440 BELL SYSTEM TECHNICAL JOURNAL 



fields.^' ^' -' In my opinion this tendency is to be deplored since it is 

 unnecessary and places too much emphasis on zero field. Richardson's 

 equation, and the theories underlying it are just as applicable for 

 accelerating fields as they are to zero field. Since the work function 

 depends on T as well as F, it would be just as logical to coin a new name 

 for the work function at any temperature other than 7" = 0. It 

 seems to me more desirable to retain " work function " in its general 

 sense and to recognize that it may depend on temperature and on the 

 accelerating field. The work function or more precisely the quantity 

 Pm/c would be defined as the work required to take an electron at rest 

 inside the metal to a point at distance Zc from the surface, where Zc is 

 the distance at which the accelerating field is equal to the surface field. 



The Effect of Non-uniform Work F'unctions: Patch Theory 



We shall now consider how the emission is altered if the cathode 

 work function is non-uniform. Here again we shall find it necessary 

 to consider the effect of such non-uniformities on the P vs. z curves, 

 i.e., on the curves for the potential energy of the electron versus dis- 

 tance from the surface. For the present we shall not consider the 

 causes for the mechanism which is responsible for the non-uniformities. 

 We shall assume that the surface work functions are non-uniform. 

 As a consequence, local fields must exist between the various regions 

 having different work functions. The effect of these fields on the 

 log i vs. F curve will depend on the size, shape and degree of the 

 non-uniformities. 



The Simple Condenser A nalog 

 Consider a simple case: The cathode is uniform except in a circular 

 region of radius R which is covered with a positive charge density a, a 

 short distance / above the surface. There is induced at a distance / 

 below the surface the image charge density — a. These two sheets of 

 charge act like a finite circular condenser. The field between the 

 condenser plates will be Aiva e.s.u. or 300 X 4x0- volts/cm. if a is 

 expressed in e.s.u. If the zero of potential is taken at the surface of 

 the metal or at the center of the condenser, the potential just outside 

 the outer sheet of charge will be 300 X 4x0-/. If the sheet of charge 

 were infinite in extent or if R were several times the distance from 

 cathode to anode, then the field outside the condenser would be zero, 

 and the work function of the patch for electrons would be reduced by 

 300 X 47r<7/ or by 300 X IttM; where M = 2<tI the moment per cm.- 

 of surface. Actually there is a field outside the finite condenser which 

 tends to pull an electron back to the surface. The integral of this 



