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Using a semi-classical approach, we derive a fully analytical expression forthe ionization rate of excitons in two-dimensional materials due to an externalstatic electric field, which eliminates the need for complicated numericalcalculations. Our formula shows quantitative agreement with more sophisticatednumerical methods based on the exterior complex scaling approach, which solvesa non-hermitian eigenvalue problem yielding complex energy eigenvalues, wherethe imaginary part describes the ionization rate. Results for excitons inhexagonal boron nitride and the $A-$exciton in transition metal dichalcogenidesare given as a simple examples. The extension of the theory to includespin-orbit-split excitons in transition metal dichalcogenides is trivial.

Analytical Quantitative Semi-Classical Approach to the LoSurdo-Stark Effect and Ionization in 2D excitons