Most of the theoretical derivations in the field emission theory are done under the assumption that the barrier takes the Schottky–Nordheim form eq. (3). However, this barrier form is not valid for emitters with radii of curvature R comparable to the length of the tunnelling barrier. The latter depends on the work function and the field, but in cases of practical interest, the SN barrier approximation can be considered valid for emitters with radii R > 20 nm , as explained in the next paragraph.