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Device performance of armchair graphene nanoribbon field effect transistors in the presence of surface roughness scattering is studied. A 2-D Gaussian autocorrelation function is employed to model the surface roughness. Tight-binding Hamiltonian and nonequilibrium Green's function formalism are used to perform atomic scale electronic transport simulation. The effect of geometrical and surface roughness parameters on the ON-current, the OFF-current, the transconductance, and the subthreshold swing is investigated. Surface roughness can strongly affect the device performance depending on how large is the roughness amplitude or how small is the roughness correlation length.