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Applied Surface Science
Volume 141, Issues 3-4, March 1999, Pages 357-365

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PII: S0169-4332(98)00524-8
Copyright © 1999 Published by Elsevier Science B.V. All rights reserved

Surface roughness of thin layers_¯¯a comparison of XRR and SFM measurements

O. Filies^a, O. Böling^a, K. Grewer^a, J. Lekki^b^,^*, M. Lekka^b, Z. Stachura^b and B. Cleff^a

^a Institute of Nuclear Physics, University of Münster, Münster, Germany
^b Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Cracow, Poland

Received 29 May 1998; accepted 12 August 1998. Available online 10 March 1999.

Abstract

X-ray reflectivity (XRR) studies of thin layers (3 to 120 nm thick) were performed for the determination of layer thickness, density and roughness. The simulations of X-ray reflectivity measurements were performed using Parrat's recursive algorithm, while those of the reflection of X-rays from interfaces were performed using Fresnel formulae. Using this approach, the roughness of the interface was described by intensity damping by gaussian type functions. This allowed for the determination of layer thickness and density and average interface roughness. As an extension of this simple model, an enhanced theoretical description of rough interfaces proposed by Sinha was applied, where the X-ray reflection from interfaces was separated into a direct fraction and a diffuse scattered one with the use of the first Born approximation. A simulation procedure, calculating both fractions of the reflection was developed, that enabled the detailed characterisation of layers and inner layers. The complementary information required for proper adjusting of input simulation parameters was obtained from SFM measurements of the investigated surfaces. Surface roughness was described using fractal surface functions instead of simple gaussian peaks. A comparison between this method and SFM measurement shows a reasonable agreement, particularly in the estimation of shapes of interface structures.

Author Keywords: X-ray reflectivity (XRR); SFM; Thin layers; Surface roughness; Fractal surface scaling

Article Outline

1. Theoretical background
2. Interface roughness_¯¯Névot's model
3. Fractal approach_¯¯Sinha's model
4. Experimental
5. Conclusion

References

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Fig. 1. The idea of the recursive approach: X-rays coming from medium 0 (air or vacuum) are scattered and deflected at the first interface (medium 1). The scattered fraction is again scattered and deflected at the next interface. This mechanism is reproduced until the last significant layer is reached. Every reflected fraction interferes with fractions reflected at previous interfaces, producing finally a measurable pattern.

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Fig. 2. Interface roughness according to Névot. The distribution of peaks and valleys on a mean interface level is described using the gaussian function and its parameter.

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Fig. 3. TOF-RBS spectra of Co/Ag thin layers deposited on a Si substrate at 10°C (left) and 130°C (right). The measured mass density values are shown in figure insets (numbers in parentheses represent values expected from deposition conditions).

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Fig. 4. XRR spectra and simulations performed according to Névot's and Sinha's algorithms for the following layers deposited on a Si substrate: (a) 7.3 nm Co/4.4 nm Ag double layer (Table 1, sample 1), (b) 96 nm Al/16 nm Ti double layer (sample 9), (c) 19 nm single In layer (sample 5), (d) 21 nm single Sn layer (sample 8). Layers' thickness were obtained from simulation following either Névot's or Sinha's model.

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Fig. 5. Topography of four samples presented in Fig. 4 measured using SFM in air.

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Fig. 6. A comparison of surface fractal scaling properties of four example surfaces (Fig. 4 and Fig. 5) measured using SFM (directly) and XRR (simulation according to Sinha's model).

Table 1. The comparison of roughness parameters obtained for several selected samples from XRR and SFM measurements

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References

1. L.G. Parrat. Phys. Rev. 95 (1954), pp. 359_¯369.

2. C. Rhan et al.. J. Appl. Phys. 74 1 (1993), pp. 146_¯152.

3. L. Névot et al.. Rev. Phys. Appl. 15 (1980), pp. 761_¯779. Abstract-INSPEC | $Order Document

4. O. Filies, Röntgenreflektometrie zur Analyse von Dünnschichtsystemen-Charakterisierung ultradünner Schichten, PhD thesis, Part I, Institute of Nuclear Physics, Münster, 1997.

5. P. Doig et al.. J. Appl. Cryst. 14 (1981), pp. 321_¯325. Abstract-INSPEC | $Order Document | Full Text via CrossRef

6. S.K. Sinha. Acta Phys. Pol. A 89 2 (1996), pp. 219_¯234. Abstract-INSPEC | $Order Document

7. S.K. Sinha et al.. Phys. Rev. B 38 4 (1988), pp. 2297_¯2311. Abstract-INSPEC | $Order Document | Full Text via CrossRef

8. G. Palasantzas. Phys. Rev. E 49 2 (1994), pp. 1740_¯1742. Abstract-INSPEC | $Order Document | Full Text via CrossRef

9. M. Kardar et al.. Phys. Rev. Lett. 56 (1986), pp. 889_¯892. Abstract-INSPEC | $Order Document | Full Text via CrossRef

10. G. Palasantzas et al.. Phys. Rev. B 48 5 (1993), pp. 2873_¯2877. Abstract-INSPEC | $Order Document | Full Text via CrossRef

11. A.-L. Barabasi, H.E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, 1995.

12. A. Bunde, S. Havlin, Fractals in Science, Springer-Verlag, 1995.

13. O. Filies, DiffTool_¯¯Program zur Analyse von Röntgenspektren, PhD thesis, Part II, Institute of Nuclear Physics, Münster, 1997.

14. J. Wang. Europhys. Lett. 42 3 (1998), pp. 283_¯288.

15. J. Lekki, Scanning Force Microscopy of Implanted Silicon, PhD thesis, Institute of Nuclear Physics, Cracow, 1996.

^*Corresponding author. Tel.: +48-12-637-0222 ext. 271; Fax: +48-12-637-1881; E-mail: lekki@alf.ifj.edu.pl

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Applied Surface Science
Volume 141, Issues 3-4, March 1999, Pages 357-365

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