474 



BELL SYSTEM TECHNICAL JOURNAL 



the capacitance Cg is assumed to be so large that the first term in 

 (17) may be ignored. The ratio between "hot" and "cold" capaci- 

 tance may then be written : 



y^ 1 — Jq ;s 



Co 



Write the conductance 1/p as 



1 - /( 



TV 

 6di 



p ri 



(18) 



(19) 



and note that the first factor of the right member is always positive. 

 F may be termed the relative input conductance. 



Before the theoretical curves are discussed a few words about the 



J T i 2"" 3 



functions -^ and Jo -rr- are in order. Thev will be expressed in 



2z<o2 oai 



terms of two parameters, i.e., ^ and ^ where 



Fo2 



ip = 



Vol 



(20) 



and ^ is a constant of integration which assumes different values 

 depending upon the type of space charge present.^ In terms of these 

 parameters one may show that : 



Jo^ = 



Jo 



J 



[V^l/2 ^ 1 _ V(g^)l/2 + 1]3 



6di (|i/2 _ 2)VFMn; 



- {{^<py" - 2)V(i^F^TT 



Tr- _ \:<e'' + 1 - <(^<py^' + 1]- 



2«o2 {^fY'- 



Type 

 < t < «,, 



(21) 



[_\e" - 1 - V(^«^)^/' - 1? 



/o 



Ti^ [V^ 



1/2 



- ((^^)i/2 + 2)V(^^)i/2 - 1 [ 



1 - V(i^F^"^T]2 



2uc 



U^pY" 



1 



Type 

 < ^ < ^, 



(22) 



2 The parameters I /a and 1//3 used by Fay, Samuel and Schockley are related 

 to ^ as follows: 



i = a Type Di 



I = - Type D2. 



