Electron diffusion under the influence of an electric field near absorbing boundaries

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Abstract
Numerical solutions have been obtained for the electron distribution function as a function of both energy and position for the case of a uniform stream of electrons being absorbed at a collecting electrode under the influence of a uniform electric field. Solutions are obtained from the Boltzmann equation for various power-law dependences of the momentum-transfer cross section on electron energy. It is found that the electron density distribution obtained by integrating the distribution function over energy varies significantly from the conventional solution obtained by solving the electron continuity equation with drift velocities and either transverse or longitudinal diffusion coefficients taken to be independent of position. The average electron energy increases by ∼ 50% near the boundary for a cross section increasing linearly with energy making the effective drift and diffusion coefficients a function of position.