In this article a two-dimensional field emission diode system is simulated. The blade-shaped emitter is located on a flat substrate. The anode is a plane parallel to the substrate. The internal region of the system is filled with three layers of dielectrics. To calculate the electrostatic potential distribution in the entire area of the system under study, the influence of the field emitter is replaced by the influence of a charged plane. The boundary problem for the Poisson equation is solved in the Cartesian coordinate system by the method of separation of variables. The problem solution is obtained in an analytical form, in the form of series of eigenfunctions. All geometric dimensions, dielectric permittivities of the layers, potentials of the electrodes are the parameters of the problem.