Physica B 248 (1998) 62-66 X-ray reflection and diffuse scattering from sputtered gold films C. Schug, P. Lamparter*, S. Steeb Max-Planck-Institut fu(r Metallforschung, Seestrasse 92, D-70174 Stuttgart, Germany Abstract Gold films were prepared by DC sputtering on quartz glass substrates under two different conditions, once in argon at 3;10\ mbar (Au1-films), and once in residual air at 0.3 mbar (Au2-films). Specular X-ray reflection showed that the surface of the Au1-films was as smooth as that of the substrate, whereas the Au2-films were distinctly rougher. The diffuse scattering could be measured with a laboratory equipment by recording rocking curves and detector scans. The application of existing theories to the diffuse scattering data showed that slight modifications of the given equations were necessary. With these modifications the experimental data could be fitted very well, and the height-height correlation functions of the surfaces of the films and of the substrate were determined. In the Au1-films the surfaces of the film and the substrate are perfectly correlated, whereas in the Au2-films no cross correlation is found. 1998 Elsevier Science B.V. All rights reserved. Keywords: Gold films; X-ray reflection; Diffuse scattering 1. Introduction to sputtered Au films is demonstrated. Two repre- sentative examples were selected from Ref. [5], Specular reflection from thin films provides in- where the experimental methods and the data re- formation about their thickness, density and mean- duction procedures are described in detail. square roughness, more generally spoken, about the structure perpendicular to the surface (z-direc- tion) [1]. The diffuse scattering is measured under 2. Experimental the nonspecular condition where the angle between the diffracted wave and the sample surface, , is The films were deposited on quartz glass substra- different from the angle of incidence, . It yields tes by DC sputtering, applying two different sput- information about structural features along the sur- tering conditions. Au1-films were prepared in a face (x, y), such as the height-height correlation magnetron DC sputtering device under a high- function c(x,y) of a rough surface. In the present purity argon atmosphere at 3;10\ mbar. Au2- work we study the feasibility of diffuse diffraction films were DC sputtered in residual air at 0.3 mbar. work by means of a laboratory setup with a sealed The measurements of the specular reflectiv- X-ray tube. The application of the diffuse scattering ity and the diffuse scattering were performed with theories by Sinha et al. [2], Sinha [3] and Pynn [4] a Siemens D 500 diffractometer, equipped with a 0921-4526/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 2 0 4 - X C. Schug et al. / Physica B 248 (1998) 62-66 63 cutting edge above the sample surface, a detector slit of 67 m, and a secondary monochromator to select Cu K? radiation. 3. Results and discussion 3.1. Specular reflection Fig. 1 shows the experimental reflectivities of the Au-films (dots). From fitting theoretical expressions (lines) using the well established optical matrix method (see e.g. [1]) the parameters in Table 1 were Fig. 1. Specular reflection with gold films Au1 and Au2: ( ) derived. experimental, (-) theoretical fit. The curves for Au2 are shifted The Au1-film appears rather perfect. Its reflec- in the plot. tivitiy curve exhibits pronounced oscillations. Its roughness, $"7.7A>, is about the same as that of the quartz glass substrate, Table 1 1"7.0 A>, and its den- sity, Parameters derived from specular reflectivity $"19.0 g/cm is only slightly lower than the density of bulk gold, "19.25g/cm . d (A>) (A>) (g/cm ) In contrast to this, the Au2-film is obviously much less perfect. The rather large roughness, Substrate - 7.0 2.20 Au1-film 282 7.7 19.0 $"23.0 A>, causes a rapid damping of the oscilla- tions. The low apparent density, Au2-film 235 23.0 15.5 $"15.5 g/cm , indicates that the film is not homogeneous. The introduction of nitrogen and oxygen atoms during the sputtering process reduces the lateral mobility of the Au atoms in the film plane, and thus enhan- ces the tendency for island formation. 