On the modeling of surface roughness limited mobility in SOI MOSFETs and its correlation to the transistor effective field

In this paper, we discuss in detail the modeling of surface roughness (SR) scattering in single- and double-gate silicon-on-insulator (SOI) MOSFETs, where the conventional formulation based on the expected value of the electric field cannot be used. By reconsidering the Ando's original approach, we show that a model based on the eigenfunction derivatives at the Si-oxide interface can be naturally extended to SOI MOSFETs, and, furthermore, we also derive a formulation based on appropriate integrals of the eigenfunctions in the silicon film, which must replace the expected value of the field used in bulk MOSFETs. All the analytical identities used in the derivation of the model have been verified by using numerically calculated eigenvalues and wavefunctions. Our results indicate that, in ultrathin-film SOI MOSFETs, the effective field is no longer a good metric for the SR scattering and, furthermore, SR scattering affects the total mobility even at lower inversion densities than it does in bulk transistors.