THE FORWARD CHARACTERISTIC OF THE PIN DIODE 693 



From (26) the potential drop in the middle region can be written 



(35) 



(36) 



Thus the total applied bias y as a function of total current density / is 

 given by 



/5F = (iij - V^ ^^ ^ + ^^ 1 , J / v> + ^^^ T- (^^) 

 /o 7^ - Too 1 + 0(7/7 J- Ips 



where y{I) is the (positive) solution of (31). 



Thus far we have referred the problem of the V — I characteristic to 

 the problem of calculating 7(7) from (31). We see that in the limits of 

 high and low current 7 approaches the limits 



7 -> 1 / « /o 



(38) 



7 — ^ 7oo i » io 



and in general lies between these limits. A good approximate solution is 

 readily obtained by replacing (31) with the cjuadratic equation 



7=1- 4(7/700)' - 1] 



z = {i/ur (1 + hr" 



which has the solution 



V7co' + 4(1 + z)zyJ - 7. 



7 = 



2z 



(40) 



A plot of this solution is shoAvn in Fig. 2 as a function of z for 7oo = x^"^, 

 7oo = 2. Since 7(7) is bounded by unity and 700 , which usually will be of 

 order unity, we can reject some of the dependence of V upon 7 and re- 

 tain only its essential dependence upon 7. This appears in the first and 

 second terms of (37). By means of (31) this second term can be written 



/n7 (7/7.)^ + 1 



^^' [7 - 1 \/l + 6(7/7jd T h 



7 



(41) 



Retaining only the essential dependence on 7 we write this equation 



i87p = C(7/7„)^^' (42) 



