We employ a tight-binding parametrization based on the Slater Koster model in order to fit the band structures of single-layer, bilayer and bulk black phosphorus obtained from first-principles calculations. We find that our model, which includes 9 or 17 parameters depending on whether overlap is included or not, reproduces quite well the ab-initio band structures over a wide energy range, especially the occupied bands. We also find that the inclusion of overlap parameters improves the quality of the fit for the conduction bands. On the other hand, hopping and on-site energies are consistent throughout the different systems, which is an indication that our model is suitable for calculations on multilayer black phosphorus and more complex situations in which first-principles calculations become prohibitive, such as disordered systems and heterostructures with a large lattice mismatch. We also discuss the limitations of the model and how the fit procedure can be improved for a more accurate description of bands in the vicinity of the Fermi energy.
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