Theory and Simulation of Dopant Diffusion in SiGe
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Theory and Simulation of Dopant Diffusion in SiGe Chun-Li Liu1, Marius Orlowski1, Aaron Thean1, , Alex Barr1, Ted White1, Bich-Yen Nguyen1, Hernan Rueda2, and Xiang-Yang Liu3 1
Advanced Process Research and Development Laboratory, Digital DNA Laboratories, Motorola, inc., Tempe, AZ 85284, USA 2 RF/IF Technology Laboratory, Digital DNA Laboratories, Motorola, inc., Tempe, AZ 85284, USA 3 Computational Nanoscience Group, Physical Sciences Research Laboratories, Motorola, inc., Los Alamos, NM 87544, USA
Abstract Strained Si-based technology has imposed a new challenge for understanding dopant implantation and diffusion in SiGe that is often used as the buffer layer for a strained Si cap layer. In this work, we describe our latest modeling effort investigating the difference in dopant implantation and diffusion between Si and SiGe. A lattice expansion theory was developed to account for the volume change due to Ge in Si and its effect on defect formation enthalpy. The theory predicts that As diffusion in SiGe is enhanced by a factor of ~10, P diffusion by a factor of ~2, and B diffusion is retarded by a factor of ~6, when compared to bulk Si. These predictions are consistent with experiment. Dopant profiles for As, P, and B were simulated using process simulators FLOOPS and DIOS. The simulated profiles are in good agreement with experiment. I.
A Lattice Expansion Theory Dopant diffusion solely depends on the defects in Si and SiGe. The effect of adding Ge to Si is to increase the lattice constant from that of Si and also to narrow the band gap. The narrowed band gap in SiGe was observed long time ago [1]. And its effect on dopant diffusion was also discussed before [2]. Fermi models were developed to account for the effect of Ge on dopant diffusion [3]. However, a theory that can satisfactorily explain the physical effect of Ge in Si on various dopant diffusion behaviors in SiGe does not exist. Here we describe such a theory based on an atomic picture of lattice expansion or contraction, their effect on defect formation, and the resulting changes of dopant activation energies. From Vegard’s law, the strain, S, is related to Ge fraction in SiGe, x, by the following relationship: (1) S = (1 – aSiGe / aSi) x = - 0.042x Where aSiGe is the lattice constant in SiGe for a given x and aSi is the lattice constant of Si. The negative sign indicates SiGe is under compressive stress relative to pure Si. The difference in the lattice constants between Si and Ge is ~4%, with the Ge lattice constant being larger. So when adding Ge to Si, the resulting SiGe will always have a larger lattice constant than Si. This lattice expansion will directly affect the defect formation as discussed below. When creating a defect in Si under constant stress or pressure P, one can view the process at atomic level. When a vacancy is created, one atom leaves a lattice site and migrates to the surface. So the volume of the crystal increases by one atomic volume. The interstitial formation is the reverse process: One atom leaves the
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