Phonon sattering by nutral donors in n-type silicon

The scattering of phonons by neutral n-type impurities in silicon is studied. Following Keyes, who determined the phonon relaxation time for scattering by neutral impurities in n-type germanium, the relaxation time for the silicon band structure is developed. This scattering comes about due to the large effect of strain on the hydrogen-like donor ground-state energy level. The change in energy of the ground state due to the strain caused by phonons is calculated and the resulting phonon scattering relaxation rate is derived.     

Numerical Analysis of Heat Transport Behavior in the Ferromagnetic Metallic State of La0.80Ca0.20MnO3 Manganites

The lattice contribution to the thermal conductivity (κ_ph) in La_0.80Ca_0.20 MnO₃ manganites is discussed within the Debye-type relaxation rate approximation in terms of the acoustic phonon frequency and relaxation time. The theory is formulated when heat transfer is limited by the scattering of phonons from defects, grain boundaries, charge carriers, and phonons. The lattice thermal conductivity dominates in La–Ca–MnO manganites and is an artifact of strong phonon-impurity and -phonon scattering mechanisms in the ferromagnetic metallic state. The electronic contribution to the thermal conductivity (κ_e) is estimated following the Wiedemann–Franz law. This estimate sets an upper bound on κ_e, and in the vicinity of the Curie temperature (240 K) κ_e is about 1% of total heat transfer of manganites. Another important contribution in the metallic phase should come from spin waves (κ_m). It is noticed that κ_m increases with a T² dependence on the temperature. These channels for heat transfer are algebraically added and κ_tot develops a broad peak at about 55 K, before falling off at lower temperatures. The behavior of the thermal conductivity in manganites is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between electron, magnon, and phonon contributions. The numerical analysis of heat transfer in the ferromagnetic metallic phase of manganites shows similar results as those revealed from experiments.      

The Relaxation of High Energy Phonons in Anisotropic Distributions in Superfluid 4He

Anisotropic distributions of low energy phonons in momentum space, in superfluid helium, create high energy phonons with energy /k _B>10K. It has been shown that phonons with /k _B>11K cannot decay by the inverse of the process that creates them, if the low energy phonons are in such a momentum cone of 11°. Here we investigate other possible phonon scattering processes that could annihilate high energy phonons. We find that interactions between two high energy phonons, which can create one low and one high energy phonon, is effective. We calculate the scattering rates for all the four phonon processes as functions of momentum of the high energy phonon, cone angle and the temperature of the low energy phonons. We obtain analytic results from which we can understand the physical reasons for all the functional dependencies. The analytic results are in good agreement with our computer evaluations. We show that a dynamic equilibrium number of high energy phonons can be established in a propagating pulse of phonons and the distribution will be suprathermal.     

Effects of the Non Equilibrium Phonons and the Band Non Parabolicity on the Small Signal High Frequency ac Mobility in Narrow Gap Semiconductors in the Extreme Quantum Limit at Low Temperatures

The small signal high frequency ac mobility of the hot electrons in n-HgCdTe and n-InSb has been calculated in the extreme quantum limit at low temperatures considering the non equilibrium phonon distribution as well as the thermal phonon distribution. The energy and the momentum losses of the carriers have been considered due to acoustic phonon scattering via deformation potential and piezoelectric coupling. The ac mobility is found to remain constant up to about 110 GHz for n-HgCdTe and up to about 100 GHz for n-InSb and then it decreases at higher frequencies. The ac mobility for the non equilibrium phonon distribution at lower frequency is found to be higher compared to the thermal phonon distribution and the variation at higher frequency is faster for the thermal phonons. The inclusion of the non equilibrium phonons increases the cut off frequency i.e. the cut off frequency is higher for the non equilibrium phonon distribution. The phase lag of drift velocity is found to increase with the frequency both for the nonequilibrium and the thermal phonon distribution respectively. The influence of the band non parabolicity based on simplified Kane’s model for the extreme quantum limit has also been investigated on the ac mobility of hot electrons and the phase angle. It is observed that at lower frequencies the normalized ac mobility is same both for the parabolic and the non parabolic band but at higher frequencies it is higher for the non parabolic than that of the parabolic band structure. The phase angle increases with frequency and is found to be higher for the parabolic band compared to the non parabolic band. These results can be explained by the Drude theory for ac conductivity.      

