Percolative Properties of Al-Ge Composite thin Films
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PERCOLATIVE PROPERTIES OF AI-Ge COMPOSITE THIN FILMS A. Kapitulnik, J.W.P. Hsu, and M.R. Hahn, Department of Applied Physics, Stanford University, Stanford, CA 94305 PREFACE (by A.K.) Part of the work described below was delivered as an invited talk by one of us (A.K.) at the special symposium to honour Dr. Ben Abeles for his 65th birthday. During the questions part of my talk, I was asked by Ben Abeles: "what about magnetoresistance...". I answered that this is a complicated issue and I don't have time to discuss this matter. After my talk Ben explained that he always asks this question because his thesis was on magnetoresistance measurements. I remembered this question and decided that this paper would be an excellent place give to the answer. Hence section IV.2 is specialy dedicated to Dr. Ben Abeles. 1. INTRODUCTION Metal-insulator mixture films can show a metallic behavior when the metal fraction is increased above a certain value. Such films can be produced, for example, by coevaporation or co-sputtering of metal and insulator which are not soluble. Here, the metal occupies a certain fraction p of the total volume, which can be determined by the appropriate calibration of the condition of deposition. For this kind of films, an appreciable rise in the conductivity appears above a certain metallic fraction Pc. Thus, we distinguish three main regimes as the metal concentration increases. First, isolated metallic islands of all sizes appear. Then, as more metal is added, a continuous metallic path coexisting with metallic islands is found. Finally, on the metal rich side, isolated insulating islands exist in the metallic continuum. The process described above can adequaly be modeled with percolation theory as was first suggested by Abeles et al.[l]. In particular it is expected that the conductivity of the composite will vanish in the metallic side as
S=0[oP-P]
(1)
as was indeed observed by Abeles et al.[1] with p-=1.9. This result was in good agreement with theoretical predictions (g=1.93)for the exponent of percolation theory [2]. However, the experimental value of Pc, more than 0.5 found for the critical volume fraction , was much higher than the pc= 0 .15 calculated for a three dimensional random continuum [31. It was later shown that this apparent dissagreement was due to the the presence of short range correlations [4], vasdy different for the metal and the insulator. In this respect we introduce the difference between granular materials and random mixtures. Of course, the universality Mat. Res. Soc. Symp. Proc. Vol. 195. 01990 Materials Research Society
154
hypothesis implies that, although the Pc are differ'ent, we expect similar critical behavior near the metal-insulator transition from the classical percolation point of view. A granular system will consist of metallic grains embedded in an insulating matrix. The strong tendency for the formation of droplets of the (usually) crystallite in the insulator, results in a randomly closed packed arrangement of metallic spheres coated with insulating mant
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