p-n JUNCTIONS IN SEMICONDUCTORS 461 



sistivity. We can also say that the hole current depends only on the ?;-type 

 material and vice versa. For a p-ii junction emitter in a transistor with an 

 w-type base, it is thus advantageous to use high conductivity /'-type ma- 

 terial so as to suppress an unwanted electron current. 



For comparison with experiment, it is advantageous to express the values 

 of pn and lip in terms of the conductivities (r„ and (Xp . If the conductivity of 

 the intrinsic material is written as 



ai = qnn,(\ + b), (4.15) 



then, if pn « «« and iip « pp , we find 



qnPn = 6(7-/(l + bfan (4.16) 



qnbup = bcVil -^b)\p. (4.17) 



Using these equations, we may rewrite (4.11) and a corresponding equation 

 for electron current into the />-region so as to express their dependence ond-c. 

 bias tq and the properties of the regions: 



/.c(tv) = ,,,^; , ■ - («""'" - 1) 



(1 + bfcTnLp q 

 -G,o-(.'-'^-^-l) ^^-^^^ 



^ Ip.ie""'"'' - 1) 



(1 + b)'apLn q 



_r kT .n.onr .X (4.19) 



^ lUe'"^'''' - 1). 

 The values of G^o and Co (which are readily seen to be the values of the low- 

 frequency, low-voltage (j'o < kT/q) conductances) and the saturation 

 reverse currents are given by 



, 2 



The expression for direct current then becomes 



wo = !-;. + Co! (■-)!/••'" -11 ^^^^^ 



