The Electrical Conductivity of Sputtered Films
TT has been known for a long time that the specific resistance of the very *• thinnest metal films is abnormally high. 1 Two theories have been advanced to explain this fact; one by J. J. Thomson 2 depends upon a shortening of the mean free path of the conducting electrons by the surface of the film; the other by Swann 3 depends upon an assumed granular * structure of the film and consequent opposition offered to the motion of the electrons by the gaps between the grains. Swann 3 has raised one
... nn 3 has raised one objection to Thomson's theory. Another has developed as a result of the present work. Thomson gives as the expression for the mean free path of an electron in a film X being the mean free path for the metal in bulk, and t being the film thickness. Evidently X' varies less rapidly than the first power of t; and since the specific conductivity, other things being the same, is probably proportioned to X/ we find that the specific conductivity of a film should vary less rapidly than the first power of t. This, however, is certainly very seldom if ever the case. The writer finds this exponent, instead of having a value less than unity, to have values ranging between . 10 and 50, and sometimes reaching as high as 200. Swann's theory, on the other hand, seems open to at least two objections. First, it .is difficult to picture the mechanism by means of which in all cases the grains of the film are distributed so as to lie separated from one another by gaps of practically uniform width. The natural supposition would appear to be (as indeed Swann suggests) that of a more or less random distribution, in which certain grains would undoubtedly touch some of their neighbors and be quite distantly separated from others. When two grains actually touch, it would seem reasonable to suppose 1 1. Stone, PHYS.