1246 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



length. For germanium at room temperature £ = 6.8 10~* cm and Ei = 

 383 volts per cm. 



Both / and / are the sum of a drift term and a diffusion term. For 

 charge neutrahty, where p — nis small compared to p + n, both charge 

 diffusion and particle drift can be neglected. We shall see later that, 

 except right at the junctions, charge diffusion is negligible. 



The Equations of Continuity 

 The two equations of continuity are 



I 



(.ttJ p (J/fJ fi 



dx dx 



= g - r (2.9) 



where g is the rate of pair generation and r the rate of recombination. In 

 terms of / and /, these become I 



^ = (2.10) 



or / = constant and 



^ = 2(^ - r) (2.11) 



which says that the gradient of particle flow is equal to the net rate of 

 particle generation, that is, twice the net rate of pair generation. 



To complete the statement of the problem it remains to express g and 

 r in terms of n and p. 



Generation and Recombination 



The direct generation and recombination of holes and electrons follows 

 the mass action law, in which g — r is proportional to w/ — np. The con- 

 stant of proportionality can be defined in terms of a lifetime t as fol- 

 lows: Let 8p = 871 <$C Ui be a small disturbance in carrier density. Then 

 defining T(g — r) = —8n, we see that the proportionality constant in 

 the mass action law is (2niT)~ . So 



, _ , = !^ipi!£ (2.12) 



and the generation rate 



g = ^ (2.13) 



is independent of carrier concentration. 



