668 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



. ^ = -E. (40 



dy 



Equations (2')-(4') will also be used within the n-type extrinsic 

 region {y < 0) and the p-type extrinsic region (y > L). However, for 

 the n-type region (1') is replaced by 



^ = 2(N + p-n), (I'a) 



dy K 



where N denotes the excess concentration of ionized donor over ac- 

 ceptor centers for y < 0. Similarly, for the p-type region (1') is replaced 

 by 



^ = ?(_P + p-n), (I'b) 



dy K 



where P denotes the excess concentration of ionized acceptor over 

 donor centers for y > L. 



In order to solve the equation set (l')-(40 for the intrinsic region 

 < y < L, it will be necessary partially to solve the sets (I'a) (2')- 

 (4') and (I'b) (2')-(4') governing the two extrinsic regions because only 

 in this way can a sufficient number of appropriate boundary conditions 

 be imposed. 



Deep inside the extrinsic regions the electric field intensity will be 

 negligible and the mobile carrier concentrations will have their equi- 

 librium values. This leads to the conditions 



E =^ 0, np = n], n — p = Nsity=— ^ (7) 



and 



E = 0, np = n% p - n = P at ?/ = + 00 . (8) 



It will further be supposed that there is no infinite charge concentration 

 at the extrinsic-intrinsic interfaces so that the electric field intensity is 

 continuous at the interfaces. The concentration of the (local) majority 

 carrier will also be assumed continuous at an interface. In short, 



E and n are continuous at ?/ = (9) 



