SHOT NOISE IN DIODES 613 



electrons at the plate are very large in comparison with their initial 

 velocities for practically all of the electrons. This means that the 

 transit time for the various electrons is practically the same for all 

 of them which leave the cathode within a particular very short time 

 interval, even though the initial velocities of the various electrons are 

 statistically distributed among them. It results that the various 

 individual velocities of the electrons in the /3-region may be replaced 

 by an average value, which at the potential minimum may be defined 

 as follows : 



u'n{ii,)duc 



-a--^ (55) 



n{uc)duc 



f 



Physically, the meaning of this expression is the average velocity 

 of these electrons which cross a plane in the )3-region close to the po- 

 tential minimum in a unit of time. Inasmuch as the unit of time may 

 be taken to be very small, it follows that (55) expresses the effective 

 instantaneous value of the initial velocity which may, and does, 

 fluctuate as time goes on. 



On the basis of an equation of the form 



the planar diode has been extensively investigated by a number of 

 workers and it has been shown ^ that the relation between current 

 and voltage is completely specified as soon as two boundary conditions 

 are given. These may be the initial velocity and acceleration, or 

 they may equally well be the initial velocity and conduction current 

 pu. However, the analysis based on (56) applies strictly to the case 

 where all of the charge moves with the same velocity and hence 

 contains a certain approximation when electrons are considered whose 

 velocities have a certain dispersion around some mean value. The 

 error will be small until frequencies are considered which are so high 

 that a large proportion of the electrons which left the cathode in a 

 time interval which is very short compared with the period of the 

 high frequency arrive at the anode in a time interval which is not 

 small compared with the high frequency period. Normally this means 

 that the error is small even for frequencies so high that the majority 

 of the electrons require several cycles to make their transit from 

 potential minimum to anode. 



