Hot electron in a polar crystal. II. Loss to single phonon modes

1976 ◽  
Vol 54 (20) ◽  
pp. 2101-2109
Author(s):  
B. Hede ◽  
T. McMullen
Keyword(s):  
Quantum Interference ◽  
Golden Rule ◽  
Eikonal Approximation ◽  
Injection Velocity ◽  
Hot Electron ◽  
Phonon Modes ◽  
Polar Crystal ◽  
Initial Injection ◽  
Important Interaction ◽  
Average Loss

A quantum theory of momentum and energy loss of a fast electron based on the eikonal approximation but including quantum interference effects is applied to a hot electron in a polar crystal. The important interaction is assumed to be the electron–polar LO phonon coupling, and this is represented by the Fröhlich polaron model. Numerical results are presented for loss, as a function of time since injection of the hot electron, to phonon modes with wave vectors parallel to the initial injection velocity. A smaller average loss rate than predicted by the golden rule is found, and quantum oscillations are seen in the time dependence of the rate.

Hot electron in a polar crystal. I. The eikonal approximation

1976 ◽  
Vol 54 (20) ◽  
pp. 2093-2100
Author(s):  
B. Hede ◽  
T. McMullen
Keyword(s):  
Energy Loss ◽  
Fast Electron ◽  
Quantum Interference ◽  
Eikonal Approximation ◽  
High Energy ◽  
Function Technique ◽  
Hot Electron ◽  
Polar Crystal ◽  
The Individual ◽  
High Energy Scattering

A quantum theory of the rates of momentum and energy loss by a fast electron to the optic modes of a polar crystal as a function of time elapsed since injection of the fast electron is developed. A nonequilibrium Green function technique is used to formulate the problem, and permits inclusion of quantum interference between the individual phonon processes. An approximation, which has been called the eikonal approximation in high energy scattering and is valid when the fractional electron energy loss in a single phonon collision is small, enables us to sum the resulting diagrams. The relationship of this method to a Boltzmann equation approach is discussed.

scholarly journals Resonance and antiresonance in Raman scattering in GaSe and InSe crystals

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Osiekowicz ◽  
D. Staszczuk ◽  
K. Olkowska-Pucko ◽  
Ł. Kipczak ◽  
M. Grzeszczyk ◽  
...  
Keyword(s):  
Raman Scattering ◽  
Temperature Effect ◽  
Band Gap ◽  
Raman Spectra ◽  
Quantum Interference ◽  
Optical Band Gap ◽  
Phonon Coupling ◽  
Phonon Modes ◽  
Electron Phonon Coupling ◽  
Resonant Raman

AbstractThe temperature effect on the Raman scattering efficiency is investigated in $$\varepsilon$$ ε -GaSe and $$\gamma$$ γ -InSe crystals. We found that varying the temperature over a broad range from 5 to 350 K permits to achieve both the resonant conditions and the antiresonance behaviour in Raman scattering of the studied materials. The resonant conditions of Raman scattering are observed at about 270 K under the 1.96 eV excitation for GaSe due to the energy proximity of the optical band gap. In the case of InSe, the resonant Raman spectra are apparent at about 50 and 270 K under correspondingly the 2.41 eV and 2.54 eV excitations as a result of the energy proximity of the so-called B transition. Interestingly, the observed resonances for both materials are followed by an antiresonance behaviour noticeable at higher temperatures than the detected resonances. The significant variations of phonon-modes intensities can be explained in terms of electron-phonon coupling and quantum interference of contributions from different points of the Brillouin zone.

Influence of Hot Electron Scattering and Electron–Phonon Interactions on Thermal Boundary Conductance at Metal/Nonmetal Interfaces

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Ashutosh Giri ◽  
Brian M. Foley ◽  
Patrick E. Hopkins
Keyword(s):  
Phonon Scattering ◽  
Energy Levels ◽  
Golden Rule ◽  
Energy Coupling ◽  
Hot Electron ◽  
Nonequilibrium Electron ◽  
Simplified Approach ◽  
Thermal Boundary Conductance ◽  
Order Of Magnitude ◽  
Unique Mechanism

