Figure 4: Thermopower calculation plotted along with experimental data (black points) from a 20-nm-wide Si nanowire p-type doped at 3 × 10¹⁹ cm^-3.

The black curve is the fitted expression for the total thermopower S_e + S_ph. The red curve is the phonon contribution S_ph and the blue line is the electronic term S_e arising from the fit. The fit has maximum error 6.1 μV K^-1 and root-mean-square error 1.8 μV K^-1. The experimental error bars represent 95% confidence limits and at 150, 200 and 225 K are smaller than the data points. The blue data points are experimental values for bulk wires (doping 2 × 10²⁰ cm^-3; crosses), 10-nm-wide nanowires (doping 7 × 10¹⁹ cm^-3; diamonds), and 20-nm-wide wires (doping 1.3 × 10²⁰ cm^-3; triangles) where only a linear-T electronic contribution was found. This data are close to the extracted electronic contribution from the black data points (blue line) and shows that the fitted linear term is reasonable. The drop in S to 0 as T→0 occurs because the phonon mean free path reaches the sample size and the specific heat tends to 0 according to the third law of thermodynamics. The inset shows the character of a three-dimensional bulk longitudinal acoustic phonon mode (top) and a one-dimensional mode when the wavelength is larger or of the order of the width (bottom). The one-dimensional mode incorporates the existence of the boundary by transverse expansion (or compression) for longitudinal compression (or expansion). The ratio of the transverse strain to the longitudinal strain is the Poisson ratio (0.29 for Si).