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The physics of space-charge-limited current (JSCL) in diodes with finite electron injection velocities v0 is investigated within the Lagrangian flow description. The space-charge-limited (SCL) current is shown to be given by JSCL=(X+1+X2)3JCL, where JCL∼U3/2/L2 is the familiar Child–Langmuir current, X=(mv02/2eU)1/2, 𝒰 and L are the diode voltage and length, respectively. It results from an intrinsic property of the diode rather than from electron reflexion, the current picture of SCL accepted since Langmuir’s days. For field emitted electrons, on the other hand, JCL is proved to be universally valid, because in this case v0=0 holds. A number of further diode properties are derived analytically and presented numerically.
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Akimov et al. (2001) studied this question.
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