12 THE BELL SYSTEM TECHNICAL JOUENAL, JANUARY 1956 



to the fre(iuency response of the transistor. In addition the base re- 

 sistance will be dependent on the distribution of both diffusants. These 

 three factors are discussed in detail below. 



Moll and Ross have determined that the minority current, /,„ , that 

 will flow into the base region of a transistor if the base is doped in a non- 

 uniform manner is given by 



f N(x) dx 



where rii is the carrier concentration in intrinsic material, q is the elec- 

 tronic charge, V is the applied voltage, Dm is the diffusion coefficient of 

 the minority carriers, and the integral represents the total number of 

 uncompensated impurities in the base. The primary assumptions in this 

 derivation are (1) planar junctions, (2) no recombination in the base 

 region, and (3) a boundary condition at the collector junction that the 

 minority carrier density at this point equals zero. It is also assumed that 

 the minority carrier concentration in the base region just adjacent to the 

 emitter junction is equal to the equilibrium minority carrier density at 

 this point multiplied by the Boltzman factor exp (qV/kT). It is of special 

 interest to note that Im depends only on the total number of uncom- 

 pensated impurities in the base and not on the manner in which they 

 are distributed. 



In the double diffused transistor, it has been convenient from the 

 point of ease of fabrication to make the emitter layer approximately the 

 same thickness as the base layer. It has been observed that heating sili- 

 con to high temperatures degrades the lifetime of n- and p-type silicon 

 in a similar manner. Both base and emitter layers have experienced the 

 same heat treatment and to a first approximation it can be assumed that 

 the lifetime in the two regions will be essentially the same. Thus as- 

 sumptions (1) and (2) should also apply to current flow from base to 

 emitter. If we assume that the surface recombination \'elocity at the 

 free surface of the emitter is infinite, then this imposes a boundary 

 condition at this side of the emitter which under conditions of forward 

 bias on the emitter is equivalent to assumption (3). Thus an equation 

 of the form of (3.1) should also give the minority current flow from base 

 to emitter. Since the emitter efficiency, y, is given by 



^ J. Tj. Moll and I. M. Ross, The J)opendencc of Transistor Paramotors on tlie 

 Distribution of Base Layer liesistivity, Proc. I.R.E. in press. 

 8 G. Bemski, private comnmnication. 



