THERMIONIC ELECTRON EMISSION 439 



Experimental log i versus yJF plots are found to be straight and to 

 have approximately the right slope for sufificiently high applied fields. 

 At low fields, the line is curved and the experimental slopes are greater 

 than the predicted values. These deviations from Schottky's law are 

 slight in the case of clean surfaces but become quite pronounced for 

 composite surfaces such as thorium on tungsten or caesium on tungsten. 

 We shall show below that these deviations can be ascribed to non- 

 uniformities in the work function for different regions of the cathode 

 surface. The prediction that the slope should vary as 1/7" has been 

 verified by Dushman's experiments.^" 



In so far as Schottky's law is verified by experiment, we can conclude 

 that the escaping electron must in certain regions overcome the forces 

 due to its own image and no other forces. Thus for clean surfaces the 

 electron is acted on only by its image force from about 10~^ to about 

 50 X 10~^ cm. from the surface ; for composite surfaces this region will 

 depend on the size and degree of the non-uniformities ; for a particular 

 surface of thorium on tungsten the image law held from 6 X 10"'' to 

 about 20 X 10""^ cm. When the critical distance is very small, the 

 emission is modified because of sharp points on the surface and because 

 of " intense field " emission.-^ When the critical distance is larger 

 than about 100 X 10"' or 1 X 10"^ cm. there are apparently other 

 fields superimposed on the image field. These are larger than the 

 image field at these distances and thus cause deviations from the 

 Schottky law. As we shall see later these fields are due to non-uni- 

 formities on the surface. From all this we can conclude that an 

 appreciable part of the work function is due to the image force and to 

 other surface fields. 



Table II shows values of A(p, Zc, log i/io and i/io if the surface field 



is given by the image law. 



TABLE II 



Values of A(p, Zc, log ijio and iji^ if the Surface Field is Given by the Image 



Law 



F, volts/cm 100 1000 10,000 40,000 



VF 10 31.6 100 200 



A v', volts 0.0038 0.0120 0.0378 0.0755 



2ecm 00 1.89X10-5 5.98X10-6 1.89 X 10-^ 9.45X10"^ 



log iAo, r= 1000° K... 0.0191 0.0604 0.191 0.382 



ijio " .. 1.000 1.045 1.149 1.553 2.410 



log iAo, r = 2000° K. . . 0.0096 0.0302 0.096 0.191 



iJH " .. 1.000 1.022 1.072 1.25 1.55 



The Use of the Term ''Effective Work Function " 

 There has been a tendency to restrict the term work function to 

 zero field and to use " eff'ective work function " for accelerating 



