Ionization equilibrium between electrons and holes in bilayers and adiabatic approximations

We analyze the ionization equilibrium between the charges in nonlinear bilayers formed by triangular planar atomic lattices. We consider a system consisting of two separated buy a dielectric medium and independently gated layers 1 and 2 separated by a dielectric medium with ???? with equal density of electrons in first layer 1 and holes in second layer 2. Assuming that the upper layer is doped with electrons and in the lower layer is doped with holes, we study of the formation, the dynamics and the thermodynamics of bound states. Beside electron – hole pairing we are including bound states with solitonic excitations. We investigate the ionization of electron – hole pairs and discuss the influence of solitons on bound electron-hole pairs; her we use the adiabatic approximation assuming at any time local equilibrium. So far we concentrated here on several thermodynamics and dynamic effects, as the Coulomb attraction between electrons and holes, the formation of electron – hole atoms and degeneration effect. Further we investigated the ionization equilibrium and the coupling to solitonic excitations.