I. G. Kuleev

Elastic waves in cubic crystals with positive or negative anisotropy of second-order elastic moduli

Elastic waves in cubic crystals are considered. A new classification of cubic crystals is proposed based on their elastic properties. All cubic crystals are shown to be divided into crystals with a positive or negative anisotropy of their second-order elastic moduli. The vibrational-branch spectra of crystals of these two types differ qualitatively in shape. The angular dependences of the polarization vectors are analyzed. The transverse component in quasi-longitudinal vibrations in cubic crystals is shown to be small and can be neglected. The longitudinal component in quasi-transverse modes is not small: its maximum value is 16.5% for Ge and reaches 27% for KCl.

The effect of normal phonon-phonon scattering processes on the maximum thermal conductivity of isotopically pure silicon crystals

The effect of normal phonon-phonon scattering processes on the thermal conductivity of silicon crystals with various degrees of isotope disorder is considered. The redistribution of phonon momentum in normal scattering processes is taken into account within each oscillation branch (the Callaway generalized model), as well as between different oscillation branches of the phonon spectrum (the Herring mechanism). The values of the parameters are obtained that determine the phonon momentum relaxation in anharmonic scattering processes. The contributions of the drift motion of longitudinal and transverse phonons to the thermal conductivity are analyzed. It is shown that the momentum redistribution between longitudinal and transverse phonons in the Herring relaxation model represents an efficient mechanism that limits the maximum thermal conductivity in isotopically pure silicon crystals. The dependence of the maximum thermal conductivity on the degree of isotope disorder is calculated. The maximum thermal conductivity of isotopically pure silicon crystals is estimated for two variants of phonon momentum relaxation in normal phonon-phonon scattering processes.

Normal phonon-phonon scattering processes and the thermal conductivity of germanium crystals with isotope disorder

The influence of the normal phonon-phonon scattering processes on the thermal conductivity was theoretically studied for germanium crystals with various degrees of the isotope disorder. The theory takes into account redistribution of the phonon momentum in the normal scattering processes both inside each oscillation branch (Simons mechanism) and between various phonon oscillation branches (Herring mechanism). Contributions to the thermal conductivity due to the drift mobility of the longitudinal and transverse phonons are analyzed. It is shown that the momentum redistribution between longitudinal and transverse phonons according to the Herring relaxation mechanism leads to a significant suppression of the drift motions (and to the corresponding drop in contribution to the thermal conductivity) of the longitudinal phonons in isotopically pure germanium crystals. The results of the thermal conductivity calculations involving the Herring relaxation mechanism agree well with the experimental data available for germanium crystals with various degrees of the isotope disorder.

Normal processes of phonon-phonon scattering and the drag thermopower in germanium crystals with isotopic disorder

A strong dependence of the thermopower of germanium crystals on the isotopic composition is experimentally found. The theory of phonon drag of electrons in semiconductors with nondegenerate statistics of current carriers is developed, which takes into account the special features of the relaxation of phonon momentum in the normal processes of phonon-phonon scattering. The effect of the drift motion of phonons on the drag thermopower in germanium crystals of different isotopic compositions is analyzed for two options of relaxation of phonon momentum in the normal processes of phonon scattering. The phonon relaxation times determined from the data on the thermal conductivity of germanium are used in calculating the thermopower. The importance of the inelasticity of electron-phonon scattering in the drag thermopower in semiconductors is analyzed. A qualitative explanation of the isotope effect in the drag thermopower is provided. It is demonstrated that this effect is associated with the drift motion of phonons, which turns out to be very sensitive to isotopic disorder in germanium crystals.

Longitudinal-phonon relaxation mechanisms in cubic crystals of germanium, silicon, and diamond

The relaxation rates of thermal and high-frequency longitudinal phonons are calculated using an anisotropic-continuum model. Three-phonon scattering mechanisms (L ↔ L + L, L ↔ T + L) for the phonon relaxation are considered. Anisotropic anharmonic phonon scattering in cubic crystals is described in terms of the second-and third-order elastic moduli. The parameters determining the longitudinal-phonon relaxation rates are found for germanium, silicon, and diamond crystals. The long-wavelength limit and the transition to the isotropic-medium model are considered, and the dependences of the relaxation rates of thermal and high-frequency phonons on temperature and phonon wave vector are analyzed for these crystals.

