21 research outputs found
Generalization of Child-Langmuir Law for Non-Zero Injection Velocities in a Planar Diode
The Child-Langmuir law relates the voltage applied across a planar diode to
the saturation value J_CL of current density that can be transmitted through it
in case the injection velocity of electrons into the diode is zero. The
Child-Langmuir current density J_CL is, at the same time, (i) the maximum
current density that can be transmitted through a planar diode, (ii) the
current density below which the flow is steady and unidirectional in the long
time limit and (iii) the average transmitted current density for {\em any}
value of injected current density above J_CL. Existing generalizations of
Child-Langmuir law to non-zero velocities of injection are based on the
characteristics (i) and (ii) of J_CL. This paper generalizes the law to
non-zero velocities of injection based on the characteristic (iii) by deriving
an analytical expression for the saturation value of current density. The
analytical expression for the saturation current density is found to be well
supported by numerical computations. A reason behind preferring the saturation
property of the Child-Langmuir current density as the basis for its
generalization is the importance of that property in numerical simulations of
high current diode devices.Comment: revtex, 4 figure
ON THE LINEAR THEORY OF ELECTRON PROCESSES IN THE COLLISIONLESS DIODE
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