Resonant tunneling in two dimensions via an impurity

We solve an exact model of two-dimensional resonant tunneling through a potential barrier with a point defect. The model shows that the scattering amplitude has a very narrow spreading angle, and gets its maximal value for a small incoming angle. Even when the incoming wave is a narrow beam of electrons, the transmission coefficient depends very strongly on the position of the impurity. This characteristic can be used to detect the position of an impurity (or defect) in a two-dimensional layer.