THEORY OF THE SWEPT INTRINSIC STRUCTURE 1277 



To find E when s is known we express the current I = qiJp — Jn) 

 in terms of s and E. Since w — p is small compared to n + p, we set 

 /; = p = sUi in (2.2) and obtain 



I = 



[ j^ 1 - h kT dsl ,„ ,„v 



Thus the current contains both a drift and a diffusion term. This is to be 

 expected for unequal mobilities. When holes and electrons have the 

 same concentration gradient, the electrons, which have the higher dif- 

 fusion constant, diffuse faster than the holes; hence the diffusion gives a 

 net current. It is seen that in the recombination region the total carrier 

 concentration has a symmetrical distribution about the point where it 

 is a maximum but the field remains unsymmetrical. 



Junction Solution 



When (Eo/Eif is large compared to I/cEi the junction solution is 

 independent of 6; so the solution obtained in Section V is valid. In all 

 cases the junction solution can be found using the method of Section V. 

 The effect of h will be small over most of the range where the junction 

 solution holds because the concentration of one type of carrier will be 

 negligible. To be exact, / in (5.8) should be multiplied by the factor 

 (1 + ^Xo/L), which can be taken to be (1 + b)/2b at the NI junction 

 and (1 -f b)/2 at the IP junction. Instead of equation (5.7) we have 



as can be seen by differentiating (6.10) with Ei = 2Li = o- =1. 



VII. EFFECT OF FIXED CHARGE 



This section will deal briefly with the case where there is some fixed 

 charge but where the carrier charge cannot be neglected. For no recom- 

 bination, the field distribution is given by a first order differential equa- 

 tion. Solutions in closed form are obtained for the case of pure drift flow. 

 For recombination and charge neutrality the solution in Section IV is 

 valid provided the fixed charge is small compared to Ui . We have seen 

 that at large fields the E versus x curve becomes linear, correspond- 

 ing to a fixed charge density of A''; where Ni = \/2n{£/L,- . Thus 

 the fixed charge may have a dominant effect on the space charge while 

 having a negligible effect on the solution in the range where recombi- 

 nation is important. 



