Kinetics of multilayer deposition: Models without screening

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Abstract
The kinetics of irreversible multilayer deposition on one- and two-dimensional uniform substrates was studied. It was assumed that the distribution of sizes of parking objects, intervals in 1D and disks in 2D, have a small-size and a large-size cutoff, l and L, respectively. The general case when the parking distribution function varies as (x−l)α near the small-size cutoff was studied. It was found that the coverage in each layer approaches to the jamming limit according to a power law as t−ν, with the exponent ν=(α+1+D)−1. The jamming coverages approach the infinite-layer limiting value exponentially as exp(−𝓀/s), with the correlation length s=ln[(α+3)/(α+1)].

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