Doping in Carbon Nanotubes Probed by Raman and Transport Measurements

In situ Raman experiments together with transport measurements have been carried out on carbon nanotubes as a function of gate voltage. In metallic tubes, a large increase in the Raman frequency of the $G^{-}$ band, accompanied by a substantial decrease of its linewidth, is observed with electron or hole doping. In addition, we see an increase in the Raman frequency of the $G^{+}$ band in semiconducting tubes. These results are quantitatively explained using ab initio calculations that take into account effects beyond the adiabatic approximation. Our results imply that Raman spectroscopy can be used as an accurate measure of the doping of both metallic and semiconducting nanotubes.

Figure 1

(a) $I_{\mathrm{DS}}$ vs gate voltage ($V_g$). The inset shows the derivative of current as a function of $V_g$. The vertical lines (red and blue) correspond to the 1st van Hove singularities of semiconducting tubes. (b) The SEM picture of our nanotube-based FET. The nanotube bundles are connected between two gold electrodes (left and right sides). (c) RBM of nanotube bundles at 1.96 eV showing peaks at $151$ ($d=1.6\mathrm{nm}$) and $170{\mathrm{cm}}^{-1}$ ($d=1.4\mathrm{nm}$).

Figure 2

(a) Tangential Raman modes of SWNTs recorded using an excitation energy of 1.96 eV at several $V_g$. The open circles (dark yellow) show the raw Raman spectra, and the black lines are the fitted one. The shaded Raman spectra show the LO phonon component of the metallic nanotubes. $V_g$ dependence of (b) $L1$, (c) $L2$, and (d) $L3$ modes: Frequency (top panel), FWHM (middle panel), and total integrated area (bottom panel).

Figure 3

$G^{-}$ peak in metallic tubes: (a) Linewidth (${\gamma }_{\mathrm{LO}}$, FWHM) and (b) frequency shift ($\Delta {\omega }_{\mathrm{LO}}$) as a function of the doping. The Fermi energy (${ϵ}_F$) is zero at the charge neutrality point. ${\gamma }_{\mathrm{LO}}$ and $\Delta {\omega }_{\mathrm{LO}}$ are multiplied by the tube diameter ($d$) to obtain a universal behavior. Diamonds are measurements ($L1$ line). Lines are calculations done by considering (full line) or not considering (dashed line) an inhomogeneous fluctuation of ${ϵ}_F$. ${\omega }_{\mathrm{LO}}$ is the frequency of the LO phonon.

Figure 4

$G^{+}$ and $G^{-}$ peaks in 1.6 nm semiconducting tubes: (a) Theoretical charge doping per C atom. (b),(c) Frequency shift ($\Delta {\omega }_{\mathrm{LO}}$, $\Delta {\omega }_{\mathrm{TO}}$) as a function of the Fermi energy (${ϵ}_F$). Open dots are measurements ($L3$ line). Dotted lines are adiabatic calculations (BOA). Full lines are our most accurate theoretical results that take into account dynamical effects (TDPT). Vertical lines are the theoretical position of the first van Hove singularities.