Consistent analytical solution of the time-dependent Schr\"odinger equation for nanoscale circuits with laser-assisted quantum tunneling

TL;DR

This paper develops an analytical approach to solve the time-dependent Schrödinger equation for nanoscale circuits, accounting for quantum effects throughout the entire system, including connections, especially under laser-assisted tunneling conditions.

Contribution

It introduces a novel analytical method for modeling coherent wavefunction transfer in nanoscale circuits, addressing limitations of traditional tunneling estimations.

Findings

Provides a consistent analytical solution for quantum tunneling in nanoscale circuits.

Highlights the importance of considering quantum effects across entire circuits.

Enables better estimation of tunneling currents in nanoscale devices.

Abstract

It is now common practice to solve the Schr\"odinger equation to estimate the tunneling current between two metal electrodes at specified potentials, or the transmission through a potential barrier by assuming an incident, reflected, and transmitted wave. However, we suggest that these methods may not be appropriate for nanoscale circuits. The electron man-free path may be as long as 68.2 nm in metallic elements so we consider the possibility that quantum effects may occur throughout a nanoscale circuit, including the connections. Analytical methods are presented for modeling the coherent transfer of the wavefunction through a closed circuit.