HOLE CONCENTRATION AND POINT CONTACTS 



487 



Haynes' measurements may be fitted by an empirical equation of the 

 following form: 



/ = h\\ + ypa/m)\, (51) 



in which /o is the normal collector current flow for a given collector volt- 

 age, / is the collector current flowing for the same collector voltage when 

 the hole concentration is increased by pa , and Hq is the normal electron 

 concentration. Values of h and 7 for four different formed phosphor- 

 bronze collector points are given in Table IV. The collector bias is —20 

 volts in each case. It can be seen that the variations in 7 are much less 

 than those in /q. It will be shown below that 7 is related to the intrinsic 

 a of the point contact. 



COLLECTOR 

 Vf, = -20 VOLTS 



■* lb SWEEPING CURRENT 



Fig. 8. — Experimental arrangement used b}' J. R. Haynes to determine relation be- 

 tween hole concentration and current to collector point biased with large voltage in re- 

 verse direction. 



In Haynes' experiment, holes are attracted to the collector by the field 

 produced by the electron current and diffusion plays a minor role. In 

 contrast to the preceding examples, the terms involving the field F in 

 Eqs. (21) and (22) are large and the diffusion terms represented by the 

 concentration gradients are small. It follows from (21) and (22) that the 

 ratio of electron to hole current density is then: 



in/ip = bn/p, (52) 



which is equal to the ratio of the electron and hole contributions to the 

 conductivity. If n and p do not vary with position, the ratio is the same 

 everywhere and equal to the ratio of total electron and hole currents, 

 /„ and Ip'. 



Inllp = inlip = hnl p. (53) 



The currents /„ and /,, can also be related to the intrinsic a for the con- 

 tact by use of an equation of the form: 



/ = /„o + a/p, (54) 



