Metal homoepitaxial growth at very low temperatures: Lattice-gas models with restricted downward funneling

Abstract

We develop and analyze 1+1-and 2+1-dimensional (d) models for multilayer homoepitaxial growth of metal films at low temperatures (T), where intralayer terrace diffusion is inoperative. This work is motivated by recent variable-temperature scanning tunneling microscopy studies of Ag/Ag(100) homoepitaxy down to 50 K. Adsorption sites are bridge sites in our 1+1d models, and fourfold hollow sites in our 2+1d models for fcc(100) or bcc(100) surfaces. For growth at 0 K, we introduce a "restricted downward funneling" model, wherein deposited atoms can be trapped on the sides of steep nanoprotrusions rather than always funneling down to lower adsorption sites. This leads to the formation of overhangs and internal defects (or voids), and associated "rough" growth. Upon increasing T, we propose that a series of interlayer diffusion processes become operative, with activation barriers below that for terrace diffusion. This leads to "smooth" growth of the film for higherT (but still within the regime where terrace diffusion is absent), similar to that observed in models incorporating "complete downward funneling. " Disciplines Chemistry | Mathematics | Physical Chemistry CommentsThis article is from Physical Review B 64 (2001) We develop and analyze 1ϩ1-and 2ϩ1-dimensional ͑d͒ models for multilayer homoepitaxial growth of metal films at low temperatures (T), where intralayer terrace diffusion is inoperative. This work is motivated by recent variable-temperature scanning tunneling microscopy studies of Ag/Ag͑100͒ homoepitaxy down to 50 K. Adsorption sites are bridge sites in our 1ϩ1d models, and fourfold hollow sites in our 2ϩ1d models for fcc͑100͒ or bcc͑100͒ surfaces. For growth at 0 K, we introduce a ''restricted downward funneling'' model, wherein deposited atoms can be trapped on the sides of steep nanoprotrusions rather than always funneling down to lower adsorption sites. This leads to the formation of overhangs and internal defects ͑or voids͒, and associated ''rough'' growth. Upon increasing T, we propose that a series of interlayer diffusion processes become operative, with activation barriers below that for terrace diffusion. This leads to ''smooth'' growth of the film for higher T ͑but still within the regime where terrace diffusion is absent͒, similar to that observed in models incorporating ''complete downward funneling.''

Vacancy trapping and annealing in noble-metal films grown at low temperature

“…Although theoretical studies and simulations have been quite successful 2,3 in reproducing many of the features observed in experiments, the reliability of these theoretical predictions largely depends on knowing the specific kinetic mechanisms that are operative on the surface. It is, therefore, surprising that the role of vacancy formation in homoepitaxy has received little attention, in spite of recent simulations 4,5 demonstrating kinetic channels that allow the formation of vacancies or voids in the growing film. These simulations proposed 4 that ''downward funneling'' ͓a mechanism that has been employed to explain the reentrant smooth growth of ͑001͒ surfaces at low temperature͔ can be ''restricted,'' causing the atomic mobility at step edges to be modified, thereby leading to overhang formation and vacancy incorporation.…”

“…It is, therefore, surprising that the role of vacancy formation in homoepitaxy has received little attention, in spite of recent simulations 4,5 demonstrating kinetic channels that allow the formation of vacancies or voids in the growing film. These simulations proposed 4 that ''downward funneling'' ͓a mechanism that has been employed to explain the reentrant smooth growth of ͑001͒ surfaces at low temperature͔ can be ''restricted,'' causing the atomic mobility at step edges to be modified, thereby leading to overhang formation and vacancy incorporation. It was also suggested that vacancy formation strongly affects the surface morphology.…”

Nanoclustering of vacancies in thin metal films revealed by x-ray diffuse scattering

“…15 At even lower temperatures Ͻ50 K, Ag͑001͒ exhibits reentrant rough growth that has been modeled by restricting the downward funneling mechanism. 16 Although this enables the formation of vacancies, restricted funneling in the higher temperature range of our experiments would lead to surfaces that are much rougher than observed experimentally and, therefore, inconsistent with known kinetics. Indeed, homoepitaxial Ag͑001͒ films grow layer by layer at room temperature.…”

X-ray diffuse scattering study of vacancy nanoclusters in homoepitaxial Ag(001) films

“…In addition, Botez et al 5 found that the strain increased with decreasing temperature concomitantly with a low-temperature reentrant roughening observed by STM 7,8 . The reentrant roughening was reproduced in KMC simulations by relaxing the funneling condition which introduced internal voids or vacancy clusters, thereby, giving theoretical support for the presence of such incorporated defects 9 . An alternative explanation was later suggested by Shim et al 10 whose accelerated molecular dynamics (MD) simulations reported that large off-normal deposition angles cause nanoscale surface roughness which, in turn, leads to compressive strain comparable in size to that observed in the x-ray reflectivity studies .…”