High-Resolution X-Ray Diffraction Analysis of Epitaxial Films
LI Changji1,ZOU Minjie1,2,ZHANG Lei1(),WANG Yuanming1(),WANG Sucheng1
1. Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China 2. School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China
Cite this article:
LI Changji,ZOU Minjie,ZHANG Lei,WANG Yuanming,WANG Sucheng. High-Resolution X-Ray Diffraction Analysis of Epitaxial Films. Acta Metall Sin, 2020, 56(1): 99-111.
Epitaxy technique has been widely used for semiconductor, ferroelectric and optical materials in the development of electronic and optoelectronic devices. Epitaxial structures with strain and defects may tune the physical properties or affect the performance of devices. High-resolution X-ray diffraction (HRXRD) has significant advantages over traditional XRD with the features of small divergence, monochromatic incident beam and high resolution detection of the diffracted beam. It is a key technique for accurate characterization of epitaxial structures in non-destructive way. In this paper, the techniques of HRXRD for epitaxial film structure characterization are outlined in terms of the relationship between diffraction and reciprocal space, the difference between high-resolution diffraction and powder diffraction such as the optical system and the geometry mode of scanning etc. Based on the corresponding relationship between the epitaxial film and the matrix structure in the reciprocal space, various factors affecting the shape of the diffraction spots are analyzed, including the state of lattice match in coherence and non-coherence, super lattice and inclined growth. The other effective factors are also demonstrated, such as finite size of film, tilt and strain of epitaxial film etc. Real examples, such as Si1-xGex(x=0.1) etc., are used to explain how to obtain the structure parameters of the epitaxial films by HRXRD spectrum analysis, including lattice constant, lattice mismatch, thickness and superlattice information. To obtain more epitaxy information, reciprocal space map (RSM) analysis can be feasibly used by reconstruction of a series of HRXRD patterns. By combining HRXRD spectrum and RSM, microstructure characterizations of PbTiO3 epitaxy films, such as micro-strain, domain structure, phase transformation can be quantitatively analyzed.
Fig.1 Schematics of reciprocal space and diffraction condition for the SrTiO3 single crystal (2θ—diffraction angle, —incident vector of X-ray, —diffracted vector of X-ray, —scattering vector)(a) reciprocal lattice points of reflections with [0v0] zone axis for the SrTiO3 single crystal(b) Ewald construction of the symmetric SrTiO3 (002) reflection(c) Ewald constructure of the asymmetric SrTiO3 (103) reflection(d) range in reciprocal space which can be probed by
Fig.2 Schematics of optics for powder X-ray (a) and high-resolution X-ray (b) diffractometers
Fig.3 Schematic illustration (a) and physical map (b) for the rotation axes of sample and detector (—the rotation angle around ZL axis by right-hand spiral rule; the azimuthal angle; —the rotation angle around the normal direction of sample surface; XL, YL, ZL—laboratory coordinate axes; X, Y, Z—sample translation coordinate axes)
Fig.4 Illustration of scan types and scattering geometries (—angle between incident X-ray and sample surface, —angle between diffracted X-ray and sample surface)(a) scan types including , 2θ-ω and 2θ(b) scattering geometry for symmetric (002) reflection of single crystal SrTiO3(c) scattering geometry for asymmetric (103)+ reflection of single crystal SrTiO3(d) scattering geometry for asymmetric (103)- reflection of single crystal SrTiO3
