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.     

Effect of isotopic composition on the linear thermal expansion coefficient of a germanium crystal lattice

Features of the thermal expansion coefficient α(T) of crystal lattices with different isotopic compositions have been analyzed. The case of germanium lattices has been studied in detail. Zh. éksp. Teor. Fiz. 114, 654–668 (August 1998)     

Effect of normal processes on thermal conductivity of germanium,silicon and diamond

The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch — KK-S model and (b) between different phonon branches — KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.      

Isotope effect in the thermal conductivity of germanium single crystals

The thermal conductivity of chemically, structurally, and isotopically highly pure germanium single crystals is investigated experimentally in the temperature range from 2 to 300 K. It is found that the thermal conductivity of germanium enriched to 99.99% ⁷⁰Ge is 8 times higher at the maximum than the thermal conductivity of germanium with the natural isotopic composition. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 463–467 (25 March 1996)     

Phonon thermal conductivity of amorphous selenium doped by germanium

The thermal conductivity of the amorphous semiconducting system Se-Ge in the temperature range of 100 to 300°K was measured. The Debye model was used for the analysis of the experimental values and the calculated mean free path of phonons was related to the size of the basic structure units of the selenium glass. The shift of the thermal conductivity of amorphous selenium doped with germanium was explained by means of the increase of the velocity of sound observed together with the occurrence of the covalent bond Se-Ge between the basic structure units of the studied amorphous system.     

Low-temperature thermal conductivity of highly enriched and natural germanium

Experimental data on the thermal conductivity K(T) of crystals of natural and highly enriched germanium (99.99%) ⁷⁰Ge with lapped and polished surfaces are analyzed in the temperature range ∼1.5–8 K. In all the samples in the temperature range ∼1.5–4 K the standard boundary mechanism of scattering dominates. As the temperature is raised, an isotopic scattering mechanism is observed in the natural samples. In the highly enriched samples the theoretical values of K(T) turn out to be much smaller than the experimental ones. It is conjectured that a Poiseuille viscous flow regime of the phonon gas emerges in this case. Zh. éksp. Teor. Fiz. 114, 1757–1764 (November 1998)     

Molecular-dynamics calculation of the thermal conductivity coefficient of the germanium single crystal

The thermal conductivity coefficient of the germanium crystal lattice has been calculated by molecular dynamics simulation. Calculations have been performed for both the perfect crystal lattice and the crystal lattice with defects such as monovacancies. For the perfect germanium single crystal, the dependence of the thermal conductivity coefficient on the lattice temperature has been obtained in the temperature range of 150–1000 K. The thermal conductivity coefficient of the germanium lattice has been calculated as a function of the monovacancy concentration.     

Characteristic features of the low-temperature thermal conductivity of highly-enriched and natural germanium

Experimental data on the thermal conductivity K(T) of natural and highly enriched (99.99%) Ge⁷⁰ crystals with ground and polished surfaces are analyzed in the temperature interval ∼2–8 K. In all samples, the boundary scattering mechanism predominates in the interval from 2 to 4.0 K. As temperature increases, in highly enriched samples N processes start to contribute to phonon transport and the behavior of K(T) corresponds to viscous Poiseuille flow of a phonon gas. The isotopic scattering mechanism plays a large role in isotopically nonideal samples. Fiz. Tverd. Tela (St. Petersburg) 40, 1604–1607 (September 1998)     

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.     

On the thermal conductivity of diamond under changes to its isotopic character

We show that the 50% increase of the room-temperature thermal conductivity of single-crystal diamond [1] upon increasing its isotopic purity is unlikely to be due to a decrease in phonon-isotope scattering alone. In addition, removal of the¹³C isotope can sharpen the phonon dispersion in a heretofore unappreciated way and thereby decrease the phonon-phonon Umklapp scattering enough to cause the observed results. In addition, the order-of-magnitude increase [1] in the UV damage threshold in the isotopically purer diamond is probably caused by similar effects. In fact, all physical processes wherein phonon wave-vector or energy thresholds are important should be affected by this mechanism.     

The solution of the kinetic equation for phonon heat conductivity by the method of momenta and the influence of isotopic disorder on phonon heat conductivity of germanium and silicon crystals at T=300 K

The problem of solving the kinetic equation for the heat conductivities of dielectric substances and semiconductors by the method of momenta is discussed. Microscopic models are used to estimate the effect of isotopic disorder on the thermal resistance of germanium crystals in the multimomentum approximation. The contributions of acoustic and optical phonons are taken into account. Excess thermal resistance ΔW of samples with a natural isotopic composition compared with highly enriched samples is calculated. For germanium, the theoretical and experimental Δ W values are in close agreement with each other. For silicon, the theoretical ΔWvalue is much smaller than its experimental excess thermal resistance.     

