A mathematical framework for modeling the compositional depth profiles obtained by pulsed laser ablation

This paper presents a simple mathematical model relevant to studies of depth-profile analysis utilizing pulsed laser ablation. The main model predictions (the amount of analyte ablated by a given laser shot, and the resulting crater profile) are independent of the method used to detect the analyte, so that the results are relevant to several techniques: laser-induced breakdown spectrometry (LIBS), laser-ablation inductively coupled plasma optical emission spectrometry or mass spectrometry (LA-ICP-OES or LA-ICP-MS) or laser-ablation time-of-flight mass spectrometry (LA-TOF-MS). The main focus of the model is on the influence of the laser beam radial energy distribution on the depth profiles. Accordingly, super-Gaussian (top-hat) as well as Gaussian laser beams can be modeled. Although the model can be used to simulate depth profiles in samples where the analyte concentration varies continuously as a function of depth, a particular emphasis of this paper is on multilayer samples. The notion of fluence threshold for ablation is also introduced, and the influence of crater aspect ratio is studied. The model is tested in relation to LIBS studies of galvannealed coatings on steel that use a Gaussian Nd: YAG laser beam at 1064 nm. The simulated depth profiles are found to correctly reproduce the shape of an experimental depth profile of the zinc signal, and the influence of specific model parameters is investigated.