[en] The possibility of amplification of terahertz-range electromagnetic waves due to optical transitions between a two-dimensional continuum and shallow-level donor states in GaAs/AlGaAs superlattices with selectively δ-doped quantum wells is analyzed theoretically. The population inversion required for the gain is attained under the conditions of vertical transport in the superlattice due to the hybridization of states in neighboring quantum wells coupled via electron tunneling through the barrier. It is shown that, at a doping level of 5 x 10¹⁰ cm^-2 per period, the gain can be as high as 50 cm^-1 at wavelengths 100-120 μm. The current density under operating conditions is ∼50 A/cm²