HOLE CONCENTRATION AND POINT CONTACTS 489 



> 



with a given by Eq. (6). Using (63) for pb, we get: 



I J, = kTtxnpiA/n = {kT<roA/ebrb){pi/no). (64) 



With kT/e = .025 volts, co = bnoe^l^ = 0.2 (ohm cm)-i, A - lO"* cm^ 

 and fd = 5 X 10~* cm, we get for the diflfusion current: 



/p = (5 X I0-^){pi/no) amps. (65) 



Comparing (65) with (57) we see that diffusion of holes will not be im- 

 portant if 



Ino » 5 X 10-« amps. (66) 



This condition is satisfied in Haynes' experiments. 



In the case of point contacts formed to have a high reverse resistance 

 as diodes, /o may be of the order of 10"'' to 10~® amps at room tempera- 

 ture. Diffusion of holes will then play a role, and the hole current will 



Table IV 

 Relation between hole concentration and collector current from data of J. R. Haynes. 

 Data represented by 



/ = /o(l + (ypa/no)) 

 where / is current flowing to collector point biased at —20 volts and pa/tto is ratio of added 

 hole concentration to the normal electron concentration. 



be larger than indicated by Eq. (53). As discussed in reference (4) there 

 is still a question as to the importance of holes in the saturation current 

 observed by Benzer in diodes with high reverse resistance. Experiments 

 similar to those of Haynes would be valuable to determine the influence 

 of hole concentration on reverse current. 



Acknowledgment 



The author is indebted to G. L. Pearson, J. R. Haynes, W. H. Brattain, 

 and H. Suhl for use of the experimental data presented herein; to W. 

 Shockley for a critical reading of the manuscript and a number of valuable 

 suggestions, and to W. van Roosbroeck for aid with some of the anal- 

 yses and for suggestions concerning the manuscript. 



APPENDIX A 



Diffusion of Holes with Surface Recombination 



In the calculation of the diffusion of holes given in Section III of the 

 text it was assumed that no recombination of electrons and holes oc- 