An attempt to observe phonon dimensionality crossover effects in the inelastic scattering rate of thin free-standing aluminum films

We compare the inelastic scattering rate in 220-Å-thick free-standing films with nearly identical films on substrates. The scattering rate was determined by fitting the magnetoresistance to theories of quantum transport. Although the films are sufficiently thin so as to modify the three-dimensional spectrum of thermal phonons, we find no significant difference between the scattering rates in free-standing and supported films. While experiments on other materials down to lower temperatures are necessary, we conclude that the cubic temperature dependence of the inelastic scattering rate in these thin aluminum films is not strongly affected by the phonon dimensionality.     

Hierarchical Coherent Phonons in a Superatomic Semiconductor

The coupling of phonons to electrons and other phonons plays a defining role in material properties, such as charge and energy transport, light emission, and superconductivity. In atomic solids, phonons are delocalized over the 3D lattice, in contrast to molecular solids where localized vibrations dominate. Here, a hierarchical semiconductor that expands the phonon space by combining localized 0D modes with delocalized 2D and 3D modes is described. This material consists of superatomic building blocks (Re₆Se₈) covalently linked into 2D sheets that are stacked into a layered van der Waals lattice. Using transient reflectance spectroscopy, three types of coherent phonons are identified: localized 0D breathing modes of isolated superatom, 2D synchronized twisting of superatoms in layers, and 3D acoustic interlayer deformation. These phonons are coupled to the electronic degrees of freedom to varying extents. The presence of local phonon modes in an extended crystal opens the door to controlling material properties from hierarchical phonon engineering.     

Breaking the Minimum Limit of Thermal Conductivity of Mg3Sb2 Thermoelectric Mediated by Chemical Alloying Induced Lattice Instability

Thermal properties strongly affect the applications of functional materials, such as thermal management, thermal barrier coatings, and thermoelectrics. Thermoelectric (TE) materials must have a low lattice thermal conductivity to maintain a temperature gradient to generate the voltage. Traditional strategies for minimizing the lattice thermal conductivity mainly rely on introduced multiscale defects to suppress the propagation of phonons. Here, the origin of the anomalously low lattice thermal conductivity is uncovered in Cd-alloyed Mg₃Sb₂ Zintl compounds through complementary bonding analysis. First, the weakened chemical bonds and the lattice instability induced by the antibonding states of 5p-4d levels between Sb and Cd triggered giant anharmonicity and consequently increased the phonon scattering. Moreover, the bond heterogeneity also augmented Umklapp phonon scatterings. Second, the weakened bonds and heavy element alloying softened the phonon mode and significantly decreased the group velocity. Thus, an ultralow lattice thermal conductivity of ≈0.33 W m⁻¹ K⁻¹ at 773 K is obtained, which is even lower than the predicated minimum value. Eventually, Na_0.01Mg_1.7Cd_1.25Sb₂ displays a high ZT of ≈0.76 at 773 K, competitive with most of the reported values. Based on the complementary bonding analysis, the work provides new means to control thermal transport properties through balancing the lattice stability and instability.     

Superconductivity and electrical resistivity in alkali metal doped fullerides: Phonon mechanism

We consider a two- peak model for the phonon density of states to investigate the nature of electron pairing mechanism for superconducting state in fullerides. We first study the intercage interactions between the adjacent C₆₀ cages and expansion of lattice due to the intercalation of alkali atoms based on the spring model to estimate phonon frequencies from the dynamical matrix for the intermolecular alkali- C₆₀ phonons. Electronic parameter as repulsive parameter and the attractive coupling strength are obtained within the random phase approximation. Transition temperature,T _c, is obtained in a situation when the free electrons in lowest molecular orbital are coupled with alkali-C₆₀ phonons as 5 K, which is much lower as compared to reportedT _c (≈ 20 K). The superconducting pairing is mainly driven by the high frequency intramolecular phonons and their effects enhance it to 22 K. To illustrate the usefulness of the above approach, the carbon isotope exponent and the pressure effect are also estimated. Temperature dependence of electrical resistivity is then analysed within the same model phonon spectrum. It is inferred from the two- peak model for phonon density of states that high frequency intramolecular phonon modes play a major role in pairing mechanism with possibly some contribution from alkali-C₆₀ phonon to describe most of the superconducting and normal state properties of doped fullerides.     

