Analytical modeling and performance benchmarking of on-chip interconnects with rough surfaces

Abstract

In planar on-chip copper interconnects, conductor losses due to surface roughness demands explicit consideration for accurate modeling of their performance metrics. This is quite pertinent for high-performance manycore processors/servers, where onchip interconnects are increasingly emerging as one of the key performance bottlenecks. This paper presents a novel analytical model for parameter extraction in current and future on-chip interconnects. Our proposed model aids in analyzing the impact of spatial and vertical surface roughness on their electrical performance. Our analysis clearly depicts that as the technology nodes scale down; the effect of the surface roughness becomes dominant and cannot be ignored. Based on AFM images of fabricated ultra-thin copper sheets, we have extracted roughness parameters to define realistic surface profiles using the well-known Mandelbrot-Weierstrass (MW) fractal function. For our analysis, we have considered four current and future interconnect technology nodes (i.e., 45, 22, 13, 7 nm) and evaluated the impact of surface roughness on typical performance metrics, such as delay, energy, and bandwidth. Results obtained using our model are verified by comparing with industry standard field solver Ansys HFSS as well as available experimental data that exhibits accuracy within 9 percent. We present signal integrity analysis using the eye diagram at 1, 5, 10, and 18 Gbps bit rates to find the increase in frequency dependent losses due to surface roughness. Finally, simulating a standard three line on-chip interconnect structure, we also report the computational overhead incurred for different values of roughness and technology nodes.