Two-dimensional model of space-limited current in the weakly collisional regime for an inhomogenous medium

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<α≤1), where α = 1 denotes a perfect homogenous medium. The calculated SCL current density is enhanced by finite emission area effects by a factor of 1+F×G, 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 α) 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.