Modeling and analysis of 3-D solenoid embedded inductors

Investigation of the statistical variation of integrated passive components is crucial for designing and characterizing the performance of multichip module (MCM) substrates. In this paper, the statistical analysis of three-dimensional (3-D) solenoid inductors manufactured in a multilayer low-temperature cofired ceramic (LTCC) process is presented. A set of integrated inductor structures is fabricated, and their scattering parameters are measured for a range of frequencies from 50 MHz to 5 GHz. Using optimized equivalent circuits obtained from HSPICE, mean and absolute deviation is calculated for each component of each device model. Monte Carlo Analysis for the inductor structures is then performed using HSPICE. Using a comparison of the Monte Carlo results and measured data, it is determined that for even a small number of sample structures, the statistical variation of the component values provides an accurate representation of the overall inductor performance.