Intrinsic thermoelectric figure of merit of bulk compositional SiGe alloys: A first-principles study

A systematic study based on state-of-the-art first-principles calculations has been carried out to determine intrinsic thermoelectric properties in $n$- and $p$-type SiGe alloys. Both electronic and thermal transport coefficients have been evaluated using the Boltzmann transport equation, applied on the electronic and phonon band structure, respectively. The Seebeck coefficient, electrical conductivity, and thermal conductivity have been analyzed focusing on the effect of carrier concentration, temperature, and alloy composition. The resulting figure of merit is highest for heavy doping and at elevated temperatures ($>$1000 K) in the SiGe alloy with Ge content from 50% to 80%.

Figure 1

Absolute value of the Seebeck coefficient at 300 K as a function of temperature for $n$-type (solid lines) and $p$-type (dotted lines) ${\mathrm{Si}}_{0.75}{\mathrm{Ge}}_{0.25}$ at various carrier concentrations.

Figure 2

Absolute value of the Seebeck coefficient of $n$-type ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ alloys with varying carrier concentration $N$, Ge content $x$, and temperature $T$.

Figure 3

Electrical conductivity at 300 K as a function of carrier concentration in ${\mathrm{Si}}_{0.75}{\mathrm{Ge}}_{0.25}$ in comparison with previous experimental [9] and theoretical [67] studies. The inset shows a magnified view of the range ${10}^{18}\le N\le {10}^{20} {\mathrm{cm}}^{-3}$ for better visualization of the results.

Figure 4

Electrical conductivity of $n$-type ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ alloys with varying carrier concentration $N$, Ge content $x$, and temperature $T$.

Figure 5

Power factor $\sigma S^2$ as a function of carrier concentration $N$ in $n$-type ${\mathrm{Si}}_{0.75}{\mathrm{Ge}}_{0.25}$ at 300 K (green) and 1000 K (red) in comparison to experimental data for samples close to ${\mathrm{Si}}_{0.7}{\mathrm{Ge}}_{0.3}$ by Dismukes et al. [9] (triangles).

Figure 6

Thermal conductivity in ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ alloys as a function of $x$ at 300 K in comparison to previous experimental [9, 80] and theoretical [16] studies. The inset shows a magnified view of the range $0.1\le x\le 0.9$ for better visualization of the differences in lattice thermal conductivity between various experimental and theoretical studies.

Figure 7

Overall thermal conductivity (${\kappa }_e+{\kappa }_L$) of $n$-type ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ alloys with varying carrier concentration $N$, Ge content $x$, and temperature $T$.

Figure 8

Figure of merit $ZT$ in ${\mathrm{Si}}_{0.75}{\mathrm{Ge}}_{0.25}$ alloys as a function of the carrier concentration $N$ at 300 K (red lines) and 1000 K (green lines) with $n$-type (solid lines) and $p$-type (dotted lines) doping.

Figure 9

Figure of merit of $n$-type ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ alloys with varying carrier concentration $N$, Ge content $x$, and temperature $T$.