Analysis of the electrical activation data in thermally annealed implanted Al/4H–SiC systems: A novel approach based on cooperativity

The dependence on the annealing temperature, Tann, of the Al asymptotic substitutional fraction φ∞ in implanted silicon carbide (4H–SiC), is addressed from a statistical mechanical point of view. Concepts relating to the cooperative nature of atomic motion in (extremely) viscous liquids or in plastic crystals are applied for the first time in describing Si ⇄ Al substitution and the tendency of the system towards a regularization of its crystalline structure during annealing. The worked out model, although inspired by Al/4H–SiC literature data, can be applied to similar systems with the due changes. The slope ΔEs of the Arrhenian lnφ∞ vs. 1/kBTann dependence encompasses both the energy that would characterize a single Si ⇄ Al ideal substitution in a regular lattice, and a negative contribution associated to the irregularity of the lattice at the substitution sites. The early evolution of the substitutional fraction φ(t;Tann) in implanted systems during annealing is then considered. The slope of lnφ vs. 1/kBTann at short annealing times, when the asymptotic state is not yet reached, provides information about the average energy barrier ΔEw characterizing on average the preliminary molecular rearrangements preceding the Si ⇄ Al substitution. Values of ΔEs in the order of 1 eV or a bit less are envisaged and worked out from φ∞-fittings, while ΔEw∼3 eV is found from the analysis of incomplete annealing. The theory applied in this work represents a reference for a more complete description of the structural evolution of implanted systems.