Energy bands and gaps near an impurity

•Energy bands can bend near an impurity in the host lattice.•We confirm possibility of energy band bending by using Kronig–Penney model.•The impurity can have profound effect on wave function structure.

It has been suggested that in the neighborhood of a certain kind of defect in a crystal there is a bend in the electronic band. We confirm that this is indeed possible using the Kronig–Penney model. Our calculations also have implications for photonic crystals.