Size-Governed Dielectric Properties of Matrix-Isolated and Percolating Mesoscopic Conductors

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Abstract
The dielectric function (DF) = 1 + i2 is a key property of condensed matter. Contact-free measurements of constitute a non-invasive method to characterize size-effects in mesoscopic matrix-isolated conductors with crystal sizes s in the range 10 nm < 8 10 m. At measuring frequencies = 2 well below the plasma frequency P , the dynamic response is not determined by collective excitations of the electron system. We present dielectric data of phase-sensitive spectroscopy in the frequency range 5 Hz 10 GHz. The experiments yield the effective DF ē = ē(,M,∫) of the investigated heterostructures (particles and insulating matrix) which depends on the microstructure, the DF and the volume filling factor ∫ of the disperse component and on the DF M of the pure matrix. At constant filling factor, the size dependent electromagnetic response was studied in a series of experiments at various frequencies. In liquid-matrix colloids with low-melting metal particles, the size of the embedded conductors was varied within the mesoscopic range by means of in-situ thermal coalescence at filling factors ∫ 0.2. This procedure revealed the relationship 3 1 2 2. The size dependence of was quantitatively deduced from by means of an effective medium analysis which yielded 1 s2 and 2 s3. The strongly size-governed DF (s) is a general property of all matrix-isolated metal particles investigated. In order to distinguish the effect of clustering from the response of isolated particles, the complementary microstructure, percolating nanocrystals (s~ 10 nm) with low filling factors ∫~ 0.01 , was studied as well. The DF of nanocrystal networks in air, where ∫ can be changed easily, is dominated by the interparticle contacts and strongly increases with ∫. This corresponds to the strong size dependence for isolated particles. Generally, the temperature dependence (T) for both structures is found to be conspicuously weak compared with the pronounced dependences of (s) for isolated and (f) for percolating particles. On the other hand, the frequency dependence () can be used to distinguish between colloids (where () is quite weak) and percolating networks where 2() -1 (i.e., the conductivity does not depend on ). This, however, does not necessarily imply Drude behavior as the value of 2 lies below the value expected for a dilute classical metal by several orders of magnitude. Moreover, the response of both colloids and networks is capacitive (i.e., 1 > 0 ). For the time being, there is no full theoretical explanation of the non-metallic dielectric behavior observed in either microstructure. The experimental results demonstrate that can be varied in a wide range by adjusting the relevant parameters and thus suggest various possibilities to design artificial heterostructures with dielectric properties tailored for technical applications.