Sec. 1-1] 



UFA 7/1 .\7< '. I /„ IXl'l ' T 77,'. I \S/,l y </7,'N 



If, 



where s is the thickness of the plates. Values of the function /(s/ri) 

 are tabulated in Table 1 . 



Table 1. Fringe -effect Correction Factors 

 for capacitive transducers 



Equation (3) is strictly valid only if the capacitor plates are com- 

 pletely surrounded by the medium with the dielectric constant e. 1 



The method is applicable for the thickness determination of thin 

 insulator layers; the minimum thickness is determined by voltage- 

 breakdown considerations. The dielectric constant of the insulator 

 must be known and constant. Humidity variation is likely to change 

 the value of e. Sharbough and Fuoss 2 have applied the capacitive 

 method for the determination of the width of small gaps used in 

 breakdown studies. The (relatively large) distance d 2 between two 

 semispherical electrodes is measured with a mechanical gauge and 

 the capacitance between the electrodes is observed. The spheres are 

 then moved closer together to the distance d x , which is too small to be 

 measured mechanically. The distance d x can be determined from 

 the change of capacitance 



AC = 2kae In % 

 d x 



where k = 0.0885 (for linear dimensions in centimeters), a the radius 

 of the spheres, and e the dielectric constant of the medium surround- 

 ing the spheres. Distances as small as 1 [x can be determined with an 

 error of less than 5 per cent. 



Capacitive displacement transducers, which can also be used for 

 thickness determination, are treated in detail in 1-23. 



1 For other capacitors see A. H. Scott and H. L. Curtis, J. Research Natl. 

 Bur. Standards, 22, 747 (1939). 



2 A. H. Sharbough and R. M. Fuoss, Rev. Sci. Instr., 26, 657 (1955). 