3.2. Diffuse scattering Fig. 2 (dots) shows a detector scan of the Au1- film at "1.88 °, where the specular reflection in Fig. 1 exhibits a peak. The lines show an attempt to fit the experimental data, using theories from literature: the dashed line according to Sinha (Eqs. (13) and (14) in Ref. [3]) and the solid line Fig. 2. Detector scan with Au1-film at "1.88 °: ( ) experi- according to Pynn (Eqs. (25) and (29) in Ref. [4]). mental, (-) theoretical fit according to Pynn, (! ! !) ac- The slit geometry of the measurements was taken cording to Sinha. The fit curves are shifted in the plot. into account by integrating the equations over the component qW of the scattering vector q perpendicu- lar to the scattering plane x-z. This corresponds to data, in particular with respect to the phase of the a transition from the two-dimensional correlation oscillations. function c(x, y), to the one-dimensional case c(x) in Therefore the equations from Refs. [3] and [4] the equations. Obviously, it is not possible to ob- were modified in the present work. With the ap- tain good agreement between fit and experimental plied modifications the contributions of the free 64 C. Schug et al. / Physica B 248 (1998) 62-66 surface of the film (F), the substrate-film interface The F (S), and the cross-correlation between the two sur- L, fL and gL are the same as defined in Ref. [4] (Eqs. (26) and (27)). faces (C), respectively, to the total scattering cross- section (d /d ) are written as follows exp[ !(q "k B. X $#Re[q X 1] 1)/2] According to Sinha: d d . ! ! qX"qX 1" d exp(!Re[q "k B1 X 1] 1) d 1 1 ; dxcos(q 1 "qX 1" V x) +exp[qX"qX 1" c!(x)]!1,, (2c) ; dxcos(qVx)+exp["qX 1" c1(x)]!1,, where B. (1a) !"2 $ 1 "¹?" "¹@" Re[exp(i qX $ d)]. The modifications to the equations given in Refs. where B1 [3,4] are: Substrate, Eq. (1a): the component q 1" 1 "¹?" "¹@" . X of the wave vector transfer is substituted by the cor- d exp(!Re[q "k B1 X $] $) responding value in the substrate, q d 1 $ X 1. Then $ "qX $" (d /d )11"(d /d ).1. Film, Eq. (1b): qX $ instead of qX and t? $,t@ $ instead of ¹?,¹@. Cross correlation, ; dxcos(qVx)+exp["qX $" c$(x)]!1,, Eq. (1c): qX $ instead of qX; Eq. (2c), qX $ instead of q (1b) X 1 and 2 "¹?" "¹@" instead of ¹? ) ¹@. For the height-height correlation functions c(x) where B1 an expression for self-affine rough surfaces (see e.g. $" $ "t? $" "t@ $" . Ref. [3]) was applied: d exp(!Re[q "k B1 X $][ $# 1]/2) d 1 ! ! "qX $" c(x)" exp[!(x/ ) &], (3) ; dxcos(q where is the lateral correlation length of the V x) +exp["qX $" c!(x)]!1,, height fluctuations, and H is the roughness expo- (1c) nent. where B1 Fig. 3a shows the fits to the experimental data !"2 $ 1 "¹?" "¹@" cos(Re[qX $]d). The calibration constant k contains all q-inde- of Fig. 2 using the modified equations. With the pendent quantities. is the electron density differ- modifications, the detector scan and the rocking ence, q is the wave vector transfer, t curve in Fig. 3b can be fitted very well, both with ? $ and t@ $ are the transmission coefficients at the film surface at the Sinha approach, Eqs. (1a), (1b) and (1c), and the angle of the incoming and the angle of the with the Pynn approach, Eqs. (2a), (2b) and (2c). reflected wave, ¹ The results for "1.51 °, where the specular reflec- ? and ¹@ are the transmission coefficients of the entire film-substrate system, and tivity in Fig. 1 has a minimum, are