466 BELL SYSTEM TECHNICAL JOURNAL 



since for equilibrium conditions the rates balance so that raiti = ga . The 

 net hole current recombining in the layer per unit area is thus 



lX<Pr> - <Pn) = qgaW''^-'"'"' - 1] (4.35) 



There must, therefore, be a discontinuous decrease of hole current across 

 the layer. The total hole current flowing in at x = Xa , which is also the total 

 current /, thus does three things: for x < xrp, it combines with I„o{d<p); 

 for Xtp < X < xTn , it combines with electrons at rate Ir{5<p);iov x > Xm , 

 it flows into the «-region in amount Ipoi^^)- This leads to 



/ = InoM + hoM + IrM. (4.36) 



In other words the layer of high recombination acts like a rectifier 

 in parallel with /„o(M + IpoM. The frequency characteristic of IrM, 

 however, will be independent of frequency and will contribute a pure con- 

 ductance to the admittance of the junction. 



If the layer is considered to have finite width, however, it will exhibit 

 frequency effects just as does Ip in the w-region. In Appendk III, we treat 

 a case in which the layer is a part of the j7-region itself but has a recombina- 

 tion time different from the main layer. If the time is shorter, a large amount 

 of the hole current may recombine in this layer. For high frequencies, the 

 current may not penetrate the layer, in which case the admittance for hole 

 current is determined by the thin layer rather than by the whole «-type 

 region. A case of this sort is shown in Fig. 7. In this case the thickness of the 

 layer is I of its diffusion length and in it the lifetime of a hole n is i the 

 value Tp in the main body of the w-region. The hole current will thus be 

 restricted to this layer when the diffusion distance -y/D/u is less than the 

 layer thickness (i) y/Drt; this corresponds to cot/ > 9 or oiTp > 81. The 

 presence of the high rate of combination in the layer is evidenced by the 

 tendency of G to be greater than S at high frequencies. If the layer were 

 infinitely thin, as discussed above, it would simply add a constant conduct- 

 ance to the admittance. 



4.7 Patch Effect in p-n Junctions 



If there are localized regions of high recombination rate, a "patch effect" 

 may be produced in an n-p junction. As an extreme example, suppose the 

 value of ga for the layer just considered is allowed to become very large; then 

 the recombination resistance may become small compared to R\ in Section 3 

 and the junction will become substantially ohmic. If the region of high 

 rate of recombination is relatively small compared to the area of the rest 

 of the junction, then the behavior of the junction as a whole may be re- 

 garded as being that due to two junctions in parallel. Over most of the area, 



