Modeling study of thermoelectric SiGe nanocomposites

Nanocomposite thermoelectric materials have attracted much attention recently due to experimental demonstrations of improved thermoelectric properties over those of the corresponding bulk material. In order to better understand the reported data and to gain insight into transport in nanocomposites, we use the Boltzmann transport equation under the relaxation-time approximation to calculate the thermoelectric properties of $n$-type and $p$-type SiGe nanocomposites. We account for the strong grain-boundary scattering mechanism in nanocomposites using phonon and electron grain-boundary scattering models. The results from this analysis are in excellent agreement with recently reported measurements for the $n$-type nanocomposite but the experimental Seebeck coefficient for the $p$-type nanocomposite is approximately 25% higher than the model’s prediction. The reason for this discrepancy is not clear at the present time and warrants further investigation. Using new mobility measurements and the model, we find that dopant precipitation is an important process in both $n$-type and $p$-type nanocomposites, in contrast to bulk SiGe, where dopant precipitation is most significant only in $n$-type materials. The model also shows that the potential barrier at the grain boundary required to explain the data is several times larger than the value estimated using the Poisson equation, indicating the presence of crystal defects in the material. This suggests that an improvement in mobility is possible by reducing the number of defects or reducing the number of trapping states at the grain boundaries.

Figure 1

(Color online) Experimental (symbols) and computed (curves) thermoelectric properties of $n$-type bulk ${\text{Si}}_{0.7}{\text{Ge}}_{0.3}$ (data from Ref. 28). Doping concentrations $\left(\times {10}^{19}{\text{cm}}^{-3}\right)$: $◇=0.22$; $△=2.3$; $◻=7.3$; and $○=17$.

Figure 2

(Color online) Experimental (symbols) and computed (curves) thermoelectric properties of $p$-type bulk ${\text{Si}}_{0.7}{\text{Ge}}_{0.3}$ (data from Ref. 51). Doping concentration $\left(\times {10}^{19}{\text{cm}}^{-3}\right)$: $◻=3.4$; $△=8.9$; $◇=18$; $○=24$; and $▽=35$. $\times$ symbols in the $ZT$ figure indicate the accuracy of the data is questionable as the $ZT$ value is much higher than previously reported values for bulk $p$-type ${\text{Si}}_{1-x}{\text{Ge}}_x$.

Figure 3

(Color online) Experimental (symbols) and calculated (curves) thermoelectric properties of state-of-the-art $n$-type bulk ${\text{Si}}_{0.8}{\text{Ge}}_{0.2}$. (Solid line—model including carrier-concentration variation with temperature; dashed line—model without carrier-concentration variation with temperature; dotted lines—electronic and lattice components of thermal conductivity.)

Figure 4

(Color online) Experimental (symbols) and calculated (curve) thermoelectric properties of state-of-the-art $p$-type bulk ${\text{Si}}_{0.8}{\text{Ge}}_{0.2}$. (Solid line—model; dotted lines—electronic and lattice components of thermal conductivity.)

Figure 5

(Color online) Computed results for the electron mean-free path versus electron wavelength (left axis), and percent accumulation of electron occupation number versus electron wavelength (right axis) for $n$-type $\left(N_D\approx 2\times {10}^{20}{\text{cm}}^{-3}\right)$ bulk ${\text{Si}}_{0.8}{\text{Ge}}_{0.2}$ at 300 K.

Figure 6

(Color online) Schematic of the cylinder model for electrical grain-boundary scattering.

Figure 7

(Color online) Calculated mobility for each scattering mechanism (phonon, GB, IIS) and total mobility (curves) with experimental data (symbols) for the $n$-type nanocomposite. (Solid line—total mobility; broken lines—mobility for each scattering mechanism.)

Figure 8

(Color online) Extracted carrier concentration versus temperature for the $n$-type and $p$-type ${\text{Si}}_{0.8}{\text{Ge}}_{0.2}$ nanocomposites.

Figure 9

(Color online) Calculated (curves) and experimental (symbols) thermoelectric properties for the $n$-type nanocomposite (data from Ref. 18). (Solid lines—model including GB scattering; dashed lines—model without GB scattering; dotted lines—electronic and lattice components of thermal conductivity.)

Figure 10

(Color online) Calculated mobility for each scattering mechanism and total mobility (curves) with experimental data (symbols) for the $p$-type nanocomposite. (Solid line—total mobility; broken lines—mobility for each scattering mechanism.)

Figure 11

(Color online) Calculated (curves) and experimental (symbols) thermoelectric properties for the $p$-type nanocomposite (data from Ref. 19) along with the bulk experimental data shown earlier for reference. (Solid lines—model including GB scattering; dashed lines—model without GB scattering; dotted lines—electronic and lattice components of thermal conductivity; dash-dotted line—Seebeck coefficient calculated using the bulk effective mass of $1.2m_e$.)