Spectral phonon thermal properties in graphene nanoribbons

This work provides a comprehensive investigation on the spectral phonon properties in graphene nanoribbons (GNRs) by the normal mode decomposition (NMD) method, considering the effects of edge chirality, width, and temperature. We find that the edge chirality has no significant effect on the phonon relaxation time but has a large influence to the phonon group velocity. As a result, the thermal conductivity of around 707 W/(m K) in the 4.26 nm-wide zigzag GNR at room temperature is higher than that of 467 W/(m K) in the armchair GNR with the same width. As the width decreases or the temperature increases, the thermal conductivity reduces significantly due to the decreasing relaxation times. Good agreement is achieved between the thermal conductivities predicted from the Green–Kubo method and the NMD method. We find that optical phonons dominate the thermal transport in the GNRs while the relative contribution of acoustic phonons to the thermal conductivity is only 10.1% and 13% in the zigzag GNR and the armchair GNR, respectively. Interestingly, the ZA mode is found to contribute only 1–5% to the total thermal transport in GNRs, being much lower than that of 30–70% in single layer graphene.     

High temperature thermal conductivity of free-standing diamond films prepared by DC arc plasma jet CVD

Free-standing diamond films with 1.68 mm in polished thickness have been prepared by DC arc plasma jet CVD. By means of simply changing the placing orientation of diamond films along the laser transmission direction while testing, the through-thickness thermal conductivity (κ_⊥) together with the in-plane (κ_//) thermal conductivity of free-standing diamond films were measured by laser flash technique over a wide temperature range. Results show that the thermal conductivity κ_⊥ and κ_// of free-standing diamond films are up to 1916 and 1739 Wm^− 1 K^− 1 at room temperature, respectively, showing small anisotropy (9%), and following the relationship κ ~ T^− n as temperature rises. The conductivity exhibits similar value compared to that of high-quality single crystal diamond above 500 K for both through-thickness and in-plane directions of CVD diamond films. The effects of impurities and grain boundaries on thermal conductivity of diamond films with increasing temperature were discussed.     

Heat transport across the metal–diamond interface

Thermal conductivity of the aluminium–diamond (Al–diamond) composites, prepared by the gas pressure infiltration method, is measured by steady state technique. A detailed theoretical investigation on the heat conduction mechanism across the Al–diamond interface is presented. It was confirmed that both electrons and phonons actively take part in the flow of heat at the interface. In the Al side, electrons of Al couple with the phonons and carry the heat up to the interface. This electron–phonon pair which predominantly carries heat in the Al, breaks down at the Al–diamond interface. The coupling between phonons of both Al and diamond takes place at the interface which eventually leads the heat conduction across the interface to the diamond. The phonon–phonon coupling across the interface is discussed by scattering mediated acoustic mismatch model (SMAMM). It is shown that for Al–diamond composite, the implementation of the SMAMM yields an interface thermal resistance (ITR) value of 4.44 × 10^− 9 m²K/W, which is in fairly good agreement with values derived from experimental thermal conductivity values of this composite implemented in the Hasselman–Johnson (HJ) mean field scheme.     

Electronic thermal conductivity and thermopower of armchair graphene nanoribbons

A theoretical investigation of the diffusion contribution to thermopower, S_d, and the electronic thermal conductivity, κ_e, of semiconducting armchair graphene nanoribbons (GNRs) is made for T ⩽ 300 K. Considering the electrons to be scattered by edge roughness, impurities and deformation-potential coupled acoustic phonons and optical phonons, expressions for S_d and κ_e are obtained. Numerical calculations of S_d and κ_e, as functions of temperature and linear carrier density, bring out the relative importance of the contributing scattering mechanisms. A GNR of width 5 nm, supporting an electron density 2 × 10⁸ m⁻¹, is found to exhibit room temperature values of S_d and κ_e as 42 μV/K and 26.5 W/mK, respectively. A decrease in armchair GNR width, is found to enhance S_d and reduce κ_e. The effect of varying the electron density is to increase their magnitude when Fermi energy moves into the second subband. An analysis of thermopower and thermal conductivity data in clean armchair GNR samples will enable better understanding of the electron–phonon interaction.     

