Insulator to semimetallic transition in conducting polymers

W. A. Muñoz, Sandeep Kumar Singh, J. F. Franco-Gonzalez, M. Linares, X. Crispin, and I. V. Zozoulenko

Phys. Rev. B 94, 205202 – Published 17 November 2016

Abstract

We report a multiscale modeling of electronic structure of a conducting polymer poly(3,4-ethylenedioxythiopehene) (PEDOT) based on a realistic model of its morphology. We show that when the charge carrier concentration increases, the character of the density of states (DOS) gradually evolves from the insulating to the semimetallic, exhibiting a collapse of the gap between the bipolaron and valence bands with the drastic increase of the DOS between the bands. The origin of the observed behavior is attributed to the effect of randomly located counterions giving rise to the states in the gap. These results are discussed in light of recent experiments. The method developed in this work is general and can be applied to study the electronic structure of other conducting polymers.

Received 5 July 2016
Revised 10 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.205202

Physics Subject Headings (PhySH)

Electronic structure Polarons

Conducting polymers Organic semiconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

W. A. Muñoz^1,*, Sandeep Kumar Singh¹, J. F. Franco-Gonzalez¹, M. Linares^2,3, X. Crispin¹, and I. V. Zozoulenko^1,†

¹Laboratory of Organic Electronics, ITN, Linköping University, 601 74 Norrköping, Sweden
²Department of Physics, Chemistry and Biology, IFM, Linköping University, 581 83 Linköping, Sweden
³Swedish e-Science Research Centre (SeRC), Linköping University, 581 83 Linköping, Sweden

^*william.armando.munoz@liu.se
^†igor.zozoulenko@liu.se

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Vol. 94, Iss. 20 — 15 November 2016

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Images

Figure 1
(a) A representative morphological conformation of PEDOT (blue) with tosylate counterions (green) obtained from MD simulations. (b) A model of crystallite used in semiempirical calculations. The crystallite is composed of five $π − π$ stacked PEDOT chains of the length of 12 monomer units. Negative point charge counterions (red) are randomly distributed around the crystallite.
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Figure 2
DOS of representative crystallites for different carrier concentrations (a) $n_{e} = 0 %$ , (b),(c) $n_{e} = 18 %$ , and (d) $n_{e} = 34 %$ . (For visualization purposes, each level is plotted as a Lorentzian with a finite width.) Note that (b) and (c) correspond to the same $n_{e}$ but different counterion realizations. Blue and red peaks correspond to occupied and unoccupied electronic states, respectively. V.B., C.B., and B.B. correspond to valence, conduction, and bipolaron bands, respectively. States in the B.B. and C.B. are plotted as unfilled and filled curves, respectively. $E_{g} = E_{LUMO} - E_{HOMO}$ is the gap between the valence and bipolaronic bands.
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Figure 3
(a),(b) DOS of (poly)crystalline PEDOT for different carrier concentrations $n_{e}$ [(b) is the same as (a), but curves are vertically shifted for clarity]. Arrows in (b) point to successive bumps vanishing in the valence band and growing in the bipolaronic band as $n_{e}$ is increased. Dotted lines indicate the position of the calculated $E_{HOMO}$ and $E_{LUMO}$ . (c) Fitting the Gaussian and exponential models to the calculated DOS for a representative charge density $n_{e} = 10 %$ ; a broadening of the fitted Gaussian DOS, $Ω_{D O S} = 0.1 eV$ , is indicated. (d) Dependence $E_{g} = E_{LUMO} - E_{HOMO}$ extracted from (b).
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Figure 4
Inverse participation ratio (IPR) for different carrier concentrations $n_{e} = 4 %$ , 18%, and 34%. The curves are averaged; gray dots represent data for $n_{e} = 34 %$ for 1000 configurations. Dashed lines indicate the averaged highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy for each case. A horizontal line shows the IPR for one bipolaron on a single chain. The inset shows the electronic localization of a bipolaron state in a representative crystallite for $n_{e} = 34 %$ .
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Figure 5
A comparison of DFT and semiempirical calculations (left and right panels, respectively) for a single PEDOT chain with one bipolaron in a presence of counterions. (a),(c) Visualization of a molecular orbital for the lowest bipolaron state. (b),(d) Band diagram of the PEDOT chain. The occupied and unoccupied electronic states are denoted in red and blue. For visualization purposes, each level is plotted as a Lorentzian with a finite width. Unfilled Lorentzians correspond to the bipolaron states. V.B., B.B., and C.B. correspond to the valence, bipolaron, and conduction bands, respectively. ${Cl}_{3}^{-}$ and $(- e)$ point charges were used as the counterions in DFT and semiempirical calculations, respectively. The PEDOT chain consists of 16 monomers.
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Figure 6
A comparison of DFT and semiempirical calculations (left and right panels, respectively) for two $π − π$ stacked PEDOT chains with two bipolarons in the presence of counterions. (a),(f) Position of the chains and counterions; (b)–(d) and (g)–(i) Visualization of a molecular orbital for the lowest bipolaron state. [(b),(g) is a side view and (c),(d) and (h),(i) is a top view for the upper and lower chains.] (e),(j) band diagram of a PEDOT chain with one bipolaron. The occupied and unoccupied electronic states are denoted in red and blue. For visualization purposes, each level is plotted as a Lorentzian with a finite width. Unfilled Lorentzians correspond to the bipolaron states. V.B., B.B., and C.B. correspond to the valence, bipolaron, and conduction bands, respectively. ${Cl}_{3}^{-}$ and $(- e)$ point charges were used as the counterions in DFT and semiempirical calculations, respectively. The PEDOT chain consists of 15 monomers.
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