436 BELL SYSTEM TECHNICAL JOURNAL 



abundantly confirm the theory that the distribution of velocities of 

 thermions is that given by Maxwell's law for an ideal gas. 



Accelerating Fields 



As illustrated in Fig. 3, when positive potentials are applied to the 

 anode, log i increases continuously ; but the rate of increase becomes 

 progressively less so that the current is almost independent of the 

 anode potential. For many purposes one can safely say that the 

 current is saturated ; for some purposes, however, it is very important 

 to consider this lack of saturation. More specifically a consideration 

 of this effect gives us direct evidence of some of the forces which are 

 responsible for the work function. Thus, as the electron escapes from 

 the surface, it must overcome certain forces which tend to pull it back. 

 The electrical fields responsible for these forces presumably decrease 

 with the distance from the surface. Call them surface fields Fs. 

 When a positive potential is applied to the anode, a field Fa is produced 

 near the surface of the cathode which tends to help the electrons 

 escape. The value of the field depends on the dimensions of the 

 cathode and anode. This applied field neutralizes the surface field at 

 some distance s from the surface ; call this distance the critical distance 

 Zc. If an electron can reach the critical distance, it will escape, since 

 beyond this distance the sum of the applied and surface fields pulls the 

 electron toward the anode. Obviously the critical distance moves 

 closer toward the cathode as the applied field is increased. 



A more quantitative concept is obtained by considering the effect 

 of the applied field on the potential energy-distance curve similar to 

 Fig. 4. Now, however, we will be concerned more particularly with 

 regions close to the cathode, so that we will greatly enlarge the distance 

 scale. Figure 7, curve 1 , shows such a curve when the true field between 

 cathode and anode is zero. The true field F is the algebraic sum of the 

 applied field Fa and the field produced by the contact potential. Fre- 

 quently it is convenient to use the term " applied field " in the sense 

 of " true field," i.e., including the contact potential field. An applied 

 field decreases the potential energy of the electron as shown in curve 2. 

 The net potential energy is shown in curve 3. 



The maximum height in curves 1 or 3 represents the work function 

 v? in the classical theory or the quantity Pv,/e in the quantum theory. 

 In the latter case, since <pe = P,„ — K from eciuation (24) and since 

 K does not depend on the applied field, 



^<f= APJe (47) 