Heat transfer in YBaCuO thin film/sapphire substrate system

The thermal boundary resistance at the YBaCuO thin film/Al₂O₃ substrate interface was investigated. The transparency for thermal phonons incident on the interface as well as for phonons moving from the substrate was determined. We have measured a transient voltage response of current-biased films to continuously modulated radiation. The observed knee in the modulation frequency dependence of the response reflects the crossover from the diffusion regime to the contact resistance regime of the heat transfer across the interface. The values of transparency were independently deduced both from the phonon escape time and from the time of phonon return to the film which were identified with peculiarities in the frequency dependence. The results are much more consistent with the acoustic mismatch theory than the diffuse mismatch model.We are grateful to A. Elantev for helpful discussion. We acknowledge the financial support of the Russian Scientific Council on the HTS problem (Project No. 90462).     

Lattice Dislocations Enhancing Thermoelectric PbTe in Addition to Band Convergence

Phonon scattering by nanostructures and point defects has become the primary strategy for minimizing the lattice thermal conductivity (κ_L) in thermoelectric materials. However, these scatterers are only effective at the extremes of the phonon spectrum. Recently, it has been demonstrated that dislocations are effective at scattering the remaining mid‐frequency phonons as well. In this work, by varying the concentration of Na in Pb_0.97Eu_0.03Te, it has been determined that the dominant microstructural features are point defects, lattice dislocations, and nanostructure interfaces. This study reveals that dense lattice dislocations (≈4 × 10¹² cm^?2) are particularly effective at reducing κ_L. When the dislocation concentration is maximized, one of the lowest κ_L values reported for PbTe is achieved. Furthermore, due to the band convergence of the alloyed 3% mol. EuTe the electronic performance is enhanced, and a high thermoelectric figure of merit, zT , of ≈2.2 is achieved. This work not only demonstrates the effectiveness of dense lattice dislocations as a means of lowering κ_L, but also the importance of engineering both thermal and electronic transport simultaneously when designing high‐performance thermoelectrics.     

Interpretation of Thermal Conductivity in the Ferromagnetic Metallic Phase of La0.83Sr0.17MnO3 Manganites: Scattering of Phonons and Magnons

The lattice contribution to the thermal conductivity (κ _ph) is theoretically analyzed within the framework of Kubo model in La_0.83Sr_0.17MnO₃ manganites. The theory is formulated when thermal conduction is limited by the scattering of phonons from defects, grain boundaries, charge carriers, and phonons. The lattice thermal conductivity dominates in La-Sr-MnO manganites and is artifact of strong phonon-impurity and -phonon scattering mechanism in the ferromagnetic metallic state. The electronic contribution to the thermal conductivity (κ _e) is estimated following Wiedemann-Franz law. This estimate sets an upper bound on κ _e, and in the vicinity of Curie temperature (T _c ) is about 1% of total heat transfer of manganites. Another important contribution in the metallic phase should come from spin waves (κ _m). It is noticed that κ _m increases with a T ² dependence on the temperature. These channels for heat transfer are algebraically added and κ _tot develops a broad peak at about 120 K, before falling off at lower temperatures. The behaviour of the thermal conductivity in manganites is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between electron, magnon, and phonon contributions. The numerical analysis of heat transfer in the ferromagnetic metallic phase of manganites shows similar results as those revealed from experiments.     

Heat Transfer in Solid Solutions Hydrogen-Deuterium

The thermal conductivity of parahydrogen-orthodeuterium solid solutions with the orthodeuterium concentration of 0.01 to 100% has been investigated in the temperature range from 1.8 K to the melting point. The experimental data have been analyzed in terms of the Callaway model. It has been found that the intensity of phonon scattering by isolated orthodeuterium impurities in solid hydrogen is much higher than that in classical crystals. The impurity additional scattering of phonons has been supposed to be due to variations in force constants and lattice distortions in the vicinity of impurity molecules in quantum crystals. The above effects have been quantitatively estimated. The concentration dependences of the thermal conductivity and phonon scattering intensity have been considered.     

