| Summary: | 碩士 === 國立臺灣大學 === 電機工程學研究所 === 94 === On-chip inductance modeling is one of the most popular issues in VLSI designs nowadays. It is important to calculate on-chip inductance values efficiently and accurately according to the operating frequencies.
As the operating frequency reaches over gigahertz, the effect of inductance can no longer be ignored as it used to be. There are many of different researches focusing on modeling on-chip inductance and most of them are field solvers such as FastHenry. Field solvers provide accurate evaluated results but they require much more computational complexity and are time consuming.
In this Thesis, we proposed a new method of modeling on-chip inductance that features the skin effect phenomenon. We first apply the volume filament model to divide the traces into smaller filaments and then evaluate the inductance value of each filament. After that, we multiply each filament with a weighting factor, which is derived from the current density distribution in the trace. Here we made the prediction of current density distribution easy to calculate by using mathematical approximation. Having all the weighted inductance value of each filament, we can therefore derive the inductance value of the whole trace.
By using the approximated formulation of current density distribution, we can tremendously decrease the time of evaluating both self-inductance and mutual inductance values without losing accuracy. Therefore, the whole chip inductance extraction can be completed accurately and efficiently.
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