488 BELL SYSTEM TECHNICAL JOURNAL 



in which /„o is the electron current for zero hole current. The electron 

 current is: 



In = /„o + (a - l)/p . (55) 



Thus we have 



[n ^ /no + (« - l)/p ^bn ^ bjXf + p) , 



Ip Ip p p ' 



This equation may be solved for Ip to give: 



Ip = pIno/{bNf + (a - 1 - b)p). (57) 



The term (a — I — b)p is generally small compared with bN/ and may 

 be neglected. We thus have approximately for p/Nf small and Nf <^ tio, 



I = Ino+ alp = /„o[l + (ap/bn,)l (58) 



When expressed in terms of the normal current, 



h = /nod + (apo/bno)], (59) 



the equation for / is of the form (51) : 



/ = /o [1 + iaPa/bm)l (60) 



From a comparison of (51) and (60) it can be seen that: 



7 = a/b or a = by. (61) 



Values of a determined from empirical values of y for the four point 

 contacts of Haynes are given in Table IV. The values are of a reasonable 

 order of magnitude for formed collector points. 



An estimate of the importance of diffusion can be obtained by compar- 

 ing the hole current in Haynes' experiments with the hole current which 

 would exist if the electron current were zero, so that holes move by diffu- 

 sion alone. Equations (28) to (33) apply to the latter case. In addition to 

 {33} we need an equation which expresses the hole current flowing into 

 the contact in terms of the hole concentration, pb, at the contact. If the 

 reverse bias is large, no holes will flow out and the entire hole current is 

 that from semiconductor to metal as given by an equation similar to (3) : 



Ip = —epbVaA/4:. (62) 



Substituting this value for Ip into equation (33) we get an equation which 

 may be solved for Pb, to give: 



Pb = api{\ 4- c) ^ api, (63) 