It has recently been demonstrated that under certain conditions of electron nonequilibrium, electron to substrate energy coupling could represent a unique mechanism to enhance heat flow across interfaces. In this work, we present a coupled thermodynamic and quantum mechanical derivation of electron–phonon scattering at free electron metal/nonmetal substrate interfaces. A simplified approach to the Fermi's Golden Rule with electron energy transitions between only three energy levels is adopted to derive an electron–phonon diffuse mismatch model, that account for the electron–phonon thermal boundary conductance at metal/insulator interfaces increases with electron temperature. Our approach demonstrates that the metal-electron/nonmetal phonon conductance at interfaces can be an order of magnitude larger than purely phonon driven processes when the electrons are driven out of equilibrium with the phonons, consistent with recent experimental observations.

scholarly journals On the dynamics of polarons in the strong-coupling limit

2017 ◽  
Vol 29 (10) ◽  
pp. 1750030 ◽  
Author(s):  
Marcel Griesemer
Keyword(s):  
Strong Coupling ◽  
Longitudinal Optical ◽  
Strong Coupling Limit ◽  
Poisson System ◽  
Phonon Modes ◽  
Polar Crystal ◽  
Effective Dynamics ◽  
Optical Modes ◽  
Non Local ◽  
With Memory

The polaron model of H. Fröhlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strong-coupling limit, one expects that the phonon modes may be treated classically, which leads to a coupled Schrödinger–Poisson system with memory. For the effective dynamics of the electron, this amounts to a nonlinear and non-local Schrödinger equation. We use the Dirac–Frenkel variational principle to derive the Schrödinger–Poisson system from the Fröhlich model and we present new results on the accuracy of their solutions for describing the motion of Fröhlich polarons in the strong-coupling limit. Our main result extends to [Formula: see text]-polaron systems.

scholarly journals Plasmonic Hot Electron Induced Layer Dependent Anomalous Fröhlich Interaction in InSe

2021 ◽  
Author(s):  
Mahfujur Rahaman ◽  
Muhammad Aslam ◽  
Lu He ◽  
Teresa Madeira ◽  
Dietrich Zahn
Keyword(s):  
Electrical Transport ◽  
Finite Element Method Simulation ◽  
Localized Surface Plasmon ◽  
Plasmonic Nanostructures ◽  
Hot Electron ◽  
Phonon Modes ◽  
Electron Doping ◽  
Fundamental Understanding ◽  
Optoelectronic Applications ◽  
Shed Light

Abstract InSe is one of the most promising two-dimensional (2D) materials for electronic and optoelectronic applications because of its favourable bandgap and superior electron mobility compared to other layered semiconductors. However, due to the polar nature of InSe, Fröhlich interaction plays an important role in electrical transport, which becomes more significant in reduced dimensionality. Until now, it is not yet known how the dimensionality influences the strength and nature of the Fröhlich polaronic effect in InSe. Here, we report on layer dependent anomalous Fröhlich interaction in InSe from bulk to monolayer with the aid of plasmonic hot electron doping. When excited near the localized surface plasmon resonance, plasmonic nanostructures produce highly energetic electrons (known as hot electrons), which can be captured by a semiconductor such as InSe at the interface. These electrons then couple to the polar optical phonons via the Fröhlich interaction in InSe. With the aid of the strong plasmonic field, the Fröhlich interaction enabling us to monitor the polar phonons in conventional Raman measurements. We prepared nanostructures with three different metals (Ag, Au, and Al) using nanosphere lithography on InSe to study the hot electron doping effect by means of Raman spectroscopy. A finite element method simulation was used to understand the coupling between the plasmonic nanostructures and InSe. We observed that the intensity of polar LO phonon modes initially increases gradually with decreasing layer number and then drops drastically from 7L to 6L, i.e. at the thickness where the transition from quasi-direct to indirect bandgap occurs at room temperature. Additionally, a gradual decrease of intensity of the polar modes with decreasing layer thickness below this transition point is observed, which is due to the increasing indirect bandgap nature of InSe suggesting reduced Fröhlich coupling. Our results shed light on fundamental understanding of Fröhlich interaction in InSe, which is crucial for electronic and optoelectronic applications of this promising 2D material.

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