Unipolar charge injection transients in insulators of various geometries

Abstract

Single-carrier space-charge-limited (SCL) effects in planar, cylindrical, and spherical samples are considered. A novel approach facilitates approximate analytical solutions to the current transients following application of a voltage step. The SCL transit time varies by only about 15% with geometry, even for large ratios of outer to inner radii. In that case, large initial current spikes occur and there is an absence or weakening of the familiar current cusp. Injection from electrode edges in planar geometry samples can show similar behaviour.

A new positive finite volume scheme for two‐dimensional convection‐diffusion equation

“…Sõ( +1 ) is weak diagonal dominance in column, that is, ( +1 ) is diagonal dominant in the columns. We use the Picard nonlinear iteration method to solve the nonlinear system (25): choose a small value  > 0 and initial vector ( +1,0) > 0, and repeat for nonlinear iteration index = 1, 2, ....…”

“…Hence, in order to finish the proof existence of solution in (25), we only need to prove that the map has a fixed point +1 ≥ 0. We know that ( + Δ̃( +1 )) is a strict -matrix.…”

“…Meanwhile, we do not need to introduce any slope limiting technique. Moreover, it is very effective on large deformed meshes, such as Kershaw mesh . In addition, the method is suitable for those problems with discontinuous, anisotropic and heterogeneous full tensor coefficients on deformed meshes.…”

“…Moreover, it is very effective on large deformed meshes, such as Kershaw mesh. [25] In addition, the method is suitable for those problems with discontinuous, anisotropic and heterogeneous full tensor coefficients on deformed meshes. For the unsteady problem, the existence of a solution for the nonlinear discrete system is proved.…”

Nanosecond laser spectrofluorimeter with automated data processing

“…A difficulty with the use of general distorted quadrilateral meshes is the necessity to use a finite discretization for the diffusion operator with a minimum of nine points. When the mesh is not orthogonal, the requirement of having a difference operator that is conform to the initial differential operator, and that of having a positive definite difference operator (needed to ensure positive mass and energy) are known to be incompatible [6]. Indeed, Kershaw illustrated how skewness in the mesh could induce distortions in the solution of a transient diffusion problem.…”