Fitting of RBS data including roughness: Application to Co/Re multilayers
Introduction
Rutherford backscattering (RBS) is often used to study the thickness, composition, and interfaces of thin films and multilayers. If interfacial mixing and roughness, or substrate and surface roughness are present, data analysis is difficult. Several approaches have been adopted to account for these effects, and several codes have been developed for the analysis of samples with surface roughness, normally in the few μm scale (see e.g. [1], [2], [3], [4], [5], [6]). Some of them reproduce experimental data very well. However, they involve calculating, for a given surface, the trajectory of many ions (normally around 100, but up to several thousand) with entrance and exit at different points of the surface, and then averaging the result. This requires a good knowledge of the nature of the surface to be investigated, and it is slow and cumbersome.
In this work, a different approach is taken, which is appropriate for thin films and multilayers with roughness values up to a few tens or hundreds of nm. By calculating the broadening due to roughness, and assigning it as an extra contribution to the energy straggling, an apparent energy resolution is obtained. This is then convoluted with the theoretical spectrum in the normal way. The effect of roughness can thus be included in a standard code with little effort, paying only a small price in terms of calculation time.
The broadening depends on the exact type of roughness. Three different models were implemented: inhomogeneous layer thickness, corrugated sample, and rough substrate surface. These models have been introduced in the well-known code IBA DataFurnace [7]. It can perform automatic fits to several spectra collected from the same sample, ensuring all the information in the data is used to obtain the final depth profile and roughness parameters.
The code is tested and validated by applying it to a well-known system, that we have previously thoroughly studied with different techniques. The system is substrate/Re 50 Å/(Co 20 Å/Re 5 Å)16, where the substrate is either glass or Si, and the roughness depends on the substrate.
Section snippets
Experimental details
The RBS analysis was done using a 1.0 MeV He+ beam. A surface barrier detector with 15 keV energy resolution was located under the beam at 160° to the beam direction (Cornell geometry). For each sample, spectra were collected at different angles of incidence, that is the tilt angle ϑ, defined as the angle between the beam direction and the sample surface. The beam was 0.2 mm wide and 0.6 mm high. The detector aperture was circular with 3 mm diameter. The detector-sample distance was 75 mm. The
Roughness models
The energy resolution degrades with depth. The result is a broadening of any interface signals in the spectra obtained, and also a distortion of the spectral shape relative to what it would be if the resolution were constant with depth. This distortion is, in a bulk sample, an increased yield at low energies. Any interface studies with RBS (or other IBA techniques) must take energy straggling into account as precisely as possible, or the results will be an artefact. In particular, any values
Results and discussion
We previously studied with RBS, transmission electron microscopy (TEM), perturbed angular correlations (PAC) and magnetisation measurements the system substrate/Re 50 Å/(Co 20 Å/Re 5 Å)16, where the substrate was either glass or Si [1], [13], [14]. The magnetic properties of the multilayers depended on the substrate: ferromagnetic coupling due to contact between Co layers was observed for Si, while for glass a perfect antiferromagnetic coupling existed, proving that the Co layers were well
Conclusions
Due to modelling and coding difficulties, RBS data analysis normally ignores the effect of substrate, layer and surface roughness on the data. The approaches taken when roughness cannot be ignored have been either ad hoc or very cumbersome.
In this work, a new approach has been developed. The effect of roughness in the few tens of nm range is similar to that of energy straggling, that is, it leads to an additional broadening of spectral features. By calculating the broadening due to roughness
Acknowledgments
I would like to thank Dr. Edit Szilágyi for many useful discussions on energy straggling and L. Wartig Barradas for early encouragement to work. The support of the Fundação para a Ciência e Tecnologia is gratefully acknowledged.
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