Statistical analysis of embedded capacitors using Monte Carlo simulation

In this paper we describe a method of accurately modeling new passive devices by deembedding the many building blocks, from which they are built, using just a few test structures. We use a nonlinear optimizer to find the optimal equivalent circuit models for the building blocks by fitting extensive high frequency measurements of the test structures behavior. We also demonstrate that the variation in the complete equivalent circuit models, based only on the circuit building blocks, can be used to predict such variations in actual fabricated devices. Three sets of gridded parallel plate capacitor structures are fabricated on a Low Temperature Co-fired Ceramic (LTCC) process, using 2-layers of a 12-layer process. S-parameter measurements are taken and element values from Partial Element Equivalent Circuits (PEEC) deembedded using an HSPICE Optimization algorithm. Statistical variations in the deembedded element values of the structures building blocks are calculated and used in an HSPICE Monte Carlo Simulation tool. S-parameters are converted to y-parameters for convenience, and both measured and predicted y-parameters compared. The comparison between the Monte Carlo simulation results and the measured data, determines that the statistical variation of the component values provides an accurate representation of the overall capacitor performance. The key results in this research are: the number of test structures needed is much less than the number of parameters and building blocks to be extracted; this methodology is much faster than other finite element like methods; and the equivalent circuit models and the process used to create them is accurate enough to also model the variations in the actual fabricated devices.