690 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



Since \/Lp « 1 we can write for the junction at x = id 



piw) = e-''- U^y-^ - (P- - y^^"") j e'^'dx 



w 



/?u>to6 



p "WW 



(15)1 



I 



where 0(X/Lp) means a term of order X/Lp . Thus we see that if we may: 

 neglect X/Lp and X/L„ we have the following simple boundary conditions 

 at the junctions 



(16). 



It is clear that in order to divide the device into three neutral regions we 

 must also be able to neglect \/w. 



Finally, we have the condition of space charge neutrality 



p - n = P (17) 



It can be shown that the term K~ dE/dx is of order (A/L)" or (X/w) | 

 and therefore negligible in our approximation. Therefore (17) is the 

 Poisson equation for the middle region in our approximation. When we > 

 use (17) we are not saying that E{x) is constant but only that K~ dE/dx 

 is negligible compared to p(x) and 7i(x). The basic eciuations then are 

 (10), (11), (13), (16), (17). 



Large Injection, No Recomhinalion 



In this section we consider current densities of the order of magnitude 

 of those that flow in normal operation of the diode as a power rectifier. 

 These currents inject large densities of electrons and holes into the 

 middle region greatly increasing its conductivity. The result is that the 

 \'oltage drop Vp is small even though the normal resistivity of the middle 

 region is high. For this reason the device has been called a conductivit}' 

 modulated rectifier. Also in this section we shall neglect recombination 

 in the middle region, which makes In{x) and Ip{x) constant and greatly 

 simplifies the analysis. The effect of recombination is to remove carrieis 

 and increase the drop across the middle region. Therefore, it is desirable 

 to keep recombination in the middle region as low as possible. 



