CNN-Cap: Effective Convolutional Neural Network-based Capacitance Models for Interconnect Capacitance Extraction

Abstract

Accurate capacitance extraction is becoming more important for designing integrated circuits under advanced process technology. The pattern matching-based full-chip extraction methodology delivers fast computational speed but suffers from large error and tedious efforts on building capacitance models of the increasing structure patterns. In this work, we propose an effective method for building convolutional neural network (CNN)-based capacitance models (called CNN-Cap) for two-dimensional (2-D) and three -dimensional (3-D) interconnect structures. With a novel grid-based data representation, the proposed method is able to model 2-D pattern structure and 3-D window structure with a variable number of conductors to largely reduce the number of patterns or increase the accuracy. Based on the ability of ResNet architecture on capturing spatial information and the proposed training skills, the obtained CNN-Cap exhibits much better performance over the multilayer perception neural network-based capacitance model while being more versatile. Extensive experiments on a 55 nm and a 15 nm process technologies have demonstrated that the error of total capacitance produced with 2-D CNN-Cap is always within 1.3%, and the error of produced coupling capacitance is less than 10% in over 99.5% probability. For 3-D structures, CNN-Cap predicts the total capacitance with less than 5% error in 99% probability and with a maximum error of 7.7%. For the tested 2-D and 3-D structures, the CNN-Cap run on a GPU server is more than 4,000× and 12,000×, respectively, faster than the conventional field solver Raphael, while consuming negligible memory.