High-Resolution X-Ray Diffraction Analysis of Epitaxial Films

doi:10.11900/0412.1961.2019.00006

Acta Metall Sin

2020, Vol. 56

Issue (1): 99-111 DOI: 10.11900/0412.1961.2019.00006

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High-Resolution X-Ray Diffraction Analysis of Epitaxial Films

LI Changji¹,ZOU Minjie^1,²,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.

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Abstract

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 Si_1-_xGe_x_{(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.}

Key words: film growth epitaxial film high-resolution X-ray diffraction reciprocal space mapping

Received: 29 September 2019

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	Changji LI
	Minjie ZOU
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	Sucheng WANG

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https://www.ams.org.cn/EN/10.11900/0412.1961.2019.00006 OR https://www.ams.org.cn/EN/Y2020/V56/I1/99

Fig.1 Schematics of reciprocal space and diffraction condition for the SrTiO₃ single crystal (2θ—diffraction angle,

k i

—incident vector of X-ray,

k d

—diffracted vector of X-ray,

S

—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

S

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 (

ω

—the rotation angle around Z_L axis by right-hand spiral rule;

ψ —

the azimuthal angle;

?

—the rotation angle around the normal direction of sample surface; X_L, Y_L, Z_L—laboratory coordinate axes; X, Y, Z—sample translation coordinate axes)

Fig.4 Illustration of scan types and scattering geometries (

ω i

—angle between incident X-ray and sample surface,

ω e

—angle between diffracted X-ray and sample surface)(a) scan types including

ω

, 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 Si_1-_xGe_x/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 Si_1-_xGe_x with nominal composition x=0.1 for Ge)

Fig.8 Intensity (

I G

) 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 (La_0.3Sr_0.7MnO₃/PbTiO₃)₈/DyScO₃ (In the inset,the substrate is DyScO₃, the layer 1 is La_0.3Sr_0.7MnO₃, the layer 2 is PbTiO₃, layer 1 and layer 2 as one period compose an 8 period (La_0.3Sr_0.7MnO₃/PbTiO₃)₈ superlattice)

Fig.10 Curve of intensity vs

2 θ

of low angle X-ray reflectivity for the Si_1-_xGe_x/Si epitaxial structure (In the inset, layer is Si_1-_xGe_x, substrate is Si)

Fig.11 Origin of the angle differences Δθ=θ_L-θ_S and Δτ=τ_L-τ_S 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, θ_L—Bragg angle of asymmetric diffraction for epitaxial layer, θ_S—Bragg angle of asymmetric diffraction for substrate, τ_L—the angle between asymmetric diffraction plane of epitaxial layer and surface of sample, τ_S—the angle between asymmetric diffraction plane of substrate and surface of sample, d_L—the plane spacing of asymmetric diffraction for epitaxial layer, d_S—the plane spacing of asymmetric diffraction for substrate, a_S—the lattice parameter of substrate,

a L p

—the lattice parameter of layer in parallel direction,

a L v

—the lattice parameter of layer in vertical direction)

Fig.12 Curves of intensity vs

2 θ

for asymmetric (206)+ reflection and (206)- reflection from an inclined Si_1-_xGe_x/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 (

q x

and

q z

are along [100]^* and [001]^* directions, respectively. a_{p, PTO} and a_{v, PTO} are the lattice parameters of PbTiO₃ along [100] and [001] directions, respectively. a_{p, LAO} and a_{v, 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

α

satisfies the relation of

2 c 12 c 11 t a n α = t a n (ω - θ)

c 11

and

c 12

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

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