The physics of space-charge-limited current in diodes with finite electron injection velocities is investigated within the Lagrangian flow description. The space-charge-limited (SCL) current is shown to be given by where is the familiar Child–Langmuir current, 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, is proved to be universally valid, because in this case holds. A number of further diode properties are derived analytically and presented numerically.
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