p-n JUNCTIONS IN SEMICONDUCTORS 467 



the currents will flow as if the patch were not present so that one compo- 

 nent of the current will be that due to the uniform junction. In addition 

 there will be current due to recombination and generation in the patch. 

 The series resistance to the patch will be relatively high due to the constric- 

 tion of the current paths. On the other hand, the value of /r(50) associated 

 with the patch may be very high. Hence the current due to the patch will 

 be that of a low impedance ideal rectifier in series with a high resistance; 

 and if the ratio of impedances is high enough, such a series combination 

 amounts essentially to an ohmic leakage path. Thus patches in the p-n 

 junction will tend to introduce leakage paths and destroy saturation in the 

 reverse direction. 



An extreme example of a region of high rate of recombination would be a 

 particle of metal making a non-rectifying contact to both p- and «-type 

 germanium. Since holes and electrons are essentially instantly combined in a 

 metal, the boundary condition at the metal surface would be equality of 

 (fp and (fn . This would mean that near the metal particle, ipp and (r„ could 

 not differ by 8(p, the condition required, over some parts of the junction at 

 least, in order for ideal rectification to occur. 



A common source of imperfection in p-n junctions arises from dirt or 

 fragments on the surface which overlap the junction. Even if these do not 

 actually constitute a short circuit across the junction, they may furnish 

 patches of the sort discussed here and modify the junction characteristic. 



4.8 Final Comments 



Another possible cause for frequency effects may be found in the trapping 

 of holes or electrons. ^^ When an added hole concentration is introduced into 

 an n-region, a certain fraction of the holes will be captured by acceptors and 

 later re-emitted or else recombined with electrons while trapped. Investiga- 

 tion of this process is given in Appendix \T. One interesting result is that the 

 trapping of holes in a uniform ;z-region cannot produce an effective suscep- 

 tance (i.e. iwC) in excess of the conductance, as can a retarding field. 



Finally it should be remarked that important and significant variations 

 of the conductivity in the p- and w-regions may be produced by hole or 

 electron injection. Under these conditions, when the hole concentration 

 approaches w„ , i/' — ipn will vary. Under these conditions Ri may be appreci- 

 ably altered. These factors favor the p-n junction as a rectifier since they lead 

 to a reduction of series resistance under conditions of forward bias and thus 

 tend to improve the rectification ratio. 



'■' Frequency dependent effects in Cu^O rectifiers have been explained in this way by 

 J. Bardeen and W. H. Brattain, personal communication. 



