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We present an extension of the unscreened generalized Prange-Nee term used to calculate the surface roughness (SR) limited mobility in arbitrarily oriented square nanowires. The presence of non-diagonal terms in the effective mass tensor is responsible for an additional term not considered in previous studies. We assess the impact of such a modification on the SR limited mobility and on the total mobility (SR and phonon scattering are considered) for devices with different orientation and size. We show that this impact is more relevant for small devices, where the SR plays an important role, even at low inversion charge.