Fig.5 Reciprocal space illustration of the (h0l) reflections of cubic substrate and epitaxial films(a) substrate and unrelaxed film (b) substrate and fully relaxed film(c) satellites of superlattice in film (d) substrate and tilted film
Fig.6 Schematics for broadening of diffraction points from epitaxial films
Fig.7 HRXRD profiles for symmetric (004) reflection (a) and asymmetric (224) reflection (b) of the cubic Si1-xGex/Si epitaxial structure (F1 and F2 in the figure are Laue oscillation peaks which can be used to calculate the thickness of epitaxial film. The inset shows the epitaxial structure where the substrate is Si with surface normal of [001] and the epitaxial film is Si1-xGex with nominal composition x=0.1 for Ge)
Fig.8 Intensity () distribution along ΔG (The half-peak width is 0.88/t, the numbers under the figure are the diffraction order n, ΔG is the relative change quantity of vector G, t is the thickness of film)
Fig.9 Curve of intensity vs 2θ of symmetric (002) reflection for the superlattice (La0.3Sr0.7MnO3/PbTiO3)8/DyScO3 (In the inset,the substrate is DyScO3, the layer 1 is La0.3Sr0.7MnO3, the layer 2 is PbTiO3, layer 1 and layer 2 as one period compose an 8 period (La0.3Sr0.7MnO3/PbTiO3)8 superlattice)
Fig.10 Curve of intensity vs of low angle X-ray reflectivity for the Si1-xGex/Si epitaxial structure (In the inset, layer is Si1-xGex, substrate is Si)
Fig.11 Origin of the angle differences Δθ=θL-θS and Δτ=τL-τS when measuring asymmetric diffraction of epitaxial layer and substrate (Δθ—the difference of Bragg angle between epitaxial layer and substrate, Δτ—the difference of tilt angle between epitaxial layer and substrate, θL—Bragg angle of asymmetric diffraction for epitaxial layer, θS—Bragg angle of asymmetric diffraction for substrate, τL—the angle between asymmetric diffraction plane of epitaxial layer and surface of sample, τS—the angle between asymmetric diffraction plane of substrate and surface of sample, dL—the plane spacing of asymmetric diffraction for epitaxial layer, dS—the plane spacing of asymmetric diffraction for substrate, aS—the lattice parameter of substrate, —the lattice parameter of layer in parallel direction, —the lattice parameter of layer in vertical direction)
Fig.12 Curves of intensity vs for asymmetric (206)+ reflection and (206)- reflection from an inclined Si1-xGex /Si epitaxial structure and substrate shown in Fig.7
Fig.13 Schematic representation of the (010) reciprocal space map of PbTiO3/LaAlO3 epitaxial structure, where the substrate is LaAlO3 with surface normal of [001] and the epitaxial film is PbTiO3 ( and are along [100]* and [001]* directions, respectively. ap, PTO and av, PTO are the lattice parameters of PbTiO3 along [100] and [001] directions, respectively. ap, LAO and av, LAO are the lattice parameters of LaAlO3 along [100] and [001], respectively. □ shows the (003) and (103) diffraction points from substrate of LaAlO3, shows the (003) and (103) diffraction points from epitaxial layer of PbTiO3, "pseu" means that the epitaxial layer is pseudomorphic, "rel" means that the epitaxial layer is fully relaxed. The upper right color map inset shows the (103) diffraction points from the PbTiO3/ LaAlO3 epitaxial structure. The arrows "α" describes the move path of the diffraction point of the layer during relaxation. The angle of satisfies the relation of , and are the elastic stiffness constants)
Fig.14 Local reciprocal space mapping including (002) diffraction points from the PbTiO3/LaAlO3 epitaxial structure, where LaAlO3(002) is from LaAlO3 (A, B, C, D are from the domains in the epitaxial layer PbTiO3(002))
