In this paper we present a 3D coupled mode space NEGF study of the quantum features of a nanoscale Gate-AU-Around (GAA) silicon transistor. The bottom oxide of the structure is parameterized in order to progressively transform the nanowire in a tri-gate FinFET and the electron transport studied for several Fin widths, back-biases voltages and electron effective masses. Moreover, we address in detail the treatment of the boundary conditions at the channel interface to model the wave function penetration into the gate oxide. We report quantitative results of the charge density obtained by a simplified and a complete discretization approach.