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

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.

Powder Filling and Sintering of 3D In-chip Solenoid Coils with High Aspect Ratio Structure.

In this study, a 3D coil embedded in a silicon substrate including densely distributed through-silicon vias (TSVs) was fabricated via a rapid metal powder sintering process. The filling and sintering methods for microdevices were evaluated, and the effects of powder types were compared. The parameters influencing the properties and processing speed were analyzed. The results showed that the pre-alloyed powder exhibited the best uniformity and stability when the experiment used two or more types of powders to avoid the segregation effect. The smaller the particle diameter, the better the inductive performance will be. The entire structure can be sintered near the melting point of the alloy, and increasing the temperature increases strength, while resulting in low resistivity. Finally, an 800-µm-high coil was fabricated. This process does not need surface metallization and seed layer formation. The forming process involves only sintering instead of slowly growing copper with a tiny current. Therefore, this process has advantages, such as a process time of 7 h, corresponding to an 84% reduction compared to current electroplating processes (45 h), and a 543% efficiency improvement. Thus, this process is more efficient, controllable, stable, and suitable for mass production of devices with flexible dimensions.