Ab-Initio Pseudopotential Calculations of Phosphorus Diffusion in Silicon
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Ab-Initio Pseudopotential Calculations of Phosphorus Diffusion in Silicon Xiang-Yang Liu1, Wolfgang Windl2, and Michael P. Masquelier1 Computational Nanoscience Group, Physical Sciences Research Labs, Motorola, Inc., Los Alamos, NM 87545, U.S.A. 2 Department of Materials Science and Engineering, Ohio State University, Columbus, OH 43210, U.S.A. 1
ABSTRACT In traditional models of P diffusion in Si, vacancy assisted diffusion mechanism has been assumed. More recently, experiments have determined that for intrinsic P diffusion in Si, the interstitial assisted diffusion mechanism dominates. We have performed ab-initio pseudopotential calculations to study P diffusion in Si. Special care is taken with regard to structure minimization, charge state effects and corrections. We calculated the defect formation energies and migration barriers for the various competing P-interstitial complex diffusion mechanisms for low concentration P region, as well as the energetics of different charge states P-vacancy complex diffusion. For interstitial mediated diffusion of P-Sii pair in Si, we find the overall diffusion activation energies calculated are 3.1 eV for neutral case, and 3.4 eV for +1 charge case. This is in agreement with experimental observation that the interstitial mechanism dominates for intrinsic P diffusion in Si. For vacancy mediated diffusion, our calculations are in agreement with previous calculations result in the neutral case. We obtained the lower bounds for diffusion activation energy of 3.8 eV for (PV)0 and 3.4 eV for (PV)-. A further evaluation of the numbers would require a proper treatment of the energy states in the band-gap due to Jahn-Teller relaxations.
INTRODUCTION Dopant diffusion is an elementary process in ultra-large scale integrated (ULSI) device fabrications. Phosphorus is a common dopant for the fabrication of n or n+ regions in Si devices. Early experimental studies and theoretical analysis on P diffusion in Si associated the P diffusion with P-vacancy (V) complex formation and migration in Si . Later, ample experimental evidence show that P diffusion is mediated by interstitials (I) in intrinsic region [2, 3]. For example, most recent experiments based on the injection of point defects into a P doped Si substrate suggests that the fractional contributions of I mechanism to P diffusion in Si is in the range of 86% - 100% in the worst case analysis . While experiments are able to find the total diffusion coefficient and the influence of point-defects on it, they generally cannot determine the microscopic diffusion mechanisms in the physical processes involved. Several modeling efforts have been made to simulate the transient enhanced diffusions (TEDs) of P diffusion in Si using a combination of I and V mechanisms based on fitting to experimental P diffusion profiles in Si . In this regard, ab-initio calculations of the fundamental parameters in the diffusion processes contribute to our knowledge and understanding, and modeling of defects influences on dopant diffusions. C4.7.1