Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 467 Residual Stress Gradients in a Tungsten Film by Grazing-Incidence XRD T Ely*, P.K. Predecki* and I.C. Noyan # * University of Denver, Denver CO 80208 # IBM T. Watson Research Center, Yorktown Heights, NY 10598 Abstract Diffraction measurements were made on a 600 nm thick W film deposited on a silicate glass substrate by dc magnetron sputtering. Diffraction patterns of the 321, 222, 310, 220, and 211 reflections were obtained with Cu α radiation at incidence angle K α from 0.6 t α = θ, the o s Bragg angle, using pseudo parallel-beam optics. The patterns showed only th α-w phase, but many reflections were asymmetric or appeared as doublets, suggesting a two layered structure in different states of stress as reported by Vink et al and Noyan et al. Fo α<~5º, reflections appeared as single peaks. Conventional sin 2 Ψ plots showed that the left and the single peak data followed a continuous trend suggesting that both came from the upper layer of primar α-w, while the right peak data came from the lower layer of secondar α-w. Sin 2 ψ plots at constant values of 1/e penetration dept τ, showed negligible slopes h for the right peak data and pronounced negative slopes for the left and single peak data. These plots yielded a hydrostatic tensile stress of 0.28 ± 0.55 GPa for the lower layer. Assuming an equi-biaxial stress state in the 317 nm thick upper layer, the plots yielded an in-plane compressive stress of -4.8 GPa near the film surface, passing through a minimum of -6 GPa at 100 nm and increasing rapidly to near zero at a depth of 317 nm. Introduction Sputtered W films frequently deposit with two phases present: one having the stable BCC structure and the other having the metastable A15 structure (1-5). The A15 structure phase typically forms during the initial stages of deposition and subsequently transforms to the BCC structure upon annealing or even at room temperature after varying periods of time (1-5). The cubical dilation of -0.94% ( 1) on transformation from the A15 to the BCC structure, superimposed on the deposition stresses in the film, leads to a layered single phase film with a complicated stress state. The evaluation of this stress state is the subject of this paper. Experimental Procedure X-ray diffraction patterns from a 600 nm thick W film were collected using a Siemens D500 configured with pseudo parallel-beam optics (see Figure 1). The film was deposited on a silicate glass substrate via dc magnetron sputtering at 500 W and an Ar pressure of 10x10-3 Torr (1.33 Pa) (2, 3).
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Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 468 Figure 1. Asymmetric pseudo parallel-beam system used on Siemens D-50 Ω-type diffractometer. Results Raw Data Several full pattern data traces collected over a range of incidence angles α=0. 6 t θ) o were compared to Powder Diffraction File patterns of bot α-w an β-w d (BCC and A15 structures h respectively) as a means of evaluating phase content as a function of depth. In each case onl α- W appeared to be present (Figure 2). The patterns showed a mil <11 0 > fiber texture normal to the film surface. Figure 2. Diffraction patterns exhibiting absence of A15 structure. Subsequently x-ray data were collected for the 211, 220, 310, 222 and 321 reflections at 14 incidence angles ranging fro α=0. 6 to 6 (including 5 m on θ/ 2θ scan e for each reflection) at a
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 469 constant arbitrar azimuthal angl y φ = 0º. An e example of the 321 reflection data as a function of incidence angle is given in Figure 3. Seven diffraction patterns α = 1º t α = θ) o for the 321 reflection were collected after rotating the specimen 90º in-plane, to provid φ = 90 data. (a) (b) Figure 3. Raw data for the 321 reflection as a function of incidence angl α: (a) small incidence angle data, top curv α=5º, bottom curv e α=0.6º; (b) e large incidence angle data top, curv α=θ., bottom curv α=10º e For each of the five reflections considered, the data traces collected at incidence angles of or less appeared to be symmetric while those collected at large α became increasingly asymmetric with increasing incidence angle, i.e. increasing penetration depth of the incident beam. r
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 470 Data Modeling As a first approximation, the symmetric peaks were assumed to be due to a single layer (the upper layer) and the asymmetric peaks due to 2 layers (upper and lower) in different states of uniform stress. Upon fitting the asymmetric data to two peaks using Diffrac-AT v3.1 software, the peak positions obtained varied significantly with the fitting function used. In order to non arbitrarily select a fitting function the pseudo-voigt, Lorentz and Gauss functions were evaluated by modeling LaB 6 powder data (NIST standard # 660) with each function and comparing the resultant peak position values with standard values. The pseudo-voigt fits generated the best agreement and therefore this function was used to fit all of the data in this study. Typical fits for both smal α and l larg α data e are shown in Figure 4. (a) (b) Figure 4. (a) two peak fit to high incidence angle data and (b) one peak fit to low incidence angle data, the residual curve for each fit is shown above each caption.
