HOLE CONCENTRATION AND POINT CONTACTS 485 



1.8 X 10^^ the concentration corresponding to a resistivity of 7.2 ohm cm 

 is": 



no - 1.8 X 10'V7.2 = 2.5 X IQiVcm^. (43) 



The product of the equihbrium concentrations of electrons and holes is 

 about 4 X 10-^ in germanium at room temperature^-. Thus, for this sample, 



Pa = 4.x 10-V2.5 X IQi-' = 1.5 X lOi-'/cm^. (44) 



If there is an added concentration of holes, pa, resulting from injection, 

 the added conductivity is: 



o-a = (1 + b) eix,,pa = 8.4 X 10-16 Pa • (45) 



The resistivity is changed to: 



P = PoO'o/(<ro + (To) ~ PO (1 — CTaPo), (46) 



the approximate expression holding if the relative change is small. The 

 resistance per unit length of filament is: 



R = 1.15 X 10^ (1 - o-apo). (47) 



The change in voltage gradient, dV/dx = RI, resulting from hole injec- 

 tion is, for a current of 4 X 10'^ amps, 



A{dV/dx) = d(AV)/dx = -46po(r„ . (48) 



Suhl measured the change in probe potential, AF, which resulted when 1 

 ma of the total current of 4 ma was injected from the emitter instead of 

 having the entire 4 ma flowing between the ends of the filament. His 

 values of AF for the four probe points are given in Table II. We have 

 made a plot of these as a function of position and have estimated the 

 gradients at each of the four probe positions. Using these values we have 

 calculated Co from Eq. (48) and the corresponding injected hole concen- 

 tration from Eq. (45). These are given in the last column of the table. 



Suhl's measurements of conductances, G, of the probe points are given 

 in Table III. Also given are differences, AG, from the normal values with 

 no magnetic field and no injection and also these differences multiplied by 

 no/pa ' Values of pa for the case of hole injection were obtained from 

 Table II. Values of AG{n^,/pa) are to be compared with the theoretical 

 value, 



AG {no/ pa) = a^a^A/cn , (49) 



"These values are based on taking //„ = 3500 cmVvolt sec and n,, = 1700 cmVvolt 

 sec, as measured by J. R. Haynes. They correspond to room temperature (295°K). 



^ This value is obtained from an intrinsic resistivity of about 60 ohm cm for Ge at 

 room temperature and the mobility values in reference 11. 



