Calculation of Phase Diagrams and First-Principles Study of Germanium Impacts on Phosphorus Distribution in Czochralski Silicon

Abstract

Phosphorus (P) is one of the most widely used donor dopants for fabricating a low-resistivity silicon (Si) substrate. However, its volatile nature and the relatively small equilibrium segregation coefficient in Si at the melting temperature of Si impede the efficient and effective growth of low-resistivity Czochralski (CZ) Si single crystal. The primary objective of this work is to theoretically perceive the influence of germanium co-doping on the heavily P-doped Si crystal by means of CALculation of PHase Diagrams (CALPHAD) approaches and density functional theory (DFT) calculations. Phase equilibria at the Si-rich corner of the Si-Ge-P system has been thermodynamically extrapolated based on robust thermodynamic descriptions of involved binary systems, where Si-P and Ge-P have been re-assessed in this work. Phase diagram calculation results indicate that at a given P concentration (e.g. 0.33 at.% P) Ge co-doping lowers the solidification temperature of the Si(Ge, P) alloys, as well as the relevant equilibrium segregation coefficients of P in the doped Si. DFT calculations simulated the formation of (i) monovacancy in Si as well as (ii) solutions of Si(P) and Si(Ge) with one dopant substitutionally inserted in 64- and 216-atom Si cubic supercells. Binding energies were calculated and compared for Ge-Ge, Ge-P and P-P bonds positioning at the first nearest-neighbors (1NN) to the third nearest-neighbors (3NN). P-P bonds have the largest bonding energy from 1NN to 3NN configurations. The climbing image nudged elastic band method (CL-NEB) was utilized to calculate the energy barriers of P 1NN jump in the 64-atom Si cubic supercell with/without a neighboring Ge atom. With Ge present, a higher energy barrier for P 1NN jump was obtained than that without involving Ge. This indicates that Ge can impede the P diffusion in Si matrix.