Surface roughness causes random shifts in the lowest sub-band level around its ideal position. This gives rise to tail states of an otherwise step-like DOS of the 2D electron gas in the channel. These tail states cause a gradual onset of tunneling in a TFET with vertical tunnel paths and degrade the sub-threshold swing. The impact of roughness of the semiconductor/oxide interface on the transfer characteristics is analyzed in this paper. Quantum-mechanical calculations are performed on a (pseudo)-one-dimensional TFET to obtain the drain current in the presence of randomly shifted sub-band levels. It is found that, the larger the roughness amplitude, the stronger the degradation of the sub-threshold swing.