiles which corresponds to the best fitting correlate well with the Al concentration profiles measured by energy dispersive X-ray spectroscopy (EDX) in TEM (Figs. 5g–i). Thus, the calibrated Al profiles in Fig. 1 were additionally confirmed. However, the thickness oscillations of the measured scans 11 ACS Paragon Plus Environment


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are generally less pronounced, which likely indicates that the strain in the film deviates from that expected of pseudomorphic growth with composition given in Fig. 1 due to partial relaxation of the AlGaN. This partial relaxation, although small in some cases, is not negligible and can be seen as the shoulders in each curve of Figs. 2g–i.

Figure 3. Experimental (gray) and simulated (red and green) triple-crystal 2𝜃/𝜔 scans of 0002 0 42 reflection for samples S26 0 (a), S26 (b), and S0 (c), and the depth profiles of the strain (d, e, and f,

respectively) extracted from the simulations. The green and red curves in d–f are calculated from the simulated 2𝜃/𝜔 scans for pseudomorphically strained (green) and partially relaxed (red) AlGaN shown in a–c. In order to account for this non-ideality in the simulations, we conceptually separated the simulated film into several similar regions (of the same thickness as the AlGaN layer), each of which was coherently strained to a different in-plane lattice parameter, 𝑎𝐴𝑙𝐺𝑎𝑁 (𝑎𝐴𝑙𝐺𝑎𝑁 < 𝑎𝐺𝑎𝑁). 12 ACS Paragon Plus Environment

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The out-of-plane lattice parameters were then determined by strain and composition according to the Eqs. 1–3. The GaN-cap layer was then considered to adopt the in-plane lattice parameter of the AlGaN layer directly beneath it. Then the final simulation was calculated by summing the simulations of all the regions. Finally, the number of regions was increased one-by-one until a good fit between the data (gray) and simulated (red) 2𝜃/𝜔 curves was achieved (Figs. 3a–c). As a result of these fittings, the depth profiles of the strain, 𝜀 ∥ (𝑧), in each region of the AlGaN layers were calculated using Eq. 1 for the profiles of Al concentration in Fig. 1. The 𝜀 ∥ (𝑧) profiles are shown in Figs. 3d–f for two cases of a fully strained (𝑎𝐴𝑙𝐺𝑎𝑁 = 𝑎𝐺𝑎𝑁) and partially relaxed (𝑎𝐴𝑙𝐺𝑎𝑁 < 𝑎𝐺𝑎𝑁) heterostructure to illustrate the magnitude of the deviation, ∆𝜀𝑋𝑅𝐷 ∥ , in the strain from the ideal pseudomorphically strained profile (green dotted line). We find that the AlGaN layer of 0 samples S26 0 (Fig. 3d) and S26 (Fig. 3e) are entirely under tensile strain, with the magnitude of the

strain increasing with increasing Al concentration. The tensile strain is slightly reduced for partially relaxed regions of the AlGaN layer where 𝑎𝐴𝑙𝐺𝑎𝑁 < 𝑎𝐺𝑎𝑁 (see the colored areas on Figs. 3d and 3e). For sample S42 0 , both tensile and compressive strains are present in the AlGaN layer (Fig. 3f). Compressive strain results from the contraction of the in-plane lattice parameter due to the strain relaxation in the whole AlGaN layer and is seen in the bottom and upper parts of the AlGaN layer where the Al concentration is small. For all samples, the relaxation in the AlGaN layer induces compressive in-plane strain in the GaN-cap layer. The magnitude of compressive strain is calculated assuming that the GaN-cap inherits the lattice parameter of the AlGaN layer. 3.2. The strain state in the GaN-cap layers. The strain in the GaN-cap layers was more precisely studied with GIXD and low-temperature (10 K) PL spectroscopy. Because of the small penetration depth (a few tens of nanometers) of the X-ray beam in GIXD and excitation laser in PL, the resulting spectra are not influenced by the GaN-buffer or AlGaN layers. The GIXD 2𝜃/𝜔 13 ACS Paragon Plus Environment