Measurements and modeling of the thermal properties of a calorimeter having a sapphire absorber

The response of a magnetic calorimeter with a sapphire crystal serving as an X-ray absorber has been studied as a function of temperature. Several different Au films were used to connect thermally the magnetic sensor to the absorber. The amplitude and time dependence of the signal resulting from the absorption of an X-ray were fit using an idealized model for the calorimeter. The values of the various parameters resulting from a fit of the data are internally consistent and provide a physical understanding of the processes determining the performance of the calorimeter. The fraction of the energy of the X-ray that is captured by the film without having first been down-converted to thermal phonons in the sapphire is found to depend on both the area and the thickness of the film. The rate at which the energy is transferred between thermal phonons in the sapphire and the electrons in the film is determined by the electron/phonon interaction in the gold. Also, an additional heat capacity was observed to be present in the sapphire, which, for want of a better means of characterization, is ascribed to the tunneling systems. The magnitude of this additional heat capacity and its thermal coupling to the lattice has been studied.     

Polaronic Trions at the MoS2/SrTiO3 Interface

The reduced electrical screening in 2D materials provides an ideal platform for realization of exotic quasiparticles, that are robust and whose functionalities can be exploited for future electronic, optoelectronic, and valleytronic applications. Recent examples include an interlayer exciton, where an electron from one layer binds with a hole from another, and a Holstein polaron, formed by an electron dressed by a sea of phonons. Here, a new quasiparticle is reported, “polaronic trion” in a heterostructure of MoS₂/SrTiO₃ (STO). This emerges as the Fröhlich bound state of the trion in the atomically thin monolayer of MoS₂ and the very unique low energy soft phonon mode (≤7 meV, which is temperature and field tunable) in the quantum paraelectric substrate STO, arising below its structural antiferrodistortive (AFD) phase transition temperature. This dressing of the trion with soft phonons manifests in an anomalous temperature dependence of photoluminescence emission leading to a huge enhancement of the trion binding energy (≈70 meV). The soft phonons in STO are sensitive to electric field, which enables field control of the interfacial trion–phonon coupling and resultant polaronic trion binding energy. Polaronic trions could provide a platform to realize quasiparticle‐based tunable optoelectronic applications driven by many body effects.     

Electron-phonon interaction model and prediction of thermal energy transport in SOI transistor

An electron-phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscales. The high electron energy induced by the electric field in a transistor is transferred to the phonon system through electron-phonon interaction in the high field region of the transistor. Due to this fact, a hot spot occurs, which is much smaller than the phonon mean free path in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electron-phonon scattering is modeled through the intervalley and intravalley processes for silicon by introducing average electron energy. The simulation results are compared with those obtained by the full phonon dispersion model which treats the electron-phonon scattering as a volumetric heat source. The comparison shows that the peak temperature in the hot spot region is considerably higher and more localized than the previous results. The thermal characteristics of each phonon mode are useful to explain the above phenomena. The optical mode phonons of negligible group velocity obtain the highest energy density from electrons, and resides in the hot spot region without any contribution to heat transport, which results in a higher temperature in that region. Since the acoustic phonons with low group velocity show the higher energy density after electron-phonon scattering, they induce more localized heating near the hot spot region. The ballistic features are strongly observed when phonon-phonon scattering rates are lower than 4 x 10(10) S(-1).     

Determination of the alloy scattering potential in modulation-doped In<Subscript>0.53</Subscript>Ga<Subscript>0.47</Subscript>As/In<Subscript>0.52</Subscript>Al<Subscript>0.48</Subscript>As heterojunctions from magnetotransport measurements

The results of magnetotransport measurements are used to investigate the scattering mechanisms and hence to determine the alloy disorder scattering potential in modulation-doped In_0.53Ga_0.47As/In_0.52Al_0.48As heterojunction samples with spacer layer thickness in the range from 0 to 400 Å. The experimental data for the temperature dependence of Hall mobility are compared with the electron mobility calculated for major scattering processes by using the theoretical expressions available in the literature. It is found that alloy disorder scattering and polar optical phonon scattering are the dominant scattering mechanisms at low and high temperatures, respectively. However, the effects of acoustic phonon scattering, remote-ionized impurity scattering, background-ionized impurity scattering, and interface roughness scattering on electron mobility are much smaller than that of alloy disorder scattering, at all temperatures. The alloy disorder scattering potential is determined by fitting the experimental data for low-temperature transport mobility of two-dimensional electrons in the first subband of the heterojunction sample with the calculated total mobility.     

