684 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



leads to 



fc' I'nA/h' ^ a. 



Now set k' = ^e^ to obtain 



Are^ ^ a 



or 



/(r) = r — tnr — tn^/a ^ 0. 



A rough approximation to r is obtained by neglecting ^nr in comparison 

 to r, it is r ;^ in 4/a. This can be used to compute a much better ap- 

 proximation from Newton's formula: 



' ""^ fin)- 

 The resulting useful formula is 



/n4/a - 1_ 



DISCUSSION OF FIELD DISTRIBUTION CURVES 



For the symmetric case {N = P) for which numerical computations 

 were made, the electric field is a minimum in the middle of the intrinsic 

 region, and rises to symmetrical maxima at the extrinsic-intrinsic inter- 

 faces. For fixed L and relatively small U the field is very small except 

 quite near the interfaces. That is, practically all the potential drop 

 takes place in thin "space charge layers" near the intrinsic boundaries 

 at 5 = and y — L. As U is increased (for given L) the region of ap- 

 preciable field strength increases in width and the minimum field at 

 y = L/2 increases. As U is made very large the minimum field strength 

 approaches the average field over the intrinsic region. In this limit the 

 potential distribution approaches linearity across the intrinsic region. 



For N 9^ Pj the qualitative behavior of the field is the same except 

 that the minimum field (^ = 0) moves away from y = L/2 and the 

 maxima at y = and y = L are no longer equal. This minimum field 



(see (38b), (39b)) occurs at 



h L + e'" {X'" - A-^'^) 



Unless the asymmetry is very pronounced, this will not differ appreciably 

 from L/2 because of (40 c, d). It will be shown in a following section 



