1280 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



contact. The voltage is computed as the product of the dc base current 

 and the modulation of the dc base resistance. This modulation can be 

 calculated from the base region resistivity and the dependence of base 

 thickness on collector potential. 



2.5 Summary of Methods 



In developing the design theory, simple physical assumptions are 

 made concerning the behavior of the charge carriers in the semicon- 

 ductor. The transistor is studied as a one-dimensional problem and the 

 per unit area electrical characteristics of the one dimensional structure 

 are computed. The effects of current flow within the base region parallel 

 to the junctions are then calculated for a three-dimensional model. 

 Finally, the equivalent circuit representations of these electronic func- 

 tions are combined in structural fashion to give the terminal electrical 

 characteristics of the junction transistor triode. 



It should be noted that the base region thickness between emitter and 

 collector is assumed uniform, and that design theory has not been ex- 

 tended here to cover the case of non-uniform thickness. Likewise, edge 

 effects at the emitter and surface effects in general are neglected. 

 These omissions were made for mathematical simplicity and are neces- 

 sary omissions in a one-dimensional analysis. The place of surface leakage 

 among the electronic functions is discussed at the end of Section 4.0. 

 Analysis of the effects of sharp discontinuities in base layer thickness 

 requires new solutions to the continuity equation but gradual changes 

 in thickness can be accounted for by averaging over the active area of 

 the transistor the short circuit admittances which are the subject of the 

 next section. 



3.0 ONE-DIMENSIONAL TRANSISTOR 



3.1 General 



This section deals mth the small signal transmission electronics of 

 the structure of Fig. 1 . It is assumed that the emitter is biased to provide 

 a flow of carriers into the base and that the collector is reverse biased 

 sufficiently so that no majority carriers can diffuse out of the collector 

 region into the base region (a reverse voltage of 0.5 volts is more than 

 enough to prevent this). The four admittances associated with minority 

 carrier flow and the two depletion layer capacitances are indicated in 

 Fig. 3. In each case, the design expressions are given first in their most 

 exact form and are progressively simplified. For convenience in dis- 

 cussion and comparison, current densities per unit area rather than 



