588 



BELL SYSTEM TECHNICAL JOURNAL 



The electrostatic potential may be evaluated from F in a manner similar 

 to that followed in the preceding section. 



3 . 3 Detailed properties of the solutions 



The general solutions given in the figures illustrate certain properties 

 which can be established through the analytical approximations obtain- 

 able for small and for large values of the relative concentration of added 

 holes. The principal qualitative properties evident from the figures are: 



100 

 60 

 40 



OJ 0.6 



_i 



O 0.4 



S 0.2 



u 



z> 



a. 

 0.06 



0.04 

 0.02 



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



REDUCED DISTANCE VARIABLE, X 



Fig. 3, — The dependence of the reduced concentration on reduced distance for the 

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

 germanium. 



The relative hole concentration, P, and the reduced hole current, Cp , 

 depend exponentially on distance for small concentrations; and for large 

 concentrations all solutions for a given dependent variable run together, 

 independently of the value of the current parameter, and give compara- 

 tively rapid variations of hole concentration and current with distance'". 

 The property that a common solution independent of total current or 



'"These rapid variations would account for the observation of J. R. Hiynes that 

 estimates, for a given emitter current, of hole concentrations or currents in a tllament at 

 a point contact removed from the emitter, with no additional aj^plied field, arc largely 

 indejiendent of changes in/, for the emitter. 