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scans were measured around the GaN 1120 reflection and are shown in Figs. 4a–d for all samples along with their Gaussian fits. For sample S0 (Fig. 4a) the 1120 peak is relatively sharp and coincides well with bulk GaN. However, an additional shoulder at larger 2𝜃 is observed for 0 42 samples S26 0 , S26, and S0 (Figs. 4b–d) which indicates the presence in the GaN-cap layer of

compressively strained regions along with fully relaxed regions. Both the shoulder width and the amount of shift are significantly larger for sample S42 0 (Fig. 4d), which is similar to what is seen for the in-plane lattice parameter extracted from the 1104 and 1124 RSMs (Figs. 2g–i). The in0 42 plane strain, 𝜀 ∥ , in the GaN-cap layers of samples S26 0 , S26, and S0 is calculated from the position

of the shoulder in these GIXD scans, then the stress, 𝜎𝐺𝐼𝑋𝐷 = 𝑌𝜀 ∥ , is calculated using the biaxial ∥

〉, which is reported in Table 1, is determined as a modulus, 𝑌 24. Finally, the average stress 〈𝜎𝐺𝐼𝑋𝐷 ∥ weighted average using the areas under the two Gaussian peaks as weighting factors. The features observed in the PL spectra in Figs. 4e–h are similar with those in the GIXD 2𝜃/𝜔 scans. In fact, using 266 nm excitation the penetration depth of the light is about 150 nm, therefore we expect that the results of the PL are representative of only the GaN-cap layer, similar to the GIXD. For sample S0, the peak at 3.472 eV is derived from the recombination of donor bound excitons (D0X) and corresponds to strain-free GaN 27. The fluctuation of the compressive strain in 0 42 the GaN-cap layer splits and blueshifts the peak in the PL spectra of samples S26 0 , S26, and S0 .

Like the GIXD scans, the PL spectra were fitted using Gaussian functions, and the PL observed 0 stress, 𝜎𝑃𝐿 ∥ , is determined from the peak shift of GaN D X emission, ∆𝐸, as:

―1 𝜎𝑃𝐿 ∥ = ―∆𝐸𝑘

(4)

where 𝑘 = 0.022 ± 5 eV/GPa is the stress factor 27.


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Figure 4. GIXD 2𝜃/𝜔 scans of GaN 1120 reflection (a)–(d) and low temperature (10 K) PL 0 42 spectra (e)–(h) for samples S0 (a, e), S26 0 (b, f), S26 (c, g), and S0 (d, h).

Table 1. Average stresses and dislocation densities in the AlGaN buried layers and the GaN-cap layers.

Sample

GaN-cap, GPa

AlGaN, GPa

𝒄𝒓𝒌 𝑿𝑹𝑫 〈𝝈𝑮𝑰𝑿𝑫 〉 〈𝝈𝑷𝑳 ∥ ∥ 〉 〈𝝈 ∥ 〉 〈𝝈 ∥ 〉

〈𝑳𝒔𝒂𝒕〉, µm

𝑵𝒂 × 1010,

𝑵𝒂 + 𝒄 × 108,

cm-2

cm-2

GIXD

𝑵𝑨𝑭𝑴 𝒕𝒐𝒕 × 108, cm-2

XRD

SEM

AFM

S0

-

-

-

-

-

0.75

11.3

0.09

1.78

S026

-0.29

-0.36

0.14

0.11

220

0.93

12.9

0.37

4.00

S26 0

-0.34

-0.46

0.21

0.21

100

1.34

14.9

0.81

3.94

S42 0

-1.90

-0.93

0.92

1.13

5

1.62

16.4

0.76

3.84



Page 16 of 37

〉, the average stress, 〈𝜎𝑃𝐿 Like 〈𝜎𝐺𝐼𝑋𝐷 ∥ ∥ 〉, reported in Table 1 is determined as a weighted average using the areas under the two Gaussian peaks. The discrepancy observed between the 〈𝜎𝑃𝐿 ∥ 〉 and

〈𝜎𝐺𝐼𝑋𝐷 〉 might be expected due to the temporal nature of the PL process, by which light is absorbed ∥ and relaxes to the locally lowest energy state before re-emission. This process favors the lower energy system, which is in this case the fully relaxed GaN, thus shifting the weigted average stress,

