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A mode space (MS) tight binding approach for the simulation of armchair graphene nanoribbon FETs is discussed. It makes use of slab-dependent modes and a novel criterion for mode selection, going beyond the one based on the lowest energy subbands. For ideal ribbons, we show that by splitting the modes into decoupled groups, the new method provides results almost identical to the real space (RS) with a speedup of more than one order of magnitude. Even in the presence of edge roughness, which tends to couple the modes, the MS approach still offers a sizable computational advantage with respect to the RS, while retaining a good accuracy.