  In this paper, a variant of discretization of the van Roosbroeck equations in
the equilibrium state with the Composite Discontinuous Galerkin Method for the
rectangular domain is discussed. It is based on Symmetric Interior Penalty
Galerkin (SIPG) method. The proposed method accounts for lower regularity of
the solution on the interfaces of devices' layers. It is shown that the
discrete problem is well-defined and that discrete solution is unique. Error
estimates are derived. Finally, numerical simulations are presented.
