1272 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 195G 



Vj — V = Sinn — ^ — sinh - (o.28> 



q L C2 C2J 



or again joining (5.28) to the solutions in Range 1 we have in Range 2 



V - 7o = -- sinh"' - + 2Eo{x - Xo) (5.29)1 



q C2 



The total voltage drop in the junction can be found by setting V = Vy' 

 and E = Ej in (5.29). The term 2Eo(L - xo) will be negligible. Wheni 

 E'^ is large compared to Co" + 2 the junction solution reduces to the 

 zero current solution as can be seen by comparing (5.3) and (5.25). 

 Then the solution has the simple form (5.20) and (5.21). Ej will always 

 be large compared to C2 . (Ef is appi'oximately Sp/e and Co" = 2so where 1 

 So is the value of s where the junction solution joins the cubic.) Thus the 

 difference AV between Vj — T^j and the built in voltage is 



AF = --fn^ (5.30) 



q I 



Example. Fig. 8 shows the field distribution near the IP junction 

 for the case L = 2Li and /I = f , for which the intrinsic region is in- 

 finitely long. The field distribution near the junction, however, will he 

 indistinguishable from that for A = 0.6G5, or ,% = 0.95, for which the; 

 intrinsic region is about twice the effective length of current generation. 

 We have taken Ej = 30, which corresponds to an excess acceptor den- 

 sity P = 4.7 X 10' Ui in the P region. Over the range where the junc- 

 tion solution holds the cubic gives an almost constant field E = En = Ec . 

 The junction solution goes from the cubic to the zero bias solution in a , 

 distance of the order of the Debye length. The sum of the built in volt- 

 age and the voltage derived from the cubic differ from the correct voltage 

 by the order of £Ei or about kT/q. The total voltage is about 0.3 EiLi , 

 which would be about 11 volts in germanium at room temperature. 



VI. GENERAL CASE, UNEQUAL MOBILITIES 



This Section deals with the general case where the ratio of the hole 

 and electron mobilities is arbitrary. The procedure is similar to that 

 used in the preceding Sections. Many of the results for 6 = 1 are useful 

 in the present, more general, case. We shall deal first with the no-recom- 

 bination case and again find that E is given by a cubic. However, the 

 field distribution is no longer symmetrical and the coefficient of the I/E 

 term in the cubic is a linear function of x instead of a constant. The 

 differential equation foi' .s in the recombination region remains un- 



