Broadband Lumped-Element Parameter Extraction Method of Two-Port 3D MEMS In-Chip Solenoid Inductors Based on a Physics-Based Equivalent Circuit Model

Abstract

Integrated 2D spiral inductors possess low inductance per unit area, which limits their application range. However, the state of investigation into the lumped-element parameter extraction method for integrated 3D in-chip multi-turn solenoid inductors, which possess higher inductance per unit area, is inadequate. This type of inductor can thus not be incorporated into fast computer-aided design (CAD)-assisted circuit design. In this study, we propose a broadband two-port physics-based equivalent circuit model for 3D microelectromechanical system (MEMS) in-chip solenoid inductors that are embedded in silicon substrates. The circuit model was composed of lumped elements with specific physical meanings and incorporated complicated parasitics resulting from eddy currents, skin effects, and proximity effects. Based on this model, we presented a lumped-element parameter extraction method using the electronic design automation software package, Agilent Advanced Design System (ADS). This method proved to be consistent with the results of two-port testing at low to self-resonant frequencies and could thus be used in CAD-assisted circuit design. The lumped element value variations were analyzed based on the physical meaning of the elements with respect to variations in structures and the substrate resistivity of inductors. This provided a novel perspective in terms of the design of integrated in-chip solenoid inductors.

High Frequency Analysis and Optimization of Planar Spiral Inductors Used in Microelectronic Circuits

“…The ABSIF software is based on: analytical expressions for low frequency inductanc calculations, based on the current sheet method [21][22][23][24][25][26][27]; analytical expressions for electr cal parameters and for high frequency were set up by the authors using the π equivalen electrical circuit method. This method implies the use of π models with concentrated pa rameters for each side of the spiral inductor [28][29][30][31][32][33][34]. For example, a square inductor wit N turns has 4N sides; each turn is formed of four lines and a π equivalent circuit wit concentrated parameters, such as the one represented in Figure 1.…”