The mathematical model that allows obtaining wave functions of electrons and holes and Coulomb potential in dependence on the parameters of the layer is proposed. In contrast to the common approach widely used in considerable literature, the proposed method allows to find the wave functions for all layers of the structure, both inside and outside the barrier layer. It was shown that increase of tunnel barrier transparency entails a transition from the dipolar electron-hole system (EHS) with a double-peak wave function of electrons to the spatially direct EHS. The proposed model takes into account the effect of the correlation interaction on the wave functions and the density of distribution of the carriers crosswise the layers. These calculations are useful for the analysis of many-particle nonequilibrium states occurring in low-dimensional structures.