THERMIONIC ELECTRON EMISSION 429 



to get to various distances from the surface. Only when this work- 

 distance curve is postulated to have a high sharp peak within a few 

 atom diameters from the surface, is it possible to deduce values of ? 

 which are appreciable. Now we have good reasons ^ for believing 

 that no such peaks exist, and that the maximum of the work distance 

 curve occurs at relatively large distances from the surface in a region 

 where the forces on the electron are given by the well-known image law. 

 For the latter type of curve, the computed value of r is less than 0.07 

 which is negligibly small. Nordheim, who first pointed out that the 

 transmission coefficient might differ from unity says: " However, the 

 exact computation taking into account the image force which must 

 necessarily be considered, has shown that such a rounded-off potential 

 curve yields a value of D \vhich differs inappreciably from 1.0." * 

 A more complete case showing that the values of the reflection coef- 

 ficient are negligibly small is given by Becker and Brattain.^ 



The Effect of Accelerating Fields and Retarding Potentials 



Thus far we have considered how the emission current and the work 

 function depend on the emitting surface and its temperature ; we have 

 implicitly assumed that the current was " saturated " or that every 

 electron which escaped from the surface was collected by the anode. 

 It is, however, well known that the emission current depends also on 

 the applied fields and the applied potentials. In considering the effects 

 of these fields and potentials we shall incidentally obtain an insight 

 into the nature of some of the forces responsible for the work function. 



For simplicity consider a large plane cathode and parallel to it a 

 large plane anode. If the temperature of the cathode is high enough 

 to emit a small but appreciable current, log i w'xW vary with the poten- 

 tial applied to the anode in the manner shown in Fig. 3. In drawing 

 curve 1 in this figure three more simplifying assumptions have been 

 made; namely (1) that the contact potential between cathode and 

 anode is zero ; (2) that all portions of the cathode and anode have the 

 same work function, and (3) that space charge effects are negligible. 

 The effect of these assumptions will be considered later. 



The curve in Fig. 3 naturally divides itself into two portions: the 

 part to the left of Va = corresponds to retarding potentials while 

 the part to the right of corresponds to accelerating potentials. In 

 the latter region the current is said to be " saturated " although 

 strictly speaking the current is never saturated but increases indef- 



* See Section by Nordheim in Miiller-Pouillets Lehrbnch der Physik* Vol. IV, 

 "Elektrizitat und Magnetism us," Part IV, p. 294. See also footnote 2 on p. 290. 



