Formation of three-particle clusters in hetero-junctions and MOSFET structures

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 for three particles is studied to clarify the character of the binding and the energy of the three-particle bound states. The results are used to offer a possible explanation of the Metal-Insulator transition recently observed in MOSFET and hetero-junctions.