Authors:

Ziara Cato

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Space Charge Limited Current (SCLC) models of electron transport in vacuum, gas, and solid systems are governed by Mott-Gurney or Child- Langmuir. Mott-Gurney (MG) describes the maximum current for a gap filled with a solid material, whereas vacuum gaps use Child-Langmuir's (CL) Law. These models can be applied to a wide range of devices, from semiconductors and transistors to spark gap switches and other plasma devices. In previous works, a generalized SCLC (GSCLC) model with collisions and nonzero velocity demonstrated that there was no clear transition between CL and MG when one region is considered. Practical devices may be manufactured imperfectly or degrade from long-term use, which can introduce a change of material across the gap. This necessitates the analysis of a multi-region structure and the electron emission laws that govern it. The work here extends previous analysis to a gap with two distinct regions varying in collision frequencies. The equations governing how electrons move after they are emitted into the first region are solved analytically to capture how material differences affect space charge limited current behavior. We recovered GSCLC from a single material gap and analyzed the trends for different types of materials in the two regions by performing an asymptotic analysis of various collision frequencies for the two regions. For a gap between two different regions, the spatially varying collision frequency will cause complexities in the solution for the SCLC. This work provides a deeper view on how electron emission is impacted by material inhomogeneities within one electrode gap. Keywords: Space Charge Limited Emissions; Child-Langmuir; Mott-Gurney

Source:

Purdue University / 2025

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Co-authors:

Ziara Cato