Thin copper film on nickel substrate diffusion simulator

H. K. D. H. Bhadeshia and H. Yan, Queen Mary University of London

Isothermal interdiffusion of a thin copper coating of initial thickness h deposited on a semi-infinite nickel substrate bar, incorporating reflection boundary conditions at the impermeable free outer surface, complete coating dissolution, Kirkendall marker displacement, and non-equilibrium vacancy accumulation. The science behind this simulation is available separately, together with a free book containing elementary explanations

Thin film diffusion diagnostics

Parameter Calculated value Physical description
Initial film thickness (h) -- As-deposited copper coating thickness
Annealing duration -- Total elapsed diffusion time
Surface copper concentration (CCu at x = 0) -- Residual copper at free outer surface (1.00 until depleted)
Intrinsic copper diffusivity (DCu) -- Mobility of copper atoms in the lattice
Intrinsic nickel diffusivity (DNi) -- Mobility of nickel atoms in the lattice
Diffusivity ratio (DCu / DNi) -- Confirms copper outpaces nickel atomic migration
Interdiffusion coefficient (D̃) -- Effective interdiffusivity governing profile broadness
Diffusion penetration depth (2√(D̃t)) -- Characteristic penetration distance into substrate
Kirkendall marker displacement (xK - h) -- Shift of inert interface markers into copper coating
Peak vacancy supersaturation (film region) -- Maximum Cv / Cveq ratio (delamination risk)
Peak vacancy subsaturation (substrate region) -- Minimum Cv / Cveq ratio (lattice contraction zone)