Sidewall Boundary Conditions Research Articles

Application of Line-Edge Profile Simulation to Thin-Film Deposition Processes

A computer simulation program based on a segment-motion model has been developed to investigate thin-film-deposition processes. This simulation program is used to study the physical phenomena in the thin-film-deposition process as well as the effects of different tooling configurations and operating conditions. The simulated results are compared with experimental results obtained from an electron-gun evaporator with planetary tooling and from a planarizing sputtered quartz system to verify the accuracy of the simulation and to illustrate important phenomena during the deposition process. The simulation program is also used in exploratory studies to find the optimum source angle for step coverage in a typical planetary evaporator. The step coverage is found to change only slightly for wafers at different locations on the planet, but can change significantly depending on the pattern orientation on the wafers if the wafer rotation is not independent of the planet rotation. A study of the sputtered quartz planarization process shows that the growth of different topological features can be accurately predicted from the change in deposition and etching rate as a function of the angle of incidence. In particular, the increased deposition near a conductor edge is attributed to the propagation of a growth front from the sidewall boundary conditions.

On a theory of amplitude vacillation in baroclinic waves

This study contributes to the theory of amplitude vacillation for finite amplitude baroclinic waves in a two-layer, quasi-geostrophic, zonal flow as worked out by Pedlosky. In a recent paper the author has shown that Pedlosky omitted a certain side-wall boundary condition on the mean zonal flow. The neglect of this boundary condition results in an unspecified energy source at the side-wall boundaries and the physical problem is incorrectly posed.In this paper, Pedlosky's analysis is repeated but with the side-wall boundary condition included. It is shown that the side-wall energy source is negligible only when the zonal wavenumber of the disturbance is large compared with the meridional wavenumber, and not otherwise. Moreover, the energy conversions to and from mean zonal kinetic energy corresponding to Pedlosky's calculations and those given here have essential differences, although for fixed meridional wavenumber, these differences become less pronounced as the zonal wavenumber increases.It is also shown that, when the side-wall condition is included, the mean flow distortion associated with the wave is different in structure to that which occurs when the condition is omitted. However, as the total disturbance wavenumber a increases, the influence of the side wall on the mean flow structure is confined to a boundary layer of width comparable with the internal deformation radius 2½a−1.Even when the deformation radius is comparable with the channel width, the conclusions of Pedlosky (1972) concerning the existence of stable periodic solutions are correct, providing viscous effects are vanishingly small, and the criteria for stability of the steady solutions obtained herein are not significantly different from those given by Pedlosky. In this viscous regime, we have also studied the evolution to limit-cycle solutions.Evolution in the case where viscous effects are small on the time scale for the initial growth of an incipient wave, but not vanishingly small, will be discussed in a subsequent paper.

Natural convection phenomena in inclined cells with finite side-walls—A numerical solution

The effects of Rayleigh number, aspect ratio and angle of inclination on the heat transfer through an inclined air-cell are studied via the numerical solution of the relevant two dimensional governing equations. This is done for two side wall boundary conditions, namely that of perfectly insulating and infinitely conducting side walls. In addition, the effects of a finite thickness wall with a finite value of thermal conductivity is studied, by solving the two dimensional conduction equation in the wall and matching the values of temperature and heat flux at the common boundaries between the two regions. It is shown that the perfectly in sulating and infinitely conducting boundary conditions are the two extremes of the real case and, depending on the values of the fluid parameters and the value of the wall thermal conductivity, the two fixed boundary conditions can be either accurate or inaccurate representations of the real case. A discussion of the relevance of this work to solar absorbers is included, with the major conclusion being that, depending on the aspect ratio of the cell used, cellular structures can be effective in reducing convective losses in inclined absorbers.