Electron and phonon transport in silicon nanowires: Atomistic approach to thermoelectric properties

We compute both electron and phonon transmissions in thin disordered silicon nanowires (SiNWs). Our atomistic approach is based on tight-binding and empirical potential descriptions of the electronic and phononic systems, respectively. Surface disorder is modeled by introducing surface silicon vacancies. It is shown that the average phonon and electron transmissions through long SiNWs containing many vacancies can be accurately estimated from the scattering properties of the isolated vacancies using a recently proposed averaging method [Markussen et al., Phys. Rev. Lett. 99, 076803 (2007)]. We apply this averaging method to surface disordered SiNWs in the diameter range of 1–3 nm to compute the thermoelectric figure of merit ZT. It is found that the phonon transmission is affected more by the vacancies than the electronic transmission leading to an increased thermoelectric performance of disordered wires, in qualitative agreement with recent experiments. The largest $\text{ZT}>3$ is found in strongly disordered $⟨111⟩$-oriented wires with a diameter of 2 nm.

Figure 1

Sketch of a wire segment containing three different vacancies, represented by white circles. Each box represents a wire unit cell, and the two neighboring unit cells at each side of a vacancy are slightly modified as compared to the pristine wire unit cell, represented by white boxes.

Figure 2

(Color online) Thermal conductance and electronic transmission for 1.2-nm-diameter $⟨110⟩$ wires. Top row: thermal conductance vs (a) length at $T=300\text{K}$ and vs (b) temperature at $L=75\text{nm}$. Dashed line: long-wire calculations and sample averaging. Solid line: results using Eq. (11). Bottom row: electronic transmission vs energy for (c) holes and (d) electrons. Solid line: pristine wire transmission; single-vacancy estimates with $N_{\text{vac}}=5$ (dotted red curve) and $N_{\text{vac}}=20$ (dashed blue curve). The markers show sample-average results for $N_{\text{vac}}=5$ (red circles) and $N_{\text{vac}}=20$ (blue squares).

Figure 3

(Color online) Cross-sectional (top panel) and side (middle panel) views of $⟨100⟩$-, $⟨110⟩$-, and $⟨111⟩$-oriented wires (from left to right). The wires are oriented along the $z$ axis. Note that we have not plotted the passivating hydrogen atoms. Bottom panel: electronic-band structure around the band gap.

Figure 4

(Color online) Average phonon transmission from Eq. (11) through $D=2.0\text{nm}$ wires containing one (dotted red curve) and ten (dashed blue curve) vacancies. The solid black curve shows the pristine wire transmission.

Figure 5

(Color online) Average hole and electron transmissions from Eq. (11) through $D=2.0\text{nm}$ wires containing one (dotted red curve) and ten (dashed blue curve) vacancies. The solid black curve shows the pristine wire transmission.

Figure 6

(Color online) Calculated ZT values vs chemical potential at $T=300\text{K}$. Solid red curve: $N_{\text{vac}}=10$; dashed blue curve: $N_{\text{vac}}=100$; and dotted black curve: $N_{\text{vac}}=1000$.

Figure 7

(Color online) Diameter dependence of the maximum ZT in $⟨111⟩$ wires with different numbers of vacancies.

Figure 8

(Color online) Diameter dependence of the average weight of the lowest conduction-band electron Bloch state, ${\left|{\psi }_k\left(r_{\text{surf}}\right)\right|}^2$ (circles), and average of all phonon eigenmodes, ${\left|\overline{u}\left(r_{\text{surf}}\right)\right|}^2$ (squares), at the surface atoms in $⟨111⟩$ wires. Notice the log-log scale.