Umklapp Processes Research Articles

Carrier concentration effect and other structure-related parameters on lattice thermal conductivity of Si nanowires

Lattice thermal conductivity (LTC) of Si bulk and nanowires (NWs) with diameter 22, 37, 50, 56, 98 and 115 nm was investigated in the temperature range 3–300 K using a modified Callaway model that contains both longitudinal and transverse modes. Using proper equations, mean bond length, lattice parameter, unit cell volume, mass density, melting temperature, longitudinal and transverse Debye temperature and group velocity for all transverse and longitudinal modes were calculated for each NW diameter mentioned. Surface roughness, Gruneisen parameter and impurity were used as adjustable parameters to fit theoretical results with experimental curves. In addition, values of electron concentration and dislocation density were determined. There are some phonon scattering mechanisms assumed, which are Umklapp and normal processes, imperfections, phonon confinement, NW boundaries, electrons scattering and dislocation. Dislocation density less than 10 $$^{{14}}$$ m $$^{{-2}}$$ for NWs and 10 $$^{{12}}$$ m $$^{{-2}}$$ for bulk has no effect on LTC. Also, electron concentration less than 10 $$^{{22}}$$ m $$^{{-3}}$$ for NWs and 10 $$^{{16}}$$ m $$^{{-3}}$$ for the bulk has no effect. On increasing dislocation density and electron concentration, LTC comparably decreases.

Interaction effects in a chaotic graphene quantum billiard

We investigate the local electronic structure of a Sinai-like, quadrilateral graphene quantum billiard with zigzag and armchair edges using scanning tunneling microscopy at room temperature. It is revealed that besides the $(\sqrt{3}\times\sqrt{3})R30${\deg} superstructure, which is caused by the intervalley scattering, its overtones also appear in the STM measurements, which are attributed to the Umklapp processes. We point out that these results can be well understood by taking into account the Coulomb interaction in the quantum billiard, accounting for both the measured density of state values and the experimentally observed topography patterns. The analysis of the level-spacing distribution substantiates the experimental findings as well. We also reveal the magnetic properties of our system which should be relevant in future graphene based electronic and spintronic applications.

Electronic States of Silicene Allotropes on Ag(111).

Silicene, a honeycomb lattice of silicon, presents a particular case of allotropism on Ag(111). Silicene forms multiple structures with alike in-plane geometry but different out-of-plane atomic buckling and registry to the substrate. Angle-resolved photoemission and first-principles calculations show that these silicene structures, with (4×4), (√13×√13)R13.9°, and (2√3×2√3)R30° lattice periodicity, display similar electronic bands despite the structural differences. In all cases the interaction with the substrate modifies the electronic states, which significantly differ from those of free-standing silicene. Complex photoemission patterns arise from surface umklapp processes, varying according to the periodicity of the silicene allotropes.

Interlayer transport through a graphene/rotated boron nitride/graphene heterostructure

Interlayer electron transport through a graphene / hexagonal boron-nitride (h-BN) / graphene heterostructure is strongly affected by the misorientation angle $\theta$ of the h-BN with respect to the graphene layers with different physical mechanisms governing the transport in different regimes of angle, Fermi level, and bias. The different mechanisms and their resulting signatures in resistance and current are analyzed using two different models, a tight-binding, non-equilibrium Green function model and an effective continuum model, and the qualitative features resulting from the two different models compare well. In the large-angle regime ($\theta > 4^\circ$), the change in the effective h-BN bandgap seen by an electron at the $K$ point of the graphene causes the resistance to monotonically increase with angle by several orders of magnitude reaching a maximum at $\theta = 30^\circ$. It does not affect the peak-to-valley current ratios in devices that exhibit negative differential resistance. In the small-angle regime ($\theta < 4^\circ$), Umklapp processes open up new conductance channels that manifest themselves as non-monotonic features in a plot of resistance versus Fermi level that can serve as experimental signatures of this effect. For small angles and high bias, the Umklapp processes give rise to two new current peaks on either side of the direct tunneling peak.

