Approximate analytical solutions for the space-charge-limited current in one-dimensional and two-dimensional cylindrical diodes

In high-power microwave diode design, the space-charge-limited current is important because of its relation to the diode impedance, and the formation of the virtual cathode. Although the Langmuir-Blodgett law, as a numerical solution, is helpful, a simple functional expression would be more convenient for practical research. In this paper, a physical approximation has been introduced to analyze the nonlinear Poisson's equation in a one-dimensional (1-D) cylindrical vacuum diode. With the help of this physical approximation, a solution for the space-charge-limited current for 1-D cylindrical diodes has been investigated and developed. In addition, a comparison between our approximate result and the Langmuir-Blodgett numerical solution shows that the physical approximation method is valid in nonlinear differential equation analyses. This physical approximation can be used to analyze similar nonlinear differential equations. Also, a correction for the space-charge-limited current in a two-dimensional cylindrical diode is obtained within a limitation. (C) 2004 American Institute of Physics.