Callaway Model Research Articles

Lattice thermal conduction in cadmium arsenide

Lattice thermal conductivity (LTC) of cadmium arsenide (Cd3As2) is studied over a wide temperature range (1–400 K) by employing the Callaway model. The acoustic phonons are considered to be the major carriers of heat and to be scattered by the sample boundaries, disorder, impurities, and other phonons via both Umklapp and normal phonon processes. Numerical calculations of LTC of Cd3As2 bring out the relative importance of the scattering mechanisms. Our systematic analysis of recent experimental data on thermal conductivity (TC) of Cd3As2 samples of different groups, presented in terms of LTC, κ L, using a nonlinear regression method, reveals good fits to the TC data of the samples considered for T < ∼ 50 K, and suggests a value of 0.2 for the Gruneisen parameter. It is, however, found that for T > 100 K the inclusion of the electronic component of TC, κ e, incorporating contributions from relevant electron scattering mechanisms, is needed to obtain good agreement with the TC data over the wide temperature range. More detailed investigations of TC of Cd3As2 are required to better understand its suitability in thermoelectric and thermal management devices.

Hydrostatic pressure effect on melting temperature and lattice thermal conductivity of bulk and nanowires of indium arsenide

The Morelli–Callaway model was used to calculate the lattice thermal conductivity (LTC) of indium arsenide in both zinc blende and wurtzite phases of bulk and nanowire (NW) forms under applied hydrostatic pressures. Calculations were performed for NWs with diameters of 50, 63, 66, 100, and 148 nm in the temperature range of (0–400) K. The melting temperature and hydrostatic pressure phase diagram of the bulk and NW forms were predicted using the Clapeyron equation. A new method was developed to examine various related parameters, such as bulk modulus and mass density. The influence of pressure on melting temperature, melting enthalpy, melting entropy, surface energy, and stress. Results indicate that the calculated values of group velocity increased with the increase in NW size. The melting temperature dropped sharply with the rise in pressure. The pressure and temperature dependencies of the LTC were obtained, and they decreased with applied hydrostatic pressure.

Electron delocalization enhances the thermoelectric performance of misfit layer compound (Sn1−x Bi x S)1.2(TiS2)2

The misfit layer compound (SnS)1.2(TiS2)2 is a promising low-cost thermoelectric material because of its low thermal conductivity derived from the superlattice-like structure. However, the strong covalent bonds within each constituent layer highly localize the electrons thereby it is highly challenging to optimize the power factor by doping or alloying. Here, we show that Bi doping at the Sn site markedly breaks the covalent bonds networks and highly delocalizes the electrons. This results in a high charge carrier concentration and enhanced power factor throughout the whole temperature range. It is highly remarkable that Bi doping also significantly reduces the thermal conductivity by suppressing the heat conduction carried by phonons, indicating that it independently modulates phonon and charge transport properties. These effects collectively give rise to a maximum ZT of 0.3 at 720 K. In addition, we apply the single Kane band model and the Debye–Callaway model to clarify the electron and phonon transport mechanisms in the misfit layer compound (SnS)1.2(TiS2)2.

Calculated Lattice Thermal Conductivity of Magnetite Thin Films based on Modified Callaway Model

Thermal conductivity is an important parameter for semiconductor materials used in the nanoscale applications. In this study, the lattice thermal conductivity (LTC) of magnetite thin films was simulated by Modified Callaway Model. To fit the experimental data, some quantities, such as mean bond length, the lattice constant, and volume per atom were calculated. Also, the model is based on some other quantities, such as gruneisen parameter, electron concentration, and surface roughness that were found through fitting theoretical with experimental LTC. As a result, this model could work comparably well in all sizes, and the relationship between the fitting parameters and the thickness of the magnetite films was estimated.

Pressure-driven thermoelectric properties of defect chalcopyrite structured ZnGa2Te4: ab initio study.

