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A two-dimensional, cellular automata model for atomic layer etching (ALE) is presented and used to predict the etch rate and the evolution of the roughness of various surfaces as a function of the efficiencies or probabilities of the adsorption and removal steps in the ALE process. The atoms of the material to be etched are initially placed in a two-dimensional array several layers thick. The etch follows the two step process of ALE. First, the initial reaction step (e.g., Cl reacting with Si) is assumed to occur at 100% efficiency activating the exposed, surface atoms; that is, all exposed atoms react with the etching gas. The second reaction step (e.g., Ar ion bombardment or sputtering) occurs with efficiencies that are assumed to vary depending on the exposure of the surface atoms relative to their neighbors and on the strength of bombardment. For sufficiently high bombardment or sputtering, atoms below the activated surface atoms can also be removed, which gives etch rates greater than one layer per ALE cycle. The bounds on the efficiencies of the second removal step are extracted from experimental measurements and fully detailed molecular dynamics simulations from the literature. A trade-off is observed between etch rate and surface roughness as the Ar ion bombardment is increased.