1283 



(A4) 



Setting AE equal to some fraction, say 20 per cent of E^ gives a family 

 of curves for V versus L with ?? as a parameter. Prim has plotted such 

 curves in Fig. 11 of his paper. His curves will be good approximations 

 when V for a given L and 77 lies above the V given by (A4). 



Prim's results are expressed in terms of the parameters U = 

 qV/2kT and L = 2L/£e where £e is the Debye length in the extrinsic 

 material. £e is given by the same formula as £ except that A'' replaces n» . 

 Substituting these into (A4) and setting AE = Ei/5 gives 



L = 3.57 — '■ r,U (A5) 



ni£ 



Prim's U versus L curves will be accurate up to the point where they 

 intersect the corresponding curves from (A5). For germanium a reason- 

 able value of NLi/ni£ is about 10 . This says that Prim's curves go bad 

 at about L = 10 , which would be about 2.1 X 10~^ cm in germanium 

 at 300°C. 



Branching of the V versus L Curves 



An effect which does not emerge from the zero-current analysis is 

 that V may have several values for the same L and 7/. In other words 

 the V versus L curve for given ?? will have more than one branch. Specifi- 

 cally, there will be a single V versus L curve up to a certain L at which 

 the curve splits into three branches that diverge as L increases. This 

 may be seen as follows: Consider an intrinsic region that is long compared 

 to the diffusion length. Suppose a bias is applied that is low enough not 

 to appreciably affect the space charge and potential drop at the junc- 

 tions. A current will flow and a proportional, ohmic voltage drop will be 

 developed across the intrinsic region. If the intrinsic region is long 

 enough, this ohmic voltage may become large compared to the built-in 

 voltage before the voltage drop at the junctions has changed appre- 

 ciably. In this range the field penetration parameter will be rising from 

 zero to about unity as V increases from the built-in voltage and ap- 

 proaches the ohmic voltage. As the voltage continues to increase, the 

 space charge begins to penetrate the intrinsic region and a majority of 

 the voltage drop comes in the space charge regions. Let L be the ef- 

 fective length of current generation. When L is larger than a diffusion 



