The GaAs AlGaAs semiconductor insulator semiconductor (SIS) structure used for high-performance field effect transistors has also been used in the study of parallel coupled transport between electrons in the FET n+ gate (3D) and channel (2D). At temperatures above 50K the predominant coupling involves momentum transfer via Coulomb Mutual Scattering (CMS). At lower temperatures the sign of the coupling reverses and the results may be explained as a CMS mediated thermo-electric effect. The coupling is much stronger for a 2D - 2D EG configuration, where a maximum current to current transfer ratio of 6 × 10-4 was obtained. Theory developed for this case predicts a temperature dependence of μ1μ2T where μ1 and μ2 are the mobilities in the gate and channel respectively, and an inverse fifth power thickness dependence. © 1991.