scholarly journals Hydrodynamic Approach to Electronic Transport in Graphene: Energy Relaxation

2021 ◽  
Vol 9 ◽  
Author(s):  
B. N. Narozhny ◽  
I. V. Gornyi
Keyword(s):  
Phonon Scattering ◽  
Local Equilibrium ◽  
Energy Relaxation ◽  
Weak Decay ◽  
Electron Phonon Interaction ◽  
Hydrodynamic Approach ◽  
Continuity Equations ◽  
Viscous Hydrodynamics ◽  
Electron Phonon Scattering ◽  
Number Of Particles

In nearly compensated graphene, disorder-assisted electron-phonon scattering or “supercollisions” are responsible for both quasiparticle recombination and energy relaxation. Within the hydrodynamic approach, these processes contribute weak decay terms to the continuity equations at local equilibrium, i.e., at the level of “ideal” hydrodynamics. Here we report the derivation of the decay term due to weak violation of energy conservation. Such terms have to be considered on equal footing with the well-known recombination terms due to nonconservation of the number of particles in each band. At high enough temperatures in the “hydrodynamic regime” supercollisions dominate both types of the decay terms (as compared to the leading-order electron-phonon interaction). We also discuss the contribution of supercollisions to the heat transfer equation (generalizing the continuity equation for the energy density in viscous hydrodynamics).

Electron–phonon interaction in P-, As-, and Sb-doped germanium in the intermediate concentration region

1980 ◽  
Vol 58 (9) ◽  
pp. 1268-1274 ◽  
Author(s):  
V. Radhakrishnan ◽  
P. C. Sharma
Keyword(s):  
Thermal Conductivity ◽  
Conduction Band ◽  
Phonon Scattering ◽  
Metallic State ◽  
Deformation Potential ◽  
Concentration Region ◽  
Electron Phonon Interaction ◽  
Impurity Atoms ◽  
Intermediate Concentration ◽  
Electron Phonon Scattering

The electron–phonon scattering, in the analysis of low temperature thermal conductivity of n-type germanium, is studied in the intermediate donor concentration region. At low concentrations, below metal–insulator transition, the donor electrons are bound to the impurity atoms, and at high concentrations they are free in conduction band. The properties in the intermediate concentration are explained by Mikoshiba's "inhomogeneity model". According to this model, the electrons are in a mixed state both in non-metallic and metallic state. The electron concentrations in the non-metallic and metallic regions are calculated for each sample and the theory of both bound electron–phonon scattering and free electron–phonon scattering are applied. This theory of mixed electron–phonon scattering explains the thermal conductivity results of P-, As-, and Sb-doped germanium samples between 1 and 20 K for intermediate donor concentrations from 1.1 × 1017 to 5.6 × 1017 cm−3. The values of density-of-states effective mass are kept constant (= 0.22) without variation with temperature. The values of shear and dilatation-deformation potential constants are obtained from our calculations. The values of shear-deformation potential for the electrons in the bound region are found to be between 14 and 16 eV, while the values of dilatation-deformation potential are between 1 and 3.5 eV for the electrons in the conduction band and these values are in agreement with the experimentally measured values.

Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

2007 ◽  
Vol 7 (11) ◽  
pp. 4094-4100 ◽  
Author(s):  
Jae Sik Jin ◽  
Joon Sik Lee
Keyword(s):  
Energy Density ◽  
Group Velocity ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Dispersion Model ◽  
Hot Spot ◽  
Interaction Model ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering

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 × 1010 s−1.

Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

2007 ◽  
Vol 7 (11) ◽  
pp. 4094-4100
Author(s):  
Jae Sik Jin ◽  
Joon Sik Lee
Keyword(s):  
Energy Density ◽  
Group Velocity ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Dispersion Model ◽  
Hot Spot ◽  
Interaction Model ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering

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 × 1010 s−1.

Coupled Non-Equilibrium Green’s Function (NEGF) Electron-Phonon Interaction in Thermoelectric Materials

2011 ◽  
Author(s):  
T. D. Musho ◽  
D. G. Walker
Keyword(s):  
Thermoelectric Materials ◽  
Thermal Transport ◽  
Phonon Scattering ◽  
Computational Method ◽  
Direct Result ◽  
Inelastic Electron ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering ◽  
Non Equilibrium

Over the last decade, nano-structured materials have shown a promising avenue for enhancement of the thermoelectric figure of merit. These performance enhancements in most cases have been a direct result of selectively modifying certain geometric attributes that alter the thermal or electrical transport in a desirable fashion. More often, models used to study the electrical and/or thermal transport are calculated independent of each other. However, studies have suggested electrical and thermal transport are intimately linked at the nanoscale. This provides an argument for a more rigorous treatment of the physics in an effort to capture the response of both electrons and phonons simultaneously. A simulation method has been formulated to capture the electron-phonon interaction of nanoscale electronics through a coupled non-equilibrium Greens function (NEGF) method. This approach is unique because the NEGF electron solution and NEGF phonon solution have only been solved independently and have never been coupled to capture a self-consistent inelastic electron-phonon scattering. One key aspect of this formalism is that the electron and phonon description is derived from a quantum point of view and no correction terms are necessary to account for the probabilistic nature of the transport. Additionally, because the complete phonon description is solved, scattering rates of individual phonon frequencies can be investigated to determine how electron-phonon scattering of particular frequencies influences the transport. This computational method is applied to the study of Si/Ge nanostructured superlattice thermoelectric materials.

scholarly journals A COMPARISON OF THE RESISTIVITY BEHAVIOR OF MgB2, AlB2 AND AgB2 SYSTEMS

2006 ◽  
Vol 20 (16) ◽  
pp. 989-994 ◽  
Author(s):  
R. LAL ◽  
V. P. S. AWANA ◽  
K. P. SINGH ◽  
R. B. SAXENA ◽  
H. KISHAN ◽  
...  
Keyword(s):  
Phonon Scattering ◽  
Weak Localization ◽  
Impurity Scattering ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Maximum Minimum ◽  
Electron Phonon Scattering

Measurements have been performed on the resistivity of samples MgB 2, AlB 2 and AgB 2. The samples show presence of impurities. By analyzing the data in terms of impurity scattering, electron-phonon scattering, and weak localization, it has been found that the AlB 2 ( AgB 2) sample involves maximum (minimum) effect of the impurity, electron-phonon interaction and weak localization.