Fig.15 Local reciprocal space mapping including (002) diffraction points from the PbTiO3/SrRuO3/SrTiO3 epitaxial structure, where SrTiO3(002) is from SrTiO3, SrRuO3(002) is from the buffer layer of SrRuO3, PbTiO3(002) is from PbTiO3, Pb2O3 is from the new phase formed in PbTiO3
[1]
Queisser H J, Haller E E. Defects in semiconductors: Some fatal, some vital [J]. Science, 1998, 281: 945
[2]
Liu J F. SSMBE epitaxial growth and structure characterization of SiC thin films [D]. Hefei: University of Science and Technology of China, 2007
Spaldin N A. Multiferroics: Past, present, and future [J]. MRS Bull., 2017, 42: 385
[4]
Damodaran A R, Agar J C, Pandya S, et al. New modalities of strain-control of ferroelectric thin films [J]. J. Phys. Condens. Matter, 2016, 28: 263001
[5]
Shang J. Preparation and laser induced thermoelectric votalge of ferroelctric thin films [D]. Kunming: Kunming University of Science and Technology, 2010
[5]
(尚 杰. 铁电氧化物薄膜的制备及其激光感生电压效应 [D]. 昆明: 昆明理工大学, 2010)
[6]
Birkholz M, Fewster P F, Genzel C. Thin Film Analysis by X-ray Scattering [M]. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2006: 303
[7]
Gao G Y. Studies on the strain states and thickness effects of epitaxial (La1-xCax)MnO3 thin films [D]. Hefei: University of Science and Technology of China, 2008
Liu Y. Aberration corrected transmission electron microscopy investigation of domains and interfaces in ferroelectric thin films [D]. Beijing: University of Chinese Academy of Sciences, 2017
Moram M A, Vickers M E. X-ray diffraction of III-nitrides [J]. Rep. Prog. Phys., 2009, 72: 036502
[10]
Fewster P F. X-ray analysis of thin films and multilayers [J]. Rep. Prog. Phys., 1996, 59: 1339
[11]
Li C R, Wu L J, Chen W C. Studies of the impurity effects on crystalline quality by high-resolution X-ray diffraction [J]. Acta Phys. Sin., 2001, 50: 2185
Moram M A, Vickers M E, Kappers M J, et al. The effect of wafer curvature on X-ray rocking curves from gallium nitride films [J]. J. Appl. Phys., 2008, 103: 093528
[13]
Mzoughi T, Fitouri H, Moussa I, et al. High resolution X-ray diffraction study of InAs layers grown with and without bismuth flow on GaAs substrates by metalorganic vapor phase epitaxy [J]. J. Alloys Compd., 2012, 524: 26
[14]
Li X F, Zhang J W, Gao H K, et al. The analysis on the reciprocal space mapping of the AlGaAs/GaAs epitaxial layer in the transparent GaAs photocathode [J]. Acta Photon. Sin., 2002, 31: 312
Fulthorpe B D, Ryan P A, Hase T P A, et al. High-resolution X-ray diffraction studies of roughness and mosaic defects in epitaxial Fe/Au multilayers [J]. J. Phys., 2001, 34D: A203
[16]
Kopp V S, Kaganer V M, Jenichen B, et al. Analysis of reciprocal space maps of GaN(0001) films grown by molecular beam epitaxy [J]. J. Appl. Cryst., 2014, 47: 256
[17]
Chen Y, Deng H, Ji H. Characterization of structure of GaN films by high resolution X-ray diffraction analysis [J]. Anal. Test. Technol. Inst., 2009, 15: 21
Yu G J, Xu M S, Hu X B, et al. High resolution X-ray diffraction analysis of GaN epitaxial layer grown on SiC substrate [J]. J. Synth. Cryst., 2014, 43: 1017
Cui Y X, Xu M S, Xu X G, et al. High resolution X-ray diffraction analysis of defect density of gallium nitride epitaxial layer [J]. J. Inorg. Mater., 2015, 30: 1904
Ayers J E. The measurement of threading dislocation densities in semiconductor crystals by X-ray diffraction [J]. J. Cryst. Growth, 1994, 135: 71
[21]
Christen H M, Nam J H, Kim A J, et al. Stress-induced R-MA-MC-T symmetry changes in BiFeO3 films [J]. Phys. Rev., 2011, 83B: 144107
