824 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



the denominator is eveiy where positive and x increases monotonically 

 with E. If J is only a little larger than J„, , there will be a large region of 

 X in which E is nearly equal to Em . Outside of this region, E increases 

 much more rapidly with x. The relative scale of these distances may be 

 estimated as follows: Suppose J is only a little larger than Jm , and con- 

 sider the situation where E is about twice E^ so that u is about one half 

 of Um ■ Then 



dx/dE = K/pa . 



(5.6) 



Under these conditions an increase of E by an additional E„> will require 

 a distance 



Ax = KE„,/pa ■ 



(5.7) 



If this value is much smaller than L, then the situation represented in 

 Fig. 5.2(c) and (d) will occur. On the other hand if L is smaller than 

 Ax, the region of space charge and high field will extend throughout 

 most of the structure. 



In any event eciuation (5.4) leads to positive resistance. This can be 

 seen from the fact that increasing J always means a decrease in x for 

 the same value of E and hence an increase in E at all values of x and 

 thus an increase in voltage at any fixed value of :r. 



The above conclusion that a positive dc resistance will be exhibited by 

 a structure like that discussed above may also be reached by considering 

 the transient response. The theory of Section 4 may be once at be apphed 

 to this case by simply taking account of the fact that v is negative for 

 part of the structure and thus that 8Em increases with increasing s. 



In Fig. 5.3 we illustrate a stmcture to which these considerations may 

 be relatively simply apphed, at least in a limiting case. It consists of 

 four layers, the two outer being p^ as before. Space-charge limited emis- 

 sion then enters the intrinsic layer which is of such a width that at its 

 right hand boundary the electric field has a value E^ that exceeds E^ ■ 

 At this point the hole space charge is 



P.3 = J/lh 



(5.8) 



Fig. 5.3 

 ductance. 



A structure having a region of uniform negative differential con- 



