Atomistic calculation of the thermoelectric properties of Si nanowires

The thermoelectric properties of 1.6-nm-thick Si square nanowires with $\left[100\right]$ crystalline orientation are calculated over a wide temperature range from 0 K to 1000 K, taking into account atomistic electron-phonon interaction. In our model, the $\left[010\right]$ and $\left[001\right]$ facets are passivated by hydrogen and there are Si-Si dimers on the nanowire surface. The electronic structure was calculated by using the $s{p}^3$ spin-orbit-coupled atomistic second-nearest-neighbor tight-binding model. The phonon dispersion was calculated from a valence force field model of the Brenner type. A scheme for calculating electron-phonon matrix elements from a second-nearest-neighbor tight-binding model is presented. Based on Fermi's golden rule, the electron-phonon transition rate was obtained by combining the electron and phonon eigenstates. Both elastic and inelastic scattering processes are taken into consideration. The temperature dependence of transport characteristics was calculated by using a solution of the linearized Boltzmann transport equation obtained by means of the iterative orthomin method. At room temperature, the electron mobility is 195 ${\mathrm{cm}}^2$ ${\mathrm{V}}^{-1}$ ${\mathrm{s}}^{-1}$ and increases with temperature, while a figure of merit $ZT=0.38$ is reached for n-type doping with a concentration of $n={10}^{19}$ ${\mathrm{cm}}^{-3}$.

Figure 1

Schematic diagram representing the Si NW structure passivated by hydrogen atoms. The Si (H) atoms are represented by large (small) spheres.

Figure 2

The electron band structure computed for the [100]-oriented Si NW with a thickness of 1.6 nm. The graph includes 40 subbands, including degenerate ones. The zero of energy is set to the valence band top of bulk Si.

Figure 3

The phonon band structure computed for the [100]-oriented Si NW with a thickness of 1.6 nm. The graph includes 410 phonon modes. The energy of the Si-H stretch modes is outside the scale of the graph.

Figure 4

The momentum relaxation time ${\tau }_n\left(k\right)$ for the first five electron subbands computed for the [100]-oriented Si NW with a thickness of 1.6 nm at room temperature.

Figure 5

The dependence of the total scattering rate on the electron energy and temperature computed for the [100]-oriented Si NW with a thickness of 1.6 nm.

Figure 6

The dependence of the transport distribution function on the electron energy and temperature computed for the [100]-oriented Si NW with a thickness of 1.6 nm.

Figure 7

The temperature dependence of the electron mobility computed for the [100]-oriented Si NW with a thickness of 1.6 nm and dopant atoms concentration of ${10}^{17}$, ${10}^{18}$, and ${10}^{19}$ ${\mathrm{cm}}^{-3}$.

Figure 8

The temperature dependence of the electrical conductivity computed for the [100]-oriented Si NW with a thickness of 1.6 nm and dopant atoms concentration of ${10}^{17}$, ${10}^{18}$, and ${10}^{19}$ ${\mathrm{cm}}^{-3}$.

Figure 9

The temperature dependence of the Seebeck coefficient computed for the [100]-oriented Si NW with a thickness of 1.6 nm and dopant atoms concentration of ${10}^{17}$, ${10}^{18}$, and ${10}^{19}$ ${\mathrm{cm}}^{-3}$.

Figure 10

The temperature dependence of the electron thermal conductivity computed for the [100]-oriented Si NW with a thickness of 1.6 nm and dopant atoms concentration of ${10}^{17}$, ${10}^{18}$, and ${10}^{19}$ ${\mathrm{cm}}^{-3}$.

Figure 11

The temperature dependence of the figure of merit computed for the [100]-oriented Si NW with a thickness of 1.6 nm and dopant atoms concentration of ${10}^{17}$, ${10}^{18}$, and ${10}^{19}$ ${\mathrm{cm}}^{-3}$.

Figure 12

Position of the first (labeled $\mathit{j})$ and the second (labeled $\mathit{M})$ nearest neighbors of atom $\mathit{i}$.