# Fileset [Al-composition-xrd(APEX)2nd.pdf](https://mdr.nims.go.jp/filesets/b1077a29-9f78-4566-91d1-9c4dfb5de763/download) ## Creator [Yuichi Oshima](https://orcid.org/0000-0001-8293-4891), Elaheh Ahmadi, Stefan C. Badescu, Feng Wu, James S. Speck ## Rights @2016 The Japan Society of Applied Physics
This is an author-created, un-copyedited version of an article accepted for publication/published in Applied Physics Express. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.7567/APEX.9.061102.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Composition determination of beta-(AlxGa1-x)2O3 layers coherently grown on (010) beta-Ga2O3 substrates by high-resolution x-ray diffraction](https://mdr.nims.go.jp/datasets/42387f9b-f2d2-496f-ab6c-9ad9b860d55c) ## Fulltext Title of Paper Goes Here: Template for APEX (Jan. 2014) 1 Composition determination of -(AlxGa1-x)2O3 layers coherently grown on (010) -Ga2O3 substrates by high-resolution x-ray diffraction Yuichi Oshima1*, Elaheh Ahmadi1, Stefan C. Badescu2, Feng Wu1, and James S. Speck1 1University of California, Santa Barbara, CA, 93106 USA 2Wright Patterson Air Force Base, Sensors Directorate, Dayton, OH 45433, USA E-mail: yuichi@engineering.ucsb.edu We demonstrate x-ray diffraction based composition estimation of -(AlxGa1-x)2O3 coherently grown on (010) -Ga2O3. The relation between the strain along the [010] direction and the Al composition of the -(AlxGa1-x)2O3 layer was formulated by using stress-strain relationship in the monoclinic system. This formulation allows us to estimate the Al composition using out-of-plane lattice spacing determined by conventional x-ray -2 measurements. This method was applied to MBE-grown coherent -(AlxGa1-x)2O3/Ga2O3 heterostructures, and the Al composition in the -(AlxGa1-x)2O3 are in close agreement with composition determined directly by atom probe tomography. Template for APEX (Jan. 2014) 2 -Ga2O3 is a wide bandgap semiconductor (Eg = 4.7 - 4.9 eV),1-3) which crystalizes in the monoclinic structure. -Ga2O3 is attracting a remarkable attention due to its great potential to realize power devices with higher breakdown voltages and lower energy losses than its counterparts GaN and SiC. In reality, several promising results have already been reported on -Ga2O3 based power devices such as Schottky barrier diodes,4) metal-semiconductor field effect transistors (MESFETs),5) and metal-oxide field effect transistors (MOSFETs).6) In addition, -(AlxGa1-x)2O3 solid solutions and -(AlxGa1-x)2O3/-Ga2O3 hetero-structures have been studied intensively since these will enable band engineering and lead to the realization of further high-performance -Ga2O3 based devices such as high electron mobility transistors (HEMTs).7,8) Ga2O3 and Al2O3 crystalize in different crystal structures, i.e., the -gallia structure and the corundum structure, respectively. They therefore make solid solutions -(AlxGa1-x)2O3 under certain solubility limit xmax. Hill et al. investigated the equilibrium phase diagram of Al2O3-Ga2O3 system by using powder synthesis technique and reported the lattice parameters of -(AlxGa1-x)2O3.9) The phase diagram shows that xmax