1256 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



scale to show the behavior at low values of field and carrier density. 

 In the region of no-recombination the field distribution is indistinguish- 

 able from that for A = ^, which is plotted in Fig. 3 on a linear scale. In 

 the region where recombination is important the solution is found from 

 the assimiption of charge neutrality as will be discussed in Section IV. 

 The cubic and charge neutrality solutions are each shown dashed outside 

 of their respective ranges of validity. For A = 0.665 the half length of 

 the intrinsic region is 2.098 X 2Li . Thus the length of the intrinsic re- 

 gion is more than twice the effective length 2L in which current is 

 generated. The effective length will be discussed in more detail in Section 

 IV and it will be shown that the effective length 2L of current generation 

 is equal to the twice the distance from the IP junction to the minimum on 

 the cubic. As explained earlier, it is convenient to take x = at the mini- 

 mum on the cubic. 



Inirinsic-Exirinsic Junction Under Large Bias 



Consider the limiting case of an intrinsic-extrinsic junction as the 

 bias is increased and the space charge penetrates many diffusion lengths 

 into the intrinsic material. Then the field distribution approaches the 

 straight line E/Ei = x/2Li . This, by Poisson's equation, means that 

 there is a constant charge density of Ni where 



2aLi Li 



Thus in the limit, the field in the intrinsic region approaches that in a 

 completely swept extrinsic region having a fixed charge density of Ni . 

 In germanium at room temperature Ni is about 4.10^" cm~^ As the 

 field approaches the limiting form, the voltage V approaches EiL^/iLi . 

 Thus the limiting form of the current voltage curve is 



aEi L, y 2EiL 



So in the limit the current varies as the square root of the voltage. Typical 

 values for germanium at room temperature are a-Ei = 7 amps cm"""', 

 £/Li = 10"^ and 2EiLi = 50 volts. 



Equivalent Generation Length for an Lntrinsic-Extrinsic Junction 



It should be noted that for an IP structure the current is the same as 

 for an NIP structure with an infinite / i-egion, or at least an / region 

 that is long compared to the distance of penetration of the space charge. 



