Rate Equations and Scaling in Pulsed Laser Deposition

TL;DR

This paper analyzes a simplified rate equation model for pulsed laser deposition, including an improved model that accounts for island size, and investigates the scaling behavior of nucleation density.

Contribution

It introduces an improved rate equation model that considers island size and accurately captures the crossover from continuous to pulsed deposition.

Findings

Exact solution for the basic rate equations with limited predictive range.

Numerical integration of the improved model matches simulations well.

Logarithmic scaling of nucleation density is not supported by numerical results.

Abstract

We study a simplified model for pulsed laser deposition [Phys. Rev. Lett. {\bf 87}, 135701 (2001)] by rate equations. We consider a set of equations, where islands are assumed to be point-like, as well as an improved one that takes the size of the islands into account. The first set of equations is solved exactly but its predictive power is restricted to a few pulses. The improved set of equations is integrated numerically, is in excellent agreement with simulations, and fully accounts for the crossover from continuous to pulsed deposition. Moreover, we analyze the scaling of the nucleation density and show numerical results indicating that a previously observed logarithmic scaling does not apply.