A new model for calculating Coulomb perturbation potentials in bidimensional semiconductor structures is proposed. The main advantage of this model is that it can be applied for an arbitrary number of layers with different permittivities. As an example of how it could be used, we studied the influence on Coulomb scattering of high-κ materials used as gate insulators in silicon-on-insulator structures. This study was carried out with insulators of different physical and effective oxide thicknesses. The results show that when a silicon dioxide is replaced by a high-κ dielectric with the same thickness, Coulomb scattering is reduced. However, the strength of this beneficial effect might be diminished in actual devices for two reasons. The first is that an interfacial layer of silicon dioxide is usually placed between the silicon slab and the high-κ dielectric, lessening its influence. Second, a gate high-κ dielectric is normally wider than its silicon dioxide counterpart. As a consequence, the metal or polysilicon gate is further from the silicon channel, and its beneficial screening effect on the perturbation charges is then reduced. Both these effects on Coulomb scattering were examined in this study.