Reduced-Order Stochastic Testing of Interconnects Subject to Line Edge Roughness

In this contribution we study the propagation constant of interconnects subject to line edge roughness by means of an efficient stochastic framework. By employing the stochastic testing method, we succeed in limiting the number of calls to the full-wave electromagnetic field solver at the core of the system. Additionally, the computationally burdensome solution of the eigenvalue problem is eased by reducing its order through projection on an appropriate basis. The resulting two-step accel-eration leads to an effective approach to assess the effect of line edge roughness on the characteristics of interconnects. The novel framework is applied to a rough rectangular waveguide and a microstrip.

I. Introduction

The push towards ever higher frequencies, more compact components and increasing heterogeneous integration raises the complexity in the design of electronic circuits and systems. Physical phenomena that could previously be ignored without detrimental consequences are now more than ever inevitable and should be included in the designer's tools to assess their influence from the get-go. Surface roughness and line edge roughness (LER) [1] are prime illustrations of such phenomena that refer to the non-ideal, irregular profile of conductors. Whether present due to the production process or intentionally applied to obtain cohesion between various layers, its effect on the performance is getting stronger due to miniaturization and a more developed skin effect. Given the random nature of line edge and surface roughness, stochastic methods built around full-wave electromagnetic modeling simulators are the most appropriate tools. However, dealing with the complicated geometry of a coarse surface or edge is a time-consuming effort for full-wave tools, not to mention the numerous runs required for distribution estimation in a stochastic context.