Origin of quasi-constant pre-exponential factors for adatom diffusion on Cu and Ag surfaces

Many-body interaction potentials from the embedded atom method with two functionals and electronic structure calculations based on density functional theory and the plane-wave pseudopotential method are used to calculate the pre-exponential factors for self-diffusion of adatoms via hopping on Cu(100) and Ag(100) surfaces with and without steps. The pre-exponential factors are found to be in the range of ${10}^{-3}{\mathrm{cm}}^2∕\mathrm{s}$ for all investigated processes regardless of whether substrate vibrational dynamics are included or omitted. When substrate dynamics are ignored, compensation effects between stiffening and softening of the vibrational frequencies of the diffusing atom are responsible for this quasi-constant pre-exponential. When these dynamics are included, subtle cancellations in the vibrational free energy make the local contribution of the diffusing atom the dominant one.

Figure 1

Investigated processes of adatom diffusion via hopping on fcc(100).

Figure 2

Comparison of the calculated frequencies for adatom diffusion processes shown in Fig. 1. (a) For Cu(100) using EAM-FBD and EAM-VC; (b) for Ag(100) using EAM-FBD and EAM-VC; (c) for Cu(100) using EAM-FBD and DFT-GGA; (d) for Ag(100) using EAM-FBD and DFT-GG.