1254 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



As A decreases and becomes negative the cubic approaches the form 



E' = Eo' + Ei 



(3.6) 



where Eq = —AEi is the minimum value of E". This form of the solu- 

 tion will be valid when the minimum E is large compared to {lEi/a). 

 As Eq increases, the voltage increases and the curve becomes flatter. 

 This is because the increasing field sweeps the carriers out and reduces 

 the space charge; so the drop in field decreases. 



If (3.4) for E/Ei versus x/2Li is extended to indefinitely large values 

 of x/2Li , it approaches the straight line of slope 1 going through the 

 origin. Since E is always positive the curve is above this straight line at 

 X = 0. li A is negative the curve is always above the straight line and 

 always concave upward. If A is positive, the curve crosses the straight 



1.5 



1.4 

 1.3 



1.2 



1.1 



1.0 



0.9 





0.8 

 0.7 

 0.6 

 0.5 

 0.4 

 0.3 

 0.2 

 0.1 







0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1,0 

 X/2Ll 



Fig. 3 — Field Distributions for L = 2L,- 



