Modeling of TSV-based solenoid inductors for 3-D integration

Circuit model for TSV-based solenoid inductors is presented and investigated. Based on the measurement, the related lumped circuit elements can be extracted, and they are independent of the operating frequency by virtue of the RL ladder. Hence, the circuit model is compatible with the SPICE simulators. Based on the circuit model, the impacts of design parameters on the quality factor and inductance are studied. Finally, the frequency-thermal analysis of TSV-based solenoid inductors is carried out.