The effective diffusion barriers of Cu monomers and dimers on Ag(111) are compared to those on Cu(111), as obtained by calculations and in experiment.

[Phys. Rev. B 82, 085405 (2010)] Understanding materials growth has been a subject of interest already for several decades. The dynamical processes involved in these phenomena in fact bear importance for several aspects of material science; metal oxidation rates and functionality (catalytic, magnetic, etc.) of supported heterogeneous materials when complex structural pattern formation become important, for example.

Local minima of the potential-energy surface of a Cu dimer on Ag

Local minima of the potential-energy surface of a Cu dimer on Ag111 found by our DFT calculations. The abbreviations f and h correspond to the hollow sites where Cu atoms sit and stand for fcc and hcp, respectively. The energy at the bottom-right corner of each configuration is the total energy of the corresponding configuration. Note that the zero of the total energy has been arbitrarily set at the energy of the dimer at the ff configuration, which has lowest energy. Figure take from Phys. Rev. B 82, 085405 (2010)

The diffusivity of adatom clusters is long recognized as a critical controlling factor in material growth. A good deal of work has thus been dedicated to reveal the motion of adatom clusters on surfaces in homo-epitaxial metallic systems and, more recently, in hetero-epitaxial systems. Hetero-epitaxy offers a greater range of applications than homoepitaxy but of course exhibits a broader variety of growth modes that need to be unraveled to predict and/or understand the mesoscopic ordering of interest.

Growth of copper (Cu) on silver (Ag), for example, is a prototype case of hetero-epitaxy subject to effects caused by bond-length misfit and by binding energy disparity between the two metals involved. Still, investigation of such systems, by means of low-temperature scanning-tunneling microscopy (STM), has started relatively recently. This technique allowed experimentalist to estimate the diffusion barriers of Cu monomers and dimers on a silver surface, Ag(111). Contrary to expectations, the experiment indicated that Cu dimers displayed a remarkably high mobility, contrasting that of the Cu monomer and contrasting also the homoepitaxial case. The “effective” diffusion barriers obtained via STM measurements, however, are not conclusive because critical parameters to extract them are taken a priori. Furthermore, it remains the challenge of identifying the specific processes that govern diffusivity. One way to approach both problems is by using a classical-mechanics and statistical method, molecular dynamics (MD) simulations. In reference [1], my coworkers performed those MD simulations, which remarkably reproduced the results derived from the STM measurements.


Energy barriers for four diffusion processes of a Cu dimer on Ag(111) obtained by our DFT calculations. The abbreviations f, h, and b correspond to the sites where Cu atoms sit, and stand for fcc, hcp, and bridge respectively. No distinct name to the various transition states is given since their configuration is off-latice, except for the transition state of the first process, which is the bb configuration.

A major disadvantage to using the classical-mechanics simulations for modeling diffusion is that they cannot capture any quantum phenomenon that may present itself at the temperature at which the experiment is performed and/or that they wash out low energy processes, for which no rationale can be grasped. I have therefore performed quantum-mechanics first-principles calculations of the energy barriers of all possible diffusion processes [1]. I found that the “effective” barriers obtained from the MD simulation are actually supported by my first-principles calculations. But more importantly, I have revealed that, while the relatively high barrier for a Cu monomer is certainly caused by the interatomic bond-length mismatch between Ag and Cu, the same mismatch works to endow configurations of the Cu dimer on Ag(111) not operating in the homo-epitaxial case, Cu dimer on Cu(111).

Such configurations of the Cu dimer on Ag(111) empower novel processes that have low-energy barriers. Still, novel configuration and processes for the Cu dimer alone do not provide an entire foundation for their observed high diffusivity on Ag(111), both in STM and the MD simulations. However, based on my previous investigation of AgCu nanoparticles, I have established that the close similarity between Cu-Cu and Cu-Ag bonds in respect to bond strength and bond length causes a competition between optimizing either one of the two types of bonds. This struggle can in fact be appreciated in the MD simulations and is ultimately responsible for the low energy barrier of the process that mainly contribute to the kinetics of Cu dimers on Ag(111). Along these lines, I have postulated that the Ag-Cu lattice mismatch and the bond-optimization hierarchy that minimizes the energy mark the dimer as the turning point of a generalized enhanced mobility of larger Cu islets on Ag(111), as compared with that on Cu(111).


Sequence of diffusion processes exemplifying how alternation of
the ff-short — fh and the ff-long — fh processes may assist intercell diffusion by zig-zag steps that require energies of ~ 80 meV. At the bottom we show the energy-barrier profile that the dimer encounters in such sequences of processes.


[1] S. S. Hayat, M. Alcántara Ortigoza, M. A. Choudhry, and T. S. Rahman; “Diffusion of Cu monomers and dimers on Ag(111): Molecular dynamics simulations and density functional theory calculations“; Phys. Rev. B 82, 085405 (2010)