Strained thin-films

When a mismatch is inevitable, as in the combination Gej-Sii j. — Si, it is found that up to a value of jc = 0.4, there is a small mismatch which leads to a strained silicide lattice (known as commensurate epitaxy) and at higher values of jc there are misfit dislocations (incommensurate epitaxy) at the interface (see p. 35). From tlrese and other results, it can be concluded that up to about 10% difference in the lattice parameters can be accommodated by commensurately strained thin films. 

As an indication of the changes in deformation modes that can be produced in ionomers by increase of ion content, consider poly(styrene-co-sodium methacrylate). In ionomers of low ion content, the only observed deformation mode in strained thin films cast from tetra hydrofuran (THF), a nonpolar solvent, is localized crazing. But for ion contents near to or above the critical value of about 6 mol%, both crazing and shear deformation bands have been observed. This is demonstrated in the transmission electron microscope (TEM) scan of Fig. 3 for an ionomer of 8.2 mol% ion content. Somewhat similar deformation patterns have also been observed in a Na-SPS ionomer having an ion content of 7.5 mol%. Clearly, in both of these ionomers, the presence of a... 

Let us examine the instability oi strained thin films. In Fig. 3, thin films of30 ML are coherently bonded to the hard substrates. The film phase has a misfit strain, e = 0.01, relative to the substrate phase, and the periodic length is equal to 200 a. The three interface energies are identical to each other = yiv = y = Y Both phases are elastically isotropic, but the shear modulus of the substrate is twice that of the film (p = 2p). On the left-hand side, an infinite-torque condition is imposed to the substrate-vapor and film-substrate interfaces, whereas torque terms are equal to zero on the right. In the absence of the coherency strain, these films are stable as their thickness is well over 16 ML. With a coherency strain, surface undulations induced by thermal fluctuations become growing waves. By the time of 2M, six waves are definitely seen to have established, and these numbers are in agreement with the continuum linear elasticity prediction [16]. 

Figure 3. Moiphological evolution of strained thin-films under the infinite- and zero-torque conditions. Thin films of 30 ML and are coherently bonded to the hard substrates whose shear modulus is twice that of the film (q =2q). The film phase has amisfit strain, e= 0.01, relative to the substrate phase.

From TEM studies on strained thin films, Donald and Kramer shown... 

Below we demonstrate that the surface PM and PE effects coupled with the surface (nanoparticles) or mismatch strains (thin films on substrates) lead to the appearance of built-in magnetic and electric fields. These fields generate the magnetization or polarization and hence alter the corresponding phase diagrams. 

For the case of a strained thin film of mean thickness / on a relatively thick unstrained substrate, the depth of the valleys in this equilibrium configuration determine whether the material separates into distinct islands or it reaches equilibrium before doing so. The valley depth in this two degree of freedom idealization is a distance ai - - a2 below the mean film thickness. Therefore, the material will separate into islands if h < ai + a2 and it will not do so otherwise. For the case of A = Acr, this depth is approximately 0.135A = O.lSAcr- This observation implies that a strained film will divide up into islands only if the mean thickness is less than about 18% of the system specific critical wavelength. The particular model is too idealized... 

Several processes contribute to the mobility behavior in the alloy. The mobility is reduced by alloy scattering due to fluctuations in the atomic core potentials. Also, in biaxially strained thin films the cubic symmetry of the solid is eliminated by the strain field, and individual branches of the band structure are split to different energies. This reduces scattering from one band to another near the band minimum and consequently increases mobility. Alloy scattering dominates the behavior overall. 

Physical Properties. Raman spectroscopy is an excellent tool for investigating stress and strain in many different materials (see Materlals reliability). Lattice strain distribution measurements in siUcon are a classic case. More recent examples of this include the characterization of thin films (56), and measurements of stress and relaxation in silicon—germanium layers (57). 

Besides phase identification XRD is also widely used for strain and particle size determination in thin films. Both produce peak broadenings, but they are distinguishable. Compared to TEM, XRD has poor area resolution capability, although by using synchrotron radiation beam diameters of a few pm can be obtained. Defect topography in epitaxial films can be determined at this resolution. 

