Phonon-Phonon Interactions in Strongly Bonded Solids: Selection Rules and Higher-Order Processes

Exposing the hidden influence of selection rules on phonon–phonon scattering by pressure and temperature tuning

“…The κ ( P , T ) of BP and 3C-SiC are calculated using a recently developed unified ab initio theoretical framework, which combines the use of density functional theory to obtain phonon dispersions and phonon scattering rates, with a numerical solution of the phonon Boltzmann transport equation 31 . The theory has no adjustable parameters, and it has demonstrated good agreement with the measured κ of several materials over a broad temperature and pressure range 5 , 18 , 31 – 33 , including BP and 3C-SiC. Both three-phonon and higher-order four-phonon scattering processes are included in the calculations along with phonon scattering by mass disorder arising from the natural isotope mixture on the constituent atoms (naturally occuring boron is 19.9% 10 B, 80.1% 11 B, and phosphorus is 100% 31 P).…”

“…Thus, for a phonon with wave vector, q , and polarization, j , and phonon frequency, ω q j , the phase space of energy and momentum conserving three-phonon scattering corresponds to all processes satisfying 2 – 6 : and , where G is a reciprocal lattice vector. Specific features in these dispersions activate selection rules that can severely restrict the phase space of certain three–phonon scattering channels 2 – 5 , 7 – 13 . Though not arising from underlying symmetries as is the case for other selection rules, the phase space selection rules have a similar effect and can lead to anomalously long phonon lifetimes.…”

“…The influence of this selection rule on κ was long thought to be negligible, since intrinsic thermal resistance is dominated by scattering processes involving phonons in different branches, particularly at higher temperatures. However, it was recently pointed out that, even around and above room temperature (RT; 300 K), this selection rule can be activated in materials whose three acoustic branches come close to each other in some high frequency region of the Brillouin zone 4 , 5 , 12 . Acoustic phonons in such a region then see a severely restricted phase space available for decay into two others (AAA processes).…”

“…First principles calculations 4 predicted an unusually weak AAA scattering in BAs, resulting from activation of the AAA selection rule. Other features in the BAs phonon dispersions open a frequency window in which only the weak AAA scattering occurs 4 , 5 , 12 , 13 . While inclusion of higher-order four-phonon scattering was found to reduce the BAs κ 17 , 18 , a RT value of around 1300 Wm −1 K −1 was predicted, by far the highest κ of any semiconductor, and behind only diamond and graphite among naturally occurring materials.…”

“…Recently, we have identified several other compounds, such as cubic boron phosphide (BP) and silicon carbide (3C-SiC), where the AAA selection rule is activated, giving anomalously weak AAA scattering channels 5 . However, unlike in BAs, for these compounds, the weak AAA scattering is masked by another strong three-phonon scattering channel involving two acoustic phonons and an optic (O) phonon (AAO scattering channel), thus drastically reducing its impact on κ .…”