Improvement of thermoelectric performance of oxygen reduced Sr0.7Ba0.3Nb2O6-δ ceramics by Lanthanides doping

Thermoelectric properties of lantanide doped Sr_0.7Ba_0.3Nb₂O₆ ceramics were investigated in the temperature range from 323 K to 1073 K. A better electrical conductivity is obtained in the sample with larger ionic radius of doping element. Thus, the highest PF value is achieved in La-doped sample. The NbO₂ second phase is counterproductive to reduce the lattice thermal conductivity, so La-doped sample without impurity shows low thermal conductivity. Thus, La-doped sample shows an excellent thermoelectric performance ZT ∼ 0.35. The small average grain size and the nano-sized phases are observed in Gd and Dy doped samples, both of which contribute to scattering phonons, resulting in low thermal conductivities.     

A new estimation method for the intrinsic thermal conductivity of nonmetallic compounds: A case study for MgSiN2, AlN and β-Si3N4 ceramics

A new method for estimating the maximum achievable thermal conductivity of non-electrically conducting materials is presented. The method is based on temperature dependent thermal diffusivity data using a linear extrapolation method enabling discrimination between phonon-phonon and phonon-defect scattering. The thermal conductivities estimated in this way for MgSiN₂, AlN and β-Si₃N₄ ceramics at 300 K equal 28, 200 and 105 W m⁻¹ K⁻¹, respectively in favourable agreement with the highest experimental values of 23, 266 and 106–122 W m⁻¹ K⁻¹. This suggests the general applicability of the proposed estimation method for non-metallic compounds. It is expected that when optic phonons contribute to the heat conduction (as is the case for AlN) the intrinsic thermal conductivity at lower temperatures (e.g. 300 K) is underestimated. However, the reliability and accuracy of the presented ‘easy to use’ estimation method seems to be much better than several other estimation methods. Furthermore the needed input for this method can provide information about which processing parameters should be optimised to obtain the highest thermal conductivity.     

Synthesis of superconducting boron-doped diamond compacts with high elastic moduli and thermal stability

Polycrystalline bulk compacts (3.5–4.0 mm in diameter and 2.5 mm in height) of superconducting boron-doped diamond with high elastic moduli have been synthesized from mixtures of graphite and boron carbide at pressures 8–9 GPa and temperature of 2500 K. We show that graphite-to-diamond transformation in the presence of liquid boron–carbon growth medium leads to formation of polycrystalline diamond matrix at B₄C concentration in the initial mixture ranging from 3.5 to 5%. Resistive transition of the samples to the superconducting state starts at 4 K and ends at 2.2 K. The thermal conductivity of the samples slightly increases in the temperature range of 230 to 400 K, and at room temperature it is as low as ~ 0.4 W/cm K. The boron-doped diamond demonstrates very high oxidation resistance up to 1200 K, and can be used as electrical structural material that can be exploited at elevated temperatures in air.     

Phonon-limited electron mobility in III-nitride heterojunctions

Low-field electron mobility limited by phonons in GaN-, InN- and AlN-based heterojunctions (HJs) for temperatures T < 300 K is studied within the framework of Boltzmann transport formalism by an iterative method. Electrons are assumed to occupy the lowest subband and scattered by the inelastic polar LO phonons and by quasi-elastic acoustic phonons through the deformation potential and piezoelectric couplings. Numerical calculations of the energy dependence of the first-order perturbation distribution function ϕ(E) for the polar LO phonons and of the acoustic phonon relaxation rates τ^− 1(E) bring out the characteristic features of phonon scattering in nitride HJs. The temperature and concentration dependences of phonon-limited mobility are compared with the low-temperature and high-energy relaxation time approximations, commonly used for ϕ. Calculations, taking into account other relevant scattering mechanisms, obtain good agreement with available Hall mobility data for GaN/AlGaN HJ.     

