450 



BELL SYSTEM TECHNICAL JOURNAL 



neighboring "valley" square into nine subsquares each, as indicated in 

 Fig. lie. It is apparent that the B squares are all alike; similarly the 

 C, B' and C squares are alike. Determine the /3 for the center of each 

 subsquare. For the A, B, C, A' , B' and C subsquares the values of /3 



1600 



pJ 1200 



E 



Q. 



10.0 



9.8 



9.6 







3b 



2 



2b f- 



3b 



Fig. 14 — A. Distance to critical plane for various points of hill and valley checker- 

 board. B. Potential energy at critical plane for various points of hill and valley 

 checkerboard. 



are, respectively, 1, 2. i. ~ 1. ~ i and — j. Then compute the P 

 vs. z curve for the normals at the center of each subsquare. These 

 are the curves shown in Fig. 13. Next compute the current for each 

 subsquare assuming this to be the same as it would be for an equal area 

 of a large surface having the same work function as that for the center 

 of the subsquare. This is equivalent to assuming that the effect of 

 the velocity components in the x and y directions average out. Do 

 this for various values of F. At each F, add up the currents for all 18 

 subsquares and multiply this by 1/2^^, the number of pairs of squares in 

 a cm.^ This will give the current per cm.^ of surface for various values 

 of F. 



Figure 15 shows the values of the current for the various subsquares; 

 more precisely it shows log i/iao vs. V F where iao is the current that 

 would be obtained from an equal area at zero field for a surface covered 

 with a charge density p which is the average value of the charge 

 density for the entire surface, iao is equal to the current from the hill 

 or active subsquares at zero field, but the current from the valley 



