  Understanding the nature of metal/1D-semiconductor contacts such as
metal/carbon nanotubes is a fundamental scientific and technological challenge
for realizing high performance transistors\cite{Francois,Franklin}. A Schottky
Barrier(SB) is usually formed at the interface of the $2D$ metal electrode with
the $1D$ semiconducting carbon nanotube. As yet,
experimental\cite{Appenzeller,Chen, Heinze, Derycke} and numerical
\cite{Leonard, Jimenez} studies have generally failed\cite{Svensson} to come up
with any functional relationship among the relevant variables affecting carrier
transport across the SB owing to their unique geometries and complicated
electrostatics. Here, we show that localized states called the metal induced
gap states (MIGS)\cite{Tersoff,Leonard} already present in the barrier
determines the transistor drain characteristics. These states seem to have
little or no influence near the ON-state of the transistor but starts to affect
the drain characteristics strongly as the OFF-state is approached. The role of
MIGS is characterized by tracking the dynamics of the onset bias, $V_o$ of
non-linear conduction in the drain characteristics with gate voltage $V_g$. We
find that $V_o$ varies with the zero-bias conductance $G_o(V_g)$ for a gate
bias $V_g$ as a power-law: $V_o$ $\sim $ ${G_o(V_g)}^x$ with an exponent $x$.
The origin of this power-law relationship is tentatively suggested as a result
of power-law variation of effective barrier height with $V_g$, corroborated by
previous theoretical and experimental results\cite{Appenzeller}. The influence
of MIGS states on transport is further verified independently by temperature
dependent measurements. The unexpected scaling behavior seem to be very generic
for metal/CNT contact providing an experimental forecast for designing state of
the art CNT devices.