increases with temperature. For example, xmax is more than 0.6 at 800C or higher, while xmax is about 0.25 at 650C, which is the growth temperature of molecular beam epitaxy (MBE) in the present work. Recently, Karnert et al. investigated the lattice parameters of their -(AlxGa1-x)2O3 ceramics.10) The lattice parameters exhibited linear dependence on x when x is 0.3 or lower regardless of the sintering temperature. A prompt and non-destructive composition measurement is essential in materials development. In the case of relaxed -(AlxGa1-x)2O3, the Al composition can be determined immediately through lattice parameters measurement by x-ray diffraction (XRD). However, the Al composition of strained -(AlxGa1-x)2O3 cannot be estimated directly through lattice parameters measurement since the crystal lattice is elastically deformed and the lattice parameters are different from the relaxed values. There are a few reports on the estimation of Al composition of strained -(AlxGa1-x)2O3. Oshima et al. utilized x-ray photoelectron spectroscopy (XPS) to estimate the Al composition of their films coherently grown on (100) -Ga2O3 substrates by MBE.7) However, XPS can collect the data only from the outermost surface (typically a few nanometers deep). Therefore, the measurement can be disturbed when the surface composition is different from that of the body layer. Kaun et al. utilized transmission electron microscopy and energy dispersive X-ray spectroscopy (TEM-EDS) to estimate the Template for APEX (Jan. 2014) 3 Al composition of -(AlxGa1-x)2O3 coherently grown on (010) -Ga2O3 by MBE.8) However, the measurement is destructive and time-consuming. In an analogous case of AlxGa1-xN, Al composition of a coherently grown film has been estimated from the out-of-plane lattice spacing with considering the Poisson effect.11) In the present work, we demonstrate a quick and non-destructive estimation of Al composition of coherently grown (010) -(AlxGa1-x)2O3 films using a methodology similar to the case of AlxGa1-xN. First, we formulate the relation between the Al composition and the strain along [010]. In the following calculations, the -(AlxGa1-x)2O3 layer is assumed to be grown coherently. The unit cells is placed in the Cartesian system so that [100] || 𝑥̂1 and [010] || 𝑥̂2, where 𝑥̂1 and 𝑥̂2 are the Cartesian unit vectors. We used standard matrix notation to express elastic stiffness tensor c, stress tensor , and strain tensor . The notation rule can be found in Ref. 12, for example. When -(AlxGa1-x)2O3 is grown on (010) -Ga2O3 coherently, -(AlxGa1-x)2O3 is subjected to in-plane biaxial stress. Accordingly, only in-plane stress components have non-zero values. Similarly, the shear strain ε4 and ε6 are zero . Therefore, stress-strain relation in a coherently grown (010) -(AlxGa1-x)2O3 film is expressed as follows: [ 𝜎10𝜎30𝜎50 ] =[ 𝑐11 𝑐12 𝑐13 0 𝑐15 0𝑐12 𝑐22 𝑐23 0 𝑐25 0𝑐13 𝑐23 𝑐33 0 𝑐35 00 0 0 𝑐44 0 𝑐46𝑐15 𝑐25 𝑐35 0 𝑐55 00 0 0 𝑐46 0 𝑐66] [ 𝜀1𝜀2𝜀30𝜀50 ] (1) From the second line in eq. (1), we obtain the following relationship: 𝜀2 = −𝑐12𝜀1 + 𝑐23𝜀3 + 𝑐25𝜀5𝑐22 (2) When the crystal lattice of -(AlxGa1-x)2O3 deforms elastically so