Space-charge-limited current in a gap composed of materials with different collision frequencies

Derivations of the space-charge-limited-current (SCLC) are well known in vacuum and semiconductors.¹ Since practical devices may not operate in vacuum, a recent study derived a SCLC for general collisionality that recovered the appropriate asymptotes for zero or infinite collision frequency ν.² However, vacuum devices may consist of only small regions of plasma near the electrodes due to erosion and semiconductors may be surrounded by vacuum.³ We modify the general ν approach² to account for two different materials with 0 ≤ ν ≤ ∞. We recover the Child-Langmuir law (CLL) with both regimes to ν = 0, the Mott-Gurney law with both regimes set to ν → ∞, prior results with one material vacuum and the other semiconductor,³ and the general approach² with matched ν. We further quantify how changing ν for small regimes near the cathode and anode, which might represent plasma formation due to electrode erosion, will alter the CLL.

1. 1. P. Zhang, Y. S. Ang, A. L. Garner, Á. Valfells, J. W. Luginsland, and L. K. Ang, J. Appl. Phys. 129, 100902 (2021).
   
   2. L. I. Breen and A. L. Garner, Phys. Plasmas 31, 032102 (2024).
   
   3. W. Chandra and L. K. Ang, Appl. Phys. Lett. 96, 183501 (2010).