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 471 At this point it is convenient to introduce the following nomenclature; the data resulting from a one peak fit (smal α) will be referred l to as single peak data while that corresponding to a two peak fit (hig α) will be h identified as being either left or right peak data. The uniqueness of each fit was tested by selecting at least three different starting positions in the profile fitting software. The resulting fits were deemed unique only if all three fits converged to the same set of peak position values. Data not satisfying this criterion were not included in further analysis. This test was particularly important in the case of the 222 reflection for α 2 5. These data were smoothed and re-tested but the software was still unable to generate unique fits despite obvious asymmetry in the data traces. The peak position data obtained a φ = 90º (321 reflection for 7 selecte α angles d ) agreed with th φ = 0º data at the sam e α angles to ± 0.079º, e which was within the ± 0.110º repeatability (321 reflection for 4 selecte α angles) of 5 repeat determinations a φ = 0º, moving or remounting the specimen each time. These results indicated that the stresses in the film were isotropic in-plane. d Data Processing and Analysis The peak position values obtained from the fitting process (single, left and right) were corrected for refraction using the James 6 equation (1) in conjunction with published material values for W (7). δ Sinα 2 θ = 2 θ B 2θL = 2 + Sin2θL Sin L ( 2θ α) ( 2θ α) Sin L + Sinα where θ B 2 is the measured Bragg angle, θ L is the peak position 2 for the case where the refraction correction is zero (symmetric Laue transmission), or true position, an δ is the refractive index decrement given, in SI units, for an elemental substance by: δ 2 2 [ ( )] 1 Ne λ 8 ρλ = 2 = 2 70 110 + 4 πε 2πmc. M Z f (2) o 2 wher ρ e is the mass density λ the x-ray wavelength,, M the molar mass of the element, Z i the atomic number an f i ' the real d part of the dispersion correction to the scattering factor for the element. θ L was 2 approximated to be θ B in this work. 2 Using the wavelength for Cu α 1 radiation and the K appropriate planar indices the peak positions were subsequently converted to lattice parameter an ψ values using the Bragg law and equation d 3, wher ψ was e considered positive when in the same sense as θ. Figure 5 displays this data in 2 the form of a conventional sin 2 ψ plot. ψ = θ + α (3) (1)
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 472 Figure 5 Conventional sin 2 ψ plot showing all of the data from five reflections The left and single peak data in this figure appear to follow the same trend indicating that the left and single peaks must be from the upper layer. Therefore, by default the right peak data must be from the lower layer. It can be seen that the curves for a given hkl in the single peak data are clearly nonlinear which is consistent with a steep stress gradient in the depth direction of the upper layer. Thus, sin 2 Ψ plots at constant 1/e penetration depth τ, are needed in order to, determine the magnitude of the stresses present in each layer. Interpolation functions (second order polynomials for the left and single peak data, linear for right peak data), were used to relate the diffraction peak positions to the incidence angles and subsequently employed to ge α an 2θ d values corresponding to constan τ values calculated from t th Wolfstieg equation (6) e, τ = 2 2 si nθ sin ψ 2µ si θ n cosψ (4), wher µ e is the linear absorption coefficient. Constan τ plots of lattice parameter versus sin 2 ψt values were then generated using the interpolated peak position values (Figures 6-8).
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 473 Figure 6 Sin 2 ψ plot at constan τ for left peak t data Figure 7 Sin 2 ψ plot at constan τ for single peak t data
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 474 Figure 8 Sin 2 ψ plot at constan τ for right peak t data The left and single peak sin 2 ψ plots are much more linear than the conventional sin 2 ψ plots (R values range from 0.997 to 0.966) and have comparable large negative slopes (indicating compressive stresses) supporting the assumption that the left and single peaks are due to the upper layer. The right peak sin 2 ψ plots have more scatter with much smaller slopes (Fig. 8). Averaging all the right peak data and using a o = 0.31648 nm (9), a hydrostatic stress of 0.28 ±0.55 GPa was obtained for the lower layer indicating near zero or slightly tensile stresses in the lower layer. Using the linear fit functions from Figs 6 and 7 and assuming an equi-biaxial in-plane stress in the upper layer, stress-free lattice parameters a o were calculated by Hauk s method (8) (eq. 5) usin ν g for W = 0.28 (7) leading to a valu ψ* = 41.41º for e the stress fre ψ angle. The results for e a o are scattered between 0.3177 nm and 0.3181 nm and are somewhat larger than 0.31648 nm as shown in Fig. 9. Sin 2 ψ * = 2ν 1 ( + ν) (5)
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 475 Figure 9. Stress free lattice parameter values obtained from sin 2 ψ plots at constan τ. t Stress value σ 11 as a s function o τ were obtained f using equation 6 with E = 384.6 GPa (7) along with slopes of the sin 2 ψ plots in Figs. 6 and 7, and are shown in Fig 10. The stress values were not sensitive to the value of a o used. a 1+ ν = a σ 2 11 sin ψ + a = 0 (6) E φψ ο φψ Figure 10. Calculated stress values for the upper layer of the W film, versus penetration dept τ. The plot shows a minimum i σ 11 around 40 nm n increasing gradually wit τ. Even though the film thickness was 600 nm, measurements could be made a τ values > 600 nm. t To convert th τ-profile e in Fig. 10 to a z-profile, where z is the physical distance from the film surface, a numerical method and software developed by Zhu et al ( 10) were used. The results are shown in Fig. 11. The invers Laplace method could e not be used since most of th τ values used h