as to fit that of -Ga2O3, strain components in eq. (2) are given as: Template for APEX (Jan. 2014) 4 𝜀1 =𝑎𝑐 − 𝑎𝑟𝑎𝑟 (3a) 𝜀3 =𝑐𝑐𝑠𝑖𝑛𝛽𝑐𝑐𝑟𝑠𝑖𝑛𝛽𝑟− 1 (3b) 𝜀5 =𝑐𝑐𝑐𝑜𝑠𝛽𝑐𝑐𝑟𝑠𝑖𝑛𝛽𝑟−𝑎𝑐𝑐𝑜𝑠𝛽𝑟𝑎𝑟𝑠𝑖𝑛𝛽𝑟 (3c) Here, ac, cc, c are the in-plane lattice parameters of coherently grown -(AlxGa1-x)2O3, which coincide with those of -Ga2O3 (a0 = 12.21 Å, b0 = 3.04 Å, c0 = 5.81 Å, 0 = 103.87°).10) ar, cr, r are the in-plane lattice parameters of relaxed -(AlxGa1-x)2O3. Kranert et al.10) have reported these values as functions of x: 𝑎𝑟 = 𝑎0 − 𝑘𝑎𝑥 [Å] (4a) 𝑏𝑟 = 𝑏0 − 𝑘𝑏𝑥 [Å] (4b) 𝑐𝑟 = 𝑐0 − 𝑘𝑐𝑥 [Å] (4c) 𝛽𝑟 = 𝛽0 + 𝑘𝛽𝑥 [deg.] (4d) Here, ka = 0.42, kb = 0.13, kc = 0.17, and k = 0.31. On the other hand, 2 can also be expressed as follows: 𝜀2 = −𝑏𝑟 − 𝑏𝑐𝑏𝑟 (5) bc is the length of b-axis of coherently grown -(AlxGa1-x)2O3, which can be experimentally determined through XRD -2 measurement. We can determine x by equating eqs. (2) and (5), and solving the equation for x with using eqs. (3a)~(3c) and (4a)~(4d). The result is as follows: 𝑥 ≅𝑏0 − 𝑏𝑐𝑏0∙ [𝑘𝑏𝑏0+𝑐12𝑐22∙𝑘𝑎𝑎0+𝑐23𝑐22∙𝑘𝑐𝑐0+𝑐25𝑐22(𝑘𝑐𝑐0−𝑘𝑎𝑎0) 𝑐𝑜𝑡𝛽0]−1 (6a) Eq. (6a) is also expressed as follows by using on-axis peak separation of the film and the substrate , and substrate peak position 0: Template for APEX (Jan. 2014) 5 𝑥 ≅ ∆𝜃𝑐𝑜𝑡𝜃0 ∙ [𝑘𝑏𝑏0+𝑐12𝑐22∙𝑘𝑎𝑎0+𝑐23𝑐22∙𝑘𝑐𝑐0+𝑐25𝑐22(𝑘𝑐𝑐0−𝑘𝑎𝑎0) 𝑐𝑜𝑡𝛽0]−1 (6b) To the best of our knowledge, no experimental elastic stiffness tensor is reported about -(AlxGa1-x)2O3. We therefore used a result of first-principles calculation for -Ga2O3. In general, elastic stiffness components show only a slight variation by alloying with small molar fraction, and they tend to vary toward the same direction. Therefore, the variation of their ratio is virtually negligible. The use of elastic stiffness of -Ga2O3 is therefore a good approximation since elastic stiffness components appear as their ratio in eq. (2). The calculation was carried out using the projector augmented wave (PAW) method13) under local density approximation (LDA) in the Vienna Ab-Inition Simulation Package (VASP).14) We used a plane-wave basis set with an energy cutoff Ecut = 500 eV and a 2 × 4 × 8 k-point grid. Elastic constants were calculated with the strain-stress method based on the set of six universal deformation modes proposed in ref. 15. The following result was employed in the composition estimation. [ 237 125 147 0 −18 0125 354 95 0 11 0147 95 357 0 6 00 0 0 54 0 19−18 11 6 0 67 00 0 0 19 0 95] [GPa] (7) Finally, eqs. (6a) is written as: 𝑥 ≅ 15.923 − 5.238 × 𝑏𝑐[Å] (8a) When 020 diffraction is used, eq. (6b) is written as: 𝑥 ≅ 0.4727 × ∆𝜃020 (8b) To examine the methodology described above, we compared the Al compositions estimated by this new method and those measured directly by pulsed laser atom probe tomography (APT).16,17) The -(AlxGa1-x)2O3 films were grown on (010) -Ga2O3 single crystal substrates at 650C by plasma-assisted MBE. Two different samples were prepared with beam flux ratio Al / (Al + Ga) = 0.061 and 0.104. The detail of the growth is described Template for APEX (Jan. 2014) 6 elsewhere.8,18) High-resolution x-ray diffraction measurements were performed in a triple axis configuration using