XEGATIVK RESISTANCE IX SEMICOXDrcTOU DIODES SI.") 



of the effect of drift in the electric lield and neglect the effects of {liffu- 

 sioii. This })r()cedure can he justified hy the fact that as soon as a hole 

 had reached a point where the potential has fallen hy A'/'A/ helow the 

 niaxinunii, its flow is iioxcrned hy diifl rather than diffusion and the 

 |)redominance of drift continues to increase towai'ds the right.'' " 



If diift in the held is the predominant cau.se of hole flow, then the 

 equations go\-ei'ning the situation in .V are 



J + bJ = (p + 8p)(n + 8u), (4.5) 



where the terms with 8 represent the transient effects and those without 

 represent the steady state solution, p = qp is the charge density of the 

 holes and u their drift velocity. The equation for the change of E with 

 distance is 



K(d/dx)(E + 8E) = pj.^ p^ 8p, (4.6) 



where p, is the fixed charge density due to donors and acceptors. (We 

 neglect any effect of traps.) The steady state equation for E is thus 



K(dE/dx) = pf + J/u. (4.7) 



In a region where pf is independent of .r, this equation may be reduced 

 to quach-atures by writing 



K dE/(pf + J/u) = dx; (4.8) 



the left side is then a known function of E through the dependence of 

 u upon E. 



It is convenient to introduce a time-hke variable s which is the transit 

 time for the dc solution. Evidently 



ds = dx/u = KdE/(pfU + J). (4.9) 



For the case of space charge limited current, s may be conveniently 

 measured from the potential maximum. Even though the solution is 

 invalid at that point, the integrals converge and the contribution from 

 the region within kT/q of the maximum is small. 



We shall assume that the equations for the steady state case have been 

 solved and that the functional relationships are known between E, x, v 

 and s. 



The differential equation for 8E maj' then Ijc obtained as follows: 

 To the left of the pulse in 8p in Fig. 4.2(a), 8E is zero. From equation 

 (4.6) we have 



KdE(x)/dx = dp. (4.10) 



