Quantum scaling in nano-transistors

TL;DR

This paper develops a scale-invariant, effectively one-dimensional model for quantum transport in nano-transistors, revealing how device dimensions influence current-voltage characteristics and aligning with experimental observations.

Contribution

It introduces a scale-invariant framework for quantum transport in nano-transistors, connecting device dimensions to output behavior and extending understanding beyond classical models.

Findings

For large channel lengths, behavior resembles classical MOSFETs.

For small channel lengths, quantum effects cause qualitative differences.

Model shows qualitative agreement with experimental data.

Abstract

In our previous papers on ballistic quantum transport in nano-transistors [J. Appl. Phys. 98, 84308 (2005)] it was demonstrated that under certain conditions it is possible to reduce the three-dimensional transport problem to an effectively one-dimensional one. We show that such an effectively one-dimensional description can be cast in a scale-invariant form. We obtain dimensionless variables for the characteristic channel length $l$ and width of the transistor which determine the scale-invariant output characteristic. For $l \gtrsim 10$, in the strong barrier regime, the output characteristics are similar to that of a conventional MOSFET assuming an ideal form for $l \to \infty$. In the weak barrier regime, $l \lesssim 10$, strong source-drain currents lead to i-v characteristics that differ qualitatively from that of a conventional transistor. Comparing with experimental data we find qualitative agreement.