1252 THE BELL SYSTEM TECHJVICAL JOURNAL, NOVEMBER 1956 



creases). The current generated in the intrinsic region is qg per unit 

 volume. So the density of current from pairs generated in the intrinsic 

 layer is 2Lqg = qniL/r. Hence 



/ = /. + ^ 



r 



In what follows we shall assume that Is is negligibly small compared to, 

 /. Then 



r _ /^'^A J (qUiD 



'-\-7)^-\-L- 



Thus / is L/Li times a characteristic current equal to (1) the diffusion 

 current produced by a gradient rii/Li or (2) the drift current produced by ." 

 a field that gives the voltage drop kT/q in two diffusion lengths in normal 

 intrinsic material. In germanium this characteristic current is about 5 

 milliamperes per cm . 



That the current / is proportional to L and independent of voltage 

 follows from the neglect of recombination. When recombination is small 

 compared to generation, then the current has reached its maximum, or 

 saturation, value. All the carriers generated in the intrinsic region are 

 swept out before recombining. It will sometimes be convenient to take 

 (jEi as the unit of current. From the above and (2.8) 



/ „V2£L ^3_^^ 



In germanium aEi is about 7 amperes per cm*. In general we will be deal- 

 ing with currents that are small compared to this. For example, if L, 

 is 1 mm, we would have to sweep out an intrinsic region 3 meters long 

 in order to get a current this large. If we take Ei as the unit field, aEi as 

 the unit current and 2Li as the unit length then the cubic becomes E — 

 I/E = x^ - A. 



For a given structure and temperature the field versus x curves form 

 a one parameter family. A determines both the field distribution and the 

 voltage. The voltage increases as A decreases. Fig. 2 is a plot of E/Ei 

 versus x/2Li for L/2Li =0.1 and several different values of A. Fig. 3 

 is for L = 2Li and Fig. 4 for L/2L, = 3. 



There is an upper limit on A but not lower limit. The reason is as 

 follows: As A increases, the minimum value of E (at x = 0) decreases 

 and the maximum value of s increases. So if A is too large, the maxi- 

 mum 8 will be so large that we cannot neglect recombination, which 

 becomes important when np approaches n', or s approaches 1. Fre- 



I 