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 476 were greater than about 1/3 the film thickness (11). The numerical method employs a damping coefficien λ (a parameter t used to stabilize the numerical solution process) which was varied over a range of values from 0.1 to 100 and yielded similar stable (non-oscillating) stress profiles fo λ = 5 to 22.88. The best value o λ is the smallest one for f which there are no oscillations in the z profile λ=5). ( From th λ=5 profile e it can be seen that the in-plane stress at the surface decreases from 4.8 GPa compression to 6 GPa compression at 100 nm then increases toward zero at the upper layer/lower layer boundary at a depth of ~ 317 nm. The upper layer thickness of 317 ± 56 nm was calculated from the integrated intensities of the left and right peaks averaged for all the reflections neglecting texture. Figure 11. Z depth profile of residual stresses in the upper layer of W film Discussion of Results Our analysis indicates a two layered single phas α-w film structure in agreement with e other reports (1-5). It also illustrates how complicated the stress state in thin W films can be. There are several areas of concern in the assumptions used in the analysis. The first pertains to how the raw data were modeled. By fitting the asymmetric (larg α) diffraction peaks with two symmetric e peak profiles we are implicitly assuming that one uniform stress state exists in the upper layer and a different uniform stress exists in the transformed layer, whereas there is clearly a substantial gradient in the upper layer. In measurements of similarly steep gradients in single layer Mo films, peak asymmetry was negligible suggesting that gradients in the upper layer should not produce much asymmetry. Nevertheless, a more sophisticated multi-layer modeling process that fits the entire peak profile might produce more accurate results.
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 477 Secondly, part of the difficulty in obtaining an accurate stress profile is the need for accurate data over the entire depth range. For α values between 7 and 20 it was not always possible to obtain unique fits to the diffraction traces for all reflections (peaks tended to be modestly asymmetric(fig. 3)) leading to an averaging of some stress values and an absence of most stress values in the τ range of ~ 150 to 400 nm (Fig. 10). Unfortunately this region corresponds to the depth range that includes the boundary between the upper and lower layers. The higher resolution attainable with synchrotron radiation should allow useful data to be obtained from this range of depths. Thirdly, due to peak breadths of 2 to 4, for large incidence angles, τ can vary significantly across a single diffraction trace, also pointwise correction of the data for refraction, absorption, and polarization should be included. Finally, because of the presence of texture in each of the layers, the transformed layer thickness should be checked by a different method, such as layer removal (1). Conclusions 1. With the assumptions used in the analysis, the diffraction data suggest the presence of two layers: both of α-w. The upper layer, 317 ± 56 nm thick is in substantial in-plane compression near the surface changing rapidly to near zero stress at the upper/lower layer interface. The lower layer, 283 ± 56 nm thick, is by comparison nearly stress free. 2. The presence of the gradient in the upper layer suggests that a multi-layer model would be more accurate. Difficulties with unique profile fitting of the diffraction peaks at a values from 5 to 20 reveal the need for higher resolution (synchrotron) measurements. References 1. Vink, T.J., W. Walrave, J.L.C. Daams, A.G. Dirks, M.A.J. Somers and K.J.A. van den Aker, Stress, strain and microstructure in thin tungsten films deposited by dc magnetron sputtering, J. Appl. Phys. 74 (2), July 15, 1993. 2. Noyan, I.C., C.C. Goldsmith, T.M. Shaw, Inhomogeneous strain states in sputter deposited tungsten thin films, App. Phys. Lett. (in press). 3. Noyan, I.C. and C.C. Goldsmith, Origins of oscillations in d vs. sin 2 ψ plots measured from tungsten thin films, Advances in X-Ray Analysis, vol. 40 (in press). 4. O Keefe, M.J. and J.T. Grant, Phase transformation of sputter deposited tungsten thin films with A-15 structure, J. Appl. Phys 79 (12), June 15, 1996. 5. Durand, N., K.F. Badawi, and Ph. Goudeau, Residual stress and microstructure in tungsten thin films analyzed by x-ray diffraction-evolution under ion irradiation, J. Appl. Phys 80 (9), November 1, 1996. 6. R.W. James The dynamical theory of x-ray diffraction, Solid State Phys., 15, 1963. 7. Hertzberg R. W., Deformation and Fracture Mechanics of Engineering Materials, second edition, Wiley, 1976. 8 Noyan, I.C. and J.B. Cohen, Residual Stress Measurements by Diffraction and Interpretation, Springer-Verlag, 1987.
Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 478 9. JCPDS-ICDD Powder Diffraction File-2, Card 4-0806, 1994. 10. Zhu, X, B. Ballard and P. Predecki, Determination of z-profiles of diffraction data from profiles using a numerical linear inversion method, Advances in X-Ray Analysis, vol. 38 1995. 11. Zhu, X, P. Predecki and B. Ballard, Comparison of inverse LaPlace and numerical inversion methods for obtaining z-depth profiles of diffraction data, Advances in X-Ray Analysis, vol. 38 1995.