For single-walled carbon nanotube (SWNT) field effect transistors, vertical scaling of high kappa dielectrics by atomic layer deposition (ALD) currently stands at approximately 8 nm with a subthreshold swing S approximately 70-90 mV/decade at room temperature. ALD on as-grown pristine SWNTs is incapable of producing a uniform and conformal dielectric layer due to the lack of functional groups on nanotubes and because nucleation of an oxide dielectric layer in the ALD process hinges upon covalent chemisorption on reactive groups on surfaces. Here, we show that by noncovalent functionalization of SWNTs with poly-T DNA molecules (dT40-DNA), one can impart functional groups of sufficient density and stability for uniform and conformal ALD of high kappa dielectrics on SWNTs with thickness down to 2-3 nm. This enables approaching the ultimate vertical scaling limit of nanotube FETs and reliably achieving S approximately 60 mV/decade at room temperature, and S approximately 50 mV/decade in the band-to-band tunneling regime of ambipolar transport. We have also carried out microscopy investigations to understand ALD processes on SWNTs with and without DNA functionalization.