Surface roughness of thin layers—a comparison of XRR and SFM measurements

doi:10.1016/S0169-4332(98)00524-8

Applied Surface Science

Volume 141, Issues 3–4, March 1999, Pages 357-365

https://doi.org/10.1016/S0169-4332(98)00524-8 Get rights and content

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.

Section snippets

Theoretical background

X-ray reflectivity technique is a relatively simple, but powerful method for the determination of thin layer density, thickness and layer interface roughness. It allows also nondestructive studies of inner layers. Standard simulation methods of such X-ray spectra use a simple, but functional term for the description of the interface roughness in a form of X-ray intensity damping.

X-ray reflections from multilayer systems of n−1 layers and n interfaces may be calculated using Parrat's recursive

Interface roughness—Névot's model

The simple model presented above describes only ideal interfaces: flat, homogeneous and isotropic. In real measurements, such conditions are not met: in general, the real surfaces are rough, inhomogeneous and anisotropic, while the most significant role is played by interface roughness.

The first simple description of interface roughness was presented by Névot et al. [3], where Gaussian functions were used for roughness modeling. According to their model, the rough interface may be approximated

Fractal approach—Sinha's model

The simulation of real interfaces with the use of roughness coefficients ζ_n is only a rough approximation. Its weakness is particularly significant for non-gaussian type of roughness, for example, for surfaces with steps, periodical changes, etc. [5]. The simple model does not include the diffuse scattering from a rough surface, which may be significant. The model proposed by Sinha 6, 7 and Palasantzas [8] brings a vast improvement of the simple model by separating the reflected X-ray beam into

Experimental

The above approach was used for the characterization of several tens of metal and metal oxide layers, deposited on silicon substrates with the use of physical vapor deposition (PVD) and magnetron sputtering techniques. In order to assure diversified deposition conditions, deposition was performed at different temperatures, ranging from 10 to 130°C. Full results of all measurements and analyses are presented in Ref. [4]. In the present paper, several example cases will be presented.

Most of the

Conclusion

XRR and SFM measurements may be performed nondestructively in a very short time (∼5 min) and do not require any special sample preparation. By obtaining surface roughness and scaling parameters from SFM measurements and applying them to simulations using the models of Névot and Sinha, it is possible to determine the following properties of layers and their interfaces:

⋅ The average layer thickness for single- and multi-layer systems, taking into account sample porosity (which influences the

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Surface roughness of thin layers—a comparison of XRR and SFM measurements

Abstract

Section snippets

Theoretical background

Interface roughness—Névot's model

Fractal approach—Sinha's model

Experimental

Conclusion

Phys. Rev.

J. Appl. Phys.

Rev. Phys. Appl.

J. Appl. Cryst.

Acta Phys. Pol. A

Phys. Rev. B