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.

磷 (P) 是用于制造低电阻率硅 (Si) 衬底的最广泛使用的施主掺杂剂之一。然而，它的挥发性和在 Si 熔化温度下 Si 中相对小的平衡偏析系数阻碍了低电阻率直拉 (CZ) Si 单晶的高效和有效生长。这项工作的主要目标是通过相图计算 (CALPHAD) 方法和密度泛函理论 (DFT) 计算，从理论上了解锗共掺杂对重 P 掺杂硅晶体的影响。基于所涉及的二元系统的稳健热力学描述，Si-Ge-P 系统富含 Si 角的相平衡已被热力学外推，其中 Si-P 和 Ge-P 在这项工作中已重新评估。相图计算结果表明，在给定的 P 浓度（例如 0.33 at.% P）下，Ge 共掺杂降低了 Si(Ge, P) 合金的凝固温度，以及掺杂中 P 的相关平衡偏析系数西。DFT 计算模拟了 (i) Si 中的单空位以及 (ii) Si(P) 和 Si(Ge) 溶液的形成，其中一种掺杂剂替代地插入 64 和 216 原子 Si 立方体超电池中。计算并比较了位于第一最近邻 (1NN) 到第三最近邻 (3NN) 处的 Ge-Ge、Ge-P 和 PP 键的结合能。PP 键具有从 1NN 到 3NN 构型的最大键能。利用爬升图像轻推弹性带法（CL-NEB）计算具有/不具有相邻Ge原子的64原子Si立方超晶胞中P 1NN 跳跃的能垒。存在 Ge 时，P 1NN 跳跃的能垒比不涉及 Ge 时获得的能垒更高。这表明 Ge 可以阻止 P 在 Si 基体中的扩散。