The pressure induced structural, electronic, transport, and lattice dynamical properties of ZnGa2Te4 were investigated with the combination of density functional theory, Boltzmann transport theory and a modified Debye–Callaway model. The structural transition from I4̄ to I4̄2m occurs at 12.09 GPa. From the basic observations, ZnGa2Te4 is found to be mechanically as well as thermodynamically stable and ductile up to 12 GPa. The direct band gap of 1.01 eV is inferred from the electronic band structure. The quantitative analysis of electron transport properties shows that ZnGa2Te4 has moderate Seebeck coefficient and electrical conductivity under high pressure, which resulted in a large power factor of 0.63 mW m−1 K−2 (750 K). The ultralow lattice thermal conductivity (∼1 W m−1 K−1 at 12 GPa) is attributed to the overlapping of acoustic and optical phonon branches. As a result, the optimal figure of merit of 0.77 (750 K) is achieved by applying a pressure of 12 GPa. These findings support that ZnGa2Te4 can be a potential p-type thermoelectric material under high pressure and thus open the door for its experimental exploration.

Calculation of Lattice Thermal Conductivity for Si Fishbone Nanowire Using Modified Callaway Model

Calculation of Lattice Thermal Conductivity for Si Fishbone Nanowire Using Modified Callaway Model

Unravelling the phonon scattering mechanism in half-Heusler alloys ZrCo1− x Ir x Sb (x = 0, 0.1 and 0.25)

Insight about the scattering mechanisms responsible for reduction in the lattice thermal conductivity (κ L) in half-Heusler alloys (HHA) is imperative. In this context, we have thoroughly investigated the temperature response of thermal conductivity of ZrCo1−x Ir x Sb (x = 0, 0.1 and 0.25). For ZrCoSb, κ L is found to be ∼15.13 W m−1 K−1 at 300 K, which is drastically reduced to ∼4.37 W m−1 K−1 in ZrCo0.9Ir0.1Sb. This observed reduction is ascribed to softening of acoustic phonon modes and point defect scattering, on substitution of heavier mass. However, no further reduction in κ L is observed in ZrCo0.75Ir0.25Sb, because of identical scattering parameter. This has been elucidated based on the Klemen’s Callaway model. Also, in the parent alloy, phonon–phonon scattering mechanism plays a significant role in heat conduction process, whereas in Ir substituted alloys, point defect scattering (below 500 K) and phonon–phonon scattering (above 750 K) are the dominant scattering mechanisms. The minimum κ L is found to be ∼1.73 W m−1 K−1 (at 950 K) in ZrCo0.9Ir0.1Sb, which is the lowest reported value till now, for n-type Zr based HHA. Our studies indicate that partial substitution of heavier mass element Ir at Co-site effectively reduces the κ L of n-type ZrCoSb, without modifying the nature of charge carriers.

Advancing thermoelectrics by vacancy engineering and band manipulation in Sb-doped SnTe–CdTe alloys

A decrease in valence band energy offset can considerably improve the thermoelectric performance of SnTe, and alloying CdTe in SnTe has been confirmed to be efficient for inducing band convergence. However, the low solubility of CdTe in SnTe severely limits the further decrease in the energy offset and the reduction of lattice thermal conductivity. Inspired by the high solubility of Sb in SnTe-based thermoelectric materials, the trivalent Sb is introduced into SnTe–CdTe alloys, aiming at manipulating the thermoelectric transport properties. Combined with the valence band model, it is demonstrated that high concentration of Sb in SnTe–CdTe enables a further optimization in valence band structures, resulting in an improvement in density-of-state effective mass, thus significantly reinforces the power factor in the whole temperature range. Meanwhile, we propose the solid solution mode of Sb in SnTe, which always generates vacancies to balance the valence state, and the introduction of vacancies explains the reduced lattice parameters and almost constant carrier concentration. Particularly, the Debye–Callaway model quantitatively compares the contribution of Sb substitutional defects and vacancy defects. As a result, an enhanced zT of ∼1.1 has been achieved for Sn0.83Cd0.05Sb0.12Te at 823 K. This work clearly shows the critical role of Sb for enhancing the thermoelectric performance of SnTe–CdTe materials.

