Spatially Resolved Conductivity of Rectangular Interconnects Considering Surface Scattering—Part I: Physical Modeling

Surface scattering in interconnects is usually treated by using Fuchs-Sondheimer (FS) approach. While the FS model offers explicit inclusion of the physical parameters, it lacks spatial dependence of conductivity across the interconnect cross section. To capture the space-dependency of conductivity, an empirical modeling approach based on “cosh” function has been proposed, but it lacks physical insights. In this work, we present a 2-D spatially resolved FS (SRFS) model for rectangular interconnects derived from the Boltzmann transport equations (BTEs). The proposed SRFS model for surface scattering offers both spatial dependence and explicit relation of conductivity to physical parameters such as mean free path and specularity of electrons (p) as well as interconnect geometry. The solution obtained from our SRFS model is exact for diffusive scattering. For specular scattering, we approximate the solution and show that the average conductivity obtained from SRFS shows a good match with the previous models for a general value of p. We highlight the importance of physics-based spatially resolved conductivity model by showing the differences in the spatial profiles between the proposed physical approach and the previous empirical approach. In Part II of this work, we build upon the SRFS approach to propose a circuit-compatible model for spatially resolved conductivity accounting for surface scattering in rectangular interconnects.