The possibility of the giant isotope effect for ultrasound absorption in crystals

The effect of isotopic disorder on ultrasound absorption in germanium, silicon, and diamond crystals is considered. The “giant” isotope effect is predicted in the ultrasound absorption coefficient (in contrast to the isotope effect in the thermal conductivity and thermopower) of these crystals. The parameters determining the ultrasound absorption coefficients for the crystals under study with different degrees of isotopic disorder are determined from the known values of elastic moduli of the second and third order. The ultrasound absorption coefficients are analyzed as functions of temperature and wavevector for isotopically modified crystals. The possibility of experimental observation of this effect is considered.

Anisotropic attenuation of transverse ultrasound in cubic crystals of Ge, Si, and diamond with various isotopic compositions

The attenuation of transverse ultrasound in germanium, silicon, and diamond crystals is considered with allowance for competing isotopic and anharmonic scattering processes. The dependence of the attenuation of transverse ultrasound on the direction of the wave vector of quasi-transverse phonons is analyzed within an anisotropic continuum model. The Landau—Rumer mechanism is considered for anharmonic scattering processes. Given the second-and third-order elastic moduli, the parameters are found determining ultrasonic absorption in the above crystals with various degrees of isotopic disorder. The attenuation coefficients of transverse ultrasound associated with isotopic and anharmonic scattering processes are shown to have qualitatively different angular dependences. Therefore, from studying the anisotropic attenuation of ultrasound in cubic crystals, one can determine the dominant mechanism of ultrasonic absorption in isotopically modified crystals.

Reduction in the rate of phonon scattering by a spatially correlated system of iron ions and low-temperature “anomaly” of the thermoelectric phenomena in HgSe:Fe crystals

A new effect of the reduction in the rate of phonon scattering by the spatially correlated system of iron ions in HgSe:Fe crystals is detected experimentally and calculated theoretically. The thermoelectric power is measured using HgSe:Fe samples with different iron content in the temperature range 7.5–60 K. It is found that the dependence of the thermoelectric power on iron content exhibits remarkable features at T<10 K: the quantity |α(NFe)| increases as the iron concentration increases to NFe=5×1018 cm−3, reaches a maximum at NFe≈(1–2)×1019 cm−3, but then monotonically decreases with further increases in NFe. It is shown that the obseved increase in the thermoelectric power is due to a reduction in the rate of phonon scattering by the spatially correlated system of Fe3+ ions. This new effect is analyzed theoretically, and the theoretical results are compared with the experimental data.

Elastic waves and the Landau-Rumer mechanism of relaxation of quasi-transverse phonons in GaAs crystals

The dependences of the relaxation rate and the absorption coefficient of ultrasound in GaAs crystals on the direction of the wave vector of quasi-transverse phonons for the Landau-Rumer mechanism are analyzed in the framework of the anisotropic-continuum model. The calculations are performed with two sets of second-order and third-order elastic moduli experimentally measured by different authors. It is demonstrated that the angular dependences of the relaxation rates of quasi-transverse phonons and the ultrasonic absorption coefficients calculated from these data differ qualitatively. The correctness of the determination of the third-order elastic moduli available in the literature can be checked by measuring the ultrasonic absorption coefficients for GaAs crystals.

Anharmonic scattering processes and relaxation of quasi-transverse modes in cubic crystals with positive or negative anisotropy of second-order elastic moduli

Relaxation of long-wavelength quasi-transverse modes due to anharmonic scattering processes is considered. An anisotropic continuum model is used to analyze the dependence of the relaxation in cubic crystals on the direction of the wave vector of quasi-transverse phonons for the Landau-Rumar mechanism both in the quasi-isotropic approximation and in the case where the cubic anisotropy is rigorously taken into account. The quasi-isotropic approximation is shown to be inadequate for quantitative description of the anisotropy in the relaxation rates of quasi-transverse phonons. It is found that not only the spectra and polarization vectors of phonons but also the angular dependences of the relaxation rates of quasi-transverse vibrational modes are different in cubic crystals with positive and negative anisotropy in the second-order elastic moduli.