Numerical Simulations of Topographic Evolution for Sputter Deposition into Trenches and Vias
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We have performed 2D and quasi-3D numerical simulations of physical vapor deposition (PVD) into high aspect ratio trenches and vias used for modem VLSI interconnects. The topographic evolution is modeled using (continuum) level set methods. The level set approach is a powerful computational technique for accurately tracking moving interfaces or boundaries, where the advancing front is embedded as the zero level set (isosurface) of a higher dimensional mathematical function. First, we study the 2D case of long rectangular trenches including 3D out-of-plane target flux. The 3D flux is obtained from molecular dynamics computations for AI(100), and hence our approach represents a hybrid atomistic/continuum model. We obtain good agreement with X-TEM data. Secondly, we report results of axisymmetric 3D simulations of high aspect ratio vias which we then go on to compare with experimental data for Ti/TiN barrier layers. We find that the simulation data (using the cosine angular distribution) overpredict bottom coverage in some cases by approximately 20%-30% for both collimated and uncollimated deposition but in other cases provide a reasonably accurate comparison with experiment.
INTRODUCTION The topographic evolution of moving interfaces has traditionally been simulated numerically using marker-particle/segment-based methods [1,2] or front-tracking [3]. One major drawback in this approach is the formation of "swallowtails" when two adjoining line segments are advanced and cross one another. These overlapping segments (surfaces in 3D) must then be
"de-looped" in order to obtain a single-valued surface. This de-looping involves complex decision rules and programming and requires excessive CPU time. The level set technique was introduced by Osher and Sethian [4,5] as a promising and fast alternative to front-tracking and has been used by Adalsteinsson and Sethian for microelectronics applications [6]. In this paper we describe the implementation of this new mathematical technique to model deposition processes such as metal film sputtering. A third approach is the hard disk Monte Carlo model which is useful for both topographic evolution and microstructure computations [7,8]. The present state-of-the-art of continuum models for film evolution and a more complete list of
references is contained in a recent review article by Cale et al. [9].
MATHEMATICAL APPROACH Problem Statement We are concerned
'1
with deposition
into
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1
44 PR:
long
rectangular trenches and axisymmetric circular vias. In figure 1 we plot a schematic drawing of the geometry for PVD from a finite target onto a substrate with local surface normal n, inclined at an angle 6 to the vertical. We denote the left- and right-hand side visibility
Figure geometry 1: Schematic of target/wafer sputter with surface normal and target visibility angles indicated.
313 Mat. Res. Soc. Symp. Proc. Vol. 564 01999 Materials Research Society
angles OL and PR. The growth rate of the film at each point of the interface is determined by the "visible" area of
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