Efficient numerical modeling of random rough surface effects in interconnect resistance extraction

Abstract

SUMMARYOwing to the decreasing skin depth in high-speed analog and digital circuits, surface roughness is playing an increasingly important role in interconnect parasitic extraction. However, the random nature of surface roughness and the complicated electromagnetic behavior baffle satisfactory solutions to the extraction exercise. This paper utilizes a numerically formulated effective conductivity as an efficient measure of the rough surface effects in the resistance extraction to avoid the global discretization of interconnect surfaces. Two numerical methods based on different boundary element formulations are proposed to compute the mean effective conductivity for interconnects with random surface roughness. Numerical experiments compare these two methods in different rough surface patterns to evaluate their efficacy.

Process variability-induced NoC link failure: A probabilistic model

“…This is due to the systematic pattern or spatial effects (metal density, width, and space) [14]. Variations in the interconnects resistance and capacitance cause the signal received to be delayed or attenuated [32]. Finally, variations in V th , L g , and T ox of the receiver will affect the receiver resistive and capacitive loads, which in turn affect the signal received.…”

Gramian‐based model order reduction of parameterized time‐delay systems

“…In high-speed circuit design, time-delay phenomena frequently appear due to the propagation delays, for instance, caused by the transmission lines in circuit packaging and printed circuit board (PCB) design [1][2][3][4][5]. In many cases of packaging and PCB design/optimization, propagation delay can dominate circuit performance, whereby attenuation effects caused by transmission lines are negligible, and the transmission lines can be regarded as lossless.…”

Model Order Reduction for Neutral Systems by Moment Matching

“…However, direct simulation of the original high or even infinite order models is very difficult and sometimes prohibitive due to unmanageable levels of storage, high computational cost and long computation time. Therefore, model order reduction (MOR) , which replaces the original complex and high-order system by a reduced-order model (ROM), plays an important role in many areas of engineering, e.g., transmission lines in circuit packaging [31,38], PCB (printed circuit board) design [11,48,58] and networked control systems [18,28]. The obvious advantages of MOR include that the use of ROMs results in not only considerable savings in storage and computational time, but also fast simulation and verification leading to shortened design cycle [2,3,5,12,15,26,33,34,36,52,59].…”