Understanding and Modeling the Resistance of High Aspect Ratio FIB-Fabricated Tungsten Vias

Tungsten vias, made with traditional focused ion beam (FIB) techniques for the purpose of circuit edit work, exhibit higher electrical resistance than expected from the resistivity of the deposited tungsten and the via’s geometry. The resistance is a strong function of the via’s aspect ratio, defined here, to be the length of the via divided by its area. Chemical analysis of the vias shows that a poorly conductive skin of partially reacted W(CO)₆ precursor and thickness ~0.1 μm lines the perimeter of every via. The skin is an unwanted consequence of the traditional technique used for filling a via with tungsten to prohibit the formation of voids. The existence of a poorly conductive perimeter justifies an effective area model whereby the electrical area of the via is the drawn area minus the area of the poorly conductive perimeter. The effective area model lends itself to two theoretical frameworks: one employing closed-form analytical expressions, and the second using finite element analysis, for understanding electrical resistance as a function of aspect ratio. The finite element framework adheres strictly to the known geometry of the vias, accounts for current crowding, and presents a reasonable fit to the data.