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We present a self-consistent multi subband deterministic solver of the Boltzmann transport equation of the two dimensional (2D) electron gas. The Schodinger equation at each slice in the confinement direction and the two dimensional Poisson equation are self-consistently solved with the Boltzmann transport equation. The energy quantization and the scattering of the 2D electron gas are included. We apply this solver to an ultra-thin body double gate MOSFET and show the influence of the 2Dk scattering to the electron transport.