Enhanced thermal conductivity of low-temperature sintered borosilicate glass–AlN composites with β-Si3N4 whiskers

The effects of β-Si₃N₄ whiskers on the thermal conductivity of low-temperature sintered borosilicate glass–AlN composites were systematically investigated. The thermal conductivity of borosilicate glass–AlN ceramic composite was increased from 11.9 to 18.8 W/m K by incorporating 14 vol% β-Si₃N₄ whiskers, and high flexural strength up to 226 MPa were achieved along with low relative dielectric constant of 6.5 and dielectric loss of 0.16% at 1 MHz. Microstructure characterization and percolation model analysis indicated that thermal percolation network formation in the ceramic composites led to the high thermal conductivity. The crystallization of the borosilicate microcrystal glass also contributed to the enhancement of thermal conductivity. Such ceramic composites with low sintering temperature and high thermal conductivity might be a promising material for electronic packaging applications.     

Effect of seeding on the thermal conductivity of self-reinforced silicon nitride

Thermal conductivity of Si₃N₄ containing large β-Si₃N₄ particles as seeds for grain growth was investigated. Seeds addition promotes growth of β-Si₃N₄ grains during sintering to develop the duplex microstructure. The thermal conductivity of the material sintered at 1900 °C improved up to 106 W m⁻¹ K⁻¹, although that of unseeded material was 77 Wm⁻¹ K⁻¹. Seeds addition leads to reduction of the sintering temperature with developing the duplex microstructure and with improving the thermal conductivity, which benefits in terms of production cost of Si₃N₄ ceramics with thermal conductivity. ©     

Quality of diamond wafers grown by microwave plasma CVD: effects of gas flow rate

We found a strong impact of gas flow rate on diamond growth process in a 5 kW microwave plasma chemical vapour deposition reactor operated on CH₄-H₂ gas mixtures. Diamond films of 0.1–1.2 mm thickness and 2.25 in. in diameter were produced at H₂ flow rates varied systematically from 60 sccm to 1000 sccm at 2.5% CH₄. The highest growth rate, 5 μm h⁻¹, was observed at intermediate F values (≈300 sccm). Carbon conversion coefficient (the number of C atoms going from gas to diamond) increases monotonically up to 57% with flow rate decrease, however, this is accompanied with a degradation of diamond quality revealed from Raman spectra, thermal properties and surface morphology. High flow rates were necessary to produce uniform films with thermal conductivity >18 W cm⁻¹ K⁻¹. Diamond disks with very low optical absorption (loss tangent tgδ<10⁻⁵) in millimetre wave range (170 GHz) have been grown at optimized deposition conditions for use as windows for high-power gyrotrons.     

Diamond dispersed Si3N4 composites obtained by pulsed electric current sintering

30 vol.% 2 and 30 μm diamond dispersed Si₃N₄ matrix composites were prepared by pulsed electric current sintering (PECS) for 4 min at 100 MPa in the 1550–1750 °C range. The densification behaviour, microstructure, Si₃N₄ phase transformation and stiffness of the composites were assessed, as well as the thermal stability of the dispersed diamond phase. Monolithic Si₃N₄ with 4 wt% Al₂O₃ and 5 wt% Y₂O₃ sintering additives was fully densified at 1550 °C for 4 min and 60 MPa. The densification and α to β-Si₃N₄ transformation were substantially suppressed upon adding 30 vol.% diamond particles. Diamond graphitisation in the Si₃N₄ matrix was closely correlated to the sintering temperature and grit size. The dispersed coarse grained diamonds significantly improved the fracture toughness of the diamond composite, whereas the Vickers hardness was comparable to that of the Si₃N₄ matrix ceramic. The Elastic modulus measurements were found to be an excellent tool to assess diamond graphitisation in a Si₃N₄ matrix.     

Highly and heavily boron doped diamond films

From the high ionization energy E_i = 0.368 eV and high solid solubility ≥ 1.4 × 10²² cm^− 3 of boron in diamond, metallic conductivity is expected on the boron impurity band within the band gap (Mott model). On the contrary, the numerical models used to describe the superconductivity of metallic diamond mainly use the Bardeen model with a Fermi level within the valence band. Taking into account the decrease to zero of E_i through the high [B] range and the band gap narrowing through the high and heavy [B] ranges, both specific of the Bardeen model, we discuss the validity of the Mott and Bardeen models from the literature and cathodoluminescence and Raman experiments. They agree with the Mott rather than the Bardeen model. Several experiments independently show the coupling of boron related levels with the zone centre optical phonons which soften for heavy [B]. The Mott model might explain the similar range of the superconductivity temperature of homoepitaxial and polycrystalline films from the similarity of their boron impurity band.     

