Statistics – Computation
Scientific paper
Jul 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008pobeo..84..141g&link_type=abstract
Publications of the Astronomical Observatory of Belgrade, vol. 84, pp. 141-141
Statistics
Computation
Scientific paper
Materials processing is at a crossroads. Currently much of industrially viable materials processing is via plasmas. However as this processing has reached the nano-scale, development of industrially viable processes has become more and more difficult. In part this is because of all of the free parameters that exist in plasmas. To overcome this economic issue, tool vendors and semiconductor companies have turned to complex computational models of processing plasmas. For those models to work, one requires a through understanding of all of the gas-phase and surface-phase processes that are exhibited in plasmas. Unfortunately, these processes are not well understood.
Fortunately, one can examine the influence the plasma properties on the desired surface processes and through this ultimately optimize manufacturing. It is well known that the surface processes (etch or deposition), occur in the top few mono-layers of the surface. For example, growth of a film will require that molecules from the gas-phase land and bond on the surface. In order to understand the mechanism of deposition and etch on a surface, we begin with a basic reaction rate density
R_particle = int_0^infty sigma(epsilon,T)n_bonds v_particle n_particle f_particle (epsilon)d epsilon (1)
Here sigma (theta,epsilon,T) is defined as the cross section of a particle either filling or creating an available bond site on the a surface of temperature T, n_bonds is the density of surface bonds, v_particle is the gas particle velocity, n_particle is the gas particle density and f_particle (epsilon) is the gas energy distribution function. Assuming that the fraction of bond sites that are open is Theta, then at any given time the open bond density will be Theta n_bonds and the closed bond density is (1 - Theta) n_bonds. Under the assumption that most of these processes occur at open bond sites, our group has arrived at a general formula for the process rate (here applied to C_x F_y etch of SiO_2) of:
Equation (2)
Here, S.C or Y approx
In this paper we will examine the implications of Equation 2. Specifically we will examine how the surface interactions set how process tools work. From this we will examine the potential future of the plasma-processing field.
Goeckner M. J.
Jarvis Brian
Jindal A. K.
Joseph E. A.
Nelson C. T.
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