Process-variation-aware electromagnetic-semiconductor coupled simulation

Abstract

We develop a new method based on the high-frequency electromagnetic (EM)-semiconductor coupled simulation to analyze the impact of multi-type process variations happen around semiconductormetal structure. It is competent to simultaneously handle geometrical variations like surface roughness and material variations like semiconductor doping profile, which are difficult for traditional "stand alone" simulation methods. A sparse grid based stochastic spectral collocation method (SSCM) combined with principle factor analysis (PFA) is implemented to accelerate the stochastic simulation. Numerical results confirm the validity and significance of our variational coupled simulation framework. I. INTRODUCTIONWhile the operational frequency is marching into multi-gigahertz, traditional separated characterization of metallic interconnects (fullwave EM) and semiconductor devices (TCAD model) becomes insufficient due to the increasing interactions between EM and semiconductor dynamics. A method breaking the barrier between full-wave EM models and semiconductor models was first proposed in [1], [2], which is named as the A-V solver with scalar potential and vector potential A being the basic unknowns. By simultaneously solving the Maxwell's equations and the semiconductor equations (e.g., driftdiffusion equations) in the frequency domain, the A-V solver sets up a physically consistent and numerically convenient linkage between the EM models and the semiconductor carrier transport models.Process variation is another major concern in submicron technology, which brings undesirable perturbations to the characteristics of devices and interconnects [3]. Generally, process variations affecting integrated circuits can be categorized as geometrical variations and material variations. There have been a number of studies on both types of variations, e.g. surface roughness of metal wire [4] and random dopant fluctuations (RDF) in the semiconductor [5]. Nevertheless, these variations are usually studied within a pure interconnect context or a pure semiconductor context, with the geometrical variations being the major concern in the former while material variations in the latter. This decoupled characterization of process variations is also becoming insufficient given the increasing tight coupling among interconnects and semiconductor.In this paper, we propose a variational A-V solver which allows a convenient and simultaneous characterization of geometrical and material variations in the coupled simulation framework. We believe it is the first time that typical process variations in metallic interconnects and semiconductor, including their mutual intercorrelations, can be simulated in a unified manner, which is very difficult, if not impossible, to be realized with existing decoupled simulation frameworks. Stochastic spectral collocation method (SSCM), is employed to speed up the stochastic analysis. Numerical results then confirm the validity and effectiveness of the proposed method.