Exact formulas for space charge limited flow in a planar diode: New relativistic Child-Langmuir law

Author

Lin, M.C.

Author_Institution

NSSL, Fu Jen Catholic Univ., Taipei, Taiwan

fYear

2012

fDate

24-26 April 2012

Firstpage

367

Lastpage

368

Abstract

In this work, we have derived the exact formulas for the relativistic Child-Langmuir law to describe a space-charge-limited flow in a planar diode under arbitrary applied voltages. Two hypergeometric functions are obtained to relate the classic Child-Langmuir law and the ultra-relativistic formula to exact relativistic Child-Langmuir law. Both non-relativistic-to-relativistic hypergeometric function and ultra-relativistic-to-relativistic hypergeometric function are found to be dependent on applied voltages only. The formulas are elegant, compact, and intuitive, and can be easily employed.

Keywords

semiconductor diodes; space charge; hypergeometric functions; non-relativistic-to-relativistic hypergeometric function; planar diode; relativistic Child-Langmuir law; space charge limited flow; space-charge-limited flow; ultra-relativistic-to-relativistic hypergeometric function; Abstracts; Anodes; Cathodes; Cities and towns; Current density; Educational institutions; Space charge; Space charge limited flow; exact formulas; hypergeometric functions; new relativistic Child-Langmuir law; planar diode;

fLanguage

English

Publisher

ieee

Conference_Titel

Vacuum Electronics Conference (IVEC), 2012 IEEE Thirteenth International

Conference_Location

Monterey, CA

Print_ISBN

978-1-4673-0188-6

Electronic_ISBN

978-1-4673-0187-9

Type

conf

DOI

10.1109/IVEC.2012.6262198

Filename

6262198