A Novel Approach to Modeling Metal–Insulator–Metal Capacitors Over Vias With Significant Electrical Length

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In monolithic-microwave integrated-circuit design, a metalinsulatormetal (MIM) capacitor is one of the key passive components. Some commonly used MIM capacitor models are optimized for series capacitor applications. These conventional models, however, face a challenge as a need for a shunt capacitor application arises. This paper is a solution provider, ushering in a new approach to modeling a shunt capacitor of large electrical length over grounding substrate vias. Our model is derived from a set of design equations that allows asymmetric coupled lines in an inhomogeneous medium to be approximated to symmetric coupled lines in a homogeneous medium. Here we gain a theoretical insight into the rationale behind this approximation. The new approach benefits from: 1) a four-port implementation providing two connections to top and bottom plates and 2) a drastic reduction in mathematical complexity without trading off accuracy or compatibility. Circuit and electromagnetic simulations has proven to be in good agreement with measurements of a test structure of electrical length 558$^{\circ}$ at 50 GHz. </para>