Periodic multilayer film

Consider a periodic multilayered film consisting of N periods, each of thickness A, bonded to a substrate of thickness hg] the overall film thickness is then /if = XNx- A period consists of a single layer of a material with modulus Ma, thickness A/ia and mismatch strain e ia with respect to the substrate plus another single layer of material with modulus Mb, thickness A/ib = A — A/ia and mismatch strain Cmb with respect to the substrate. The quantity Cm,n, defined in (2.50), can then be evaluated in terms of the parameters N, hg, Ms, A/ia, Ma, A/ib, M , Cma and Ciab- The resulting curvature will again 

The curvature is then given by (2.51). Also, for this case. 

It can be confirmed that, if the number of periods in the multilayer is very large, the expression for curvature is consistent with the result obtained for a homogeneous layer in (2.19). This can be demonstrated by letting X/hg 0, identifying the film modulus Mi in (2.19) with Mg + Mg), and identifying the mismatch strain Cm in (2.19) with Cma- 

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Dawber M, Lichtensteiger C, Triscone J-M (2008) Phase transitions in ultra-thin ferroelectric films and fine period multilayers. Phase Transit 81 623... 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

The discussion up to this point has focused on the relationship between the curvature of an elastic substrate and the stress in a single layer or multilayer film in which the mismatch is invariant under any translation parallel to the interface. The films considered have also been continuous and of uniform thickness over the entire film-substrate interface. Within the range of small deflections, such an equi-biaxial film stress induces a spherical curvature in the substrate midplane, except very near the edge of the substrate. What is the deformation induced in the substrate if such a film does not have uniform thickness or if the mismatch stress varies with position along the interface This question is addressed in this section for the cases when the nonuniformity in mismatch stress or thickness varies periodically along the... 

Nanao and Eguchi [228] describe a general scheme whereby metal alkoxides and metal chelates are combined to form a gel. Thermal decomposition of the chelates produces composite multilayer films with applications as sensors, conductive or piezoelectric layers, or opto-electronic materials. Adair et al. [226] discuss a novel process based on Liesegang periodic precipitation to produce a layered Si02/Cu composite potentially useful for fabrieation of insulator-conductor multilayers for electronic packaging. 

Bar] Barnard, J.A., Tan, M., Waknis, A., Haftek, E., Magnetic Properties and Stmcture of Al/Fe-N Periodic Multilayer Thin Films , J. Appl. Phys., 69(8), 5298-5300 (1991) (Crys. Structure, Magn. Prop., 8)... 

Interdiffusion of bilayered thin films also can be measured with XRD. The diffraction pattern initially consists of two peaks from the pure layers and after annealing, the diffracted intensity between these peaks grows because of interdiffusion of the layers. An analysis of this intensity yields the concentration profile, which enables a calculation of diffusion coefficients, and diffusion coefficients cm /s are readily measured. With the use of multilayered specimens, extremely small diffusion coefficients (-10 cm /s) can be measured with XRD. Alternative methods of measuring concentration profiles and diffusion coefficients include depth profiling (which suffers from artifacts), RBS (which can not resolve adjacent elements in the periodic table), and radiotracer methods (which are difficult). For XRD (except for multilayered specimens), there must be a unique relationship between composition and the d-spacings in the initial films and any solid solutions or compounds that form this permits calculation of the compo-... 

Multilayer Langmuir-Blodgett films doped with a cyanine dye have been deposited on the surface of a quartz multimode optical fiber and the fluorescence properties investigated. 49 The fluorescence intensity of the films was found to be a periodic function of the number of layers due to the waveguide properties of the films. 

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