Beyond 65 nm node, the ultra-narrow channel memory device serves as a possible technology for further scaling. A self-assembled carbon nanotube (CNT) channel with self aligned metal nanocrystals is proposed as an alternative to Si based ultra-narrow channel memory. The device demonstrates large memory window and single-electron sensitivity. The analysis of the transport in the CNT channel using non-equilibrium Green's function (NEGF) formalism confirms single electron sensitivity quantitatively at room temperature. The CNT channel conductance exhibits sensitivity to position of the charge along the channel. The NEGF based analysis is easily extended to the application of CNTFET as a charge sensor. The electrostatics of the CNT-nanocrystal memory was analyzed for transport between nanocrystal and CNT. Despite the nanocrystal being in close proximity of the CNT, it is strongly coupled to the gate electrode electrostatically. This effect is not observed in the planar 2D Si- based nanocrystal memory. It obviates a major trade-off in memory design of scaling the control dielectric to decrease operational voltage, while ensuring low gate leakage and should allow ultra-low voltage operations. Large tunneling current should also enhance write times. Large electric field asymmetry should enable a better write/retention ratio.