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Many computational models have been developed to predict the rates of atomicdisplacements in two-dimensional (2D) materials under electron beamirradiation. However, these models often drastically underestimate thedisplacement rates in 2D insulators, in which beam-induced electronicexcitations can reduce the binding energies of the irradiated atoms. This bondsoftening leads to a qualitative disagreement between theory and experiment, inthat substantial sputtering is experimentally observed at beam energies deemedfar to small to drive atomic dislocation by many current models. To addressthese theoretical shortcomings, this paper develops a first-principles methodto calculate the probability of beam-induced electronic excitations by couplingquantum electrodynamics (QED) scattering amplitudes to density functionaltheory (DFT) single-particle orbitals. The presented theory then explicitlyconsiders the effect of these electronic excitations on the sputtering crosssection. Applying this method to 2D hexagonal BN and MoS$_2$ significantlyincreases their calculated sputtering cross sections and correctly yieldsappreciable sputtering rates at beam energies previously predicted to leave thecrystals intact. The proposed QED-DFT approach can be easily extended todescribe a rich variety of beam-driven phenomena in any crystalline material.

QED theory of electron beam-induced electronic excitation and its effect on sputtering cross sections in 2D crystals