Thin film thickness, thermal-wave

After raising the wall temperature in both sides, a sharp wave front develops and propagates toward the center of the physical domain which separates between the heat-affected zone from the thermally undisturbed zone (see Figure 8.13). The two thermal wavefronts from both sides collide with each other at the center of the film. After the collision, the center temperature is amplified, and reverse thermal wavefronts take place and travel toward both sides of the thin film. When thermal wave-front reaches both side walls, the film temperatures at the side walls exceed the imposed wall temperature, called temperature overshoot. For thick film, the wavefronts do not show reverse temperature waves after meeting the center of the thin film. 

Thermal-Wave Measurement of Thin-Film Thickness... 

Rosencwaig, A. In Thermal-Wave Measurement of Thin Film Thickness 5 ACS SYMPOSIUM SERIES, this volume. 

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]. 

We have developed a method for measuring the thickness of semiconductor thin films that is nondestructive, noncontact and that can make measurements with 2-um spatial resolution on both optically opaque and optically transparent films. This method is based on the use of high-frequency thermal waves. 

Finally, it should be noted that when the thickness of a thin film is known, then the thermal-wave signal can be used to characterize the composition or uniformity of the thin film material. 

The mechanism of rupture depends upon the thickness of the lamella film. Ultra-thin films, with thicknesses in the 1-20 nm range, are believed to rupture due to the amplification of thermally-generated surface waves [28-30]. However, studies by Artavia and Macosko [31] and Akabori and Fujimoto [32] demonstrated that most of the ruptured lamellae in a PU foam are in the 200-1000 nm thickness range. Therefore, it is assumed here that the mechanism of rupture of these thicker films is most important when considering PU foam. 

Finally, we consider the hydrodynamic theory of thin liquid film rupture. The stability of the liquid films to a great extent is ensured by the property of the adsorbed surfactant to damp the thermally excited fluctuation capillary waves representing peristaltic variations in the film thickness [6]. In addition to the theory of stability of free foam and emulsion films, we consider also the drainage and stability of wetting films, which find application in various coating technologies [7]. 

The influence of thermal wave is more signiflcant for thermal conduction in microscale systems compared to macrosystem. An example of thin film conduction is illustrated here to justify this point. Figures 8.13 and 8.14 compare the conduction through a thin film and thick film, respectively. Here, the film is initially at temperature Tq. There is a sudden change in the temperature of both sides to T. The nondimensional variables for the problem are defined as... 

---