Dielectric Properties of Percolating Nanocrystals
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DIELECTRIC PROPERTIES OF PERCOLATING NANOCRYSTALS
P. MARQUARDT AND G. NIMTZ II. Physikalisches Institut der Universitit zu K6ln, D-5000 K6ln 41, FRG
ABSTRACT Microwave spectroscopy revealed a non-metallic effective dielectric function E=
El +
ie
2
of non- supported nanocrystal networks. This new result is
in agreement with the size-induced metal-insulator transition (SIMIT) observed in isolated sub-pm conductors. Separating the particle contribution 6 61 + i62 from the measured effective dielectric response E leads to the conclusion that percolating networks of SIMIT particles are characterized by an enormous positive value of El and a conductivity ' -, 6 2 much smaller than expected for metallic networks. Another non- metallic feature of the networks is the weak thermal influence on e, and C2. All properties change sensitively with the filling factor f of the network. Their unusual dielectric properties make low- density nanocrystal networks candidates for applications e.g. as high permittivity capacitor materials or temperature-independent resistors.
TEXT Investigations in the microwave and radiofrequency range v = w/27r < 10GHz belong to the least invasive measuring techniques of dielectric properties and as such are suitable for experiments on mesoscopic conductors. Here, far below the plasma frequency wp of electron ensembles with metallic densities, the dielectric function (DF) 6 = 61 + i62 is governed by single electron excitations. Previously, the DF of matrix-isolated mesoscopic conductors was found to be non- metallic and to depend strongly on the particle size s. The conductivity u(s) = CoW6 2 (s) (with co the free space permittivity) decays proportional to s3 [11. This size-induced metal-insulator transition (SIMIT) is accompanied by a positive real part -I(s) which increases as s' [2]. Both E2 (s) , s3 and e1 (s) , S2 are not expected within the Drude model which introduces size effects via a surface-enhanced momentum scattering
Mat. Res. Soc. Symp. Proc. Vol. 195. ©1990 Materials Research Society
176
rate 1/r(s) = 1/r(oo) + vF/8 with VF the Fermi velocity [3]. In contrast to the SIMIT behavior, the Drude DF of conductors larger than the mean free path, some 10-s m at room temperature, is expected to have a large negative real part dominating the positive lattice contribution and a bulk conductivity u(oo) = ew"2 'r(oo). Microwave experiments indicate that el(s) passes a pronounced maximum before the negative classical value el - -(wPr(00))2 is reached. From the effective response of various metal colloids a positive value of ei(s) ce 105 can be extrapolated for s lym [2]. Further experimen1p tal evidence for non-metallic behavior of minute conductors comes from the weak dependence of c on temperature T and frequency w in the investigated
ranges T < 400K, w < 10GHz, and 10 nm < s < l1m [4]. Some applications as capacitor materials require highly polarizable materials without dominating losses (i.e. e 2 < el). Due to the s"- dependence of e 2 and the weaker ,2 dependence of cl, the loss tang
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