ON ANALYTICAL SOLUTION OF THE NEAR ISOTROPIC APPROXIMATION TO THE BOLTZMANN EQUATION FOR HOT ELECTRONS IN A SEMICONDUCTOR BASE IN AN ELECTRIC FIELD

1985 ◽  
Vol 4 (4) ◽  
pp. 183-193 ◽  
Author(s):  
W. COX
Keyword(s):  
Boltzmann Equation ◽  
Analytical Solution ◽  
Electric Field ◽  
Hot Electrons ◽  
Isotropic Approximation ◽  
The Boltzmann Equation

scholarly journals Calculation of Electron Swarm Parameters in Tetrafluoromethane

2020 ◽  
Vol 8 (2) ◽  
pp. 22-28
Author(s):  
Idris H. Salih ◽  
Mohammad M. Othman ◽  
Sherzad A. Taha
Keyword(s):  
Boltzmann Equation ◽  
Field Strength ◽  
Electric Field ◽  
Cross Sections ◽  
Electron Attachment ◽  
High Energy ◽  
Longitudinal Diffusion ◽  
Characteristic Energy ◽  
The Boltzmann Equation ◽  
High Energy Tail

The electron swarm parameters and electron energy distribution function (EEDF) are necessary, especially onunderstanding quantitatively plasma phenomena and ionized gases. The EEDF and electron swarm parameters including the reduce effective ionization coefficient (α-η)/N (α and η are the ionization and attachment coefficient, respectively), electron drift velocity, electron mean energy, characteristic energy, density  normalized longitudinal diffusion coefficient, and density normalized electron mobility in tetrafluoromethane (CF4) which was analyzed and calculated using the two-term approximation of the Boltzmann equation method at room temperature, over a range of the reduced electric field strength (E/N) between 0.1 and 1000 Td(1Td=10-17 V.cm2), where E is the electric field and N is the gas density of the gas. The calculations required cross-sections of the electron beam, thus published momentum transfer, vibration, electronic excitation, ionization, and attachment cross-sections for CF4 were used, the results of the Boltzmann equation in a good agreement with experimental and theoretical values over the entire range of E/N. In all cases, negative differential conductivity regions were found. It is found that the calculated EEDF closes to Maxwellian distribution and decreases sharply at low E/N. The low energy part of EEDF flats and the high-energy tail of EEDF increases with increase E/N. The EEDF found to be non-Maxwellian when the E/N> 10Td, havingenergy variations which reflect electron/molecule energy exchange processes. In addition, limiting field strength (E/N)limit has been calculated from the plots of (α-η)/N, for which the ionization exactlybalances the electron attachment, which is valid for the analysis of insulation characteristics and application to power equipment.

scholarly journals A Thermodynamic Treatment of Anisotropic Diffusion in an Electric Field

1972 ◽  
Vol 25 (6) ◽  
pp. 685 ◽  
Author(s):  
RE Robson
Keyword(s):  
Boltzmann Equation ◽  
Electric Field ◽  
Drift Velocity ◽  
Anisotropic Diffusion ◽  
Diffusion Tensor ◽  
Charged Particles ◽  
Equilibrium Thermodynamics ◽  
Neutral Gas ◽  
The Boltzmann Equation ◽  
Diffusive Processes

Non-equilibrium thermodynamics is used to analyse the diffusive processes associated with a swarm of charged particles (ions or electrons) drifting in a neutral gas under the influence of an electric field. A simple approximate phenomenological relationship connecting components of the diffusion tensor with the drift velocity of the swarm is derived and the utility of the formula is illustrated in several cases where previous analyses have been carried out using the Boltzmann equation.

Analytical Solution for Boltzmann Collision Operator for the1-D Diffusion equation

2021 ◽  
Vol 9 (9) ◽  
pp. 1514-1517
Author(s):  
Wasif Almady
Keyword(s):  
Boltzmann Equation ◽  
Analytical Solution ◽  
Diffusion Equation ◽  
Collision Operator ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
The Boltzmann Equation ◽  
Boltzmann Collision Operator ◽  
The One

Abstract: In this paper, we have presented the analytical solution of the collision operator for the Boltzmann equation of onedimensional diffusion equation using the analytical solution of the one-dimensional Navier Stoke diffusion equation. Keywords: Boltzmann equation; analytical collision operator; one-dimensional diffusion equation.

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

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