Optimization of the Intrinsic Electrical and Thermal Transport Properties of Sb2Si2Te6 via Tensile Strain: A First-Principles Study

A promising thermoelectric material, Sb2Si2Te6, which has an intrinsically low thermal conductivity and a considerable figure of merit (ZT) of 1.08 at 823 K, was recently reported. In this work, we study the effect of strain on the electronic structure and electrical transport performance of Sb2Si2Te6 via density-functional calculations. When the out-of-plane tensile strain is applied, the Seebeck coefficient of p-type Sb2Si2Te6 increases due to the flattened electronic dispersion near the valence band edge and the larger DOS effective mass. An enhancement of the power factor along the out-of-plane direction of strained p-type Sb2Si2Te6 is observed in a wide range of carrier concentrations. Meanwhile, the change of lattice thermal conductivity of strained Sb2Si2Te6 is estimated by the modified Debye–Callaway model. The lattice thermal conductivity of Sb2Si2Te6 decreases under out-of-plane tensile strain due to the smaller phonon group velocities and larger Grüneisen parameters.

A transient heat conduction phenomenon to distinguish the hydrodynamic and (quasi) ballistic phonon transport

Previous studies have predicted the failure of Fourier’s law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regimes only by this phenomenon. In this work, the transient heat propagation in homogeneous thermal system is studied based on the phonon Boltzmann transport equation (BTE) under the Callaway model. Given a quasi-one or quasi-two (three) dimensional simulation with homogeneous environment temperature, at initial moment, a heat source is added suddenly at the center with high temperature, then the heat propagates from the center to the outer. Numerical results show that in quasi-two (three) dimensional simulations, the transient temperature will be lower than the lowest value of initial temperature in the hydrodynamic regime within a certain range of time and space. This phenomenon appears only when the normal scattering dominates heat conduction. Besides, it disappears in quasi-one dimensional simulations. Similar phenomenon is also observed in thermal systems with time varying heat source. This transient heat propagation phenomenon of hydrodynamic phonon transport distinguishes it well from (quasi) ballistic phonon transport.

High Thermoelectric Performance of ZnO by Coherent Phonon Scattering and Optimized Charge Transport

AbstractZnO is identified as a potentially attractive n‐type oxide thermoelectric material due to its abundance, nontoxicity, and a high degree of stability. However, working with ZnO is challenging due to its high thermal conductivity from its strong ionic bonds and low electrical conductivity due to its low charge concentrations. Here, it is demonstrated that the electrical and thermal transport properties of ZnO can be simultaneously improved via the successful doping of Al and ZnS coating. The ZnS coating in Al‐doped ZnO is observed and analyzed through microstructure and spectroscopic studies. The power factor for 1% ZnS‐coated Zn0.98Al0.02O is increased to ≈0.75 mW m−1K−2at 1073 K, 161% higher than pure ZnO. This enhancement in the power factor can be explained by the aliovalent Al3+doping and modifications in intrinsic defects, leading to an increased carrier concentration. Interestingly, ZnS coating significantly reduces lattice thermal conductivity to ≈2.31 W m−1K−1at 1073 K for 2% ZnS‐coated Zn0.98Al0.02O, a 62% decrease over pure ZnO. This large reduction in lattice thermal conductivity can be elucidated based on coherent phonon scattering via Callaway's model. Overall, the figure of merit,zT, increases to 0.2 in 2% ZnS‐coated Zn0.98Al0.02O, which is 272% higher than pure ZnO at 1073 K.

