I came across a paper (which is currently available online) which discussed how 248 nm radiation at doses exceeding 10 mJ/cm^2 could cause ionization by means of two 5 eV photons being added up to give a single 10 eV effect. Of course higher doses increases the effect (proportional to intensity squared). So ~ 100 mJ/cm^2, the effect is about 1% for benzene, even higher for diethylaniline.

Of course this was never a concern when 248 nm was used for lithography, because the optical resolution never had a chance to approach the range of electrons produced by the ionization. But for EUV and electron-beam, since the optical spot resolution can be less than the ionized electron range, the traditional resolution definition is no longer meaningful.

A footnote for the interested:

Reilly and Kompa (J. Chem. Phys. 73. 5468 (1980)) compared two-photon process for KrF (248 nm) vs. ArF (193 nm) for benzene and found that ArF was less ionizing than KrF (though of same order of magnitude) because the nonionizing single-photon absorption mechanism was more dominant.

I estimate the 2-photon KrF or ArF ionized electron dose to be on the order of ~100 uC/cm^2, not negligible at all.