The true nature of space-charge-limited currents in electron vacuum diodes: A Lagrangian revision with corrections

The physics of space-charge-limited current (J(SCL)) in diodes with finite electron injection velocities v(0) is investigated within the Lagrangian fl ow description. The space-charge-limited (SCL) current is shown to be given by J(SCL)=(X+root1+X-2)(3)J(CL), where J(CL)similar toU(3/2)/L-2 is the fa miliar Child-Langmuir current, X=(mv(0)(2)/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 h and, J(CL) is proved to be universally valid, because in this case v(0)=0 h olds. A number of further diode properties are derived analytically and pre sented numerically. (C) 2001 American Institute of Physics.