Modulation of Thermoelectric Power of Individual Carbon Nanotubes

Thermoelectric power (TEP) of individual single walled carbon nanotubes (SWNTs) has been measured at mesoscopic scales using a microfabricated heater and thermometers. Gate electric field dependent TEP modulation has been observed. The measured TEP of SWNTs is well correlated to the electrical conductance across the SWNT according to the Mott formula. Strong modulations of TEP were observed in the single-electron conduction limit. In addition, semiconducting SWNTs exhibit large values of TEP due to the Schottky barriers at SWNT-metal junctions.

Figure 1

(a) The inset shows a scanning electron micrograph of a typical SWNT device used in this study. Two stripe electrodes, $R_n$and $R_f$, contacting the SWNT, are used as thermometers to probe junction temperatures by measuring their four-probe resistance. The graph shows the normalized change in $R_n$ and $R_f$ as a function of the heater current, $I_h$, at $T=300\mathrm{K}$. Changes in resistance are mapped to the change in temperature difference, $\Delta T$, across the SWNT. (b) The thermoelectric voltage measured as a function of $I_h$ at $T=300\mathrm{K}$. Dashed ($a$), dotted ($b$), and solid ($c$) lines correspond to data taken at various applied gate voltages marked by arrows in the inset. The inset shows the conductance of the SWNT as a function of gate voltage.

Figure 2

Measured conductance and TEP (solid line) vs applied gate voltage at $T=300\mathrm{K}$ (a) and 100 K (b). Vertical dashed lines correspond to values of gate voltage where the conductance is extremal. Horizontal dashed lines indicate the offset of TEP matching the small TEP of the metal electrodes. The dotted lines in the lower panel represent the Mott formula calculated from the measured conductance (see text).

Figure 3

(a) Conductance of a metallic SWNT as a function of gate voltage taken at various temperatures. The inset shows the conductance at finite source drain bias voltage ($V_{\mathrm{s}\mathrm{d}}$) in gray scale. The white and black represent 0 and $3\mu \mathrm{S}$, respectively. (b) The corresponding TEP of the SWNT device in (a). The graphs at different temperatures are shifted for clarity. Dashed lines represent $S=0$ for each data set. The inset shows the root-mean-squared TEP ( $S_{\mathrm{r}\mathrm{m}\mathrm{s}}$) calculated from the data set at different temperatures. The dotted line corresponds to a simple fit to $1/T$.

Figure 4

Conductance (upper panel) and TEP (lower panel) versus gate voltage of a semiconducting SWNT device at $T=300\mathrm{K}$. The conductance plot exhibits typical $p$-type SWNT FET behavior. The inset shows the band alignment of the SB model in different regions of the gate voltage.