Film stress from x-ray diffraction measurement

X-ray diffraction is a readily available experimental method that can be used to infer values of stress in thin crystalline films on substrates. With this method, the normal spacing between adjacent crystallographic planes within a family of planes with indices hkl) is determined by means of Bragg s law in the form 

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Table 7.1. Representative values of the flow stress of polycrystalline thin films of metals and alloys as a function of film thickness (h ) and average grain size (g.s.). Data obtained from micro-tensile tests, microbeam deflection and x-ray diffraction measurements.

Several attempts to induce orientation by mechanical treatment have been reviewed 6). Trans-polyacetylene is not easily drawn but the m-rich material can be drawn to a draw ratio of above 3, with an increase in density to about 70% of the close-packed value. More recently Lugli et al. 377) reported a version of Shirakawa polyacetylene which can be drawn to a draw ratio of up to 8. The initial polymer is a m-rich material produced on a Ti-based catalyst of undisclosed composition and having an initial density of 0.9 g cm-3. On stretching, the density rises to 1.1 g cm-3 and optical and ir measurements show very high levels of dichroism. The (110) X-ray diffraction peak showed an azimuthal width of 11°. The unoriented material yields at 50 MPa while the oriented film breaks at a stress of 150 MPa. The oriented material, when iodine-doped, was 10 times as conductive (2000 S cm-1) as the unstretched film. By drawing polyacetylene as polymerized from solution in silicone oil, Basescu et al.15,16) were able to induce very high levels of orientation and a room temperature conductivity, after doping with iodine, of up to 1.5 x 10s S cm-1. 

Vibrational Raman band intensities and frequencies are also dependent on temperature, applied pressure, and the intrinsic microstructure of the material. These second-order parameters may be extracted from measured spectra. Both X-ray diffraction lines and Raman bands from polycrystalline materials show increased broadening as the microcrystallite grain sizes decrease. In fact, for the hexagonal phase of BN, bandwidths vary linearly with the reciprocal grain size (13). Inherent stress in thin films is manifested in vibrational line shifts. Based on pressure-dependent measurements of vibrational frequencies in bulk solids, inherent stress and stress inhomogeneity can be determined in thin films. Since localized stress can influence the optical and electronic properties of a thin film, it appears to be an important parameter in film characterization studies. Vibrational features also exhibit temperature-dependent frequency shifts. Therefore, an independent measurement of temperature is sometimes necessary to deconvolute these effects. Reference to Figure 1 shows that the molecular temperature of a material may be determined from the Stokes/anti-Stokes... 

The strain in thin crystalline films can also be detected by X-ray diffraction. A deviation of the lattice parameter from the respective bulk value, o, establishes the strain. The stress is then calculated from the elastic constants of the film and the geometry of the experiment. For example, the usual diffractometer geometry is widely enployed to measure the spacing of planes parallel to the substrate. The stress can be calculated from... 

Stresses produced in sol-gel-derived films modify the lattice parameters of the film and its orientation or texture. These effects are clearly observed in the X-ray diffraction (XRD) patterns of Figure 27.16 [55]. The XRD pattern of a (Ca, Pb) TiOs perovskite thin film on a Pt-coated silicon substrate shows a textured film with a (100) preferred orientation and with the cell parameters for the perovskite indicated in Table 27.5. When this film is electrolytically separated from the substrate, it recovers the random orientation of the ceramic powder and its preferred orientation disappears observe the lattice parameters and strains measured in a (Ca, Pb)TiOs thin film on the substrate and this film is separated from the substrate in comparison with those of the bulk ceramic (Table 27.5) [55]. 

X-ray and electron diffraction methods are applied in order to measure atomic distances in the crystal lattice and their changes. Hence, the diffraction methods are also basically suitable for measuring the strain/stress behaviour in thin films. However, since the film thickness and the crystallite size in thin films are small, some line broadening already arises from this. In order to determine what contribution the mechanical stresses have on the diffuse lines, careful analysis of the line profiles must be undertaken [148, 151]. This method is less suitable for routine determination of stresses in thin films. In some cases, it is possible though rarely applied to determine the stresses in the films through their influence on other, known film properties, at least approximately. Such properties are, for example, the position of an absorption edge [152], the Hall effect [153], electron spin resonance spectra [155] and in the case of superconducting films, variations in the critical transition temperature [156]. However, these effects can, unfortunately, also arise for other reasons, and thus these techniques can usually only be used as supplemental experiments. 

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