Fast Domain Growth through Density-Dependent Diffusion in a Driven Lattice Gas

TL;DR

This paper investigates how density-dependent diffusion in a driven lattice gas leads to rapid domain growth, with growth rates influenced by vacancy concentration, temperature, and external electric fields, relevant to electromigration phenomena.

Contribution

It introduces a model showing exponential and power-law domain growth under electromigration, highlighting the effects of density-dependent mobility and external driving forces.

Findings

Exponential domain growth at low vacancy and temperature conditions.

Power-law growth with exponents between 0.55 and 0.75 depending on filling.

Growth rate increases with external field strength, following a crossover length scale.

Abstract

We study electromigration in a driven diffusive lattice gas (DDLG) whose continuous Monte Carlo dynamics generate higher particle mobility in areas with lower particle density. At low vacancy concentrations and low temperatures, vacancy domains tend to be faceted: the external driving force causes large domains to move much more quickly than small ones, producing exponential domain growth. At higher vacancy concentrations and temperatures, even small domains have rough boundaries: velocity differences between domains are smaller, and modest simulation times produce an average domain length scale which roughly follows $L \sim t^{\zeta}$, where $\zeta$ varies from near .55 at 50% filling to near .75 at 70% filling. This growth is faster than the $t^{1/3}$ behavior of a standard conserved order parameter Ising model. Some runs may be approaching a scaling regime. At low fields and early times, fast growth is delayed until the characteristic domain size reaches a crossover length which follows $L_{cross} \propto E^{-\beta}$. Rough numerical estimates give $\beta= >.37$ and simple theoretical arguments give $\beta= 1/3$. Our conclusion that small driving forces can significantly enhance coarsening may be relevant to the YB$_2$Cu$_3$O$_{7- \delta}$ electromigration experiments of Moeckly {\it et al.}(Appl. Phys. Let., {\bf 64}, 1427 (1994)).