456 BELL SYSTEM TECHNICAL JOURNAL 



is the diffusion length for holes in the intrinsic region. The inequality states 

 that the diffusion length must be much larger than /.„ • This is equivalent 

 to the previous statement that the hole current must penetrate the w-region 

 for the rectifier to have a good characteristic. (If a local region of high re- 

 combination is present in the transition region, this result just quoted need 

 not apply. See Section 4.6.) 



If the hole current penetrates deeply into the w-region and Ri is negligible, 

 then we can conclude that the current-voltage characteristic will fit the 

 ideal formula. For these assumptions 5^Rp on Fig. 5 will be small and the 

 principal change in (pp will occur relatively deep in the w-region, at least 

 beyond the transition region. So long as the hole concentration introduced 

 in the w-region is much smaller than «„ , the hole current into the w-region 

 will be a linear function of the value of p at the right edge of the transition 

 region, being zero when p equals pn , the equilibrium value of p. This 

 leads at once to a hole current proportional to p — pn and since the shift 

 of <pp in respect to ^ at the edge of transition region is 8<p, p — pn is 

 equal to pniexpiaSip/kT)-].). (These ideas are discussed in detail in Sec- 

 tion 4.) A similar relationship will hold for electrons entering the p-reg\on; 

 hence the total current will vary as exp{q8<p/kT)-l. This is a theoretical 

 rectification formula" givmg the maximum rectification for carriers 

 of charge q. 



4. Treatment of Particular Models 



4.1 Introduction and Assumptions 



In this section we shall deal chiefly with good rectifiers so that the IR 

 drop, discussed in connection with Ri in Section 3, is negligible. We shall 

 deal chiefly with the case for which the transition region is narrow com- 

 pared to the diffusion length; consequently, there is little change in Ip in 

 traversing the transition region. In Fig. 6(a) we consider a hypothetical 

 junction in which the properties are uniform outside the transition region. 

 The division of the specimen into three parts as shown is seen to be reason- 

 able for germanium: In ;/-type germanium, the diffusion constant for holes 

 is about 40 cmVsec and the lifetime is greater than 10~® sec so that the 

 diffusion distance is Lp = \/l>rp > 6 X 10"' cm. This is much greater than 

 most transition regions. 



The major drop in ipp must occur to the right of the transition region. This 

 follows from our assumptions: First, we may neglect the IR drop in the 

 ^-region; hence (pp is substantially constant from :v = Xa to x = Xrp • Second, 

 the decrease in ipp is much less in the transition region than in the «-region; 

 this follows from two considerations: the resistance for hole flow is lower in 



"C. Wagner, Pliys. Zeils. 32, 641-645 (1931). 



