706 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



The value to use for 7^^ is very uucertain, but it certainly is much less 

 than /o , so I\ » h • Thus we would not expect to observe ^Vp , and the 

 characteristic should have the form 



I'^he"^ (103) 



up to the highest attainable currents. 



We have shown in this section how the law of recombination in the 

 contacts affects the dependence of Vp upon /. In particular if a = i^ 

 there is no dependence of Vp upon /, which means that the conductivitj' 

 due to injection increases just as rapidly as the current. We may con- 

 clude from (97) that the smaller the A^alue of a the more effective is con- 

 ducti\'ity modulation in keeping down the drop Vp in the middle region. 



Discussion 



We have considered the PIN structure of Fig. 1 having typical param- 

 eters given in (3). We find that the presence of the middle region causes) 

 no significant deviation in the voltage-current characteristic from that 

 of a simple PN diode until very high current densities are reached, of 

 the order of 200 amp/cm' in silicon. In particular the middle region is 

 not responsible for an anomalous slope in the plot of V versus log /. We 

 find that recombination in the middle region can be accounted for by re- 

 placing the characteristic current density elo of the device with eIog(w/L) 

 where g(w/L) < 1 is shown in Fig. 5. Thus qualitatively there is no 

 change in the form of the voltage-current characteristic due to recombi- 

 nation in the middle region, although the effect of g(iv/L) is to make the 

 voltage drop somewhat higher than if recombination were absent. 



We have suggested that the anomalous slope of V versus log / usually I 

 observed in silicon diodes might be due to non-linear recombination. If; 

 the recombination obeys a power law chosen to give a typical (anoma- 

 lous) V— I characteristic for a PN diode, we have shown that the PIN 

 diode should manifest the same characteristic up to extremely lai-ge 

 current densities many times elo . Thus the drop across the middle region l 

 should be even more negligible with non-lineai- than with linear rccom- ■ 

 bination . 



I am pleased to acknowledge my great benefit from discussions with 

 M. B. Prince and I. M. Ross. 



