Dielectric constant and charging energy in array of touching nanocrystals

K. V. Reich, B. I. Shklovskii

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Abstract

We calculate the effective macroscopic dielectric constant εa of a periodic array of spherical nanocrystals (NCs) with dielectric constant ε immersed in the medium with dielectric constant εm 蠐 ε. For an array of NCs with the diameter d and the distance D between their centers, which are separated by the small distance s = D - d 蠐 d or touch each other by small facets with radius ρ 蠐 d what is equivalent to s < 0, | s | 蠐 d we derive two analytical asymptotics of the function εa(s) in the limit ε/εm 蠑 1. Using the scaling hypothesis, we interpolate between them near s = 0 to obtain new approximated function εa(s) for ε/εm 蠑 1. It agrees with existing numerical calculations for ε/εm = 30, while the standard mean-field Maxwell-Garnett and Bruggeman approximations fail to describe percolation-like behavior of εa(s) near s = 0. We also show that in this case the charging energy Ec of a single NC in an array of touching NCs has a non-trivial relationship to εa, namely, Ec = αe2ad, where α varies from 1.59 to 1.95 depending on the studied three-dimensional lattices. Our approximation for εa(s) can be used instead of mean field Maxwell-Garnett and Bruggeman approximations to describe percolation like transitions near s = 0 for other material characteristics of NC arrays, such as conductivity.

Original languageEnglish (US)
Article number113104
JournalApplied Physics Letters
Volume108
Issue number11
DOIs
StatePublished - Mar 14 2016

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