Quantum scaling in nano-transistors

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 $l \to \infty$\mathrm{.}Intheweakbarrierregime,$l \lesssim 10$, 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.