Thermal Conductivity of a Molecular Crystal with Rotational Degrees of Freedom: Orientational Defect Scattering

Measurements of thermal conductivity of solid methane-deuteromethane solutions at equilibrium vapor pressure in the temperature range 1.2÷20 K are reported. The obtained dependences of thermal conductivity on temperature and concentration can be explained qualitatively assuming that the dominant mechanism of phonon scattering is connected with the interaction of phonons with the rotational motion of the molecules in all of the three orientational phases of the CH₄-CD₄ system. The contribution of the orientational defect scattering to the thermal conductivity is discussed in frame of the model of local changes in the moments of inertia of molecules.      

The reflection of low energy phonons at the free surface of liquid4He. I. Theory

The scattering of a low energy phonon at the free surface of liquid⁴He at finite temperature is discussed in relation to the reflection measurements in the accompanying paper (II). If not specularly reflected, the phonon may be inelastically scattered, with the emission or absorption of a single ripplon, or it may be absorbed with the emission of two ripplons. The inelastic scattering produces deviations from ideal specular reflection that depend logarithmically on the angular sensitivity of the measurement. For the experiment described in II, the predicted deviations due to scattering and absorption are roughly equal and too small (5×10^–4) to be measured. In addition, there should be a small broadening (less than 1 ° in angle) of the reflected image of the phonon source due to phonon decay in the bulk liquid. This was calculated from the curvature of the phonon spectrum measured by Rugar and Foster. Phonon decay also determines the distribution of the incident phonon beam with respect to energy. From the known decay rate, the average incident phonon energy in our experiment is calculated to be 0.5 K. We also discuss the attenuation of surface second sound due to the inelastic scattering and absorption of thermal phonons at the surface. We find that two ripplon absorption is the dominant effect. Below 0.7 K, the attenuation due to phonons is probably just small enough for pure ripplon surface sound to exist in a narrow range of low frequencies. To show this, we have recalculated the ripplon lifetime using the 3-ripplon interaction as recently revised by Rocheet al. The results for the ripplon lifetime are displayed in a simple scaling format.     

Phonon Interactions in an Anisotropic Phonon System Leading to a Suprathermal Distribution in Liquid 4He

The relaxation rates of high energy phonons are calculated for a highly anisotropic phonon system which can be realised by phonon pulses in liquid ⁴He. We find that the creation rate for these phonons is very much greater than the decay rate over almost all of the momentum range. As a consequence, we have the unusual behaviour of the distribution function, for the high energy phonons, not being the Bose–Einstein distribution function. From our results we expect that the distribution function will be very much greater than the Bose–Einstein one and also to have a quite different momentum dependence. The analytic expressions which are derived, enable us to explain the physical reasons for a suprathermal distribution of high energy phonons which are predicted to occur in highly anisotropic phonon systems.     

Interpretation of Resistivity of Nd1.85Ce0.15CuO4: Electron–Phonon Mechanism

The temperature-dependent normal state resistivity of single crystal Nd_1.85Ce_0.15CuO_{4 ? δ} is theoretically analyzed within the framework of classical electron–phonon i.e., Bloch-Gruneisen model of resistivity. For the reason of inherent acoustic (low frequency) phonons (ω_ac) as well as high-frequency optical phonons (ω_op), the contributions to the resistivity were first derived. The optical phonons of the oxygen breathing mode yields a relatively larger contribution to the resistivity compared to the contribution of acoustic phonons. Estimated contribution to in-plane resistivity by considering both phonons, i.e., ω_ac and ω_op, along with the zero-temperature-limited resistivity, when subtracted from single crystal data infers a quadratic temperature dependence over most of the temperature range [25 ≤ T ≤ 300]. Quadratic temperature dependence of ρ_diff. = [ρ_exp. ? {ρ₀ + ρ_e–ph (=ρ_ac + ρ_op)}] is understood in terms of 3D electron–electron inelastic scattering. The comparison of single crystal experimental data appears favorable with the present analysis.