Experimental and modeling evidence for the reduction of thermal conductivity in Mg2Si by fine tuning the nano & micro-structural features

In this paper, experimental and modeling evidence for reduced thermal conductivity in Bi-doped Mg2Si is presented. Upon doping, lattice thermal conductivity was reduced monotonically and, at the same time, MgO content was increased while grain size was decreased. A model has been developed, which takes into account various phonon-scattering mechanisms, the 3-phonon (Umklapp) process, electron-phonon interaction and phonon-scattering by the grain-boundaries or nano-scale MgO inclusions. The model was successfully applied and excellently describes the temperature dependence of lattice thermal conductivity as well as its evolution vs. doping. Application of the model suggests that lattice thermal conductivity is mainly affected by both nano-MgO precipitates and Umklapp processes. Exploring the effect of the grain size and nano-precipitates, our model predicts that the two phonon-scattering mechanisms are interconnected; for a given grain size there is an optimal value for nano-precipitate concentration, and vice-versa. This conclusion may lead to a general approach in the optimization of lattice thermal conductivity in thermoelectric materials, by fine tuning both the nano- as well as the micro-structural features.

Minority Carrier Diffusion Coefficient &lt;i&gt;D&lt;/i&gt;*(&lt;i&gt;B,T&lt;/i&gt;): Study in Temperature on a Silicon Solar Cell under Magnetic Field

This work deals with minority carrier diffusion coefficient study in silicon solar cell, under both temperature and applied magnetic field. New expressions of diffusion coefficient are pointed out, which gives attention to thermal behavior of minority carrier that is better understood with Umklapp process. This study allowed to determine an optimum temperature which led to maximum diffusion coefficient value while magnetic field remained constant.

Temperature Dependence of Anisotropic Thermal‐Conductivity Tensor of Bulk Black Phosphorus

The anisotropic thermal-conductivity tensor of bulk black phosphorus (BP) for 80 ≤T ≤ 300 K is reported. Despite the anisotropy, phonons are predominantly scattered by Umklapp processes in all the crystallographic orientations. It is also found that the phonon mean-free-paths of BP are rather long (up to 1 µm) in the through-plane direction.

Growth and electronic properties of Tb silicide layers on Si(111)

The formation, atomic structure, and electronic properties of Tb silicide layers on the Si(111) surface were studied using scanning tunneling microscopy as well as core-level and angle-resolved photoelectron spectroscopy. For Tb exposures around one monolayer, the formation of a hexagonal TbSi2 monolayer was found, while higher coverages led to the formation of a hexagonal Tb3Si5 multilayer with a 3×3R30° superstructure in the bulk layers. For the monolayer silicide, Si-2p core level spectra show a Fermi level position very close to the conduction band minimum of the silicon substrate, while the Fermi level shifts toward midgap in the multilayer case. The electronic structure of the monolayer is characterized by a Fermi surface consisting of electronlike ellipses around the M¯ points and a holelike state around the Γ¯ point. The effective masses of the band around the M¯ points are strongly anisotropic, with values around 1.45 m0 in the long direction and 0.16 m0 in the short direction of the ellipses. In the case of the multilayer, the ellipses around the M¯ points are less eccentric, and there are indications for Umklapp processes due to the 3×3R30° superstructure in the silicide bulk layers. The overall behavior of Tb is found to be similar to that of other trivalent rare earths on Si(111).

Magnetism and superconductivity in a quasi-2D anisotropic system doped with charge carriers

The theory of multiband superconducting systems with variable density of charge carriers is analyzed. The possibility of emergence of nonphonon high-temperature superconductivity due to the predominance of electron–electron interband interactions over intraband interactions, as well as due to the fact that the thermodynamic and magnetic properties of multiband systems in the superconducting phase differ qualitatively from those of single-band systems, is indicated. Phase transitions in a quasi-2D anisotropic medium upon a change in the carrier concentration, i.e., a transition from the commensurate to the incommensurate state of the spin density wave, are analyzed. Such a transition is observed when the Umklapp processes in the lattice structure are taken into account. These processes facilitate a deviation of wavevector Q of the spin density wave from 2k F , as well as a displacement of the bandgap relative to the Fermi surface. This leads to the generation of free charge carriers and the possibility of superconductivity. It is shown that superconductivity accompanies the magnetism. The conditions for the coexistence of these two phenomena are determined.

