Observation of strong higher-order lattice anharmonicity in Raman and infrared spectra

The fundamental theory of Raman and infrared (IR) linewidth has been well established as the third-order lattice anharmonicity (three-phonon scattering). In this work, we use both rigorous density functional calculations and Raman experiments to find, surprisingly, that the fourth-order anharmonicity universally plays a significant or even dominant role over the third-order anharmonicity at room temperature, and more so at elevated temperatures, for a wide range of materials including diamond, Si, Ge, GaAs, boron arsenide (BAs), cubic silicon carbide ($3C\text{−}\mathrm{SiC}$), and $\alpha$-quartz. This is enabled by the large four-phonon scattering phase space of zone-center optical phonons. Raman measurements on BAs were conducted, and their linewidth verifies our predictions. The predicted infrared optical properties through the Lorentz oscillator model, after including four-phonon scattering, show much better agreement with experimental measurements than those three-phonon-based predictions. Our work advances the fundamental understanding of Raman and IR response and will broadly impact spectroscopy techniques and radiative transport.

Figure 1

$T$ dependence of the phonon linewidth, $2\mathrm{\Gamma }$, of the TO (a) and LO (b) modes in GaAs, with the insets for a better view below 300 K. The solid lines represent the results of the present calculation; the dashed lines denote the calculated result from Ref. [6]; the squares denote experimental data from Ref. [28].

Figure 2

Zone-center optical phonon linewidth in diamond, Si, Ge, BAs, $3C\text{−}\mathrm{SiC}$, and $\alpha$-quartz as a function of $T$. For diamond, Si, and Ge, the solid curves represent the results of the present calculation, and the dashed curves denote the calculated results from Ref. [4]; all symbols denote experimental data from Refs. [32, 33, 34, 35]. For BAs, the solid curves represent the results of our present calculations of the TO phonon linewidth; the black squares and red up triangles denote our Raman measurement for natural abundance and isotope pure BAs, respectively. For $3C\text{−}\mathrm{SiC}$, the solid curves represent our present prediction of the TO phonon linewidth; the black squares denote experimental data from Ref. [36]; the dashed curve represents the calculated result from Ref. [41]. For $\alpha$-quartz, all curves represent our predicted phonon linewidth with (solid lines) and without (dashed lines) ${\tau }_{4,\lambda }^{-1}$ for phonon modes with frequencies of 206, 465, and 1218 ${\mathrm{cm}}^{-1}$, and all symbols denote the experimental data from Refs. [37, 38].

Figure 3

(a) The contribution to ${\tau }_{4,\lambda }^{-1}$ of BAs from different scattering channels. (b) Phonon dispersion of BAs with schematic diagrams of four-phonon scattering processes dominated by recombination channels.

Figure 4

(a) The calculated dielectric function of BAs, $3C\text{−}\mathrm{SiC}$, and $\alpha$-quartz with (red lines) and without (blue lines) ${\tau }_{4,\lambda }^{-1}$ included. Solid lines represent the real part (Re) of dielectric function and dashed lines denote the imaginary part (Im) of dielectric function. (b) The calculated semi-infinite normal reflectance $R$ for BAs at 300 K, $3C\text{−}\mathrm{SiC}$ at 1000 K, and $\alpha$-quartz at 785 K along with available experimental data [38] for comparison.