Exceptionally Strong Phonon Scattering by B Substitution in Cubic SiC

We use ab initio calculations to predict the thermal conductivity of cubic SiC with different types of defects. An excellent quantitative agreement with previous experimental measurements is found. The results unveil that ${\mathrm{B}}_{\mathrm{C}}$ substitution has a much stronger effect than any of the other defect types in $3C\text{−}\mathrm{SiC}$, including vacancies. This finding contradicts the prediction of the classical mass-difference model of impurity scattering, according to which the effects of ${\mathrm{B}}_{\mathrm{C}}$ and ${\mathrm{N}}_{\mathrm{C}}$ would be similar and much smaller than that of the C vacancy. The strikingly different behavior of the ${\mathrm{B}}_{\mathrm{C}}$ defect arises from a unique pattern of resonant phonon scattering caused by the broken structural symmetry around the B impurity.

Figure 1

Calculated $\kappa$ of $3C\text{−}\mathrm{SiC}$ including, progressively, anharmonic phonon scattering, isotope scattering, grain boundary scattering ( $L_{\text{grain}}=0.8\mu \mathrm{m}$), and different concentrations of defects [ $2.2\times {10}^{20}{\mathrm{cm}}^{-3}$ ${\mathrm{N}}_{\mathrm{C}}$ (0.45%), $8\times {10}^{20}{\mathrm{cm}}^{-3}$ ${\mathrm{N}}_{\mathrm{C}}$ (1.63%), $6.6\times {10}^{20}{\mathrm{cm}}^{-3}$ ${\mathrm{N}}_{\mathrm{C}}$ (1.3%), $2.6\times {10}^{20}{\mathrm{cm}}^{-3}$ ${\mathrm{B}}_{\mathrm{C}}$ (0.5%), and $1.32\times {10}^{21}{\mathrm{cm}}^{-3}$ ${\mathrm{N}}_{\mathrm{C}}$ (2.7%), $1.23\times {10}^{21}{\mathrm{cm}}^{-3}$ ${\mathrm{B}}_{\mathrm{C}}$ (2.5%)]. The experiments are from Morelli et al. [14] and Ivanova et al. [16].

Figure 2

$3C\text{−}\mathrm{SiC}$ $\kappa$ variation with defect concentration for ${\mathrm{Al}}_{\mathrm{Si}}$, ${\mathrm{N}}_{\mathrm{C}}$, ${\mathrm{Vac}}_{\mathrm{C}}$, and ${\mathrm{B}}_{\mathrm{C}}$ defects. The low value of $\kappa$ associated with the ${\mathrm{B}}_{\mathrm{C}}$ defect is related to its anisotropic lattice relaxation seen in the inset (and in the Supplemental Material [20]). The changes in the nearest-neighbour interatomic distances are directly proportional to the bond-width variations shown in the inset.

Figure 3

(a) Phonon DOS of SiC and (b) scattering rates of phonons by different defects (with a concentration of ${10}^{20}{\mathrm{cm}}^{-3}$), isotopes, and phonon-phonon interactions at 300 K.

Figure 4

Frobenius norm of the changes in the on-site IFC submatrices of the atoms ($i$) around the defects with respect to the perfect $3C\text{−}\mathrm{SiC}$ structure as a function of the distance of the atoms from the defect center ($d$).

Figure 5

(a) Trace of the imaginary part of the scattering $\mathbf{T}$ matrix for different impurities, showing a resonance for B and a vacancy. (b) Scattering cross section $\sigma$ for the longitudinal-acoustic mode at an angular frequency of $33\mathrm{rad}/\mathrm{ps}$, as a function of scattering strength for different impurities. Similar resonance peaks for the ${\mathrm{B}}_{\mathrm{C}}$ defect are also seen for transverse-acoustic phonon modes at $\sim 33\mathrm{rad}/\mathrm{ps}$ (see Fig. S4 in the Supplemental Material [20]).