On calculation of the electric potential for 2D silicon transistor with a silicon oxide nanochannel

We study the problem on calculation of the electric potential for the 2D silicon transistor occupying a domain $\Omega$ with an adjoint silicon oxide nanochannel occupying a domain $\Omega_G$. By numerical simulations we justify the reduction of this problem in the domain $\Omega\cup\Omega_G$ to that for finding the potential only in the domain $\Omega$.