THE FORWARD CHARACTERISTIC OF THE FIX DIODE 687 



the device are 



W'^2 X 10"^ cm 



P -- 10'' cm"' 



(3) 

 Ar+ p+ ^ 10^' cm"' 



L„ , Lj, ^ 10"^ cm 



where L„ , Lp are minority carrier diffusion lengths in the contacts. 



The present treatment makes three distinct approximations. The first 



is to neglect the voltage drop in the contacts. The highest currents ordi- 



I narily used are of the order of 500 amp/cm" which should produce an 



ohmic drop in the contacts of about 1 volt/cm. Since the entire diode has 



a length of about 0.01 cm we are neglecting only about 0.01 ^'olts in this 



I approximation. 



The second approximation is to regard the Debye length as small 

 compared to w and the diffusion lengths L„ , Lp . li L„ , Lp are as small 

 as the typical values given in (3) the error made in this approximation 

 is not completely negligible. Nevertheless, we use the approximation be- 

 cause it enables us to regard the device as three relatively large neutral 

 regions and two relatively narrow space charge regions. The behavior of 

 the device can then be determined by solving for the diffusion and drift 

 of carriers in the neutral regions subject to boundary conditions con- 

 necting the carrier densities across the space charge layers. 



The third approximation is to neglect any increase in majority carrier 

 density in the contacts due to injection of minority carriers. This approxi- 

 mation is valid until the current density approaches 5 X 10 amp/cm", 

 which is well above anticipated operating currents. It is conceivable 

 that in some junctions all the current may flow through small active 

 spots at which the current density is ^'ery high, perhaps exceeding the 

 above figure. In such cases the current flow is two or three dimensional 

 and the present analysis would not apply. 



It is also necessary to assume some law for carrier recombination. We 

 shall assume that recombination in the contacts is linear in the injected 

 minority carrier density 



din ■ n — np+ 



rKJ 



ax T 



Modification of the theory to suit other recombination laws is simple in 

 principle, although considerable analytical complications might be en- 

 countered. It seems most likely that in silicon FN junctions the re- 

 combination actuallv is nonlinear. It can be shown that if the rccombi- 