X-ray Diffraction (XRD) is a powerful technique used to uniquely identify the crystalline phases present in materials and to measure the structural properties (strain state, grain size, epitaxy, phase composition, preferred orientation, and defect structure) of these phases. XRD is also used to determine the thickness of thin films and multilayers, and atomic arrangements in amorphous materials (including polymers) and at inter ces. 

XRD offers unparalleled accuracy in the measurement of atomic spacings and is the technique of choice for determining strain states in thin films. XRD is noncontact and nondestructive, which makes it ideal for in situ studies. The intensities measured with XRD can provide quantitative, accurate information on the atomic arrangements at interfaces (e.g., in multilayers). Materials composed of any element can be successfully studied with XRD, but XRD is most sensitive to high-Z elements, since the diffracted intensity from these is much lar r than from low-Z elements. As a consequence, the sensitivity of XRD depends on the material of interest. With lab-based equipment, surface sensitivities down to a thickness of -50 A are achievable, but synchrotron radiation (because of its higher intensity)... 

Thin-film XRD is important in many technological applications, because of its abilities to accurately determine strains and to uniquely identify the presence and composition of phases. In semiconduaor and optical materials applications, XRD is used to measure the strain state, orientation, and defects in epitaxial thin films, which affect the film s electronic and optical properties. For magnetic thin films, it is used to identify phases and to determine preferred orientations, since these can determine magnetic properties. In metallurgical applications, it is used to determine strains in surfiice layers and thin films, which influence their mechanical properties. For packaging materials, XRD can be used to investigate diffusion and phase formation at interfaces... 

A. Segmuller and M. Murakami. X-Ray Diffraction Analysis of Strains and Stresses in Thin Films. In Analytical Techniques for Thin Films. (K.N. Tu and R. Rosenberg, eds.) Academic, San Diego, 1988, p.l43. 

Strained set of lattice parameters and calculating the stress from the peak shifts, taking into account the angle of the detected sets of planes relative to the surface (see discussion above). If the assumed unstrained lattice parameters are incorrect not all peaks will give the same values. It should be borne in mind that, because of stoichiometry or impurity effects, modified surface films often have unstrained lattice parameters that are different from the same materials in the bulk form. In addition, thin film mechanical properties (Young s modulus and Poisson ratio) can differ from those of bulk materials. Where pronounced texture and stress are present simultaneously analysis can be particularly difficult. 

As one example, in thin films of Na or K salts of PS-based ionomers cast from a nonpolar solvent, THF, shear deformation is only present when the ion content is near to or above the critical ion content of about 6 mol% and the TEM scan of Fig. 3, for a sample of 8.2 mol% demonstrates this but, for a THF-cast sample of a divalent Ca-salt of an SPS ionomer, having only an ion content of 4.1 mol%, both shear deformation zones and crazes are developed upon tensile straining in contrast to only crazing for the monovalent K-salt. This is evident from the TEM scans of Fig. 5. For the Ca-salt, one sees both an unfibrillated shear deformation zone, and, within this zone, a typical fibrillated craze. The Ca-salt also develops a much more extended rubbery plateau region than Na or K salts in storage modulus versus temperature curves and this is another indication that a stronger and more stable ionic network is present when divalent ions replace monovalent ones. Still another indication that the presence of divalent counterions can enhance mechanical properties comes from... 

We discuss the application of atomic scale computer models to bulk crystal growth and the formation of thin films. The structure of the crystal-fluid interface and the mobility of the material at this interface are discussed in some detail. The influence of strain on thin film perfection and stability is also examined. 

Epitaxial growth of thin films usually involves the formation of strained material as a result of mismatch between the film and substrate and because of the large surface to volume ratio in the film. Surface stress can be a major factor, even when the lattice constants of film and substrate are perfectly matched. Although it appears to be difficult to eliminate the stress totally, it is important to be able to control it and even use it to produce desired qualities. 

Huse has pointed out that strain is to be expected in most thin-film systems, since even in the incommensurate case the intrinsic surface stress will strain the film (18). As a result, we conclude that incomplete wetting is expected for all crystalline films, except in the case where there is an epitaxial relationship between film and substrate and that the film is maintained at its bulk equilibrium lattice spacing. 

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