I am attaching an articles which has derived the relation between penn gap and energy band gap

Dear Vinay,

Chandra brought an interesting paper which defines the socalled Penn gap for semiconductors. But i think you could mean the Fermi level pinning at the surface of semiconductors because of the presence of allowed electronic sate populated at certain energy level near the conduction band. It is so if the density of the sates is high it can deplete the surface region and clamp the Fermi level at the surface so that it pins it at that level rendering the material not nearly responsive to the work function of the metal contacting the semiconductor. The pinning level depends on the energy position of the traps levels at the surface not in the energy gap.