CuK radiation ( = 1.5406 Å) at room temperature. Out-of-plane lattice spacing of each film was directly determined through symmetrical -2 measurement using 020 diffraction. Asymmetrical reciprocal lattice mapping (RSM) using 420 diffraction was carried out to confirm the coherent growth. After the XRD measurements, a 200-nm-thick -Ga2O3 capping layer was additionally grown by MBE on each -(AlxGa1-x)2O3 layer before producing a tip sample for APT to ensure that the whole thickness of the -(AlxGa1-x)2O3 layer was included in the tip. APT samples were prepared by focus ion beam (FIB) technique. About 150 nm wide needle like tips were polished using a FEI Helios Dual Beam Nanolab 650 instrument, milled at 30 kV and followed by a final cleaning at 5 kV. The experiment was carried out using a Cameca LEAP 3000X atom probe instrument equipped with a 532 nm green pulsed laser. The laser energy is around 0.2 nJ, the tip temperature was about 40K and evaporation rate was 1%. Figures 1(a) and (b) show the XRD -2 profiles of the -(AlxGa1-x)2O3 films. Each profile exhibited a single -(AlxGa1-x)2O3 020 diffraction peak with thickness fringes. The out-of-plane lattice spacing of the films were determined to be (a) 3.019 Å and (b) 3.009 Å, respectively. The thicknesses of the two films determined from the fringe spacing were 130 and 127 nm, respectively. Figure 2(a) and (b) show the RSMs of the two films. The 420 peaks of -Ga2O3 and -(AlxGa1-x)2O3 appeared at the same qx position in each RSM, indicating that the -(AlxGa1-x)2O3 films were grown coherently. Figure 3(a) and (b) show the depth profiles of the Al and Ga compositions for the two films measured by APT. The film composition was nearly uniform along the growth direction of the -(AlxGa1-x)2O3 films. The average Al composition in each film was 0.120 and 0.168. These values are significantly higher than those expected from the beam flux ratio. This is probably due to the low incorporation efficiency of Ga because of the formation of volatile suboxide Ga2O.12,19) The calculated Al composition of coherently grown -(AlxGa1-x)2O3 is shown in Fig. 4 as a function of bc together with the averaged APT results. We also show the relationship for relaxed -(AlxGa1-x)2O3 reported by Kranert et al.10) for comparison. The calculated result for coherent films is in good agreement with the APT results, while the application of the relaxed line to the fully strained films results in significant overestimation. In summary, the Al composition of -(AlxGa1-x)2O3 films coherently grown on (010) Template for APEX (Jan. 2014) 7 -Ga2O3 by MBE was successfully estimated by conventional XRD -2 measurement with considering the Poisson effect in the monoclinic system. Coherent growth was confirmed by RSM measurement. The elastic stiffness tensor of -Ga2O3 obtained by first-principle calculation was utilized in the estimation. The result was in a close agreement with the Al compositions directly measured by APT. This methodology enables us to estimate the Al composition of coherently grown -(AlxGa1-x)2O3 in a rapid and non-destructive manner, and thus it will boost the development of high-performance -Ga2O3 based devices. Acknowledgments This work was supported by the Air Force Office of Scientific Research (AFOSR, Program Manager Dr. Ali Sayir) through grant # FA9550-14-1-0112. Additional support for J.S.S. was provided by the MRSEC Program of the U.S. National Science Foundation under Award No. DMR-1121053. References 1) H. H. Tippins: Phys. Rev. 140, A316 (1965). 