Low-temperature thermal rectification by tailoring isotope distributions

We combine first-principles electronic structure calculated thermal conductivity data with a numerical solution of the one-dimensional heat equation to show that an asymmetric distribution of impurity scattering, if suitably designed, yields the conditions for a low-temperature thermal rectification. This happens as a result of the differences in the peaks of the temperature dependence of the thermal conductivity. We demonstrate the effectiveness of the method by probing the thermal rectification rendered by a silicon slab with a steplike position-dependent isotopic composition. The same conclusions are obtained by using experimentally measured values of the thermal conductivity of Si samples with different isotope distributions.

Figure 1

(a) Calculated thermal conductivity as a function of temperature of isotopically purified ${}^{28}\mathrm{Si}$ (black circles) and natural Si (red squares). (b) Thermal conductivity of silicon single crystals along the [100] axis as a function of temperature measured by the steady-state heat flow technique with two thermometers and one heater. Data is shown for natural Si (${}^{\mathrm{nat}}\mathrm{SiA}100$) and for two different levels of isotopic enrichment: ${}^{28}\mathrm{SiA}100$ has 99.995% of ${}^{28}\mathrm{Si}$, 0.0046% of ${}^{29}\mathrm{Si}$, and 0.0004% of ${}^{30}\mathrm{Si}$, while ${}^{28}\mathrm{SiB}100$ has 99.92% of ${}^{28}\mathrm{Si}$, 0.075% of ${}^{29}\mathrm{Si}$, and 0.005% of ${}^{30}\mathrm{Si}$. Reprinted with permission from Ref. [31], copyright 2018 The American Institute of Physics.

Figure 2

Thermal rectification as a function of $T_0=(T_H+T_C)/2$ of a junction made of a segment of length $L_A$ of isotopically purified ${}^{28}\mathrm{Si}$ and a segment of length $L_B$ of natural Si, for different values of $\mathrm{\Phi }=L_A/(L_A+L_B)$ and a thermal bias $\mathrm{\Delta }T=T_H-T_C$ of (a) 10 K and (b) 30 K.

Figure 3

Thermal rectification as a function of $T_0$ for $\mathrm{\Phi }=0.8$ and $\mathrm{\Delta }T=10$ (a) and 30 K (b). We consider different degrees of purity of the isotopically purified side of the junction; we also include a combination of isotopically purified Si and a Si segment with a higher degree of isotopical disorder than natural Si.

Figure 4

Thermal rectification for $T_0=10$ K and $\mathrm{\Delta }T=10$ (a) and 30 K (b) as a function of $\mathrm{\Phi }$ for junctions of Si segments with different degrees of isotopical purity.

Figure 5

Thermal rectification as a function of $T_0$ for a junction made of a segment of ${}^{28}\mathrm{SiA}100$ and a segment of ${}^{\mathrm{nat}}\mathrm{SiA}100$, as defined above, for different values of $\mathrm{\Phi }$ and a thermal bias $\mathrm{\Delta }T=T_H-T_C$ of 10 K (a) and 30 K (b).