Simulations of Collisional Space-Charge Limited Current: From Semiconductors toward Vacuum

The space-charge-limited current (SCLC) in a one-dimensional planar diode is given by the Child-Langmuir law (CLL) in vacuum and the Mott-Gurney law (MGL) in semiconductors. Recent studies have theoretically unified the CLL and MGL for general electron mobility¹ and extended them to nonplanar geometries using point transformations². This work presents a two-dimensional simulation study of trap-free SCLC using Silvaco TCAD. A lateral N⁺–i–N⁺ silicon diode was modeled with Ohmic contacts, uniform intrinsic doping, and heavily doped N⁺ regions. Steady-state simulations run from 0 V to 10,000 V recovered the transition from the Ohmic regime to the MGL regime that were identified based on the dependence of current density on applied voltage. We further compare the results for nonplanar geometries to theoretical results that used canonical gap distances from point transformations to extend the MGL. The possibility of adapting Silvaco’s physics models to capture ballistic transport and reproduce the MGL to CLL transition assessed analytically¹ will also be investigated.

1. L. I. Breen and A. L. Garner, Phys. Plasmas 31, 032102 (2024).

2. A. L. Garner and N. R. S. Harsha, IEEE Trans. Electron Devices 72, 1419-1425 (2025).

This work was supported by SCALE: U.S. DoD under Contract W52P1J-22-9-3009 and the ONR through Grant No. N00178-23-1-0004.