Applied Physics Letters, volume 108, issue 11, pages 113104
Dielectric constant and charging energy in array of touching nanocrystals
Publication type: Journal Article
Publication date: 2016-03-14
Journal:
Applied Physics Letters
Quartile SCImago
Q1
Quartile WOS
Q2
Impact factor: 4
ISSN: 00036951, 10773118
Physics and Astronomy (miscellaneous)
Abstract
We calculate the effective macroscopic dielectric constant $\varepsilon_a$ of a periodic array of spherical nanocrystals (NCs) with dielectric constant $\varepsilon$ immersed in the medium with dielectric constant $\varepsilon_m \ll \varepsilon$. For an array of NCs with the diameter $d$ and the distance $D$ between their centers, which are separated by the small distance $s=D-d \ll d$ or touch each other by small facets with radius $\rho\ll d$ what is equivalent to $s < 0$, $|s| \ll d$ we derive two analytical asymptotics of the function $\varepsilon_a(s)$ in the limit $\varepsilon/\varepsilon_m \gg 1$. Using the scaling hypothesis we interpolate between them near $s=0$ to obtain new approximated function $\varepsilon_a(s)$ for $\varepsilon/\varepsilon_m \gg 1$. It agrees with existing numerical calculations for $\varepsilon/\varepsilon_m =30$, while the standard mean-field Maxwell-Garnett and Bruggeman approximations fail to describe percolation-like behavior of $\varepsilon_a(s)$ 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 non-trivial relationship to $\varepsilon_a $, namely $E_c = \alpha e^2/\varepsilon_a d$, where $\alpha$ varies from 1.59 to 1.95 depending on the studied three-dimensional lattices. Our approximation for $\varepsilon_a(s)$ 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.
Top-30
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Citations by publishers
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5 publications, 41.67%
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Wiley
2 publications, 16.67%
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1 publication, 8.33%
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1 publication, 8.33%
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1 publication, 8.33%
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Springer Nature
1 publication, 8.33%
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1 publication, 8.33%
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- We do not take into account publications without a DOI.
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Reich K. V., SHKLOVSKII B. I. Dielectric constant and charging energy in array of touching nanocrystals // Applied Physics Letters. 2016. Vol. 108. No. 11. p. 113104.
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Reich K. V., SHKLOVSKII B. I. Dielectric constant and charging energy in array of touching nanocrystals // Applied Physics Letters. 2016. Vol. 108. No. 11. p. 113104.
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TY - JOUR
DO - 10.1063/1.4944407
UR - https://doi.org/10.1063/1.4944407
TI - Dielectric constant and charging energy in array of touching nanocrystals
T2 - Applied Physics Letters
AU - Reich, K V
AU - SHKLOVSKII, B. I.
PY - 2016
DA - 2016/03/14 00:00:00
PB - American Institute of Physics (AIP)
SP - 113104
IS - 11
VL - 108
SN - 0003-6951
SN - 1077-3118
ER -
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@article{2016_Reich,
author = {K V Reich and B. I. SHKLOVSKII},
title = {Dielectric constant and charging energy in array of touching nanocrystals},
journal = {Applied Physics Letters},
year = {2016},
volume = {108},
publisher = {American Institute of Physics (AIP)},
month = {mar},
url = {https://doi.org/10.1063/1.4944407},
number = {11},
pages = {113104},
doi = {10.1063/1.4944407}
}
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Reich, K. V., et al. “Dielectric constant and charging energy in array of touching nanocrystals.” Applied Physics Letters, vol. 108, no. 11, Mar. 2016, p. 113104. https://doi.org/10.1063/1.4944407.