The p-wave superconductivity in the presence of Rashba interaction in 2DEG.

We investigate the effect of the Rashba interaction on two dimensional superconductivity. The presence of the Rashba interaction lifts the spin degeneracy and gives rise to the spectrum of two bands. There are intraband and interband pairs scattering which result in the coupled gap equations. We find that there are isotropic and anisotropic components in the gap function. The latter has the form of cos φk where . The former is suppressed because the intraband and the interband scatterings nearly cancel each other. Hence, −the system should exhibit the p-wave superconductivity. We perform a detailed study of electron-phonon interaction for 2DEG and find that, if only normal processes are considered, the effective coupling strength constant of this new superconductivity is about one-half of the s-wave case in the ordinary 2DEG because of the angular average of the additional in the anisotropic gap function. By taking into account of Umklapp processes, we find they are the major contribution in the electron-phonon coupling in superconductivity and enhance the transition temperature Tc.

Lattice Dynamics and Thermal Transport in Superionic Conducting Li7La3Zr2O12 Garnet

Highly conductive solid electrolytes (SE) that are stable in contact with Li and cathodes are required for all solid state battery or high energy Li-S and Li-air batteries. With the advantages of high conductivity (>10-4 S/cm) and excellent stability, Li-stuffed garnet Li7La3Zr2O12 has emerged as one of most promising SEs for Li batteries. Even though the Li ionic dynamics in garnet have been studied extensively, the couplings between Li transport and the vibrations of framework atoms, namely phonons, have seldom been studied, and the controversies in Li transport mechanism and superionic transition have not been settled. In this study, we synthesized phase-pure tetragonal and cubic Li7La3Zr2O12 using a solid state reaction method, and systematically studied their thermal conduction, lattice dynamics, and phase transition. Cubic phase, stabilized by 0.3 mol aluminum, shows much lower thermal conductivity k than that of tetragonal phase, e. g. 1.7 vs. 4.3 W/m-K at 70 K and 1.4 vs. 2.4 W/m-K at 300 K. More specifically, k of cubic phase is almost temperature independent and approaches the amorphous limit, indicating very strong phonon scattering; while the tetragonal phase shows a decreased k with increasing temperature, typical of crystalline solids with the Umklapp processes dominating phonon scatterings. By examining the lattice dynamics and velocity auto–correlation function (VAF) in the cubic phase, we found a high frequency hopping mechanism of Li rather than a liquid-like diffusion mechanism, and Li atoms predominantly contribute to the low energy lattice excitations. This indicates that Li atoms ‘rattle’ intensively in their equilibrium position before hopping to another sites, and the ‘rattling-like’ mode strongly correlate with lattice phonons to block their transport. Moreover, the Li-framework couplings also cause the instability of Li atoms in their positions and promote the hopping responsible for the high ionic conductivity. Our study provides additional understanding of ionic transport mechanism in garnet and insights into thermal management of all solid state batteries.

Thermal rectification and negative differential thermal conductance in harmonic chains with nonlinear system-bath coupling.

Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011)]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.

Influence of the energy-band structure on ultracold reactive processes in lattices

We study theoretically ultracold collisions in quasi one-dimensional optical traps for bosonic and fermionic reactive molecules in the presence of a periodic potential along the trap axis. Elastic, reactive, and umklapp processes due to non-conservation of the center of mass motion are investigated for parameters of relevant experimental interest. The model naturally keeps into account the effect of excited energy bands and is particularly suited for being adapted to rigorous close-coupled calculations. Our formalism shows that a correct derivation of the parameters in tight-binding effective models must include the strong momentum dependence of the coupling constant we predict even for deep lattices.

Globalk-space analysis of electron-phonon interaction in graphene and application toM-point spectroscopy

Recently, optical probes have become available that can access and observe energy renormalization due to electron-phonon interaction in graphene away from the well-studied Dirac $K$ point. Using an expanded deformation potential approach, we present a theoretical study of the electron-phonon self-energy and scattering matrix elements across the entire Brillouin zone. We elucidate the roles of modulated hopping and conventional deformation potential coupling, parameterized via standard deformation potentials, the in-plane phonon modes, intra- and interband contributions, and umklapp processes. Applying the theory to nonlinear optical transmission spectroscopy in the vicinity of the $M$ point, we find very good agreement with recently published experimental data.

