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.