Effect of thermal conductivity on ultrasonic attenuation in praseodymium monochalcogenides

The ultrasonic attenuation in intermetallic praseodymium monochalcogenides are evaluated in the temperature interval 100–500 K along the crystallographic directions 〈100〉, 〈110〉, and 〈111〉 for longitudinal and shear waves. A comparison has been made with lanthanum monochalcogenides and other similar materials. Ultrasonic attenuation at different temperatures is mainly affected by the lattice thermal conductivity values of the materials at these temperatures. Thermoelastic loss is very small in comparison to the attenuation due to phonon-phonon interaction mechanism at higher temperatures.     

Laser-stimulated conductivity of amorphous germanium films

It is shown that metastable states are created in evaporated -Ge films by laser irradiation. The lifetime of the metastable state is a strong function of the incident laser power density.Supported by IRSIA (Brussels)     

Effect of phonon focussing on thermal conductivity of silicon

Thermal conductivity of a cubic crystal in the boundary scattering regime is calculated, taking into account the difference between the phonon phase and group velocities. Numerical estimates in the case of silicon indicate appreciable anisotropy in conductivity as a result of phonon focussing, its maximum value being about 90% larger than the minimum. The contributions of the individual polarization branches are found to be more strongly dependent on direction than the total conductivity. It is further observed that the angle between the phonon phase and group velocities can be sometimes as large as 10°, 24° and 18° in the case of the longitudinal and the two transverse acoustic branches, respectively.     

Effect of dislocations on the lattice thermal conductivity of superconducting niobium

Thermal conductivity measurements on single crystal Nb samples in the superconducting state have demonstrated a resonant scattering of thermal phonons at roughly 5 × 10¹⁰Hz. The assumption of a mechanical resonance associated with the dislocation structure accounts for the present data and is consistent with other data found in the literature. The thermalization of phonons at an abraded sample surface, and the attendant failure of the relation l^?1 = ∑_jl_j^?1 for phonon mean free paths, was also observed.     

Effect of structural features on the thermal conductivity of SiGe-based materials

On the basis of the experimental data concerning interactions between humans the process of epidemic spreading in a social network was investigated. It was found that number of contact and average age of nearest neighbors are highly correlated with age of an individual. The influence of those correlations on the process of epidemic spreading and effectiveness of control measures like mass immunizations campaigns was investigated. It occurs that the magnitude of epidemic is decreased and the effectiveness of target vaccination is increased.     

Effect of multipolar interaction on the effective thermal conductivity of nanofluids

Nanofluids or liquids with suspended nanoparticles are likely to be the future heat transfer media, as they exhibit higher thermal conductivity than those of liquids. It has been proposed that nanoparticles are apt to congregate and form clusters, and hence the interaction between nanoparticles becomes important. In this paper, by taking into account the interaction between nearest-neighbour inclusions, we adopt the multiple image method to investigate the effective thermal conductivity of nanofluids. Numerical results show that then the thermal conductivity ratio between the nanoparticles and fluids is large, and the two nanoparticles are close up and even touch, and the point-dipole theory such as Maxwell--Garnett theory becomes rough as many-body interactions are neglected. Our theoretical results on the effective thermal conductivity of CuO/water and Al$_{2}$O$_{3}$/water nanofluids are in good agreement with experimental data.     

Effect of triangular vacancy defect on thermal conductivity and thermal rectification in graphene nanoribbons

We investigate the thermal transport properties of armchair graphene nanoribbons (AGNRs) possessing various sizes of triangular vacancy defect within a temperature range of 200–600 K by using classical molecular dynamics simulation. The results show that the thermal conductivities of the graphene nanoribbons decrease with increasing sizes of triangular vacancy defects in both directions across the whole temperature range tested, and the presence of the defect can decrease the thermal conductivity by more than 40% as the number of removed cluster atoms is increased to 25 (1.56% for vacancy concentration) owing to the effect of phonon–defect scattering. In the meantime, we find the thermal conductivity of defective graphene nanoribbons is insensitive to the temperature change at higher vacancy concentrations. Furthermore, the dependence of temperatures and various sizes of triangular vacancy defect for the thermal rectification ration are also detected. This work implies a possible route to achieve thermal rectifier for 2D materials by defect engineering.