Title :
Exact formulas for space charge limited flow in a planar diode: New relativistic Child-Langmuir law
Author_Institution :
NSSL, Fu Jen Catholic Univ., Taipei, Taiwan
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;
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
DOI :
10.1109/IVEC.2012.6262198