2) M. R. Lorenz, J. F. Woods, and R. J. Gambino: J. Phys. Chem. Solids 28, 403 (1967). 3) M. Orita, H. Ohta, M. Hirano, and H. Hosono: Appl. Phys. Lett. 77, 4166 (2000). 4) K. Sasaki, A. Kuramata, T. Masui, E.G. Víllora, K. Shimamura, and S. Yamakoshi, Appl. Phys. Express 5, 035502 (2012). 5) M. Higashiwaki, K. Sasaki, A. Kuramata, T. Masui, S. Yamakoshi, Appl. Phys. Lett. 100, 013504 (2012). 6) M. Higashiwaki, K. Sasaki, T. Kamimura, M.H. Wong, D. Krishnamurthy, A. Kuramata, T. Masui, S. Yamakoshi, Appl. Phys. Lett. 103, 123511 (2013). 7) T. Oshima, T. Okuno, N. Arai1, Y. Kobayashi1, and S. Fujita, Jpn. J. Appl. Phys. 48, 070202 (2009). 8) S. W. Kaun, F. Wu, James S. Speck, J. Vac. Sci. Technol. A 33, 041508 (2015). 9) V. G. Hill, R. Roy, and E. F. Osborn, J. Am. Ceram. Soc. 35, 135 (1952). 10) C. Kranert, M. Jenderka, J. Lenzner, M. Lorenz, H. von Wenckstern, R. Schmidt-Grund, and M. Grundmann, J. Appl. Phys. 117, 125703 (2015). 11) T. Takeuchi, H. Takeuchi, S. Sota, H. Sakai, H. Amano, and I. Akasaki, Jpn. J. Appl. Phys. 36, L177 (1997). 12) J. F. Nye, “Physical Properties of Crystals: Their Representation by Tensors and Matrices”, Oxford Univ. Press (1985). Template for APEX (Jan. 2014) 8 13) P. Blöchl, Phys. Rev. B 50, 17953 (1994). 14) J. Hafner, J. Comput. Chem. 29, 2044 (2008). 15) R. Yu, J. Zhu, H.Q. Ye, Comput. Phys. Comm. 181, 671 (2010). 16) T. F. Kelly & M. K. Miller, The Review of Scientific Instruments, 78, 031101 (2007). 17) B. Gault, M. P. Moody, J. M. Cairney, S. P. Ringer, “Atom Probe Microscopy” (Springer Science & Business Media, 2012). 18) H. Okumura, M. Kita, K. Sasaki, A. Kuramata, M. Higashiwaki, and J. S. Speck, Applied Physics Express 7, 095501 (2014). 19) P. Vogt and O. Bierwagen, Appl. Phys. Lett. 108, 072101 (2016). Figure Captions Fig. 1. XRD -2 scan profiles of -(AlxGa1-x)2O3 films. (a) Al / (Al + Ga) = 0.061, (b) Al / (Al + Ga) = 0.104. Fig. 2. RSMs of -(AlxGa1-x)2O3 films. (a) Al / (Al + Ga) = 0.061, (b) Al / (Al + Ga) = 0.104. Fig. 3. Depth profiles of Al and Ga compositions of -(AlxGa1-x)2O3 films measured by APT. (a) Al / (Al + Ga) = 0.061, (b) Al / (Al + Ga) = 0.104. Fig. 4. Relationships between bc and Al composition x. Error bars show ±2. The calculated result for coherent films is approximated by eq. (8a). Template for APEX (Jan. 2014) 9 Figures Fig. 1. Fig. 2. -Ga2O3 020 -(AlxGa1-x)2O3 020 60.5 61.0 61.52 [deg.]Intensity [arb. units](a)(b)0.505 0.510 0.515 0.260 0.255 0.265 0.505 0.510 0.515 (a) 0.260 0.255 0.265 qx [Å-1] qx [Å-1] qz [Å-1] qz [Å-1] (b) Film Substrate Template for APEX (Jan. 2014) 10 Fig. 3. Fig. 4. 0 40 80 120Al / Ga compositionDistance [nm](b)0 40 80 12000.20.40.60.81.0Distance [nm]AlGa(a)Growth direction3.00 3.01 3.02 3.03 3.0400.10.20.3bc [Å]Al composition xAPT results