1242 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



It is necessary to take account of (1) space charge, (2) carrier drift, (3) 

 carrier diffusion and (4) recombination according to a nonlinear bi- 

 molecular law. Of these four, only space charge and recombination are 

 never simultaneously important in practical cases. Nevertheless certain 

 simplifications can be made if the problem is formulated so as to take 

 advantage of them. The field and carrier distributions in the intrinsic 

 region are found by joining two solutions: one solution is for charge 

 neutrality; the other, which we shall call the no-recombination solution 

 is for the case where the recombination rate is negligible compared to the 

 rate of thermal generation of hole electron pairs. We shall show that in 

 practical cases the ranges of validity of the two solutions overlap; that 

 is, wherever recombination is important, we have charge neutrality. 



Prim's Zero-Current Approximation 



Prim* derived the field distribution in a reverse biased NIP structure; 

 on the assumption that the hole and electron currents are negligibly small 

 differences between their drift and diffusion terms, as in the zero- bias 

 case. He showed that the average diffusion current is large compared 

 to the average current. However, as it turns out, this is misleading.: 

 Throughout almost all of the intrinsic region (where the voltage drop 

 occurs in practical cases) the diffusion current is comparable to or 

 smaller than the total current. The larger average diffusion current comes 

 from the extremely large diffusion current in the small regions of high 

 space charge at the junctions. Prim's analysis, in effect, neglects the space 

 charge of the carriers generated in the intrinsic region. These may be 

 neglected in calculating the field distribution if the intrinsic region is 

 sufficiently narrow or the reverse bias sufficiently high. In the appendix 

 we derive the limits within which Prim's calculation of the field and 

 potential will be valid. The range will increase with both the Debye 

 length and the diffusion length in the intrinsic material. However, in 

 cases of practical interest the zero-current approximation may lead to 

 serious errors in the field distribution and give a misleading idea of the 

 penetration of the field into the intrinsic region. The present, more 

 general analysis, reduces to Prim's near the junctions where the zero- 

 current assumption remains valid. The zero current approximation was, 

 of course, not intended to give the hole and electron distributions in the 

 intrinsic region or to evaluate the effects of interacting drift, diffusion 

 and recombination. 



Ibid. 



