Abstract
The frequency-variant characteristics of a pair of package power and ground net are experimentally investigated and modeled by using frequency-variant grid-type equivalent circuits, where each cell of the grid is modeled with vertically stacked RLC-ladder circuits. Various test patterns are designed and fabricated by employing a ball grid array (BGA) package process. Then the test patterns are characterized by using impedance analyzer, time domain reflectometry and time domain transmission (TDR/TDT), and vector network analyzer (VNA). Based on the experimental characterizations, not only are material constants and circuit model parameters determined, but also the conductor roughness and other frequency-variant effects are modeled. It is shown that the SPICE-based circuit simulation using the proposed circuit model has an excellent agreement with the measurement data in the range of 100 MHz - 15 GHz. Then, it is also shown that the various types of package performance evaluations can be very efficiently as well as accurately achieved with the proposed technique.
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