[22]
Chen Z H, Luo Z L, Huang C W, et al. Low-symmetry monoclinic phases and polarization rotation path mediated by epitaxial strain in multiferroic BiFeO3 thin films [J]. Adv. Funct. Mater., 2011, 21: 133
[23]
Mai Z H. Thin Film Structure Characterization by X-Ray [M]. Beijing: Science Press, 2007: 1, 11
[23]
(麦振洪. 薄膜结构X射线表征 [M]. 北京: 科学出版社, 2007: 1, 11)
[24]
Birkholz F C, Fewster P F, Genzel C. Thin Film Analysis by X-Ray Scattering [M]. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2006: 297
[25]
Darakchieva V, Paskova T, Paskov P P, et al. Structural characteristics and lattice parameters of hydride vapor phase epitaxial GaN free-standing quasisubstrates [J]. J. Appl. Phys., 2005, 97: 013517
[26]
Lee S R, West A M, Allerman A A, et al. Effect of threading dislocations on the Bragg peakwidths of GaN, AlGaN, and AlN heterolayers [J]. Appl. Phys. Lett., 2005, 86: 241904
[27]
Macrander A T, Schwartz G P, Gualtieri G J. X-ray and Raman characterization of AlSb/GaSb strained layer superlattices and quasiperiodic Fibonacci lattices [J]. J. Appl. Phys., 1988, 64: 6733
[28]
Paduano Q S, Weyburne D W, Drehman A J. An X-ray diffraction technique for analyzing structural defects including microstrain in nitride materials [J]. J. Cryst. Growth, 2011, 318: 418
[29]
Paduano Q S, Weyburne D W, Drehman A J. An X-ray diffraction technique for analyzing basal-plane stacking faults in GaN [J]. Phys. Status Solidi, 2010, 207A: 2446
[30]
Mariager S O, Lauridsen S L, Dohn A, et al. High-resolution three-dimensional reciprocal-space mapping of InAs nanowires [J]. J. Appl. Cryst., 2009, 42: 369
[31]
Mariager S O, Schlepütz C M, Aagesen M, et al. High-resolution three-dimensional reciprocal space mapping of semiconductor nanostructures [J]. Phys. Status Solidi, 2009, 206A: 1771
[32]
Cornelius T W, Davydok A, Jacques V L R, et al. In situ three-dimensional reciprocal-space mapping during mechanical deformation [J]. J. Synchrotron Rad., 2012, 19: 688
[33]
Takahasi M, Nakata Y, Suzuki H, et al. In situ three-dimensional X-ray reciprocal-space mapping of GaAs epitaxial films on Si(001) [J]. J. Cryst. Growth, 2013, 378: 34
[34]
Bauer S, Lazarev S, Bauer M, et al. Three-dimensional reciprocal space mapping with a two-dimensional detector as a low-latency tool for investigating the influence of growth parameters on defects in semipolar GaN [J]. J. Appl. Cryst., 2015, 48: 1000
[35]
Sasaki T, Takahasi M, Suzuki H, et al. In situ three-dimensional X-ray reciprocal-space mapping of InGaAs multilayer structures grown on GaAs(001) by MBE [J]. J. Cryst. Growth, 2015, 425: 13
[36]
Diffracplus Leptos (User Manual). Version 7. Karlsruhe: Bruker AXS GmbH., 2009
Luo Z L, Chen Z H, Yang Y J, et al. Periodic elastic nanodomains in ultrathin tetragonal-like BiFeO3 films [J]. Phys. Rev., 2013, 88B: 064103
[39]
Catalan G, Janssens A, Rispens G, et al. Polar domains in lead titanate films under tensile strain [J]. Phys. Rev. Lett., 2006, 96: 127602
[40]
Chen Z H, Liu J, Qi Y J, et al. 180° ferroelectric stripe nanodomains in BiFeO3 thin films [J]. Nano Lett., 2015, 15: 6506
[41]
Barchuk M, Holy V, Kriegner D, et al. Diffuse x-ray scattering from stacking faults in a-plane GaN epitaxial layers [J]. Phys. Rev., 2011, 84B: 094113
[42]
Moram M A, Johnston C F, Kappers M J, et al. Investigating stacking faults in nonpolar gallium nitride films using X-ray diffraction [J]. Physica, 2009, 404B: 2189
[43]
Moram M A, Johnston C F, Hollander J L, et al. Understanding X-ray diffraction of nonpolar gallium nitride films [J]. J. Appl. Phys., 2009, 105: 113501
