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We studied the roughness evolution of Si surfaces upon Ar ion erosion in real time. Following the theory of surface kinetic roughening, a model proposed by Majaniemi was used to obtain the value of the dynamic scaling exponent beta from our data. The model was found to explain both the observed roughening and the smoothening of the surfaces. The values of the scaling exponents alfa and beta, important for establishing a universal model for ion erosion of (Si) surfaces, have been determined. The value of beta proved to increase with decreasing ion energy, while the static scaling exponent alfa was found to be ion energy independent.