〈𝜎𝑃𝐿 ∥ 〉,

𝐺𝐼𝑋𝐷〉 to a smaller value. However, both the 〈𝜎𝑃𝐿 increase with increasing Al ∥ 〉 and 〈𝜎 ∥

concentration in the graded AlGaN layers. Also, higher compressive stress is induced in the GaNcaps of samples with -shaped profile of the Al concentration, which is concluded by comparing 𝐺𝐼𝑋𝐷〉 0 the 〈𝜎𝑃𝐿 for samples S26 ∥ 〉 and 〈𝜎 ∥ 0 and S26. Moreover, there is a strong correlation between

relaxation in graded AlGaN layers (Figs. 2 and 3) and induced stress in GaN-cap layers (Fig. 4). 3.3. The strain relaxation vs. defect microstructure. Plastic relaxation of strained epitaxial layers proceeds predominantly by nucleation of edge dislocations. Generally, however in the analysis of threading dislocations (TDs) in III-nitrides epitaxial layers, both edge and screw type are found. As such, all TDs are classified as: c-type with Burgers vector, 𝒃 = 〈0001〉, a-type with 𝒃 = 1 3〈1120〉, or a + c-type with 𝒃 = 1 3〈1123〉, which are screw, edge, or mixed TDs, respectively

28,29.

TDs in GaN have been found to be predominantly a-type and a + c-type, with

only about 2% of c-type 29. Moreover, the ratio between the a-type and a + c-type dislocations has been found to be roughly 2:1 with typical TDs densities of about 1  109 cm-2 30. Values similar to 0 42 these are observed in cross-sectional TEM images taken for samples S26 0 , S26, and S0 under

different beam conditions (see Figs. 5a-f). It is explicitly seen that a-type dislocations dominate over c and a + c-type dislocations. Moreover, as can be seen in Figs. 5a–c that the main source of c and a + c-type dislocations in the heterostructure epilayers are TDs which originate in the 16 ACS Paragon Plus Environment

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0 underlying GaN substrate. The same can be concluded also for a-type TDs in samples S26 0 and S26

(see Figs. 5d and 5e, respectively). However, for sample S42 0 , the density of a-type dislocations in GaN-cap and graded AlGaN epilayers is much higher than in the GaN-buffer (Fig. 5f). Moreover, we can clearly see the nucleation of new a-type misfit dislocations at the AlGaN/GaN heterointerface as well as inclination and annihilation of TDs in the AlGaN buried layer. This can be explained by severe plastic strain relaxation for sample S42 0 , confirming the observations by XRD and PL (see Figs. 3 and 4), and the formation of compressively strained regions at the bottom and upper parts of the AlGaN layer where the Al concentration is small (Fig. 3). An alternating strain field (compressive to tensile) in these regions can cause the inclination and annihilation of TDs from the underlying GaN substrate.

0 42 Figure 5. Cross sectional TEM images of samples S26 0 (a, d), S26 (b, e), and S0 (c, f) recorded with

g = [0002] and g = [1100] for c- and a-type dislocations. The (g)–(f) show the depth profiles of Al concentration in the AlGaN layers determined from EDX and XRD. 17 ACS Paragon Plus Environment


Page 18 of 37

The densities of TDs were quantified by 0002 XRD and 1120 GIXD 𝜔 scans measurements. The 0002 𝜔 scan is sensitive to lattice tilt which is produced by c-type and the c-component of a + c-type dislocations. The a-type and the a-component of a + c-type dislocations produce lattice twist which is the broadening source for the GIXD 1120 𝜔 scans 29,31. Since usually there are more a-type than a + c-type dislocations, it is generally considered that the 0002 𝜔 scan reflects the density of a + c-type dislocations, while the 1120 𝜔 scans measure the density of a-type dislocations. Also note that for our samples the 0002 𝜔 scan is influenced by both, the GaN-cap and GaN-buffer layers in the sample, while the grazing incidence 1120 𝜔 scan reflects the structure quality of only the GaN-cap layer. Calculation of the dislocation densities by XRD is commonly based on the measurement of the full width at half maximum (FWHM) of an ω scan 32. However, this neglects the tail regions of the rocking curve which reflect the strain fields in the near vicinity of the dislocation lines. The decay of the strain from a dislocation line is typically proportional to r-1 (where r is the distance from the dislocation line) 33. This also determines the shape of the X-ray diffraction profile, and for double-crystal geometry the intensity decay at large ω generally obeys an ω-3 law. A simple approach to calculating the densities of threading TDs by simulating the ω-3 asymptotic behavior of the diffraction peak profiles was proposed by Kaganer et al. 34,35 for highly dislocated GaN epitaxial films. The final expression for the scattered intensity was given as follows 𝐼(𝜔) =

