Resistivity-based Modeling of Substrate Non-uniformity for Resistance Extraction of Low-Resistivity Substrate

This paper discusses modeling of non-uniform substrate resistivity for substrate resistance extraction. Though substrate resistivity of each substrate layer is frequently assumed to be uniform, doping profile of each substrate layer is not uniform. We present the extraction error of substrate resistance under uniform resistivity assumption. The resistivity models we suggest enable accurate resistance extraction of substrate with non-uniform profile. We also demonstrate characterization of the suggested model using substrate resistances which are easily obtained from fabricated chips.