Self-energy Models for Scattering in Semiconductor Nanoscale Devices: Causality Considerations and the Spectral Sum Rule

2013 ◽  
Vol 1551 ◽  
pp. 17-22 ◽  
Author(s):  
John R. Barker ◽  
Antonio Martinez
Keyword(s):  
Green Function ◽  
Spectral Density ◽  
Density Of States ◽  
Inelastic Electron ◽  
Causality Condition ◽  
Nanoscale Devices ◽  
Sum Rule ◽  
Nanowire Transistors ◽  
Self Energy ◽  
Energy Models

ABSTRACTThe modelling of of silicon gate-all-around nanowire transistors by non-equilibrium Green function methods requires the computation of self-energies for inelastic electron-phonon interactions. It is shown that many approximations designed to reduce numerical complexityto these self-energies in fact fail because they do not satisfy appropriate causality conditions. Four familiar approximations are discussed and their failures resolved. It is also shown that a condition for the spectral density sum rule to hold (and hence accurate density of states in energy) depends on a simple causality condition.

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

Inelastic Electron-Proton Scattering and a Sum Rule for the Schwinger Term

1971 ◽  
Vol 3 (3) ◽  
pp. 677-681 ◽  
Author(s):  
V. Gupta ◽  
G. Rajasekaran
Keyword(s):  
Inelastic Electron ◽  
Proton Scattering ◽  
Sum Rule

ADMITTANCE FIELD METHOD FOR THE CALCULATION OF THE SPECTRAL DENSITY OF CURRENT FLUCTUATIONS

2001 ◽  
Vol 01 (01) ◽  
pp. R1-R11 ◽  
Author(s):  
PAVEL SHIKTOROV ◽  
EVGENIJ STARIKOV ◽  
VIKTORAS GRUŽINSKIS ◽  
LUCA VARANI ◽  
JEAN-CLAUDE VAISSIERE ◽  
...  
Keyword(s):  
Green Function ◽  
Spectral Density ◽  
Field Method ◽  
Current Fluctuations ◽  
Noise Sources ◽  
Field Methods ◽  
Physical Ground ◽  
Hydrodynamic Calculations ◽  
Gaas Structure ◽  
The Green Function

In the framework of the Green-function formalism the admittance field method is proposed for the calculation of the spectral density of current fluctuations of two and more terminal devices. The usefulness of the theory is illustrated by hydrodynamic calculations performed for a submicron GaAs structure. The unifying property of the formalism evidences the same physical ground of both the admittance and impedance field methods when instantaneous fluctuations of carrier accelerations during scattering events are taken as noise sources.

Spectral density of states for ferromagnetic Fe (001) surface

1978 ◽  
Vol 25 (8) ◽  
pp. 561-564 ◽  
Author(s):  
Bernardo Laks ◽  
C.E.T.Gonçalves da Silva
Keyword(s):  
Spectral Density ◽  
Density Of States

The density of states in dilute solid solutions

1966 ◽  
Vol 292 (1430) ◽  
pp. 433-440 ◽  
Keyword(s):  
Green Function ◽  
Density Of States ◽  
Solid Solutions ◽  
Level Shift ◽  
Green Function Method ◽  
Pure Solvent ◽  
Energy Level Shift ◽  
The Difference ◽  
The Green Function

The difference in the density of states in energy in a dilute solid solution, relative to its value in the pure solvent, is derived. It is shown to be simply related to the energy level shift induced by virtual electron scattering off the solute ions and to the density of states in the pure solvent. The result, which follows from a brief physical argument, is shown to be completely equivalent to that obtained from a far more laborious derivation by means of Green function techniques. An application to the determination of the specific heat of dilute metallic solid solutions is given and a former incomplete result, as derived by Jones from an approximate evaluation of the Green function method, is amended.

Modeling of Polarization-Specific Phonon Transmission Functions Through Interfaces

2008 ◽  
Author(s):  
Zhen Huang ◽  
Jayathi Murthy ◽  
Timothy Fisher
Keyword(s):  
Theoretical Prediction ◽  
Density Of States ◽  
Bulk Material ◽  
Transmission Function ◽  
Dissimilar Materials ◽  
Bulk Materials ◽  
Phonon Branch ◽  
Self Energy ◽  
Frequency Independent ◽  
Eigenvectors And Eigenvalues

The atomistic Green’s function (AGF) method has been used successfully in previous research to predict the transmission function for energy carriers at interfaces. In this work, the method is extended to capture the transmission function for each phonon polarization. The inputs for this extension are the same as for the original AGF method. Furthermore, this method does not require any complex manipulation of harmonic matrices and can be applied to different materials and geometries. The eigenvectors and eigenvalues of the overall density of states matrices are manipulated to yield the density of states matrix for each polarization. A decomposed self-energy is calculated from the density of states matrix for each polarization and used to calculate the transmission function for a particular phonon branch. In a pure bulk material such as silicon, each transmission function exhibits a frequency-independent value of unity, which matches the theoretical prediction. In heterogeneous bulk materials, the transmission function is reduced significantly due to the contact of dissimilar materials. The summation of the decomposed transmission functions is shown to reproduce the result from a direct AGF calculation in which all branches were treated together.

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