Different materials may have radically different distributions in energy of their internal electron states, so the process of integrating current-density contributions over the internal electron states may give rise to significantly different expressions for the current-density pre-exponentials, for different classes of material. In particular, the power of barrier field appearing in the pre-exponential may be different from the original Fowler–Nordheim value "2". Investigation of effects of this kind is an active research topic. Atomic-level "resonance" and " scattering " effects, if they occur, will also modify the theory.