Se-induced enhancement of the high-temperature thermoelectric performance of n-type Cu0.008Bi2(Te,Se)3 alloys due to suppressed bipolar conduction

Bipolar conduction in Bi-Te-based alloys is a critical barrier to high conversion efficiency in thermoelectric power generation applications. Herein, we investigate the effect of Te/Se ratio control on bipolar conduction in n-type Cu0.008Bi2(Te,Se)3. Based on the two-band model and Callaway model, we found that electronic and thermal transports of minority carriers (holes) were gradually decreased with an increase in Se content. The high-temperature power factor of Se-rich Cu0.008Bi2Te2.1Se0.9 was higher in value compared to reference Cu0.008Bi2Te2.7Se0.3 due to the weighted mobility ratio increase, and its bipolar thermal conductivity was significantly reduced simultaneously. As a result, a peak figure of merit (zT) of 0.92 was obtained at 440 K in Cu0.008Bi2Te2.1Se0.9.

Quasi-ballistic thermal conduction in 6H–SiC

The minimization of electronics makes heat dissipation of related devices an increasing challenge. When the size of materials is smaller than the phonon mean free paths, phonons transport without internal scattering and laws of diffusive thermal conduction need to be revisited. This work reports the temperature dependent thermal conductivity of doped epitaxial 6H–SiC and monocrystalline porous 6H–SiC below room temperature probed by time-domain thermoreflectance. Strong quasi-ballistic thermal transport was observed in these samples, especially at low temperatures. Doping and structural boundaries were applied to tune the quasi-ballistic thermal transport since dopants selectively scatter high-frequency phonons while boundaries scatter phonons with long mean free paths. Exceptionally strong phonon scattering by boron dopants are observed, compared to nitrogen dopants. Furthermore, orders of magnitude reduction in the measured thermal conductivity was observed at low temperatures for the porous 6H–SiC compared to the epitaxial 6H–SiC. Finally, first principles calculations and a simple Callaway model are built to understand the measured thermal conductivities. Our work sheds light on the fundamental understanding of thermal conduction in technologically-important wide bandgap semiconductors such as 6H–SiC and will impact applications such as thermal management of 6H–SiC-related electronics and devices.

Heat vortices of ballistic and hydrodynamic phonon transport in two-dimensional materials

Heat conduction in solid materials may behave like fluid dynamics when normal (N) scattering dominates phonon transport. In this hydrodynamic regime, the heat vortices have been predicted with frequency-independent relaxation time. So can this phenomena appear in other regimes? And what are the differences? In order to answer these questions, in this work, the heat vortices in two-dimensional materials are investigated based on the frequency-dependent phonon Boltzmann transport equation (BTE) under the Callaway model. We find that apart from the hydrodynamic regime, the heat vortices can appear in the ballistic and other transition regimes, which is a wider window of heat vortices compared to previous study (Fig. 1). The differences of heat vortices in the ballistic and hydrodynamic regime are investigated. In ribbon structure, the vortices sizes increase with system length in the ballistic regime but are confined by the system width in the hydrodynamic regime. In porous structures, the critical values of τR (or τN) about when the heat vortices disappear (or when the vortices size starts to become smaller) are found.

Ultralow Lattice Thermal Conductivity of A0.5RhO2 (A = K, Rb, Cs) Induced by Interfacial Scattering and Resonant Scattering

Recently, superionic conductors featured with melted ionic sublattices have been proved to possess ultralow thermal conductivity, but the underlying physical mechanism is under hot debate. In this article, we report ultralow out-of-plane thermal conductivity (0.4 ∼ 0.6 W m–1 K–1 at 300 K) in A0.5RhO2 (ARO, A = K, Rb, Cs) crystals with a layered structure. Analyzed by the empirical Debye–Callaway model, it reveals that both interfacial scattering and resonant scattering play dominant roles in ultralow thermal conductivity observed in RRO and CRO crystals, while in KRO crystals, resonant scattering is nearly negligible, and both interfacial scattering and three-phonon Umklapp scattering are contributed to the low thermal conductivity. Moreover, the frequency of resonant modes in ARO is dependent on ionic species, which makes it possible to modulate thermal conductivity by intercalation of different ions in the matrix. This work provides crucial information to the physical origin of ultralow thermal conductivity in superionic conductors.

