  We describe a method to fabricate clean suspended single-wall carbon nanotube
(SWCNT) transistors hosting a single quantum dot ranging in length from a few
10s of nm down to $\approx$ 3 nm. We first align narrow gold bow-tie junctions
on top of individual SWCNTs and suspend the devices. We then use a
feedback-controlled electromigration to break the gold junctions and expose
nm-sized sections of SWCNTs. We measure electron transport in these devices at
low temperature and show that they form clean and tunable single-electron
transistors. These ultra-short suspended transistors offer the prospect of
studying THz oscillators with strong electron-vibron coupling.
