In this work we investigate quasi-ballistic transport in nanowire field-effect transistors (NW-FETs) by addressing the 1D Boltzmann transport equation. First, we find its exact analytical solution for any potential profile within the constraint of dominant elastic scattering. Next, we calculate the I-V characteristics of the NW-FET, which differ from the Landauer expression for the inclusion of a transmission coefficient smaller than one. Our approach provides a methodology for the calculation of the transmission and backscattering coefficients directly from the scattering probabilities. These coefficients turn out to be functions of the ratio between the device length and a suitably-averaged momentum-relaxation distance. One of the main conclusions of the paper is that, so long as inelastic collisions are neglected, the so-called kT-layer plays no role in 1D devices.
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