Schottky effect lowering of the barrier

When an electron is at a distance of x from metal surface +ve charge induced on metal surface. The force of attraction between electron and induced +ve charge.=force that will exist between electron and (positive charge at -x) image charge. Attractive force (image force) . The work done on electron in the course of its transfer from to x

Potential energy of an electron at a distance x from the metal surface. This energy must be added to barrier energy to obtain total potential energy of electron .

This is shown in Fig 12.8

So in effect the barrier height varies with field