Abstract
This short report describes the phenomenon of space-charge-limited (SCL) current transport between ballistic and collision-dominated regimes for an inhomogeneous medium with a finite emission area. This intermediate regime can be considered as a weakly collisional regime where the collisional mean free path is comparable to the length of the medium. The SCL current density is calculated as a function of the degree of collision, inhomogeneity of the medium, and the geometrical properties of the emitting area. The inhomogeneity of the medium is characterized by a parameter of (0<alpha <= 1), where alpha = 1 denotes a perfect homogenous medium. The calculated SCL current density is enhanced by finite emission area effects by a factor of 1+FxG, where F measures the mean position of the electrons in the medium, and G is a geometrical correction factor due to finite emission area. The enhancement is found to be higher in the collisional regime as compared to the ballistic regime. A higher inhomogeneity (with smaller alpha) also increases the enhancement. Smooth transition between the fully ballistic SCL transport (Child-Langmuir model) and the collision-dominated SCL transport (Mott-Gurney model) is demonstrated and verified, respectively, by the particle-in-cell code and the device simulator. This model is useful for the characterization of high-current SCL transport where the non-ideal conditions (such as inhomogenous medium and weakly collisional regime) cannot be described by the existing SCL models. (C) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).