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