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Abstract
We calculate the effective macroscopic dielectric constant ε_{a} of a periodic array of spherical nanocrystals (NCs) with dielectric constant ε immersed in the medium with dielectric constant ε_{m} 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 ε_{a}(s) in the limit ε/ε_{m} 蠑 1. Using the scaling hypothesis, we interpolate between them near s = 0 to obtain new approximated function ε_{a}(s) for ε/ε_{m} 蠑 1. It agrees with existing numerical calculations for ε/ε_{m} = 30, while the standard meanfield MaxwellGarnett and Bruggeman approximations fail to describe percolationlike behavior of ε_{a}(s) near s = 0. We also show that in this case the charging energy E_{c} of a single NC in an array of touching NCs has a nontrivial relationship to ε_{a}, namely, E_{c} = αe^{2}/ε_{a}d, where α varies from 1.59 to 1.95 depending on the studied threedimensional lattices. Our approximation for ε_{a}(s) can be used instead of mean field MaxwellGarnett and Bruggeman approximations to describe percolation like transitions near s = 0 for other material characteristics of NC arrays, such as conductivity.
Original language  English (US) 

Article number  113104 
Journal  Applied Physics Letters 
Volume  108 
Issue number  11 
DOIs  
State  Published  Mar 14 2016 
Bibliographical note
Funding Information:The authors would like to thank Han Fu and B. Skinner for helpful discussions. This work was supported primarily by the National Science Foundation through the University of Minnesota MRSEC under Award No. DMR1420013.
Publisher Copyright:
© 2016 AIP Publishing LLC.
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 2 Finished


MRSEC IRG2: Sustainable Nanocrystal Materials
Kortshagen, U. R., Aydil, E. S., Campbell, S. A., Francis, L. F., Haynes, C. L., Hogan, C., Mkhoyan, A., Shklovskii, B. I. & Wang, X.
11/1/14 → 10/31/20
Project: Research project