Temperature dependence of thermodynamic and electrical properties of CuIrRhS4

We have investigated the thermodynamic and electrical properties of spinel CuIrRhS4. The temperature (T) dependence of the electrical resistivity (ρ) shows metallic behaviour defined as ∂ρ/∂T>0, in the range of 5≤T≤300K. The T dependence of thermal conductivity, κ(T), has a broad peak resulting from the Umklapp process at 35K and increases gradually above 80K with increasing T. κ(T) can be reproduced by the combination of the usual Debye model and the localized-vibrations hopping model. Thermoelectric power, S(T), changes from negative to positive at 32K and gradually increases with increasing T. The positive value of S(T) is due to carrier diffusion, which shows a hole-like band dispersion at the Fermi level. On the other hand, the negative value originates from phonon drag and variable-range hopping. We also estimated the T dependence of the dimensionless figure of merit, ZT, from ρ(T),κ(T), and S(T).

Ultrafast study of phonon transport in isotopically controlled semiconductor nanostructures

AbstractIsotopically modulated silicon and germanium multilayers are analyzed by means of femtosecond spectroscopy and pulsed X‐ray scattering for determining thermal conductivity and phonon modes. Isotopic modulation decreases thermal conductivity stronger than expected from a band bending model in the coherent phonon transport regime, in particular for silicon. Femtosecond spectroscopy and X‐ray scattering resolve zone‐folded vibration modes, which are located at the edge of the new, smaller Brillouin zone due to the multilayer periodicity. These modes can contribute to the reduction of thermal conductivity by Umklapp processes within the zone‐folded mini‐bands.Color‐coded increase in ultrafast X‐ray scattering in vicinity to the mini‐zone boundary of a germanium multilayer.

Magnetic Structure and Thermal Conductivity of FeVO&lt;sub&gt;4&lt;/sub&gt; Multiferroic

Multiferroics are new class of materials, attracting attention because of simultaneous presence of more than one ferroic orders, especially magnetic and ferroelectric ordering [1]. Recently, FeVO 4 has been identified a type II multiferroic, where onset of electric polarization is due to the non-col-linear spin structure at T N2 = 15 K, breaking the spatial inversion symmetry [2, 3]. We synthesized phase pure stoichiometric FeVO 4 bulk sample using solid state reaction route, as explained in Ref. [2]. The structural and microstructural characterizations of the sample were carried out using x-ray diffraction, scanning electron microscopy and x-ray photoelectron spectroscopic measurements, discussed in detail elsewhere [2]. In brief, these measurements confirmed the single phase of FeVO 4 with right valence state for Fe, V and O elements. The grain size of synthesized bulk FeVO 4 , estimated from XRD measurements, varies in the range of 1–2 mm. We carried out temperature-dependent ac magnetic measurements at different frequencies, as shown in Fig. 1. We observed two antiferromagnetic transitions at T N1 ∼ 22 K and T N2 ∼ 15 K, marked by the dashed lines in Fig. 1 for eye view, which consistent with the earlier reports [2, 3]. The magnetic structure at and below 15 K antiferromagnetic transition is complex non-collinear magnetic structure, responsible for breaking spatial inversion symmetry in FeVO 4 . Moreover, we do not observe any frequency dependence for both antiferromagnetic transitions (Fig. 1), suggesting the absence of any magnetic clustering or impurities in FeVO 4 , substantiating x-ray diffraction results. In order to understand the pho-non-magnon coupling in the system, we also measured the temperature-dependent thermal conductivity, k(T) on bulk FeVO 4 pellet, as plotted in Fig. 2a. We found that the value of k decreases quite linearly with decreasing temperature until 70 K, and then starts to increase below 70 K to reach a peak value of about ∼ 0.8 Wm−1K−1 at around 30 K followed by the deep fall below 30 K. This feature is commonly seen in crystalline solids, and the phonon peak usually appears at the temperature when the phonon mean free path is approximately equal to the crystal site distance, attributed to the phonon-phonon Umklapp process. However, its temperature-dependence above 70 K is somewhat different from that of the normal insulators [4], which usually follows 1/T-dependence at high temperatures due to the Umklapp scattering. We also noticed that there is a small slope change at 20 K near to the value of T N1 (see Fig. 1), as indicated in inset of Fig. 2a. The thermal conductivity data was analyzed using the combined Debye-Einstein phonon model with heat conduction from both acoustic (k aph ) and optical phonon (k oph ), and contribution from different phonons is plotted in Fig 2(b) with their sum as the total thermal conductivity. We observed a good fit for the low-temperature data, and the main contribution to the thermal transport is coming from the acoustic phonons below 50 K, whereas optical phonons starts to contribute significantly to heat conduction at relatively higher temperatures above 50 K. Further details about thermal transport and its mechanisms in FeVO 4 will be presented and discussed in the manuscript. Additionally, the observed variation in thermal conductivity near T N1 ∼ 22 K, suggest strong coupling between magnetic ordering and phonons. These results suggest that the phonons are strongly coupled with magnetic ordering in FeVO 4 bulk system and may provide a mechanism for the charge-lattice-spin interactions in this multiferroic material.

