High-$Q$ Solenoid Inductors With a CMOS-Compatible Concave-Suspending MEMS Process

Abstract

This paper presents micromachined solenoid inductors that are fabricated in a standard CMOS silicon substrate (with a resistivity of 1-8 Omega . cm). The solenoid is concavely embedded in a silicon cavity with the silicon wafer surface remaining a plane, and mechanically suspended to form an air gap from the bottom of the silicon cavity. In addition to facilitating flip-chip packaging, this so-called "concave-suspending" technique effectively depresses the substrate effects including eddy current and capacitive coupling between the coil and the substrate, therefore contributing to both high Q -factor and high resonant frequency of the inductors for high-performance radio-frequency (RF)/microwave integrated circuit applications. Various inductors with different solenoid layouts, e.g., several shapes of curved solenoids, have been successfully fabricated by using a post-CMOS microelectromechanical systems process that employs copper electroplating, tetra-methyl-ammonium hydroxide (TMAH) + iso- propanol etching and compensation control for convex-corner undercutting, photoresist spray coating, XeF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gaseous etching, and other steps. A lumped circuit model that accounts for inter- turn fringing capacitance, capacitance between the coil and the substrate, substrate ohmic loss and substrate capacitance, etc., is derived for the solenoid inductors. The accuracy of the model is confirmed by the testing results and can be used for optimal design of the inductors. By S-parameter testing, various types of inductors with different solenoid layouts have been evaluated. The solenoid inductors generally exhibit improved RF performance in Q-factor and self-resonance frequency compared to their conventional counterparts.