Figure 1

Gated Si nanoribbon thermoelectric device. (a) Colorized scanning electron micrograph of a device with the same structure as the one measured here. The surface is (110), and the nanowire is oriented along the $[\overline{1}10]$ direction. (b) Perspective schematic diagram of the sample. Inset: The red curve shows the charge distribution in the nanoribbon when the sheet density $n_s=2.15\times {10}^{12}{\mathrm{cm}}^{-2}$. The horizontal lines are the subbands derived from the heavy-hole band; the subbands derived from the light-hole and split-off bands are omitted from the plot, for clarity. The Fermi level is at zero energy.Reuse & Permissions

Figure 2

Thermopower of holes in a gated silicon nanoribbon as a function of $n_s$ and $V_g$ at $T=300\mathrm{K}$ (red), 200 K (black), and $T=100\mathrm{K}$ (blue). Symbols are the measurement; the curves are calculated values (dashed line: diffusion thermopower only, solid line: diffusion and phonon-drag thermopowers combined). During the measurement, the temperature difference $△T$ induced across the nanoribbon is typically below 2 K, and the thermoelectric voltage is measured using a nanovoltmeter with input impedance exceeding $10\mathrm{G}\Omega$. The contribution from the nickel electrodes [30] is subtracted from the results, and it is less than 5% of the total thermopower in all cases.Reuse & Permissions

Figure 3

Characterization of hole sheet density $n_s$ and mobility $\mu$. (a) $n_s$ and $\mu$ as a function of the gate voltage, obtained from Hall measurements on a wide ribbon ($W\times L=50\mu \mathrm{m}\times 500\mu \mathrm{m}$). Inset: Hole mobility as a function of temperature at $V_g=-55\mathrm{V}$. (b) Black curves: $I_d-V_g$ characteristics of the nanoribbon and the $50\mu \mathrm{m}$-wide ribbon, both at a source-drain voltage of 1 V. Blue curves: transconductance $g_m$.Reuse & Permissions

Figure 4

Power factor $S^2/\rho$. (a) Solid symbols show the power factor at $T=300$ (red), 200 (black), and 100 K (blue). Solid curves show the total calculated power factor, including both diffusion and phonon-drag components. Inset: mobility $\mu$ as a function of $n_s$; solid lines: calculation; dashed lines: linear fit. (b) $S^2/\rho$ as a function of the effective three-dimensional hole density $n_{\mathrm{eff}}$ at $T=300\mathrm{K}$ for four cases. Dashed black: doped nanoribbon of thickness 20 nm. Dashed blue: doped nanoribbon of thickness 2 nm. Solid blue: doped nanoribbon of thickness 2 nm with ionized impurity scattering (IIS) removed from the calculation. Solid red: gated nanoribbon corresponding to the experiment. For the cases with doping, $n_{\mathrm{eff}}=N_A$; for the gated nanoribbon, $n_{\mathrm{eff}}=n_s/w$, where $w$ is the effective thickness of the inversion layers, as described in the text.Reuse & Permissions