PRIXCiri.FS OF TRAXSISTOR ACTION 269 



liole current might be obtained as follows: The number of holes entering 

 the space charge region i)er second is''^ 



where ui,,, is the hole concentration at the semi-conductor boundar}' of the 

 space-charge layer and z'„ is an average thermal velocity (~ 10^ cm/sec). 

 The hole current, I,,, is obtained by multiplying by the electronic charge, 

 giving 



/;. = -nhbevaAc/4: (4.14) 



If we set iii,h equal to the equilibrium value for the interior, say lO'Vcm^ 

 we get a current //, ~ 4 X 10"^ amps, which is of the observed order of 

 magnitude of the saturation current at room temperature. With this in- 

 terpretation, the temperature variation of Is is attributed to that of Uh, 

 which, according to Eq. (3.11), varies as exp {-Eo/kT). The observed 

 value of e is indeed almost equal to the energy gap. 



The difficulty with this picture is to see how Uhh can be as large as Uh 

 when a current is trowing. Holes must move toward the contact area 

 primarily by diffusion, and the hole current will be limited by a diffusion 

 gradient. The saturation current depends on how rapidly holes are gener- 

 ated, and reasonable estimates based on the mean life time, — t, yield 

 currents which are several orders of magnitude too small. A diffusion 

 velocity, Vd, of the order 



vn - {D/Tyi\ (4.15) 



replaces i'a/4 is Eq. (4.14). Setting D ~ 25 cmVsec and t ~ lO"^ sec 

 gives I'D -^ 5 X 10', which would give a current much smaller than the 

 observed. What is needed, then, is some other mechanism which will 

 help maintain the equilibrium concentration near the barrier. Surface 

 effects may be important in this regard. 



Forward Current 



The forward characteristic is much less dependent on such factors as 

 surface treatment than the reverse. In the range from to 0.4 volts in 

 the forward direction, the current can be fitted quite closely by a semi- 

 empirical expression''^ of the form: 



/ = i,{/"' - 1), (4.16) 



where W is the drop across the barrier resulting from the applied voltage, 

 as defined by Eq. (4.7). Equation (4.16) is of the general form to be ex- 

 pected from theory, but the measured value of /3 is generally less than the 

 theoretical value el'kT (40 volts"^ at room temperature). Observed values 



