High-frequency electrical circuit model for integrated capacitors utilizing lossy nanostructures

A phys­ics-based mod­el is presen­ted that cap­tures the elec­tric­al high-fre­quency beha­vi­or of low-dimen­sion­al nano­struc­tures used in emer­ging tech­no­lo­gies such as the ultra-high-dens­ity capa­cit­or. Derived from trans­mis­sion line the­ory the ana­lyt­ic­al expres­sion provides a fre­quency-depend­ent admit­tance of a lossy nano­struc­ture, which can be numer­ic­ally integ­rated over arbit­rary areas com­pris­ing the nano­struc­ture. Edge effects, a dis­trib­uted nature of res­istiv­ity or dimen­sions of the nano­struc­ture com­pris­ing the device can be taken into con­sid­er­a­tion and make it a power­ful tool for design­ing future integ­rated cir­cuits. The mod­el pre­dic­tions show an excel­lent match with hard­ware meas­ure­ments up to 3 GHz on state-of-the-art car­bon nan­ofiber based MIM-capa­cit­ors with capa­cit­ance dens­it­ies up to 500 nF/​mm² at 6 μm device height.