Heat conduction mechanisms in hot pressed ZrB2 and ZrB2–SiC composites

Thermal diffusivity and conductivity of hot pressed ZrB₂ with different amounts of B₄C (0–5 wt%) and ZrB₂–SiC composites (10–30 vol% SiC) were investigated experimentally over a wide range of temperature (25–1500 °C). Both thermal diffusivity and thermal conductivity were found to decrease with increase in temperature for all the hot pressed ZrB₂ and ZrB₂–SiC composites. At around 200 °C, thermal conductivity of ZrB₂–SiC composites was found to be composition independent. Thermal conductivity of ZrB₂–SiC composites was also correlated with theoretical predictions of the Maxwell–Eucken relation. The dominated mechanisms of heat transport for all hot pressed ZrB₂ and ZrB₂–SiC composites at room temperature were confirmed by Wiedemann–Franz analysis by using measured electrical conductivity of these materials at room temperature. It was found that electronic thermal conductivity dominated for all monolithic ZrB₂ whereas the phonon contribution to thermal conductivity increased with SiC contents for ZrB₂–SiC composites.     

Free-standing diamond wafers deposited by multi-cathode,direct-current,plasma-assisted chemical vapor deposition

Free-standing diamond wafers, 100 mm in diameter, have been deposited by the multi-cathode (seven-cathode) direct-current (DC) plasma-assisted chemical vapor deposition (PACVD) method. The input power was 17.5 kW and the pressure was 100 torr. The methane concentration in hydrogen was between 3.5% and 8% at a constant flow rate of 150 sccm. Intrinsic tensile stress was controlled by introducing thermal compressive stress with step-down control of the deposition temperature during diamond deposition. A higher growth rate of 10 μm h⁻¹ was obtained by raising the methane concentration to 8%, and the deposited diamond wafer showed good thermal conductivity of 12–14 W cm⁻¹ K⁻¹. Crack-free, homogeneous and flat diamond wafers with 100 mm diameter were obtainable.     

Thermoelectric transport properties of boron-doped nanocrystalline diamond foils

Natural diamond is known for its outstanding thermal conductivity and electrical insulation. However, synthetic production allows for doping and tailoring microstructural and transport properties. Despite some motivation in the literature and the ongoing search for abundant and non-toxic thermoelectric materials, the first experimental study on a set of eight substrate-free boron-doped nanocrystalline diamond foils is presented herein. All transport coefficients were determined in the same direction within the same foils over a broad temperature range up to 900 °C. It is found that nanostructuring reduces the thermal conductivity by two orders of magnitude, but the mobility decreases significantly to around 1 cm² V⁻¹ s⁻¹, too. Although degenerate transport can be concluded from the temperature dependence of the Seebeck coefficient, charge carriers notably scatter at grain boundaries where sp²-carbon modifications and amorphous boron-rich phases form during synthesis. A detailed analysis of doping efficiency yields an acceptor fraction of only 8–18 at%, meaning that during synthesis excess boron thermodynamically prefers electrically inactive sites. Decent power factors above 10⁻⁴ W m⁻¹ K⁻² at 900 °C are found despite the low mobility, and a Jonker-type analysis grants a deeper insight into this issue. Together with the high thermal conductivity, the thermoelectric figure of merit zT does not exceed 0.01 at 900 °C.     