𝐼𝑖 ∞ 𝜋

∫

(

exp ―𝐴𝑥2ln

)

𝐵+𝑥 cos (𝜔𝑥)𝑑𝑥 + 𝐼𝑏𝑎𝑐𝑘𝑔𝑟 𝑥

(5)

0

where 𝐼𝑖 is the integrated intensity of the peak, 𝐼𝑏𝑎𝑐𝑘𝑔𝑟 is the background intensity, and 𝜔 is the angular deviation from the peak maximum. The parameters A and B describe the dislocation density and the dislocation correlation range, respectively. 18 ACS Paragon Plus Environment

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Figure 6. Experimental (gray lines) and simulated (colored lines) double-crystal 𝜔 scans of the 0002 and 1120 reflections for all samples. The profiles are shown in logarithmic scales. The inset shows the log-log scale profile for sample S26 0 . Figure 6 shows the measured double-crystal ω scans (gray lines) for the GaN 0002 and 1120 reflections and their simulations (colored lines) by Eq. (5). A good fit between the measured and simulated spectra is seen in the semilogarithmic and log-log scales. On the log-log scale (see Fig. 6, inset), the ω-3 asymptotic decay of the scattered intensity confirms the scattering from dislocation strain fields. For all samples, the calculated densities of TDs are listed in Table 1. The a-type vs. a + c-type dislocations differ by one order of magnitude which is in accordance with 𝐺𝐼𝑋𝐷 TEM data. Both, the 𝑁𝑋𝑅𝐷 are the lowest for the reference sample S0, and increase with 𝑎 + 𝑐 and 𝑁𝑎

the released stress in the graded AlGaN layers (or induced stress in GaN-cap layers) from sample 42 S026 to S26 0 to S0 , which implicates their close connection.



Page 20 of 37

42 0 Figure 7. Top-view SEM images of samples S0 (a), S26 0 (b), S0 (c), and S26 (d) after etching.

The surface defects in the GaN-cap layers were studied further combining SEM and AFM techniques. First, the as-grown surfaces of all samples were examined with an optical microscope (not shown here) and a weak pattern of cracks, which are related to the release of tensile stress 0 42 stored in the AlGaN layers, was seen for samples S26 0 , S26, and S0 . The observed interrupted

propagation of some of the crack channels indicate that probably most of the cracks are overgrown during the deposition of the GaN-cap layer. Therefore, defect-selective etching was performed to open the buried cracks. In order to open all overgrown cracks, the samples were etched in phosphoric acid at 200 °C for 10 min

36–38;

this

formed etch pits and channels on the dislocation and crack sites, respectively. SEM examinations of sample surfaces after the etching (Fig. 7) reveal high densities of pronounced crack channels 20 ACS Paragon Plus Environment

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0 42 for samples S26 0 , S26, and S0 . The cracks propagate predominantly along the 1120, 1210

and 2110 directions. The 60º and 120º angles between the adjacent cracks agree with the sixfold symmetry of the wurtzite lattice. As expected, no cracks were observed on the surface of 0 sample S0 which was grown without an AlGaN layer (Fig. 7a). For samples S26 0 (Fig. 7b) and S26

(Fig. 7d), for which the maximum Al concentration in the AlGaN layer is only, x ~ 0.26 (Fig. 1), the networks of crack channels extend over the surface separating large areas of intact film. The average crack spacing, 〈𝐿𝑠𝑎𝑡〉, however is different for the two different Al concentration profiles. 0 42 It is found to be 100 μm and 220 μm for samples S26 0 and S26, respectively. For sample S0 (Fig.

7c), in which the maximum Al concentration increases up to x ~ 0.42 (Fig. 1), the 〈𝐿𝑠𝑎𝑡〉 decreases to 20 μm. The crack channels separate the regions which have a denser network of cracks with

〈𝐿𝑠𝑎𝑡〉 ≈ 5 μm. It should be noted, that the crack pattern is observed on the surface of GaN-cap which is under compression. Therefore, we can conclude that this pattern of cracks is adopted from the graded AlGaN buried layer which has cracked to relieve the tensile stress during and after growth. 39 The average stress released in AlGaN by cracking, 〈𝜎𝑐𝑟𝑘 ∥ 〉, is estimated using Eq. 6 :