Electron–phonon scattering limited hole mobility at room temperature in a MoS2 monolayer: first-principles calculations

2019 ◽  
Vol 21 (41) ◽  
pp. 22879-22887 ◽  
Author(s):  
Fei Guo ◽  
Zhe Liu ◽  
Mingfeng Zhu ◽  
Yisong Zheng
Keyword(s):  
Room Temperature ◽  
Phonon Scattering ◽  
Hole Mobility ◽  
Interaction Matrix ◽  
First Principles Calculations ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Mos2 Monolayer ◽  
Intervalley Scattering ◽  
Electron Phonon Scattering

Electron–phonon interaction matrix elements show that (a) valence band holes have stronger intervalley scattering than (b) conduction band electrons.

scholarly journals A Wignerfunction Approach to Phonon Scattering

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 339-350 ◽  
Author(s):  
Florian Frommlet ◽  
Peter A. Markowich ◽  
Christian Ringhofer
Keyword(s):  
Phonon Scattering ◽  
Transport Model ◽  
Scaling Limits ◽  
Wigner Equation ◽  
Phonon Interaction ◽  
Second Quantization ◽  
Electron Phonon Interaction ◽  
Wigner Transformation ◽  
Quantization Formalism ◽  
Electron Phonon Scattering

We consider the motion of a single electron under phonon scattering caused by a crystal lattice. Starting from the Fröhlich Hamiltonian in the second quantization formalism we derive a kinetic transport model by using the Wigner transformation. Under the assumption of small electron-phonon interaction we derive asymptotically the operator representing electron-phonon scattering in the Wigner equation. We then consider some scaling limits and finally we give the connection of our result to the well known Barker-Ferry equation.

Electron–Phonon Scattering Times for Aluminum

1974 ◽  
Vol 52 (7) ◽  
pp. 618-623 ◽  
Author(s):  
P. T. Truant ◽  
J. P. Carbotte
Keyword(s):  
Fermi Surface ◽  
Phonon Spectrum ◽  
Phonon Scattering ◽  
Pure Aluminum ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering

The electron–phonon scattering times in pure aluminum vary with position on the Fermi surface. There are several sources of this anisotropy. Perhaps the most obvious, but not necessarily the most important, is the distortions of the Fermi surface from a sphere. Another results from the anisotropy in the electron–phonon interaction and in the phonon spectrum. We have calculated the effect on the electron–phonon scattering times of this latter source of anisotropy. We find large variations over the Fermi surface. As the temperature is increased the anisotropy reduces but it is still significant even above 100 K.

scholarly journals Electron-Phonon Scattering in Quantum-Sized Films with the Hyperbolic Pöschl–Teller Potential

2019 ◽  
Vol 64 (4) ◽  
pp. 336
Author(s):  
Kh. A. Gasanov ◽  
J. I. Guseinov ◽  
I. I. Abbasov ◽  
D. J. Askerov ◽  
Kh. O. Sadig
Keyword(s):  
Electron Scattering ◽  
Phonon Scattering ◽  
Transition Probability ◽  
Bulk Crystals ◽  
Dimensional Electron ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Dimensional Electron Gas ◽  
Analytical Expressions ◽  
Electron Phonon Scattering

A quantitative theory of electron-phonon interaction in the two-dimensional electron gas in a quantum-sized film with the hyperbolic P¨oschl–Teller confining potential has been developed. Analytical expressions for the transition probability are derived in the case of electron scattering by deformation-induced acoustic, piezoacoustic, and polar optical phonons. The results obtained for various scattering mechanisms in the film are compared with the results obtained for bulk crystals.

EFFECT OF INELASTIC SCATTERING OF HOT ELECTRONS ON THERMIONIC COOLING IN A SINGLE-BARRIER STRUCTURE

2000 ◽  
Vol 14 (14) ◽  
pp. 1451-1457
Author(s):  
C. ZHANG
Keyword(s):  
Inelastic Scattering ◽  
Room Temperature ◽  
Phonon Scattering ◽  
Hot Electrons ◽  
Electron Interaction ◽  
Barrier Structure ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Barrier Region ◽  
Electron Phonon Scattering

One of the important problems in thermionics using layered structures is the inelastic scattering of hot electrons in the electrodes and in the barrier region. Scattering in these systems is mainly via the electron–phonon interaction, or indirectly via the electron–electron interaction. In semiconductor heterostructures at room temperature, the LO-phonon plays a crucial role in thermalising electrons. In this work we study the effect of electron–phonon scattering on thermionic cooling in a single-barrier structure. Because of the asymmetry of the barrier under a bias, a larger fraction of the total energy loss will be dissipated in the hot electrode. As a result, we find that the theoretical thermal efficiency can increase due to limited electron–phonon scattering.

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