The physical mechanism of the experimentally observed dependence of passive intermodulation (PIM) in printed circuits on conductor surface roughness is studied. It is shown that electrothermal (ET) nonlinearity, arising due to heating of imperfect conductors by high-power carriers in a multicarrier system, is correlated with conductor surface roughness and has a unique signature. Carriers modulate the conductor resistivity, skin depth, and surface impedance which generate PIM products. The detailed analysis demonstrates that ET-PIM depends on the conductor resistivity, shape, and roughness profile and also on the electric and thermal properties of the substrate. Their effects on PIM are illustrated by examples of uniform microstrip lines with different conductor and substrate materials, and periodically perturbed and meandered microstrip lines.