〈𝜎𝑐𝑟𝑘 ∥ 〉=

5.8

Γ𝐸

〈𝐿𝑠𝑎𝑡〉(1 ― 𝜈2)

where 𝐸 and 𝜈 are the averaged Young’s modulus and Poisson ratio for the AlGaN alloy

(6) 24,40,

respectively; Г = 2𝛾 is the fracture resistance of the film; and 𝛾 is the surface energy of cleavage planes and was taken equal to 1.89 Jm-2 and 2.51 Jm-2 for GaN and AlN, respectively 16. 𝑋𝑅𝐷 In Table 1, 〈𝜎𝑐𝑟𝑘 ∥ 〉 is in good agreement with the average released tensile stress, 〈𝜎 ∥ 〉 = 0.5 26 0 42 𝑌∆𝜀𝑋𝑅𝐷 ∥ , in the AlGaN layers of samples S0 , S26, and S0 , which was determined from the 0002 2

𝜃/𝜔 scan simulations (Fig. 3). Therefore, the variation of the in-plane lattice parameter (and of the 21 ACS Paragon Plus Environment


Page 22 of 37

related strain), which was introduced to simulate the 2𝜃/𝜔 scans, is correlated with the sample fracture. As a result, different in-plane lattice parameters can be assigned for each region having a different 𝐿𝑠𝑎𝑡.

42 0 Figure 8. The AFM images of etched GaN surfaces of samples S0 (a), S26 0 (b), S0 (c), and S26 (d).

During etching, the TDs of different types form on the sample surface etch pits with different shapes and sizes. The small circular pits represent the surface termination of a-type dislocations (see Figs. 8a-d), and the large hexagonal etch pits are associated with c and a + c-type dislocations (Fig. 8b, inset) 37. It should be noted, that the largest etch pits seen on the AFM images appear as only small black spots on the SEM images (see Fig. 7, insets), i.e., the small pits seen in AFM, which are due to the a-type TDs are not visible in the SEM. The large pits are generally due to the c-type component of the TDs and therefore represent the density of c and a + c-type surfaceterminated dislocations (𝑁𝑆𝐸𝑀 𝑎 + 𝑐). On the other hand, the different type of TDs cannot be clearly differentiated on the AFM images, since the huge etch pits which are in close vicinity can merge 22 ACS Paragon Plus Environment

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together or potentially contain tens of smaller etch pits 37, and are thus summed together in one 𝑆𝐸𝑀 𝐴𝐹𝑀 density, 𝑁𝐴𝐹𝑀 𝑡𝑜𝑡 . For all samples, the calculated 𝑁𝑎 + 𝑐 and 𝑁𝑡𝑜𝑡 are listed in Table 1. Both, the 𝐴𝐹𝑀 𝑁𝑆𝐸𝑀 𝑎 + 𝑐 and 𝑁𝑡𝑜𝑡 are the lowest for the reference sample S0, supporting the XRD data (see Table 𝐺𝐼𝑋𝐷 1). However, both densities of surface-terminated dislocations are lower than the 𝑁𝑋𝑅𝐷 𝑎 + 𝑐 and 𝑁𝑎

by one order of magnitude. This indicates that some TDs terminate at the cracks or mosaic block boundaries. In general, it should be noted that there are at least three main sources of TDs in GaNcap: (i) penetrated TDs from GaN-substrate, (ii) TDs formed to relax tensile strain in AlGaN buried layer and (iii) TDs formed to relax compressive strain in GaN-cap. The final density of TDs in GaN-cap depends on all of these factors but mainly on the amount of stress induced by the AlGaN buried layer in GaN-matrix.

Figure 9. Stress (a) in the GaN-cap and the AlGaN buried layers as well as dislocation densities (b) in the GaN-cap layer as a function of the crack spacing.



The quantitative correlation between the stress released in the AlGaN buried layers, the stress induced in the GaN-cap layers, cracking, and TDs can be seen in Fig. 9. First, there is a good correlation between the stresses calculated for AlGaN from XRD and cracking as well as for GaN from GIXD and PL data. Second, the amount of stress released in AlGaN correlates well with the amount of stress induced in GaN-cap and with the density of cracks. Third, the density of TDs increases with the density of cracks (see Fig. 9b), which indicates a close connection between the two channels of strain relaxation. This should be expected and has been observed elsewhere 41, where it was concluded that crack formation facilitates a-type dislocation formation by creating a local pathway for their slip and subsequent glide. The nucleation of a-type TDs by grain coalescence was shown to induce tensile strain in otherwise compressively strained AlN layers on SiC substrates 42, and to partially compensate the compressive strain in GaN layers grown on Al2O3 43.

