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LII. The Electrical Resistance of Thin Metallic Films, and 

 a Theory of the Mechanism of Conduction in such Films. 

 By W. F.'G. Swann, D.Sc 9 A.R.C.S.* 



rriHE theory which attributes electrical conduction to the 

 JL presence of free electrons requires, in order that the 

 variation of the resistance of a metal with the temperature 6 

 shall be explained, that the mean free path of an electron 

 shall vary as 6~ 2 f. 



The original object of the present work was to test this 

 fact by direct experiment. Patterson % has shown that the 

 specific resistance of a very thin film is abnormally high, and 

 moreover, that it increases enormously rapidly as the thick- 

 ness diminishes below a certain critical value. Sir J. J. 

 Thomson has shown that a rapid increase of this kind can be 

 explained as due to the fact that when the dimensions of the 

 film get comparable with the mean free path of an electron, 

 those electrons which at any instant are moving in a direction 

 inclined to the plane of the film do not get a chance of 

 travelling for their complete mean free path, so that the 

 electric field does not produce in them the full velocity 

 which it would produce if the true mean free paths were 

 described. Sir J. J. Thomson shows that if t, the thickness 

 of the film, is greater than 2\, where \ is the mean free path 

 in a large mass of the metal, \' the mean free path in the 

 film is given by 



^-K 1 -*) (1) 



V-«{J + iWtr} (2) 



from which it follows that \' does not begin to diminish 

 rapidly as t decreases, until t becomes less than X. The 

 thickness at which V, and consequently the conductivity, 

 starts to diminish rapidly gives, on this theory, an approxi- 

 mate measure of the mean free path. Now if \ varies as 



* Communicated by the Author. Experiments performed at the 

 University of Sheffield. Paper read at the Meeting- of the British 

 Association, 1913. 



t Formerly it was supposed that the mean free path should vary as 

 0- 1 (see Sir J.J. Thomson, 'Corpuscular Theory of Matter,' p. 80), 

 but O. W. Richardson (Phil. Mag. [6] xxiii. p. 275) points out that in 

 the theory of the Thomson effect (which plays an important part in the 

 subject) a term has been omitted by all previous workers. The inclusion 

 of this term leads to 0~ 2 as above. 



t Patterson, Phil. Mag. [6] iv. 1902. 



2 H 2 



and if t<\ 



