Thin film surface waviness

In addition to the theories reviewed above, there are many treatments in the literature which deal with the hydraulics of wavy flow in open channels. Most of these refer to very small channel slopes (less than 5°) and relatively large water depths. Under these conditions, surface tension plays a relatively minor part and is customarily neglected, so that only gravity waves are considered. For thin film flows, however, capillary forces play an important part (K7, H2). In addition, most of these treatments consider a turbulent main flow, while in thin films the wavy flow is often... 

In general, surface morphological instabilities driven by stresses are an important subject to investigate in connection with microelectronic applications. In particular, the degree of surface waviness in thin films as a consequence of surface and volume diffusion is a matter of pivotal importance. This topic has attracted considerable attention in the last two or so decades (11). Although surface diffusion is an important kinetic process, other kinetic processes may affect the evolution of stressed surfaces. Indeed, a possibility at high temperatures is the diffusion of atoms through the bulk. 

From the brief discussion above it is apparent that the flow of viscous liquids in the form of thin films is usually accompanied by various phenomena, such as waves at the free surface. These waves greatly complicate any attempt to give a general theoretical treatment of the film flow problem Keulegan (Kl4) considers that certain types of wavy motion are the most complex phenomena that exist in fluid motion. However, by making various simplifying assumptions it is possible to derive a number of relationships which are of great utility, since they describe the limits to which the flow behavior should tend as the assumptions are approached in practice. 

The problem of turbulent flow in thin films has received comparatively little attention. Because of the great complexity of the flow processes involved, there are no theoretical treatments of the problem of wavy turbulent flow, and the usual procedure is to neglect the surface waves and obtain solutions for the case of smooth turbulent flow. 

Semenov (S7) simplified the wavy flow equations by omitting the inertia terms, which is permissible in the case of very thin films. Expressions are obtained for the wavelength, wave velocity, surface shape, stability, etc., with an adjoining gas stream the treatment refers mainly to the case of upward cocurrent flow of the gas and wavy film in a vertical tube. 

Technical issues in printed electrodes were briefly reviewed for all-printed TFT applications. Surface morphology and edge waviness of the printed electrode should be well controlled to produce uniform and stable TFT behavior and consistent thin-film device performances. This investigation fabricated solution-process TIPS-pentacene based TFT with the printed silver electrodes. Solution-process materials can be readily combined with a low-cost printing process, which can significantly reduce complexity in the fabrication and manufacturing process. In addition, these types of solution-process TFT can be fabricated at low temperatures and they can be also readily implemented on plastic substrates for flexible electronics applications. 

Because thin films range from hundreds of angstroms to several micrometers, roughness, flatness, and waviness of substrate surface are crucial to a... 

Nonlinear dynamics and breakup of free-surface flows is rewieved in the recent paper by Eggers (1997). The thin film rupture is considered also by Ida and Miksis (1996) and these authors [Ida and Miksis (1995)] are considered also the dynamics of a lamella in a capillary tube. A wavy free-surface flow of a viscous film down a cylinder is considered by A.L. Frenkel (1993). 

Figure 17 Illustration of DSA simulations of chemical epitaxy (left two columns) or graphoepitaxy (right columns). The top row shows straight or wavy chemical patterns ortopographical walls on a simulated substrate. Green regions are selective for the A block (red) and yellow regions selective forthe B block (blue) of a model block copolymer, while gray surfaces are neutral. DSA of a disordered thin film of symmetric AB diblock copolymer was simulated in the presence of each substrate pattern using single chain in mean-field Monte Carlo to produce the self-assembled structures in the bottom row.

Films under compression will try to expand. If the substrate is thin, the film will bow the substrate with the film being on the convex side. If the film has a tensile stress, the film will try to contract, bowing the substrate so the film is on the concave side. Tensile stress will relieve itself by microcracking the film. Compressive stress will relieve itself by buckling, giving wrinkled spots (associated with contamination of the surface) or a wavy pattern (clean surface), as shown in Figure 11.1. Compressive stress in a ductile material may relieve itself by generating hillocks (mounds of material). The stress distribution in a film may be anisotropic and may even be compressive in one direction and tensile in another. 

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