Circuit Models of Nanoscale Devices

On the nanoscale, equivalent circuit models are not scale invariant. An ideal equivalent circuit can be a valid model of a device at the macro or even micro-scale, but it might not reveal even the qualitative properties of the same device during downscaling. We illustrate the consequences of downscaling to the nanoscale with an example, the nanoscale capacitor. The circuit models combine four groups of state variables: (1) classical mechanical, (2) classical electromagnetic, (3) quantum mechanical, and (4) quantum electromagnetic. In general, a quantum-classical equivalent circuit is combined from four coupled “subcircuits,” representing the classical mechanical dynamics of the nuclei, the classical dynamics of the electromagnetic field, the quantum wave-dynamics of the electrons, and the QFT dynamics of photons. The modeling procedure should determine the state-variables of the four subcircuits and their couplings.