Modeling Copper Diffusion in Silicon Oxide, Nitride, and Carbide

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Modeling Copper Diffusion in Silicon Oxide, Nitride, and Carbide Vladimir Zubkov, Joseph Han1, Grace Sun, Charles Musgrave1, and Sheldon Aronowitz LSI Logic Corporation, 3115 Alfred Street, Santa Clara, CA 95054, U.S.A. 1 Departments of Chemical Engineering and Materials Science and Engineering, Stanford University Stanford, CA 94305, U.S.A. ABSTRACT Density functional theory was applied to simulate copper diffusion in silicon oxide, nitride, and carbide (SiOx, SiNx, SiCx). Because copper drift into oxide is significantly enhanced by negative bias, copper ions are the active diffusing species. Clusters and, in some cases supercells, modeling various ring configurations of the amorphous networks of silicon oxide, nitride, and carbide were employed. Interactions of both neutral copper and its cation, Cu+, with the network were explored. Calculations revealed a strong binding of Cu+ to SiOx, SiCx, and SiNx in contrast with neutral Cu. The Cu+ attraction to carbide clusters is significantly lower than to SiOx and SiNx, explaining the effective barrier properties of SiCx. The estimated lower bounds for activation energies for Cu+ hops between stable ring clusters of SiOx and SiNx are similar. This implies that the difference in Cu diffusion properties between oxides and nitrides is likely due to a higher percentage of large rings in amorphous oxides compared with nitrides. An approach to increasing the resistance of oxides to Cu+ diffusion is suggested.

INTRODUCTION The high diffusivity of Cu through low k and regular oxides under negative DC bias is well established. However, nitrides and carbides exhibit effective barrier properties for Cu drift [1,2]. The different behavior of oxides versus nitrides and carbides may be due to two effects: the different Cu+ diffusion barriers in these amorphous materials, or the different internal topology of these materials. For example, the density of amorphous SiNx is higher than that of SiOx. The presence of moisture in SiOx may be important [3]. However, a recent study of copper penetration into SiOx after annealing does not mention any role of water [4]. The goal of this work is to derive by density functional theory (DFT) a qualitative explanation of the copper diffusion differences in SiOx, SiNx, and SiCx. Because copper penetration into SiOx is induced by negative bias, positive copper ions are considered the active diffusing species. In this work the following approach was pursued. We employed molecular clusters and, in some cases supercells with periodic boundary conditions (PBC), as models of the materials studied and searched for various stable structures which might result from Cu and Cu+ interaction with the models. This enabled a confirmation that copper diffusion can only proceed as diffusion of the Cu+ cation. It also revealed that attraction of Cu+ to carbide is not enough for Cu+ penetration into it. In the case of SiOx and SiNx the elementary steps of copper diffusion consist of "hops" between various stable structures. Estimates of low bounds of activation energi

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