Film/substrate system

When infrared radiation with electric field amplitude Eo impinges on the film-covered substrate, some is reflected from the ambient/film interface while some is transmitted into the film and then reflected at the film/substrate interface. Some of the radiation reflected at the film/substrate interface is reflected back into the film at the film/ambient interface. However, some is transmitted into the ambient (see Fig. 4). The reflection coefficient (r) for the film/substrate system is calculated by summing the electric field amplitudes for all of the waves reflected into the ambient and then dividing by the electric field amplitude Eo) of the incident radiation. 

Thus, Kic can be used as an accurate descriptor of the interfacial strength in a film/substrate system. 

Far more frequently, however, measurements are made with a relatively thin film (often < 5 /rm) on a comparatively massive substrate (often > 400 //,m in thickness). In principle, the piezoelectric and electromechanical properties of the films can be extracted by fitting conventional resonance measurements. In practice, multiple resonances due to the film/substrate system are measured it is then necessary to deconvolute the data in order to extract information on the films itself. In practice, this is difficult to do unambiguously [21,22],... 

At mechanical equilibrium, the film/ substrate system is therefore curved. In the example shown in Figure 1, the curve is concave and corresponds to a residual tensile stress in the film. A stress gradient is formed in the substrate, with compression occurring at the interface. Conversely, the system would be convex if the film were subjected to a residual compressive stress. 

Residual stresses are therefore generated throughout the film/substrate system in which the dimensions of the film change in respect to those of the substrate (Figure Ic). These stresses will depend on the deposition conditions (temperature, pressure, gas flux, etc.) and on the heat treatment applied to the system after deposition. 

Leaving aside the special case of epitaxial stresses resulting from parameter differences between two monocrystalUne media, the residual stresses in a film/substrate system have two components, one thermoelastic and the other intrinsic. 

Models describing the mechanics of cracking and loss of adhesion occurring in uniaxially stretched film/substrate systems are numerous. 

Faupel et al. have analyzed the adhesion of metal films deposited on polymer substrates strained in an optical microscope. The deadhesion energy was deduced from the difference in the stress versus strain curves between the film/substrate system and the substrate only. 

The different PEC VD film/substrate systems are schematically presented in Figure 6a. The substrates correspond to 99.99% pure Al, mechanically polished with a 0.3 pm alumina powder, then finally electrolytically in a 70% methanol-30% nitric acid solution. When exposed to air, a native aluminum oxide of about 3 nm is produced. The substrates were coated with a dielectric film of a passivation material either SijN or Si02 4.5 wt.% P. These systems are, respectively, denoted as system A and system C. The SijN films were produced by plasma enhanced chemical vapor deposition at a temperature of 360°C, while the SiO 4.5 wt.% P films were chemically vapor deposited at a temperature of 420°C. For both passivation materials, the thickness of the films was 0.8 pm. 

Fig. 14 Stress distribution in a cracked film. The dotted lines correspond to the elastic behavior of the film/substrate system, the solid lines to the presence of plasticity in the substrate at the crack/interface intersection (a) crack opening in a film deposited on a substrate which is uniaxially stretched, (b) longitudinal strain distribution In the film, (c) normal stress distribution in the film, and (d) shear stress distribution In the film at the Interface.

The mechanical stability of each film/ substrate system can be characterized by three steps. 

Fig. 2. Schematic illustration of a computational procedure employed to generate a-Si H/ c-Si film/substrate systems through a sequence of steps that involve MC and MD simulations.

The presence of mechanical stresses in the films is usually undesirable. With good adhesion of the film-substrate system, strong deformation of the substrate often takes place. If the stresses are very high, depending on sign, then because of transient effects in the case of overstressing of the elasticity, undesired crack formation or blistering can occur in the films. In the worst cases, the films can even become completely detached from the substrate. 

In addition, the experimental results are correlated with optical models of the cryo-deposited film-substrate systems. 

This means that if useful information is to be obtained from a film-substrate system, there are five parameters the complex refractive index n and k) of film (two parameters) and substrate (two parameters) and a film thickness (one parameter). Usually some parameters are known or can be assumed, such as the refractive index of the substrate material and k = 0 for a transparent film. In that case the film refractive index and thickness can be obtained from a single ellipsometric measurement. If one needs to determine more parameters, the number of free parameters can be increased by varying the angle and/or the wavelength. 

The reflectivity of the film/substrate system can be calculated from Eq. 6 as ... 

Omitting the intermediate calculations, let us consider only the results summarized in Table 3.1. For the surrounding-film-substrate system, the phonon theory predicts five types of eigenstates of the electromagnetic field inside an ultrathin film normal modes) one mode has a y-component of electric polarization and therefore is named the s-polarized mode, and the other four modes... 

The band distortions are explained by the redistribution of contributions of the vertical and lateral components of the mode in the p-polarized spectrum as either the real or imaginary part of the refractive index of the substrate is changed. In spite of this, however, the SSR for dielectrics (Sections 3.3.2 and 3.11.4) is independent of the optical properties of the substrate. The phenomenon outlined above can also be considered from the viewpoint of geometric optics, rather than invoking the complex origin of the absorption bands in the p-polarized spectra (Section 3.2). The intensity of the radiation reflected from the film-substrate system can be represented as the sum of the intensities of the radiation reflected from the front fihn-snbstrate interface, 7i, and the radiation multiply reflected in and emerging from the film, I (see Fig. 1.12). Clearly, in IRRAS, the... 

Chen, S.H., Liu, L., Wang, T.C., 2007. Small scale, grain size and substrate effects in nano-indentation experiment of film-substrate systems. Int. J. Solid Struct. 44,4492—4504. 

The total potential energy of the film-substrate system is... 

Since the in-plane dimension of the film-substrate system is much larger than its total thickness, an equi-biaxial state of stress can be assumed in the system (ignoring edge effects). Therefore, ase z) = arr (z)-Prom (2.14), note that Cm = (os 0 ) (T — To). From (2.19)-(2.21), it is seen that Cq = — Cm/S and k = 3etn/(4fis)- At the interface between the film and the substrate at z = fig/2, the stress values for Mi = Ms = M are... 

If (Og-Of) < 0 and (T—To) > 0, the normal stress components in the lateral direction, Urr and <7, are both compressive as the interface is approached from the film side, and they are both tensile as the interface is approached from the substrate. Thus, similar to the trends shown in Figure 2.5 for the strain components, the magnitude of the stress discontinuity at the interface can be estimated for the film-substrate system the elastic stresses vary linearly with z in each layer. Equation (2.32) reveals that when the thickness ratio h /hs is fixed, the peak stresses occur at the interface, and that these peak stresses are independent of the individual thickness of the film or the substrate they depend only on the thickness ratio. When the biaxial moduli... 

The coherent gradient sensor (CGS) method is a full-field interferometric technique that produces fringe patterns by laterally shearing an incident wavefront. This method, developed by Rosakis et al. (1998) for curvature measurement in film-substrate systems, is amenable for use in a variety of experimental configurations in either a reflection or a transmission arrangement. 

All features of the film-substrate system introduced in Section 2.2 are retained. In addition, it is assumed that the film material carries a mismatch strain in the form of an isotropic equibiaxial extensional strain em( ) parallel to the interface. This strain may depend on distance from the interface in an arbitrary way, as suggested by writing the mismatch as a function of z] this function need not be continuous in 2. Similarly, the biaxial elastic modulus of the film Mf z) may vary through the thickness of the film. 

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