Electronic structure and thermal conductivity of zirconium carbide with hafnium additions

AbstractThe lattice thermal conductivity of ZrC with different Hf contents was investigated theoretically. The density of states and electron density differences were calculated for ZrC and (Zr,Hf)C containing 3.125 or 6.25 at% Hf. It was found that the electronic structure did not change significantly with the Hf additions. Lattice thermal conductivities were calculated for all of the compositions by combining first‐principles calculations with the Debye–Callaway model. The theoretical lattice thermal conductivity of ZrC was 68 W·m−1·K−1 at room temperature. When adding 3.125 and 6.25 at% Hf into ZrC, the lattice thermal conductivities decreased to 18 and 15 W·m−1·K−1, respectively. The mechanism for the decreased conductivity is that with the addition of Hf impurities, the frequency of the acoustic phonons decreased, which resulted in decreases in the Debye temperature and lattice thermal conductivity.

Thermal conductivity reduction in GaSb1-xTex (0 ≤ x ≤ 0.12) thermoelectric materials

XSb (X = Ga, In) based thermoelectric (TE) materials have received much attention due to the high electronic performance. However, the high lattice thermal conductivity limits further TE performance enhancement. In this work, GaSb1-xTex (x ≤ 0.12) compounds were prepared to investigate the effect of Ga vacancies induced by Te doping on the lattice thermal conductivity. The room temperature lattice thermal conductivity decreases significantly from ~24 Wm−1K−1 for GaSb to ~3.4 Wm−1K−1 for GaSb0.88Te0.12. The Callaway model was used to analyze the detailed phonon scattering mechanism. The effect of each scattering mechanism at different phonon frequencies and temperatures are investigated. The lattice thermal conductivity reduction due to vacancies combined with isoelectronic substitution is predicted. These results are of importance for further TE performance enhancement of the XSb (X = Ga, In) based TE materials.

Modified callaway model calculations for lattice thermal conductivity of a 20 nm diameter silicon nanowire

The modified Callaway model is used to calculate Lattice Thermal Conductivity (LTC) for (20-nm) silicon nanowires diameter in the temperature range from 2K to 800K. Acoustic phonon mode and group velocity in the calculations are modified by spatial confinement of phonons with that of the boundary effects. All important scattering rates such as Umklapp, Mass difference, Resonance, and Boundary are calculated at room temperature. Room temperature LTC for this diameter is about only 10.23% of its bulk value. Numerical evaluation is also investigated and the results are compared to that of the reported experimental as well as theoretical data.

Se-Induced Enhancement of the High-Temperature Thermoelectric Performance of &lt;i&gt;n&lt;/i&gt;-type Cu &lt;sub&gt;0.008&lt;/sub&gt;Bi &lt;sub&gt;2&lt;/sub&gt;(Te,Se) &lt;sub&gt;3&lt;/sub&gt; Alloys Due to Suppressed Bipolar Conduction

Bipolar conduction in Bi-Te-based alloys is a critical barrier to high conversion efficiency in thermoelectric power generation applications. Herein, we investigate the effect of compositional tuning of Te/Se ratio on bipolar conduction in n-type Cu0.008Bi2(Te,Se)3 alloys. Based on the two-band model and Callaway model, we found that electronic and thermal transports of minority carriers (holes) were gradually decreased with an increase in Se content. The high-temperature power factor of Se-rich Cu0.008Bi2Te2.1Se0.9 was higher in value compared to reference Cu0.008Bi2Te2.7Se0.3 due to the weighted mobility ratio increase, and its bipolar thermal conductivity was significantly reduced simultaneously. As a result, a peak figure of merit (zT) of 0.92 was obtained at 440 K in Cu0.008Bi2Te2.1Se0.9.

Non-Monotonic Thickness Dependent Hydrodynamic Phonon Transport in Layered Titanium Trisulphide: First-Principles Calculation and Improved Callaway Model Fitting

Non-Monotonic Thickness Dependent Hydrodynamic Phonon Transport in Layered Titanium Trisulphide: First-Principles Calculation and Improved Callaway Model Fitting