New Perspectives on Electron Emission Physics
The space-charge limited current (SCLC) is an important limit in high-power microwaves, vacuum electronics, directed energy, and sheath physics in plasma processing in the semiconductor industry. While the SCLC was derived over a century ago for a one-dimensional (1D) planar diode in vacuum, extensions to more general geometries have been challenging. This problem is exacerbated when considering conditions that may not yet be space-charge limited or when considering non-vacuum conditions.
This seminar introduces several techniques to address these issues. We demonstrate the utility of variational calculus (VC) to extremize the current in the gap, conformal mapping of the space-charge electric potential, and Lie point symmetries to derive exact solutions for multiple 1D geometries. We further derive a universal relationship between vacuum electric potential and space-charge limited potential that yields SCLC for multidimensional diodes with any geometry that depends on the capacitance with no space-charge. Finally, we extend these approaches to collisional diodes to generalize SCLC and to predict conditions between the source current (e.g., field or thermal emission) and the SCLC for nonplanar diodes. Experimental implications and the importance for serving as a benchmark to particle-in-cell simulations will be discussed.
Bio: Dr. Allen L. Garner received the B.S. degree (with high honors) in nuclear engineering from the University of Illinois, Urbana-Champaign, in 1996. He received an M.S.E. in nuclear engineering from the University of Michigan in 1997, an M.S. in electrical engineering from Old Dominion University in 2003, and a Ph.D. in nuclear engineering from the University of Michigan in 2006. He was an active duty Naval officer from 1997 to 2003 and is currently a Captain in the United States Navy Reserves. From 2006 to 2012, he was an electromagnetic physicist at GE Global Research Center. He joined Purdue University in 2012, where he is currently Professor and Graduate Program Chair in Nuclear Engineering.
Prof. Garner received a University of Michigan Reagents’ Fellowship and a National Defense Science and Engineering Graduate Fellowship. He has been awarded two Meritorious Service Medals, the Navy and Marine Corps Commendation Medal, and five Navy and Marine Corps Achievement Medal. He also received the 2024 and 2021 Purdue School of Nuclear Engineering Outstanding Research Award, 2019 Outstanding Faculty Mentor of Engineering Graduate Students, and 2016 IEEE NPSS Early Achievement Award.