594 



BELL SYSTEM TECHNICAL JOURNAL 



In the following analysis, it is assumed that the electrodes of the 

 planar diode are infinite in extent, and that the electron emission is 

 random, so that the equipotential surfaces are parallel planes perpen- 

 dicular to the A:-axis. 



The potential distribution in such a planar diode operating with 

 space charge is shown in Fig. 1. The origin of coordinates is taken at 

 the cathode, and the potential minimum formed by space charge occurs 

 at a distance x = x' from the cathode. The subscript a will be used to 

 denote the space between cathode and potential minimum while ^ 

 applies similarly to the space between minimum and anode. Of all 



Fig. 1- — Potential distribution in planar diode. 



the electrons emitted from the cathode only those whose x-velocity 

 exceeds the value uj corresponding to the potential minimum can 

 penetrate the barrier and proceed to the anode. Electrons with lesser 

 values of initial velocity will come to rest at a point in the a-region 

 where the potential corresponds to their initial velocity and will then 

 return to the cathode. The anode current density is thus given by 



■f. 



I = e i n(u,)duc, 



(1) 



while the relation between velocity u and potential V at a given value 



of X is 



2e 



u^ = u? — 



hm 



V. 



(2) 



