DIFFUSED EMITTER AND BASE SILICON TRANSISTORS 13 



/m (emitter to base) 



-y = . . . 



/^(emitter to base) + /„j(base to emitter) 



proper substitution of (3.1) will give the emitter efficiency of the double 

 diffused n-p-n transistor, 



1 



7 = 



J-'n 



Z).^''^-^"^ 



dx 



p .6 (3.2) 



\ (No - iVj dx 



In (3.2), Dp is the diffusion coefficient of holes in the emitter, /)„ is the 

 diffusion coefficient of electrons in the base and the ratio of integrals is 

 the ratio of total uncompensated doping in the base to that in the 

 emitter. 



A calculation of transit time is more difficult. Kromer has studied 

 the case of an aiding field which reduces transit time of minority carriers 

 across the base region and thus increases frequency response. In the 

 double diffused transistor the situation is more complex. Near the 

 emitter side of the base region the field is retarding (Region R, see Fig. 8) 

 and becomes aiding (Region A) only after the base region doping reaches 

 a maximum. The case of retarding fields has been studied by Lee and 

 by MoU.^ At present, the case for a base region containing both types of 

 fields has not been solved. However, at the present state of knowledge 

 some speculations about transit time can be made. 



The two factors of primary importance are the magnitude of the 

 built-in fields and the distance over which they extend. In the double 

 diffused transistor, the widths of regions R and A are determined by the 

 surface concentrations and diffusion coefficients of the diffusants. It 

 Can be shown by numerical computation that if region R constitutes no 

 more than 30-40 per cent of the entire base layer width, then the overall 

 effect of the built-in fields will be to aid the transport of minority car- 

 riers and to produce a reduction in transit time. In addition the absolute 

 magnitude of region R is important. If the point x' should occur within 

 an effective Debye length from the emitter junction, i.e., if x' is located 

 in the space charge region associated with the emitter junction, then the 

 retarding fields can be neglected. 



The base resistance can also be calculated from surface concentrations 

 and diffusion coefficients of the impurities. This is done by considering 

 the base layer as a conducting sheet and determining the sheet con- 



' J. L. Moll, private communication. 



