20 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



mined by the area enclosed by the specified contour lines. It is also 

 possible to compare the measured parameters of a specific device and 

 observe how closely they agree with what is predicted from the estimated 

 concentrations and diffusion coefficients. This is done below for the 

 transistor described in Sections 1 and 2. 



The comparison is complicated by the fact that the exact values of the 

 surface concentrations and diffusion coefficients are not known {Precisely 

 enough at present to permit an accurate evaluation of the design theory. 

 However, the following values of concentrations and diffusion coefficients 

 are thought to be realistic for this transistor. 



iVi = 5 X 10^' /)i = 3 X 10"'' /i = 5.7 X lO' 



iV2 = 4 X 10'' Di = 2.5 X 10"" t^= 1.2 X lO' 



Nz = 10'' 



From these values it is seen that 



Ti/ra = 12.5; r, = 400; X = 0.6 



From Fig. 9, a = 1.9 and from Fig. 10, /3 = 3.6 and therefore w = 1.7. 

 Measurement of the emitter and base layer dimensions showed that these 

 layers were approximately the same thickness which was 3.8 X 10" cm. 

 Thus the ifieasured ratio of emitter width to base width of unity is in 

 good agreement with the ^'alue of 1.1 predicted from the assumed con- 

 centrations and diffusion coefficients. 



From Fig. 11, lo/h ~ —0.01. If this value is substituted into (4.4), 

 7 = 0.997. This compares with a measured maximum alpha of 0.972. 



From Fig. 12, lo = —15. Assuming an average hole mobility of 350 

 cm' /volt. sec. and evaluating Li from the measured emitter thickness 

 and the calculated a, (4.5) gives a value of gb = 1.7 X 10^ mhos per 

 square. The geometry of the emitter and base contacts as shown in Fig. 

 3 makes it difficult to calculate the effective base resistance from the 

 sheet conductivity even at very small emitter currents. In addition at 

 the very high inje{;tion levels at which these transistors are operated the 

 calculation of effective base resistance becomes very difficult. However, 

 from the geometr}^ it would be expected that the effective base re- 

 sistance would l)c no greater than 0.1 of the sheet resistivity or 600 ohms. 

 This is about seven times larger than the measured \'alue of 80 ohms 

 reported in Section 2. 



From Fig. b3, A/^ is approximately 0.20. Thus there should be an over- 

 all aiding elfect of the built-in fields. In addition the impurity gradient 

 at the emitter junction is believed to be approximately lO'Vcm and the 



