Charge transport in silicon nanocrystal superlattices in the terahertz regime

H. Němec, V. Zajac, P. Kužel, P. Malý, S. Gutsch, D. Hiller, and M. Zacharias

Phys. Rev. B 91, 195443 – Published 28 May 2015

Abstract

Silicon nanocrystals prepared by thermal decomposition of silicon-rich 2–5-nm-thick ${SiO}_{x}$ layers ( $0.64 \leq x \leq 1$ ) are investigated using time-resolved terahertz spectroscopy. The samples consist of a superlattice of isolated monolayers composed of Si nanocrystals with controlled variable size and filling fraction. Experiments with variable optical pump fluence over almost two orders of magnitude allow us to determine the depolarization fields in the structure. Careful consideration of the local fields along with Monte Carlo calculations of the microscopic conductivity of Si nanocrystals supported by structural characterization of the samples provide detailed information about the electrical connectivity of nanocrystals and about the charge transport among them. Well below the percolation threshold, nanocrystals grow mostly isolated from each other. In thicker or in more Si-enriched layers, nanocrystals merge during their growth and form tens-of-nanometer-sized photoconducting Si structures with a good electrical connection. In addition, in thick ${SiO}_{x}$ layers, imperfectly connected clusters of Si nanocrystals are observed which develop probably at the end of the growth process and allow only limited charge transport due to energy barriers.

Received 23 December 2014
Revised 15 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.195443

Authors & Affiliations

H. Němec¹, V. Zajac^1,2, P. Kužel^1,*, P. Malý², S. Gutsch³, D. Hiller^3,†, and M. Zacharias³

¹Institute of Physics ASCR, Na Slovance 2, 18221 Prague 8, Czech Republic
²Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 3, 12116 Prague 2, Czech Republic
³IMTEK Faculty of Engineering, Albert-Ludwigs-University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany

^*kuzelp@fzu.cz
^†daniel.hiller@imtek.uni-freiburg.de

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Vol. 91, Iss. 19 — 15 May 2015

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Images

Figure 1
Examples of distributions of NC sizes. Symbols: distribution determined from EF-TEM images; solid lines: fit using log-normal probability distribution; vertical dashed lines: mean values. Upper panels display a direct number-of-particle distribution; lower panels show the number-of-particle distribution weighted by $d^{2}$ .
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Figure 2
Examples of spectra of the normalized transient transmission $Δ T_{norm}$ [or, following (6), to the normalized sheet conductivity] measured for pump-probe delay of 10 ps (symbols) and fits using the model described in the text (lines). Error bars denote the normal deviation (1σ) calculated over a large statistical ensemble of spectra (50–4000) measured in the time domain with 30 ms time constant. In some cases, these error bars are smaller than the size of symbols. Systematic errors are discussed in the text.
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Figure 3
Examples of the mobility spectra of Si NCs with variable size calculated using the Monte Carlo approach. In order to emphasize the difference in the shape of the real part, the spectra are normalized to the same initial slope of the imaginary part (the spectra for 4.4 nm and 15 nm NCs are multiplied by factors 40 and 3.67, respectively).
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Figure 4
Scheme of the morphology of investigated samples as deduced from THz photoconductivity measurements. (a) NCs in samples S93, M93, M85, and M100 are well isolated from each other and no tendency to aggregation is observed. (b) NCs in the sample M64 start to form clusters; some of these clusters may form a percolation network on a medium length scale (the pathways closest to the percolation are illustrated by thick dotted lines). (c) In thick layers (L93), weakly connected NCs may develop in ${SiO}_{x}$ layers at the end of the phase-separation technological step. The electron transport among these NCs is limited. Insets: Equivalent electrical circuits of the structures.
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Figure 5
Dynamics of transient conductivity spectra for samples (a) with different ${SiO}_{x}$ layer thickness and (b) with different composition $x$ . The pump fluence in all measurements was in the range $3.1 - 3.6 \times 10^{13} {photons / cm}^{2}$ . The lines serve as guides to the eye.
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Figure 6
(a) Effective absorption coefficient $α_{eff}$ of a layer with NCs as a function of the absorption coefficient of the NCs $α_{Si}$ . The vertical dashed line denotes the absorption coefficient of bulk Si. (b) Maximum achievable effective absorption coefficient as a function of the volume fraction occupied by the NCs. The symbols indicate the measured absorption coefficient of the investigated samples. Parameters of the calculation are provided in the Appendix.
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