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 $\mathrm{6}\ \mu \mathrm{m}$ device height.