Kinetic Inductance in Ballistic Transport

Electron transport in nanoscale semiconductors approaches the ballistic limit. Without scattering, the kinetic inductance of carriers becomes considerably large. Using a generalized formulation of ballistic transport, we investigate the generalized kinetic inductance in a d-dimensional conductor with various band-structures (e.g. parabolic and conical) in the ballistic limit. The kinetic inductance per unit length is evaluated as a function of carrier density and temperature at low bias voltages. Kinetic inductance is found to very weakly depend on voltage, and strongly on the electron density. An increase in kinetic inductance at low density is expected because more velocity is needed to maintain the same current. The ballistic model predicts that even without considering phonon scattering, the kinetic inductance decreases at high temperature. Because of the Fermionic nature of electrons, their collective excitation exhibits a Newtonian inertia, which decreases with an increase in temperature. The quantum mechanical ballistic kinetic inductance is compared to the standard classical inductance in the Boltzmann Transport regime, and its importance is classified for various carrier densities, and dimensions.