constitutive relation g$_{n}$ = g$_{d}$ + g$_{m}$/ 2 β which gives rise to Eq.(1). Details of screening, which are encoded in the Φ( V$_{d}$, V$_{g}$ ) functional, or temperature T$_{e}$ ( V$_{d}$, V$_{g}$ ) in f$_{s,d}$ (Φ), are implicit in Eq.(1) which can be regarded as a universal result for 1D transistors. In terms of thermal shot-noise one has ˜ F = coth ( eV$_{d}$/ 2 k$_{B}$T$_{e}$ ) ≲ 1 . 3 (for 2 k$_{B}$T$_{e}$/eV$_{d}$ ≲ 1) at low bias where g$_{m}$ < 2 βg$_{d}$ . At high bias one has g$_{m}$ ≫ 2 βg$_{d}$ whenever f$_{d}$ (Φ) ≪ f$_{s}$ (Φ) ≲ 1; one also expect Pauli noise suppression with a reduction factor (1 − f$_{s}$ (Φ)) like in the usual 2D case [12]. As a first test of the model we obtain a good fit of the g RF m ( V$_{g}$ ) data in Fig.2 with Eq.(2) by taking Φ( V$_{g}$ ) = Const. − eβV$_{g}$ and E$_{F}$ ≪ Φ in f$_{s,d}$ (Φ) according to the equivalent circuit and the potential landscape in Figs.1(b) and (c). We have used a scaling factor 0 . 6 that accounts for residual electronic diffusion above the barrier. Electronic temperatures deduced from theoretical fits corresponds to a large absolute temperature ( k$_{B}$T$_{e}$ ≃ 28 meV at V$_{d}$ ∼ 200 mV), but still a small energy spread when compared to the bias voltage ( k$_{B}$T$_{e}$ ≃ 0 . 14 eV$_{d}$ ) . The model accounts qualitatively for a full shot-noise at low bias ( ˜ F ≃ 1 for V$_{d}$ ≲ 0 . 1 V) and for the noise reduction at intermediate bias ( | V$_{d}$ | = 0 . 1–0 . 3 V). Using the electronic temperature from transconductance fits in Fig.2, we can quantitatively compare noise and transconductance in Eq.(1): At V$_{d}$ = − 0 . 2 V, where S$_{I}$/ 2 e ≃ 1 . 46 ± 0 . 1 µ A, g RF m ≃ 8 . 6 ± 0 . 5 µ S and V$_{Te}$ = k$_{B}$T$_{e}$/eβ ≃ 0 . 14 ± 0 . 02 V we obtain g RF m V$_{Te}$ ≃ 1 . 2 ± 0 . 3 µ A in good agreement with theoretical prediction S$_{I}$/ 2 e ≳ g$_{m}$V$_{Te}$ from Eq.(1). By comparison standard noise thermometry would give a smaller value S$_{I}$/ 2 e = 2 g$_{d}$k$_{B}$T$_{e}$/e ≃ 0 . 5 µ A (taking g$_{d}$ = g DC d ≃ 9 µ S). We take this agreement as a strong support for the 1D model. Further experimental investigations should involve direct measurement of g RF d to test Eq.(1) over the full bias range including the crossover g RF m ≲ 2 βg RF d . Finally we can use our data to estimate the charge resolution δq$_{rms}$ = √$_{S}$$_{I}$$_{C}$$_{g}$$_{/g}$$_{m}$$_{. The}$ best signal to noise conditions, for V$_{d}$ ∼ 0 . 3 V and I$_{d}$V$_{d}$ ∼ 1 µ W where g$_{m}$ ≳ 15 µ S and S$_{I}$/ 2 e ≲ 2 µ A, give δq$_{rms}$ ≲ 13 µ e $_{/}$√$_{Hz (}$$_{C}$$_{g}$ ≲ 40 aF [5]) for our double gate device which corresponds to an rms charge resolution of 0.4 electron in the 0 . 8 GHz bandwidth of our set- up. Within a factor five of the best resolution achieved in SETs [2], this smaller sensitivity of the present CNT-FETs is balanced by a much larger bandwidth (0 . 8 GHz here against 0 . 08 GHz in [2]) and the possibility to operate at room temperature. In conclusion, our comprehensive study of high-frequency transport and shot noise has confirmed that the single nanotube transistor is a model system and that hot electron 5