USE OF FIELD EMISSION ELECTRON MICROSCOPE 913 



perimental curves agreed fairly well with the theoretical ones for both slope 

 and intercept. The values of r, deduced from the location of the experimental 

 Hnes, ranged from 2 X 10-^ cm for low temperature treatment to 3 X 10"^ 

 cm after repeated glowing at 2800°K. 



The theoretical family of curves was based on the Fowler-Nordheim 

 equation modified for the electron image effect :^ 



i(amps/cm^) = ^-^ X 10"^ i^^F^ ^-(,3/./^,)6.8 x io7/(x) (^) 



in which the field = KXV volts/cm and x = ^'^^ ^ ^^-^KV ^ ^^^^_ 



heim* gives a table of /(x) vs x. From this we plotted f{x) ws KV ior (p = 

 4.4 volts, and found that for values of the field KV from 15 million to 95 

 milUon volts/ cm, f(x) was given by 



fix) = .968 - 5.54 X 10-» KV (7) 



This range of field covers nearly all values which are usually encountered 

 in field emission. By substituting Eq. (7) in Eq. (6) and putting (p = 4.4 

 we obtain 



j = 3A2XiO-' K'V'.'"r'''^ ''""""'' (8) 



For a W point in which the major part of the current comes from an 

 area of about r^ cm^ having a work function (p of 4.4 volts, and making an 

 angle of about 25° with the axis, the current i in amperes is given by 



log i = -5.00 + .04 + 2 log r + 2 log /^ + 2 log V - """^^ '"^ (9) 



in which K is sl function of r, h, and d given by Eq. (3). For the experimental 

 tube the point to anode distance was 4.0 cm. Since the field at the point will 

 vary only shghtly with the exact shape of the anode we have put d = 4.0 

 cm. For r = 3 X 10"^ cm 



Ko = 5300 cm-i. K;, = .924 Ko = 4900 cm-i 



and 



logi = -7 + .41 + 2 log F - 5.40 X lOVF (10) 



Similar equations can be deduced for other values of r. 



From Eq. (6) it follows that the current density and hence the screen 

 brightness depend on the work function </?, and the field KV: the current 

 density increases as <p decreases, and increases as K increases. Since the single 

 crystal point exposes all possible planes and since it is known that different 



