how to simulate insulator in a GNRFET with matlab?

I want to apply gate voltage on a graphene nanoribbon as a channel in a GNRFET. then I want to solve poisson equation but I need to know the voltage on channel as the boundary condition in poisson eq. As we know there is voltage drop in insulator of the fet, so the voltage on channel is not the same as gate voltage. so we should count insulator in our calculation and I don't know how.

It would be appreciated if you send me a matlab code for simulation of GNRFET, or introduce me a source in which I can find my answer.