590 



BELL SYSTEM TECHNICAL JOURNAL 



100 

 60 

 40 



20 



10 

 6 



1.0 

 ; 0.6 



i 0.4 

 ) 



; 0.2 



J 

 J 

 J O.t 



J 0.06 



) 



) 0.04 



) 



J 



• 0.02 



0.01 

 0.006 

 0.004 



0.002 

 0.001 



2 4 6 8 10 12 14 16 18 20 22 24 



REDUCED DISTANCE VARIABLE, X 



Fig. 5. — The dependence of the reduced electrostatic field on reduced distance for 

 the steady-state one-dimensional flow of holes with mass-action recombination in M-type 

 germanium. 



3.31 The behavior for small concentrations 



The exponential dependence of P and Cp on distance for P small is 

 given for the w-type semiconductor by the analytical approximations, 



iP = Ps exp [- h[±V0T^ - C\X] 



(46) • 1 ^ ^ 



Cp = _[±VC2-f 4 + C]P, 



where P., is a suitable constant. If C is positive, the plus sign holds for 

 field aiding^^ and the minus sign for field opposing. These approximate 



^' It is evident from the curves for C,, in Fig. 4 that the exponential extrapolation hack 

 to the emitter location of estimates of hole concentrations or currents at a point contact 

 on a germanium filament lead to values of/, for the emitter which are too small. Using 

 moderately large injected currents and no additional a])plied heids, J. R. IIa\nes once 

 obtained in this way an apparent/, of about 0.2. From the figure, this is the apparent/, 

 to be expected for moderate and large values of C for the true/, equal to unity. 



