Structure and strain of phosphorus-vacancy clusters in highly doped silicon

Ab initio calculations were used to assess the feasibility of PnV (n = 1–4) cluster defects in highly phosphorus-doped silicon (Si:P). Unit cell lattice parameters were determined by density functional theory (DFT) and compared with published experimental high-resolution x-ray diffraction data. This comparison was uniquely enabled by applying pseudomorphic constraints directly into calculations. Across the ∼1.5%–9% P range considered here, lattice parameters for PV do not match experiment while, for P3V and P4V, they are physically consistent. P2V shows experimental agreement at 3.3% P but not at higher 7.1% P. Investigating individual defects revealed PV and P2V are not energetically favorable compared to keeping phosphorus isolated and electronically active. Conversely, P3V and P4V clustering have no energy penalty further signifying their viability. Detailed structural atomic analysis shows that these two higher-order clusters negate tensile strain of an otherwise isolated vacancy, attributed to charge density from absent phosphorus bonds. The transition from P3V to P4V lacks a strong thermodynamic driving force and, using kinetic Monte Carlo simulations, is argued to be governed by dopant availability instead. DFT also indicates the possibility of P3V, P4V, active phosphorus, and V− all coexisting at the onset of this transition. A description for clustering behavior is developed from first-principles where the reduction of phosphorus bonds to the lattice, coupled with the resulting residual charge density stabilizing vacancy sites, lowers tensile strain. The broader ambiguity of PnV cluster species in Si:P is addressed with fundamental analysis, having implications on dopant activation behavior, for example, in this foundational material for microelectronics.