FLOW OF ELECTRONS AND HOLES IN GERMANIUM 601 



with m , the concentration of holes or electrons in intrinsic germanium at 

 T deg abs, given in (73). It may be estimated that temperature rises of 

 less than 100 deg C will make 10 ohm cm »-type germanium substantially 

 intrinsic in its behavior. 



The range of values of the parameter C for which the numerical solu- 

 tions are given corresponds, for example, to current densities up to the 

 order of 10 amp cm~- in germanium filaments of about 10 ohm cm re- 

 sistivity, for the mean lifetime r about 10 /xsec; for this mean lifetime, the 

 distance unit Lp is approximately 2- 10~- cm. Current densities correspond- 

 ing to the larger values of C will ordinarily produce appreciable joule 

 heating in filaments some 10~^ cm''^ in area of cross-section, cemented to a 

 backing, with temperature rises of the order of 100 deg C. 



The effect of joule heating on Lp and C may be evaluated from 



(75) 



300 



Lp= 6.6 



C = 2.6- 102 I ::^ 





where r is expressed in sec, / in amp cm~^, and p is the normal resistivity 

 in ohm cm of the germanium at T deg abs. These are obtained from the 

 definitions (8), taking the hole mobility in the thermal scattering range 

 to be proportional to T ', with the value 1700 cm- volt~^ sec~^ at 300 deg 

 abs.'^ 



5.3 Series solutions for the extrinsic semiconductor in the steady state 

 Maclaurin's series for G in the relative concentration P are of the form 



(76) G = aiP -f a^F' + a^P^ + . . . 



for the cases of field opposing and field aiding, the solutions passing 

 through the {P, G)-origin. Substituting the series (76) for G in the differ- 

 ential equation (27) for the w-type semiconductor in the steady state, it 

 is found, in accordance with (30), that 



(77) ai=HC±VCM^], 



the sign of C being taken before the radical for field opposing, the other 

 sign for field aiding. The other coefficients are given in terms of ax and 



^ loc. cit. 



