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A novel interaction mechanism in MOSFET structures and GaAs/AlGaAs hetero-junctions between the zone electrons of the two-dimensional (2D) gas and the charged traps on the insulator side is considered. By applying a canonical transformation, off-diagonal terms in the Hamiltonian due to the trapped level subsystem are excluded. This yields an effective three-particle attractive interaction as well as a pairing interaction inside the 2D electronic band. A type of Bethe- Goldstone equation fordoi:10.1103/physrevb.66.195333 fatcat:lbrlyixihjbstpvnas3jwcr5gm