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Some reasons that require modifying the Fowler–Nordheim theory of field emission, especially for nanoscale emitters, are described. One such reason is that the microtip apex curvature radius can become comparable or even less than the width of the potential barrier on the metal–vacuum boundary. Therefore, the electric field near the surface is not homogeneous. Such deviation of the barrier shape from the traditional plane model and of the interaction between the electron and image charge must have an influence upon the emission characteristics. The possible approaches to this problem are reviewed. The results of the numerical solution of Schrödinger equation for electron tunneling, that allows us to calculate the emission current density and energy distribution of emitted electrons for arbitrary barrier shape, are presented. The problem of comparing the obtained results with the prediction of conventional Fowler–Nordheim theory is discussed. © 1998 American Vacuum Society.