Inner-shell charging of multiwalled carbon nanotubes

The electrostatic properties of individual multiwalled carbon nanotubes (MWCNTs) have been investigated from charge injection and electrostatic force microscopy experiments. The MWCNT linear charge densities analyzed as a function of the nanotube diameters are found to differ from classical capacitive predictions by one order of magnitude and correspond to the response of MWCNTs in the external electric field generated at the microscope tip. The fact that MWCNTs can hold an out-of-equilibrium charge is attributed to the inner-shell charging, as a result of the MWCNT finite transverse polarizability and of the intercalation of semiconducting and metallic shells.

Figure 1

(Color online) (a) Schematics of the charge injection experiments, in which nanotubes deposited on $200\mathrm{nm}$ thick $\mathrm{Si}{\mathrm{O}}_2$ layer are addressed with an atomic force microscope tip biased at an injection voltage $V_{\mathit{inj}}$ with respect to the substrate. (b) CNT charge detection in the EFM mode. The electrostatic interaction between the cantilever and the charged CNT is detected from the resonance frequency shift of the cantilever polarized at the detection voltage $V_{\mathit{EFM}}$ and oscillated at a distance $z$ above the sample $(z\simeq 100\mathrm{nm})$. (c1) Topography image ($50\mathrm{nm}$ $z$ scale) of a MWCNT with $20\mathrm{nm}$ diameter. The scale bar is $300\mathrm{nm}$. (c2) EFM image ($20\mathrm{Hz}$ frequency scale) prior to charge injection. The detection voltage is $V_{\mathit{EFM}}=-2\mathrm{V}$. The image was scanned from top to bottom as sketched by the vertical arrow. (c3) EFM image ($V_{\mathit{EFM}}=-2\mathrm{V}$, $20\mathrm{Hz}$ scale) after a charge injection experiment using $V_{\mathit{inj}}=-6\mathrm{V}$ for $2\min$. The abrupt CNT discharge occurring during the scan is indicated by the horizontal arrow. (d1) Topography image ($50\mathrm{nm}$ $z$ scale) of an $18\mathrm{nm}$ diameter MWCNT. The scale bar is $1\mu \mathrm{m}$. (d2) EFM image ($V_{\mathit{EFM}}=-2\mathrm{V}$, $10\mathrm{Hz}$ scale) prior to injection. (d3) Same image after charge injection using $V_{\mathit{inj}}=-6\mathrm{V}$ for $2\min$. Two abrupt discharges occur during scanning from top to bottom. (e1) Topography image ($12\mathrm{nm}$ $z$ scale) of a SWCNT of diameter of $3\mathrm{nm}$. The scale bar is $300\mathrm{nm}$. (e2) EFM image ($V_{\mathit{EFM}}=-3\mathrm{V}$, $20\mathrm{Hz}$ scale) prior to injection. (e3) Same image after charge injection using $V_{\mathit{inj}}=-6\mathrm{V}$ for $2\min$.

Figure 2

(Color online) (a) Plot of the CNT linear charge density (in $e∕\mu \mathrm{m}$) normalized by $V_{\mathit{inj}}$ as a function of the CNT diameter $d_{\mathit{CNT}}$. Experimental data points correspond to charge injection experiments performed in multiwalled and single-walled CNTs with injection voltage $-4\mathrm{V}⩽V_{\mathit{inj}}⩽-10\mathrm{V}$. Experimental linear charge densities have been measured from the ratio between charge and capacitive frequency shifts and then normalized by $V_{\mathit{inj}}$. The top curves correspond to densities expected for metal cylinders. Curve (a) is derived from the cylinder-plane capacitance using a dielectric constant $\epsilon =(1+{\epsilon }_{\mathit{ox}})∕2$. Points in (b) are obtained from three-dimensional Poisson calculations with the EFM tip in contact with the CNT as in Fig. 1a. The line in (b) is a guide to the eye. Finally, curve (c) corresponds to linear charge densities expected from the inner-shell charging of nanotubes as a response to the electric field generated by the EFM tip.

Figure 3

Plot of the linear charge density associated with each shell of a MWCNT that is characterized by an inner and an outer diameter of 6.1 and $10.2\mathrm{nm}$, respectively. The MWCNT is subjected to the same external electric field as in experimental conditions (see inset). The charges are provided by a reservoir representative of the tip that is situated just above the MWCNT at $z=10.2\mathrm{nm}$. These results are obtained by applying the charge-dipole model of Ref. 18. The solid line indicates the results obtained when all shells are metallic. The other results (histograms) are obtained for MWCNTS for which only one shell out of three is metallic (no charge is carried by semiconducting shells). Three MWCNTS have been considered, with the outermost metallic shell, respectively, at the surface of the MWCNT (light gray) and one layer (medium gray) and two layers (dark gray) below the surface.