An increase of the density of a-type TDs was observed with decreasing grain diameter, while

the density of c-type TDs remained constant 43. Therefore, cracking and the partial coalescence of 0 the regions between the cracks during the growth of the GaN-cap layers of samples S26 0 , S26, and

S42 0 is concluded to promote nucleation of mainly a-type TDs which contribute to the relaxation of the compressive strain in the GaN-cap. 4. DISCUSION AND CONCLUSIONS The plastic strain relaxation in heterostructures consisting of compositionally graded AlGaN epitaxial layers tensile-strained between a GaN-buffer and a GaN-cap proceeds initially by cracking of the AlGaN buried layer. By creating new surfaces, the cracks locally relieve a substantial portion of the tensile strain build up in the growing film. Furthermore, cracked surfaces act as the nucleation sites of misfit dislocations enhancing the process of plastic strain relaxation. This mechanism was recently reported for plastic strain relaxation of a tensile strained AlGaN/GaN 24 ACS Paragon Plus Environment

Page 24 of 37

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heterointerface predominantly by nucleation of a-type misfit dislocations in the 1/3⟨11-20⟩|{0001} slip-system driven by cracking of the AlGaN graded layer 30. The cracking of a uniformly stressed thin film will occur once the film reaches a critical 0 42 thickness. For samples S26 0 , S26, and S0 , this critical thickness depends on the shape of the Al

composition profile in the AlGaN layer. The general expression for the critical thickness (ℎ𝑐) of cracking is given by: ℎ𝑐 =

Γ𝑌 𝑍𝜎2∥ (1 + 𝜈)

(7)

where 𝑍 is a dimensionless parameter which depends on the cracking geometry and is 1.976 and 3.951 for channeling and “small” cracks, respectively 39. On the other hand, the breaking of bonds and the formation of additional surfaces which are required to form a crack should be energetically favored in comparison to a further increase of the strain energy. A critical strain energy determining the onset of cracking can be estimated using Eq. 8 16,40: 𝑈𝑐 = ℎ𝑐𝑌 (𝜀 ∥ + 𝜀𝑡ℎ𝑒𝑟𝑚.)2

(8)

where 𝜀𝑡ℎ𝑒𝑟𝑚. = [𝛼𝑠𝑎𝑝𝑝ℎ𝑖𝑟𝑒 ― 𝛼𝐴𝑙𝐺𝑎𝑁(𝑥)]∆𝑇 44,45 is the thermal strain along the a-axis of the AlxGa1xN

induced by the sapphire substrate; 𝛼𝑠𝑎𝑝𝑝ℎ𝑖𝑟𝑒 and 𝛼𝐴𝑙𝐺𝑎𝑁(𝑥) are the thermal expansion

coefficients of sapphire and AlxGa1-xN, respectively, from Ref. 45. Substitution of Eq. 7 in Eq. 8 leads to: 𝑈𝑐 =

Γ 𝑍(1 + 𝜈)

(9)

Accordingly, 𝑈𝑐 depends on the fracture resistance and does not differ significantly between GaN and AlGaN, being 1.6 J/m2 and 1.81 J/m2 for GaN and Al0.42Ga0.58N, respectively. Therefore, for



Page 26 of 37

0 42 the entire compositional range in the AlGaN layers of samples S26 0 , S26, and S0 , 𝑈𝑐 varies by

~ 1.7 ± 0.1 J/m2. The calculated depth profiles of the stress and accumulated elastic energy 𝑈 in the AlGaN layers 0 42 pseudomorphicly strained to GaN (0001) of samples S26 0 , S26, and S0 are shown in Fig. 10. As can