plotted in d is the thickness of the film. The transmission Fig. 4a and b. All four scans in Figs. 3 and 4 could coefficients were calculated for rough surfaces. be fitted with a consistent set of parameters, which According to Pynn: are listed in Table 2. The contribution of the cross-correlation (d /d ). d ! is additionally plotted on a linear scale in Fig. 3a and Fig. 4a, and we note that " , (2a) d . d the pronounced oscillations of the detector scans 1 d 11 are caused by a strong cross correlation between d "k (!1)L> F the free surface of the film and that of the substrate. d . $ L $ L The high quality of the Au1-film, already observed exp[!( f with the specular reflectivity, is confirmed by the ; L#g L) $/2] f dxcos(qVx) fitting parameters of the cross-correlation function: L gL The roughness, ;+exp[(!1)L> f !"6.8 A>, is comparable to those L gL c$(x)]!1,. (2b) of the quartz glass substrate and the film, and the C. Schug et al. / Physica B 248 (1998) 62-66 65 Table 2 Parameters from diffuse scattering (according to Pynn, modi- fied). c$: free surface of the film; c!: cross-correlation. The errors refer to the variation of the single scan fits (A>) (A>) H Substrate 7.0$2.0 2000$200 0.25$0.05 Au1-film, c$ 7.8$0.7 1300$200 0.25$0.04 Au1-film, c! 6.8$0.2 1300$200 0.25$0.04 Au2-film 15.0$1.0 350$50 0.75$0.05 Fig. 3. Detector scan (a) and rocking curve (b) with Au1-film at "1.88 °: ( ) experimental, (! ! !) fit with Eqs. (1a), (1b) and (1c), (-) fit with Eqs. (2a), (2b) and (2c). The right-hand scale in (a) refers to the cross-correlation (d /d ).! (Eq. (2c)). Fig. 5. Detector scan (a) and rocking curve (b) with Au2-film: ( ) experimental, (-) fit with Eqs. (2a), (2b) and (2c), (! ! !) substrate contribution (d /d ).1 (Eq. (2a)), (! ) !) film contri- bution (d /d ).$ (Eq. (2b)). correlation length, !"1300A>, is as large as that of the film surface. In addition, the values of the roughness exponent H are the same for the three contributions. This indicates that the surface of the gold film is a replication of the substrate sur- face. A detector scan and a rocking curve of the Au2- sample are plotted in Fig. 5a and b together with Fig. 4. Detector scan (a) and rocking curve (b) with Au1-film at "1.51 °: ( ) experimental, (! ! !) fit with Eqs. (1a), (1b) the fits according to Eqs. (2a), (2b) and (2c). These and (1c), (-) fit with Eqs. (2a), (2b) and (2c). The right-hand scale fits show that no cross-correlation at all between in (a) refers to the cross-correlation (d /d ).! (Eq. (2c)). the two surfaces exists, i.e. c!(x)"0. 66 C. Schug et al. / Physica B 248 (1998) 62-66 The contributions of c1 and c$, shown separ- that smooth Au films of high quality, as proved by ately in Fig. 5a and b, are sufficient to describe the their specular reflectivity, exhibit a perfect cross- diffuse scattering. The correlation length of the correlation between the free surface of the film and surface of the Au2-film, $"350A>, is distinctly the surface of the substrate. Slight modifications of smaller than that of the Au1-film. The larger rough- theoretical expressions from literature for the dif- ness exponent, H$"0.75, indicates a less jagged fuse scattering allow a quantitative description of surface. the experimental data. 4. Conclusions References X-ray reflectivity and diffuse scattering by means [1] B. Vidal, P. Vincent, Appl. Opt. 23 (1984) 1794. of a laboratory equipment can be sucessfully em- [2] S.K. Sinha, E.B. Sirota, S. Garoff, Phys. Rev. B 38 (1988) ployed to characterize the quality of gold films 2297. [3] S.K. Sinha, Physica B 173 (1991) 25. sputtered on quartz glass substrates under different [4] R. Pynn, Phys. Rev. B 45 (1992) 602. ambient conditions. The diffuse scattering shows [5] C. Schug, Thesis, University of Stuttgart, 1997.