Graphene based transistors relying on a conventional structure cannot switch properly because of the absence of an energy gap in graphene. To overcome this limitation, a barristor device was proposed, whose operation is based on the modulation of the graphene-semiconductor (GS) Schottky barrier by means of a top gate, and demonstrating an ON-OFF current ratio up to $10^5$. Such a large number is likely due to the realization of an ultra clean interface with virtually no interface trapped charge. However, it is indeed technologically relevant to know the impact that the interface trapped charges might have on the barristors electrical properties. We have developed a physics based model of the gate tunable GS heterostructure where non-idealities such as Fermi Level Pinning (FLP) and a bias dependent barrier lowering effect has been considered. Using the model we have made a comprehensive study of the barristors expected digital performance.