Texture, residual stress and structural analysis of thin films using a combined X-ray analysis

doi:10.1016/j.tsf.2003.10.150

Thin Solid Films

Volume 450, Issue 1, 22 February 2004, Pages 34-41

https://doi.org/10.1016/j.tsf.2003.10.150 Get rights and content

Abstract

Advanced thin films for today's industrial and research needs require highly specialized methodologies for a successful quantitative characterization. In particular, in the case of multilayer and/or unknown phases a global approach is necessary to obtain some or all the required information. A full approach has been developed integrating novel texture and residual stress methodologies with the Rietveld method (Acta Cryst. 22 (1967) 151) (for crystal structure analysis) and it has been coupled with the reflectivity analysis. The complete analysis can be done at once and offers several benefits: the thicknesses obtained from reflectivity can be used to correct the diffraction spectra, the phase analysis help to identify the layers and to determine the electron density profile for reflectivity; quantitative texture is needed for quantitative phase and residual stress analyses; crystal structure determination benefits of the previous. To achieve this result, it was necessary to develop some new methods, especially for texture and residual stresses. So it was possible to integrate them in the Rietveld, full profile fitting of the patterns. The measurement of these spectra required a special reflectometer/diffractometer that combines a thin parallel beam (for reflectivity) and a texture/stress goniometer with a curved large position sensitive detector. This new diffraction/reflectivity X-ray machine has been used to test the combined approach. Several spectra and the reflectivity patterns have been collected at different tilting angles and processed at once by the special software incorporating the aforementioned methodologies. Some analysis examples will be given to show the possibilities offered by the method.

Introduction

Today film technology has greatly improved and from the technological point of view it is now becoming strategic to have the potentialities to correctly characterize both the research and the consumer production. Performances and lifetime of these films depend on several characteristics, from chemical composition, purity to other physical properties like thicknesses, crystal structures, microstructure, grain texture and residual stresses. A complete characterization of a film or multilayer can be a very demanding task and in some cases even not possible by the actual standard techniques due to its complexity. X-Ray diffraction and reflectivity are ideal tools to perform the aforementioned analyses and are normally employed to analyze the physical characteristics of films/multilayer. The principal limitation is that when two characteristics are too strong (like texture and stress, number of phases/layers and texture, or thickness and stresses) the single analysis method fails. In the present work we are proposing an integrated methodology based on ad hoc instrumentation and data collection strategy to overcome most or all of the previous limitations. Some real analysis examples will be also reported to show the potentialities of the approach.

The basic idea is to describe the sample as a set of physical characteristics and using them to fit a set of diffraction and reflectivity spectra obtained at different position of sample inside the instrument goniometer. The physical properties of the sample (layers thicknesses, phase composition, texture, residual stresses, crystal structure and microstructure) are optimized in a framework derived from the so-called Rietveld method [1].

The principal drawback of this integrated analysis is that it requires a powerful diffraction instrument to collect all the required spectra in a reasonable time. Ideally, synchrotron and neutron facilities with spectrometers equipped with large position sensitive, image plates, CCD or energy dispersive detectors can collect the necessary data in a very short time. However, we aim to demonstrate that this kind of analysis is suitable also in normal laboratories using custom diffractometers and it can be especially advantageous in the case of thin film analyses where X-ray diffraction is employed preferentially to neutron diffraction.

Section snippets

Theory

The general principles of the Rietveld method are detailed in some very good Refs. [1], [2]. We recall here just few general ideas. The method is based on the least squares fitting of a diffraction spectrum. For a spectrum collected at a specific sample orientation (χ,φ) the intensity of the point i can be computed as $I_{i}^{calc} (χ,φ)= bkg_{i} +I_{0} L_{p} 2θ_{i} A_{i} (χ,φ) ∑ n=1 N_{phases} f_{n} ∑ k=1 N_{hkl} m_{k;n} F_{k;n}^{2} S_{k;n} 2θ_{i} −2θ_{k;n} P_{k;n} (χ,φ)$ assuming the presence of a certain number of phases (N_phases) and reflections (N_h k l). In a normal

Experimental

Three thin film samples have been measured using three different diffractometers.

The first is a film composed by 400 nm of Pb_0.76Ca_0.24TiO₃ (PTCa) deposited by spin coating using a sol–gel solution over a (1 0 0) Si wafer with a 50-nm Pt buffer layer. The diffraction measurements were done at the LPEC laboratory in Le Mans using a closed Eulerian goniometer equipped with a 120° position sensitive detector and a graphite primary monochromator. Full spectra of 120° in 2θ were collected using a

Discussion

The experimental spectra of the PTCa film have been analyzed by the program maud [15] in order to test some of the texture models and the layered approach. A starting model has been defined using two layers, one of PTCa over a layer of 50 nm of Pt. To simplify the analysis the Si wafer has been neglected, and the few spectra showing a little Si peak (≈33.5° in 2θ) were removed from the refinement.

The first texture model used was the harmonic. It turns out immediately that the texture was

Conclusions

We have shown in this work that an integrated analysis approach can successfully analyze thin films and obtains quantitative results in term of texture, residual stresses, crystal structure and film structure. The result was obtained through the implementation of some new methodologies in a custom software package and a dedicated custom instrument for diffraction/reflectivity. Using the instrumentation and methodology here enlightened researchers can have powerful tools for a complete

Acknowledgements

The authors would like to thank S. Matthies for providing the routines for the BulkPathGEO method and C. Wiemer for the measurement of the SBT diffraction spectra and zirconia thin film reflectivity pattern. The work was sponsored and realized entirely inside the ESQUI European Project, contract number: G6RD-CT-1999-00169.

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Texture, residual stress and structural analysis of thin films using a combined X-ray analysis

Abstract

Introduction

Section snippets

Theory

Experimental

Discussion

Conclusions

Acknowledgements

Acta Cryst.

The Rietveld Method, IUCr

Mater. Sci. Forum

Texture Analysis in Material Science

J. Appl. Cryst.

Standard Distribution in Texture Analysis

J. Appl. Cryst.

Textures Microstruct.