1272 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



1 .2 Method and Assumptions 



The usefulness of the junction transistor derives primarily from the 

 flow of holes or electrons across two closely-spaced p-n junctions, one 

 of which is biased in the forward or conducting direction while the other 

 is biased in the reverse or non-conducting direction. Development of 

 design theory begins quite properly with analysis of this mechanism, 

 which is considered, for simplicity, as a problem in the flow of holes and 

 electrons in one dimension, at right angles to the p-n junctions. In the 

 analysis, it is assumed that these carriers are controlled largely by the 

 voltages applied to the junctions and that they move principally by 

 diffusion. The dependence of the diffusion currents on the junction volt- 

 ages is reduced to a set of two terminal-pair short-circuit admittances, 

 which form the initial and most important segment of the equivalent 

 circuit model for the junction transistor. 



Practical transistors have not only the very useful transisting mecha- 

 nism mentioned above, but also passive capacitances across the charge 

 depletion layers which separate the p and n regions at each junction. 

 These capacitances limit the useful frequency range of transistors and 

 must be considered in any practical theory. In the synthesis of the 

 equivalent circuit, these capacitances are placed in parallel with the 

 short-circuit input and output admittances which represent the flow of 

 diffusing holes and electrons. 



A further limitation on performance is imposed by the ohmic or body 

 spreading resistance of the base region. The base current of the transistor, 

 in flowing from the region between the emitter and collector to the base 

 contact, develops a base contact to emitter voltage which seriously 

 limits the frequency response. Calculation of these effects requires the 

 assumption of flow paths for the base current. The circuit elements rep- 

 resenting base spreading resistance effects appear in series in the base 

 leg of the equivalent circuit. 



1 .3 Existing Design Theory 



W. Shockley's classic paper* announcing the junction transistor also 

 initiated the design theory. Diffusion effects for dc and low frequencies 

 were analyzed, and formulae for depletion layer capacitances were de- 

 veloped. The mechanism of the frequency cutoff of the current trans- 

 mission (alpha) was reported in a subsequent article t, and the effects of 



* W. Shocklev, The Theory of p-n Junctions in Semiconductors and p-n Junc- 

 tion Transistors, B.ST.J., 28, p. 435. 



t W. Shockley, M. Sparks, and G. K. Teal, The p-n Junction Transistors, 

 Phys. Rev., 83, p. 151, July, 1951. 



