Spatially Resolved Conductivity of Rectangular Interconnects considering Surface Scattering -- Part II: Circuit-Compatible Modeling

Abstract

Interconnect conductivity modeling is a critical aspect for modern chip design. Surface scattering -- an important scattering mechanism in scaled interconnects is usually captured using Fuchs-Sondheimer (FS) model which offers the average behavior of the interconnect. However, to support the modern interconnect structures (such as tapered geometries), modeling spatial dependency of conductivity becomes important. In Part I of this work, we presented a spatially resolved FS (SRFS) model for rectangular interconnects derived from the fundamental FS approach. While the proposed SRFS model offers both spatial-dependency of conductivity and its direct relationship with the physical parameters, its complex expression is not suitable for incorporation in circuit simulations. In this part, we build upon our SRFS model to propose a circuit-compatible conductivity model for rectangular interconnects accounting for 2D surface scattering. The proposed circuit-compatible model offers spatial resolution of conductivity as well as explicit dependence on the physical parameters such as electron mean free path (${\lambda}_0$), specularity ($p$) and interconnect geometry. We validate our circuit-compatible model over a range of interconnect width/height (and ${\lambda}_0$) and p values and show a close match with the physical SRFS model proposed in Part I (with error < 0.7%). We also compare our circuit-compatible model with a previous spatially resolved analytical model (appropriately modified for a fair comparison) and show that our model captures the spatial resolution of conductivity and the dependence on physical parameters more accurately. Finally, we present a semi-analytical equation for the average conductivity based on our circuit-compatible model.