RELAXATION TIME APPROXIMATION FOR ELECTRON-PHONON INTERACTION IN SEMICONDUCTORS

1995 ◽  
Vol 05 (04) ◽  
pp. 519-527 ◽  
Author(s):  
PETER A. MARKOWICH ◽  
CHRISTIAN SCHMEISER
Keyword(s):  
Relaxation Time ◽  
Hydrodynamic Limit ◽  
Asymptotic Methods ◽  
Drift Diffusion Model ◽  
Phonon Interaction ◽  
Drift Diffusion ◽  
Time Model ◽  
Electron Phonon Interaction ◽  
Relaxation Time Approximation ◽  
Equilibrium Distributions

A Boltzmann equation for semiconductors is considered. Physical assumptions include the parabolic band approximation and a new relaxation time model for electron-phonon interaction. Thermal equilibrium distributions for this scattering mechanism are products of Maxwellian distributions with periodic functions of the energy, where the period is the energy of a phonon. The hydrodynamic limit is considered and a drift-diffusion model is derived by formal asymptotic methods.

scholarly journals Approximation of the BTE by a Relaxation-time Operator: Simulations for a 50 nm-channel Si Diode

VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 349-354 ◽  
Author(s):  
Marcello A. Anile ◽  
Jose A. Carrillo ◽  
Irene M. Gamba ◽  
Chi-Wang Shu
Keyword(s):  
Relaxation Time ◽  
Field Potential ◽  
Potential Drop ◽  
Ballistic Regime ◽  
Drift Diffusion ◽  
Time System ◽  
Mean Velocity ◽  
Time Model ◽  
Relaxation Time Approximation ◽  
Field Dependent

In this work we present comparisons between DSMC simulations of the full BTE and deterministic simulations of a relaxation-time approximation for a nowadays size Si diode. We assume a field dependent relaxation time fitted to give the same drift speed (mean velocity) as DSMC simulations for bulk Si. We compute the density, mean velocity, force field, potential drop, energy and I-V curves of both models and plot the pdf of the deterministic relaxation-time model. We also compare the results to augmented drift-diffusion models proposed in the literature to approximate the relaxation time system in the quasi-ballistic regime. The quasi-ballistic and ballistic regimes are distinguished by using local dimensionless parameters.

ELASTIC AND DRIFT–DIFFUSION LIMITS OF ELECTRON–PHONON INTERACTION IN SEMICONDUCTORS

1998 ◽  
Vol 08 (01) ◽  
pp. 37-53 ◽  
Author(s):  
CHRISTIAN SCHMEISER ◽  
ALEXANDER ZWIRCHMAYR
Keyword(s):  
Electron Transport ◽  
Characteristic Length ◽  
Mean Free Path ◽  
Macroscopic Model ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Phonon Interaction ◽  
Drift Diffusion ◽  
Electron Phonon Interaction ◽  
The Mean

This paper deals with electron transport in semiconductors when electron–phonon interaction is considered. Smallness of the mean free path compared to a characteristic length scale and of the phonon energy compared to the thermal energy of the crystal are assumed. The corresponding limits in the transport problem are carried out and shown not to commute. An intermediate limit leads to a new macroscopic model.

Simulation of Unsteady Small Heat Source Effects in Sub-Micron Heat Conduction

2003 ◽  
Vol 125 (5) ◽  
pp. 896-903 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Relaxation Time ◽  
Heat Source ◽  
Time Scales ◽  
Electric Fields ◽  
Hot Spot ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Electron Phonon Interaction ◽  
Relaxation Time Approximation ◽  
Phonon Relaxation Time

In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller than the phonon mean free path in the medium. In this paper, we present a study of unsteady hot spot behavior. The unsteady gray phonon Boltzmann transport equation (BTE) is solved in the relaxation time approximation using a finite volume method. Electron-phonon interaction is represented as a heat source term in the phonon BTE. The evolution of the temperature profile is governed by the interaction of four competing time scales: the phonon residence time in the hot spot and in the domain, the duration of the energy source, and the phonon relaxation time. The influence of these time scales on the temperature is investigated. Both boundary scattering and heat source localization effects are observed to have considerable impact on the thermal predictions. Comparison of BTE solutions with conventional Fourier diffusion analysis reveals significant discrepancies.

The Drift–Diffusion Limit for Electron–Phonon Interaction in Semiconductors

1997 ◽  
Vol 07 (05) ◽  
pp. 707-729 ◽  
Author(s):  
Peter A. Markowich ◽  
Christian Schmeiser
Keyword(s):  
Boltzmann Equation ◽  
Spherical Harmonics ◽  
Diffusion Limit ◽  
Scattering Operator ◽  
Semiconductor Crystal ◽  
Phonon Interaction ◽  
Drift Diffusion ◽  
Constant Energy ◽  
Electron Phonon Interaction

A scattering operator modeling the interaction of electrons with phonons of given constant energy in semiconductors is analyzed by means of an expansion in terms of spherical harmonics. An application is the derivation of the drift–diffusion limit of the corresponding Boltzmann equation for the transport of electrons in a semiconductor crystal.

Current Fluctuations of Hot Electrons

1970 ◽  
Vol 25 (7) ◽  
pp. 1107-1115 ◽  
Author(s):  
A. Friedmann ◽  
A. B. Fazakas
Keyword(s):  
Relaxation Time ◽  
External Field ◽  
The Other ◽  
Hot Electrons ◽  
Current Fluctuations ◽  
Phonon Interaction ◽  
Electrical Field ◽  
Electron Phonon Interaction ◽  
Electron Density Matrix ◽  
The One

In order to calculate the spectral density of current fluctuations in a high d. c. electrical field, a method using the one-electron density matrix is proposed. The nonperturbed problem is considered to be that of the electrons in an external field. The other interactions of electrons are expressed by means of a relaxation time matrix. To fit the expression of the current, given by the Boltzmannian formalism, a form of the diagonal terms of this matrix for electron-phonon interaction is suggested and closed formulae for the current fluctuations spectrum are obtained

Electron–phonon interaction and relaxation time in graphite

2004 ◽  
Vol 392 (4-6) ◽  
pp. 383-389 ◽  
Author(s):  
J. Jiang ◽  
R. Saito ◽  
A. Grüneis ◽  
G. Dresselhaus ◽  
M.S. Dresselhaus
Keyword(s):  
Relaxation Time ◽  
Phonon Interaction ◽  
Electron Phonon Interaction

The simulation of the electron-phonon interaction in silicon

2018 ◽  
Vol 30 (12) ◽  
pp. 3-16
Author(s):  
A. Berezin ◽  
◽  
Yu. Volkov ◽  
M. Markov ◽  
I. Tarakanov ◽  
...  
Keyword(s):  
Phonon Interaction ◽  
Electron Phonon Interaction
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