Thermal conductivity of diamond composites sintered under high pressures

Thermal conductivity at room temperature of diamond composites of two types: with a diamond skeleton and with diamond grains imbedded in a non-diamond matrix was evaluated in dependence of the diamond grain size (d) varied from a ten of microns to 500 μm. The thermal conductivity of the compacts with diamond skeleton obtained in the Cu–diamond system at high pressure of 8 GPa strongly increases with diamond particles size approaching the maximum value of 9 W/cm K at d ≈ 200 μm. The compacts sintered in the Cu–Ti–diamond, Al–Si–diamond and Si–diamond systems at lower pressure (2 GPa) are formed predominantly owing to the presence of the binder. It was found for these conditions that the thermal conductivity is less sensitive to the diamond grain size, reaching the value of 6 W/cm K for the composites with SiC–Si matrix.     

High resolution electron energy loss spectroscopy of hydrogenated polycrystalline diamond: Assignment of peaks through modifications induced by isotopic exchange

In this work we unambiguously determine the origin of the different peaks which appear in the High Resolution Electron Energy Loss Spectrum (HREELS) of hydrogenated polycrystalline diamond films for an incident electron energy of 5 eV and loss energies extending to 700 meV. High quality diamond films deposited by hot filament chemical vapor deposition from various isotopic gas mixtures: ¹²CH₄ + H₂, ¹²CD₄ + D₂, ¹²CH₄ + D₂, ¹²CD₄ + D₂, ¹³CH₄ + H₂ were characterized. The different vibrational modes, fundamentals and overtones, were directly identified through the modifications of the HREEL spectra induced by the isotopic exchange of H by D and ¹²C by ¹³C Three types of peaks were identified: (1) pure C–C related peaks (a diamond optical phonon at ∼ 155 meV and its overtones at 300, 450 and 600 meV), (2) pure C–H related peaks (C–H bend at ∼ 150 meV and C–H stretch of sp³ carbon at 360 meV), (3) coupling of C–H and C–C peaks (510 meV peak due to coupling of the C–H stretch at 360 meV with either the C–C stretch or the C–H bend at ∼ 155 meV). The overtones at 300, 450 and 600 meV (associated with electron scattering at diamond optical phonons) indicate a well defined hydrogenated diamond surface since they are absent in the HREEL spectrum of low energy ion beam damaged diamond surface.     

High thermal conductive diamond/Ag–Ti composites fabricated by low-cost cold pressing and vacuum liquid sintering techniques

Diamond/Ag–Ti composites were fabricated by a low-cost liquid sintering technique. The Ti addition can effectively improve wetting and promote penetration in composite pores during liquid sintering. The interface structure of the diamond/Ag–Ti composite was identified as Ag/TiC/Ag–Ti/diamond. A high thermal conductivity of 719 W/mK was obtained for the 50 vol.% diamond/Ag-1 at.% Ti composite. Using a bimodal mixture (60 vol.% 150 μm + 10 vol.% 50 μm diamond/Ag-2 at.% Ti composite), a low coefficient of thermal expansion of 6.3 × 10^− 6/K still with high thermal conductivity of 687 W/mK was achieved. These composites have potential applications for thermal management of high integration electronic devices.     

Impedance spectroscopy studies on PbFe0.5Nb0.5O3 –BiFeO3 multiferroic solid solution

(1-x) PbFe_0.5Nb_0.5O₃ (PFN) – (x) BiFeO₃ (BFO) (PFN – BFO) multiferroic solid solution (x = 0.1, 0.2, 0.3 and 0.4) were synthesized by single step solid state reaction method. Single phase was confirmed in all the samples through room temperature (RT) X-ray Diffraction (XRD) with monoclinic structure (Cm space group). Transmission Electron Microscopy (TEM) studies confirm the high crystallinity of the materials with the average particle size of 100 nm. The temperature (313–528 K) and frequency (100 Hz – 5 MHz) dependent impedance, modulus and DC conductivity of PFN – BFO solid solutions were investigated. An impedance spectroscopy result shows a significant contribution from the grains (bulk) to the conductivity and exhibits non-Debye type of relaxation. The bulk (grain) resistance reduces as the temperature increases corresponds to negative temperature coefficient of resistance (NTCR) behaviour. Electric modulus exhibits thermally dependent relaxation phenomena in the material. The Bergmann modified KWW function fitted to the imaginary modulus with non-Debye type of relaxation. DC conductivity of PFN – BFO solid solutions was found to follow the Arrhenius behaviour.