THERMIONIC ELECTRON EMISSION 



449 



points above a hill checker than for points above a valley checker. 

 Values of Zc and P,„ are shown in Fig. 14. 



Figure 14A shows Zc at various values of x iov y = Q; it also shows 

 Zc at various values of x for y = bjS. Figure 14B shows Pm for these 



10.0 



9.9 



9.8 



9.7 



h 9.6 



9.5 



9.4 



9.3 



9.2 



F= 5000 VOLTS PER CM 

 b = 1 XIO"'* CM 



Poo= 10.0 VOLTS 

 JUL = 0.1 68 VOLTS 

 P = 0.200 VOLTS 



200 



400 



z - 



600 800 tOOO 1200 1400 1600 



DISTANCE FROM CATHODE IN CENTIMETERS 



1800X10" 6 



Fig. 13 — Potential energy vs. distance from the surface above the center of the dif- 

 ferent subcheckers of hill and valley checkerboard; applied field of 5000 volts/cm, 



same values of x and y. Since P„, — K = ipe, it is clear from these 

 figures that different portions of the surface will have different work 

 functions, or stated more precisely, the energy an electron must have 

 to cross the critical surface (loci of the values of Zc) depends upon 

 where it crosses the critical surface. This in turn means that the 

 chance that a given electron will escape depends not only on its 

 normal component of velocity but also on the place at which it leaves 

 the surface and on the angle its path makes with the surface. 



To compute accurately the emission current is a very difficult task. 

 It would appear that the following procedure should give a good 

 approximation to the true current. Divide a "hill" square and a 



