  We evaluate the effect of the recombination associated with interlayer
transitions in ungated and gated double-graphene-layer (GL) structures on the
injection of electrons and holes. Using the proposed model, we derive
analytical expressions for the spatial distributions of the electron and hole
Fermi energies and the energy gap between the Dirac points in GLs as well as
their dependences on the bias and gate voltages. The current-voltage
characteristics are calculated as well. % The model is based on hydrodynamic
equations for the electron and hole transport in GLs under the self-consistent
electric field. It is shown that in undoped double-GL structures with weak
scattering of electrons and holes on disorder, the Fermi energies and the
energy gap are virtually constant across the main portions of GLs, although
their values strongly depend on the voltages and recombination parameters. In
contrast, the electron and hole scattering on disorder lead to substantial
nonuniformities. The resonant inter-GL tunneling enables N-shaped
current-voltage characteristics provided that GLs are sufficiently short. The
width of the current maxima is much larger than the broadening of the tunneling
resonance. In the double-GL structures with relatively long GLs the N-shaped
characteristics transform into the Z-shaped characteristics. % The obtained
results are in line with the experimental observations \cite{1} and might be
useful for design and optimization of different devices based on double-GL
structures, including field-effect transistors and terahertz lasers.
