Theoretical Studies of Self-Diffusion and Dopant Clustering in Semiconductors

Abstract

(a) Theoretical Division, Los Alamos National Laboratory, Los Alamos,NM 87545, USA(b) Department of Chemistry, University of Washington, Seattle, WA 98195, USA(c) Faculty of Science, VR-II, University of Iceland, 107 Reykjavi´k, Iceland(d) Department of Electrical Engineering, University of Washington, Seattle,WA 98195, USA(e) Department of Materials Science and Engineering, The Ohio State University,Columbus, OH 43210, USA(f) Computational Materials Group, Motorola, Inc., Los Alamos, NM 87545, USA(Received March 15, 2002; accepted May 25, 2002)PACS: 61.72.Ji; 66.30.Hs; 71.15.MbDensity functional theory studies have been performed to investigate the mechanisms of self-diffu-sion in Ge and the clustering of B in Si. In the case of self-diffusion of Ge, we find within theharmonic transition state theory a diffusion prefactor for the vacancy mechanism which is in goodagreement with experimental values. However, the activation energy is underestimated by nearly1 eV when the PW91 functional is used. We propose a cluster correction procedure involving thehybrid B3LYP functional which leads to an activation energy of 3.1 eV in agreement with theexperiment. The contribution of interstitial and exchange mechanisms is negligible. The reactionpathway for the B cluster formation in Si has also been studied. The cluster B