An ab initio method for the prediction of the lattice thermal transport properties of oxide systems: Case study of Li2O and K2O

A method for the prediction of the thermal transport properties of macroscopic and isotropic oxides systems, above the standard temperature of T=298.15 K, is presented. This method combines: (i) the kinetic theory, (ii) a thermodynamically self consistent method for the density of the lattice vibration energy, and (iii) the three-phonon umklapp processes for the description of the phonon-phonon scattering. The proposed approach is purely predictive, as no experimental data are required for the model parameterization; they are derived from ground sate electronic structure calculations. Case studies on Li2O and K2O are presented and discussed. The predicted thermal transport properties are found to be in excellent agreement with available experimental data. The thermal conductivity of K2O is found to differ from the thermal conductivity of Li2O by an order of magnitude. This difference is explained in terms of electron localization within the crystal.

Effect of Stone–Wales defects on the thermal conductivity of graphene

The problem of phonon scattering by strain fields caused by Stone–Wales (SW) defects in graphene is studied in the framework of the deformation potential approach. An explicit form of the phonon mean free path due to phonon-SW scattering is obtained within the Born approximation. The mean free path demonstrates a specific q-dependence varying as q−3 at low wavevectors and taking a constant value at large q. The thermal conductivity of graphene nanoribbons (GNRs) is calculated with the three-phonon umklapp, SW and rough edge scatterings taken into account. A pronounced decrease of the thermal conductivity due to SW defects is found at low temperatures whereas at room temperatures and above the phonon–phonon umklapp scattering becomes dominant. A comparison with the case of vacancy defects shows that they play more important role in the reduction of the thermal conductivity in GNRs over a wide temperature range.

Thermal properties of halogen-ethane glassy crystals: Effects of orientational disorder and the role of internal molecular degrees of freedom.

The thermal conductivity, specific heat, and specific volume of the orientational glass former 1,1,2-trichloro-1,2,2-trifluoroethane (CCl2F-CClF2, F-113) have been measured under equilibrium pressure within the low-temperature range, showing thermodynamic anomalies at ca. 120, 72, and 20 K. The results are discussed together with those pertaining to the structurally related 1,1,2,2-tetrachloro-1,2-difluoroethane (CCl2F-CCl2F, F-112), which also shows anomalies at 130, 90, and 60 K. The rich phase behavior of these compounds can be accounted for by the interplay between several of their degrees of freedom. The arrest of the degrees of freedom corresponding to the internal molecular rotation, responsible for the existence of two energetically distinct isomers, and the overall molecular orientation, source of the characteristic orientational disorder of plastic phases, can explain the anomalies at higher and intermediate temperatures, respectively. The soft-potential model has been used as the framework to describe the thermal properties at low temperatures. We show that the low-temperature anomaly of the compounds corresponds to a secondary relaxation, which can be associated with the appearance of Umklapp processes, i.e., anharmonic phonon-phonon scattering, that dominate thermal transport in that temperature range.