Band Structure, Phonon Scattering, and the Performance Limit of Single-Walled Carbon Nanotube Transistors

Semiconducting single-walled carbon nanotubes are studied in the diffusive transport regime. The peak mobility is found to scale with the square of the nanotube diameter and inversely with temperature. The maximum conductance, corrected for the contacts, is linear in the diameter and inverse temperature. These results are in good agreement with theoretical predictions for acoustic phonon scattering in combination with the unusual band structure of nanotubes. These measurements set the upper bound for the performance of nanotube transistors operating in the diffusive regime.

Figure 1

(a) The relativistic band structure of semiconducting SWNT. (b) Theoretical plot of SWNT FET conductance and mobility as functions of gate voltage according to Eqs. (5, 6). The dotted line indicates where the Fermi level reaches the second subband at zero temperature. (c) AFM image of one device. (d) Schematic of device geometry. The gray layer is 200 nm thick silicon oxide between the SWNT and highly-doped silicon wafer used as backgate.

Figure 2

The conductance of a device with $d=4\mathrm{nm}$ and $L=4\mu \mathrm{m}$ versus gate voltage at different temperatures. Upper inset: $R_{\mathrm{on}}$ as a function of $T$. Lower inset: measured peak mobility as a function of $T^{-1}$. Both are shown with linear fitting.

Figure 3

The conductance (a) and mobility (b) as functions of gate voltage for two different devices. The solid black curves are for a tube with $d=3.4\mathrm{nm}$, $L=5.4\mu \mathrm{m}$ while the dotted red curves are for a tube with $d=1.5\mathrm{nm}$, $L=10\mu \mathrm{m}$.

Figure 4

(a) Device length $L$ divided by resistance change $\Delta R$ from room temperature to 50 K versus tube diameter with linear fitting shown. Data of similar diameter tubes are averaged. (b) Room temperature peak mobility as a function of tube diameter for many devices. Two devices showing anomalously large peak mobility are circled. Inset to (b): peak mobilities versus tube diameters on log-log scale with circled two data points omitted. The solid line is a visual reference line for square law.

Figure 5

Scan gate microscopy images of (a) the device studied in Fig. 2 with normal peak mobility and (b) the circled $d=2.5\mathrm{nm}$ device with anomalously high peak mobility in Fig. 4b. The solid lines indicate the position of electrodes and dotted lines indicate the position of SWNT. The device in (b) is dominated by a few short segments of tube near the threshold region. Therefore, the mobility is overstated when the whole tube length is used to calculate the mobility.