be seen in Fig. 10a, the change of stress in the AlGaN layers corresponds to the change in the Al concentration in the depth profile. This is in contrast with the accumulated strain energy (Fig. 10b). Moreover, the Al concentration depth profile has a strong impact on the rate of 𝑈 accumulation. As a result, the critical thicknesses for sample cracking at 𝑈𝑐 are ℎ𝑐 ≈ 150 nm for S42 0 , ℎ𝑐 ≈ 165 nm for S026, and ℎ𝑐 ≈ 185 nm for S26 0 . Despite the close values of ℎ𝑐, the differences between the investigated samples can be observed by: (i) the magnitude of 𝜎 ∥ at the critical thickness and (ii) the amount of elastic energy accumulated in the AlGaN layer after the ℎ𝑐 (see colored areas on 42 Fig. 10b). Both of these quantities increase from sample S026 to S26 0 to S0 . This correlates with and 42 consequently explains the reduction of 〈𝐿𝑠𝑎𝑡〉 from sample S026 to S26 0 to S0 (Table 1). Indeed, when

samples cracked at ℎ𝑐, the difference between crack density at this growth stage can be explained by the magnitude of in-plane stress 𝜎 ∥ influenced by the profile of the Al concentration. After the next growth stage, if the peak local strain energy, occurring in the center between two cracks, exceeds the critical value, 𝑈𝑐, additional cracks should form. From Fig. 10b, we can conclude, that after ℎ𝑐, the strain energy exceeds the critical value 𝑈𝑐 only for sample S42 0 , i.e., the total energy exceeds 2𝑈𝑐. This explains the much higher crack density for this sample. Moreover, since the misfit dislocations nucleate at the cracked surfaces, a correlation is also observed between TDs and crack densities. Thus, the higher degree of plastic strain relaxation observed for sample S42 0


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leads to the formation of separate regions between cracks with different in-plane lattice parameters. This is in accordance with the described above experimental data.

Figure 10. Depth profiles of stress (a) and accumulated elastic energy (b) in the pseudomorphic 0 42 strained AlGaN layers of samples S26 0 , S26, and S0 . The patterned region 𝑈𝑐 in (b) is the critical

accumulation of elastic energy which corresponds to the critical thickness, ℎ𝑐, for cracks formation in the AlGaN alloy. In conclusion, we have studied the strain relaxation mechanism of compositionally graded AlGaN layers tensile-strained between a GaN-buffer and a GaN-cap. The magnitude and depth evolution of tensile stress inside the AlGaN layer is determined by the Al concentration and its 27 ACS Paragon Plus Environment


Page 28 of 37

depth profile, respectively. The relaxation of the strain results in a broken in-plane coherency between the AlGaN layer and the GaN-buffer, which fluctuates along the a-axis of the crystal lattice and which becomes more pronounced with increasing Al concentration. The fluctuation magnitude was determined from HRXRD reciprocal space maps and 2𝜃/𝜔 scan simulations. Cracking of the film in result of tensile stress relief in the AlGaN layer was revealed from SEM images. The amount of strain relaxation in the film determined through crack density is in good agreement with the average tensile stress determined by HRXRD, which allowed the close connection between the fluctuation of strain with the fluctuation of the sizes of the regions between the cracks which are under different strain states. The critical thickness for cracking depends, generally on the rate of accumulation of strain energy, which in-turn depends on both the maximum Al concentration as well as its depth profile. Finally, the relief of tensile stress in the AlGaN layer induces compression in the GaN-cap which was concluded to be partially reduced by the formation of a-type dislocations in the GaN-cap. These results on the prediction and control of mechanism of strain relaxation in AlGaN graded layers are important for the fabrication of GaN-based transistors/diodes using graded AlGaN layers.

AUTHOR INFORMATION Corresponding Author *(A.V.K.) E-mail: [email protected]. *(Z.M.W.) E-mail: [email protected]. Notes The authors declare no competing financial interest. 28 ACS Paragon Plus Environment

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Local Strain and Crystalline Defects in GaN/AlGaN/GaN(0001) Heterostructures Induced by Compositionally Graded AlGaN Buried Layers

Hryhorii V. Stanchu, Andrian V. Kuchuk, Yuriy I. Mazur, Chen Li, Petro M. Lytvyn, Martin Schmidbauer, Yurii Maidaniuk, Mourad Benamara, Morgan E. Ware, Zhiming M. Wang, Gregory J. Salamo


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The mechanism of strain relaxation in heterostructures composed of graded AlGaN buried layers tensile-strained in GaN-matrix is investigated. The local strain, crystalline defects and the critical thickness for crack generation are correlated with the Al concentration-depth profile in graded layers. This study showed that the tensile strain released in the buried layer is consistent with the compressive strain induced in the GaN-cap.


GaN(0001

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