III-nitride membranes offer promising perspectives and improved device designs in photonics, electronics, and optomechanics. However, the removal of the growth substrate often leads to a rough membrane surface, which increases scattering losses in optical devices. In this work, we demonstrate membranes with etched surface roughness comparable to that of the as-grown epitaxial material, accomplished by the implementation of a properly designed built-in polarization field near the top of the sacrificial layer from an AlInN interlayer, which is polarization-mismatched to GaN. This leads to a steeper reduction in free carrier density during the electrochemical etching of the sacrificial layer, limiting the etching current and thus causing an abrupter etch stop. As a result, the root mean square roughness is reduced to 0.4nm over 5x5 mu m(2). These smooth membranes open attractive pathways for the fabrication of high-quality optical cavities and waveguides operating in the ultraviolet and visible spectral regions.