Dynamic transition in etching with poisoning

We study a lattice model for etching of a crystalline solid including the deposition of a poisoning species. The model considers normal and lateral erosion of the columns of the solid by a flux of etching particles and the blocking effects of impurities formed at the surface. As the probability p of formation of this poisoning species increases, the etching rate decreases and a continuous transition to a pinned phase is observed. The transition is in the directed percolation (DP) class, with the fraction of the exposed columns as the order parameter. This interpretation is consistent with a mapping of the interface problem in d+1 dimensions onto a d-dimensional contact process, and is confirmed by numerical results in d=1 and d=2. In the etching phase, the interface width scales with Kardar-Parisi-Zhang (KPZ) exponents, and shows a crossover from the critical DP behavior (W∼t) to KPZ near the critical point, at etching times of the order of (p_c-p)^-ν_‖. Anomalous roughening is observed at criticality, with the roughness exponent related to DP exponents as α_c=ν_‖/ν_⊥>1. The main differences from previously studied DP transitions in growth models and isotropic percolation transitions in etching models are discussed. Investigations in real systems are suggested.