Kinetic simulation of the 3D growth of subsurface impurity nanoclusters during cobalt deposition onto a copper surface

Thermodynamic determination of the critical radii of surface and subsurface cobalt clusters in the cobalt-copper system

“…The specific interfacial strain energy can be expressed as follows [11]: (10) where ΔΩ is the difference of the atomic volumes of copper and cobalt and Spσ is the trace of the tensor of elastic stresses on the cluster boundary, which can be estimated as [12,13] (11) Here, E is the Young's modulus of cobalt and γ is the relative strain at the Co-Cu interface.…”

“…(2), which yields (12) Number of atoms j l in a Co cluster can be expressed via cluster volume V cl or its geometric parameters (radius R l and height h l ) as follows: (13) where Ω = /4 is the volume per atom in a Co clus ter with the fcc structure. Upon substituting this expression for the number of atoms in the Co cluster into formula (12) for the system free energy change Δ (R l , h l ) as a function of the cluster radius and height, we obtain (14) where Δ + Δ = 0.0075 eV/Å 2 [14].…”

“…Here, = exp( /kT), is the activation energy of cobalt migration on the surface (l = s) or in the subsurface region of copper (l = u), = 0.28 eV, and = 1.0 eV [13,18]. The time of nucleation delay in the regime of com plete condensation can be determined as [17] (…”