In Silico Modeling of Indigo and Tyrian Purple Single-Electron Nano-Transistors Using Density Functional Theory Approach
© The Author(s). 2017
Received: 24 April 2017
Accepted: 8 June 2017
Published: 5 July 2017
The purpose of this study was to develop and implement an in silico model of indigoid-based single-electron transistor (SET) nanodevices, which consist of indigoid molecules from natural dye weakly coupled to gold electrodes that function in a Coulomb blockade regime. The electronic properties of the indigoid molecules were investigated using the optimized density-functional theory (DFT) with a continuum model. Higher electron transport characteristics were determined for Tyrian purple, consistent with experimentally derived data. Overall, these results can be used to correctly predict and emphasize the electron transport functions of organic SETs, demonstrating their potential for sustainable nanoelectronics comprising the biodegradable and biocompatible materials.
KeywordsIndigo Tyrian purple Single-electron transistor Density functional theory
The development of organic semiconductors that are capable of both hole and electron transport is of pivotal importance in designing new organic field-effect transistors (OFET) and optoelectronic nanodevices [1, 2]. Recently, the use of indigoids has been widely explored in such devices with a view to the creation of natural and sustainable semiconductors [3–5]. These botanical substances were derived from the plants Indigofera tinctoria and Isatis tintora and have been employed as organic dyes for the textile industry .
Indigoids, including indigo and its derivative, Tyrian purple, are insoluble agents with a very high melting point, a property which is explained by the presence of inter- and intramolecular stabilizing hydrogen bonds (H-bonds). On the other hand, the existence of π-skeleton intermolecular interactions also strongly influences the charge transport within indigo thin films . Both materials are stable in terms of degradation within aerated conditions  and tend to form tiny and highly crystalline films upon evaporation, which exhibit promising charge transport properties . Recent studies have also reported the development of indigo-based OLEDs (organic light-emitting diodes) and OFET devices due to the visible and near-infrared absorption spectra and electron transport characteristics of indigoid molecules [8, 9]. In particular, indigo and Tyrian purple show high and almost perfectly balanced electron and hole charge transport in OFET, owing to their reversible two-electron reduction and oxidation . Another example of OLED devices contained a metal of 5-hydroxy-quinoxaline as a host component and indigo-based electroluminescent layer as a dopant material, comprising of a bisphenyl-squarilium compound .
Various computational approaches have been adapted and successfully implemented in the modeling of coherent transport in different types of molecular junctions, including density-functional theory (DFT), in combination with non-equilibrium Green’s functions or semi-empirical methods [11–14]. However, none of these in silico methods are applicable in the case of molecular single-electron transistors (SET) with incoherent electron transport . Therefore, Kaasbjerg and Flensberg have devised a novel methodology, where they introduced a semi-empirical model for simulating the properties of molecular SETs, including a renormalization of the molecular charge states due to the environment polarization . However, the possibility of indigoid integration within SET nanodevices remains to be investigated.
In the present work, to improve the performance of organic semiconductors, we modeled indigoid-based molecular SETs, which consist of the natural dye molecule weakly coupled to gold electrodes using the optimized DFT approach. These SET systems operate in the incoherent transport regime, and the electron transport is described by sequential tunneling of single electrons and a sequential transport mechanism, such as Coulomb blockade, rather than coherent, ballistic tunneling. The proposed in silico approach has the potential to correctly predict experimentally determined parameters and to explore the electronic properties of indigoids as bio-inspired materials for the development of novel organic semiconductors.
where K is the initial number of electrons in the drain electrode.
where W is the work function of the electrode and the V applied bias.
where ΔE island (N) = E island (N + 1) − E island (N) is the charging energy of the island.
Results and Discussion
The configuration of modeled organic SETs was adjusted where the “indigoid” island only weakly coupled to the metal electrodes, tunneling the electrons from the source to the gate in a time-dependent manner. Therefore, to model this situation correctly, the DFT with LDA and a double-ζ-polarized basis set were applied . The subsequent tunneling process from the island to the drain electrode could be in this regard referred to a transport mechanism, which is independent of the tunneling process into the island . One of the prerequisites for indigoid molecules to be exploited in SET nanodevices is the presence of many alternating double and single bonds because such patterns delocalize the molecular orbitals, making it possible for electrons to move freely over the conjugated area .
Charging energy E N–1 –E N of different charge states of indigo and Tyrian purple molecules in the gas phase
Charging energy (eV)
It is clear from Fig. 3 that the conductance is directly related to the number of energy levels inside the bias window. In this regard, for any given value of V SD (source-drain bias voltage) and V G , the calculated number of charge states in the bias window corresponded to the charge stability diagrams for indigo (Fig. 3a) and Tyrian purple (Fig. 3b). If the charging energy of the “indigoid” island in the gas phase is modified by an electrostatic gate through a tuning of the V G parameter, the energy levels of SET are moved in and out of the bias window.
The relationship between E(q, V G ) and V G is non-linear because the atoms closest to the dielectric region screen V G for the rest of the molecule, decreasing the gate coupling. A difference in the charges on different atoms in the indigoid molecule alters a molecular dipole, which in turn contributes to E(q, V G ).
In the regions starting from 0 to 5 gate voltage, the minimal E(q, V G ) states were detected for Tyrian purple due to the bromination of this molecule (Fig. 5b). Since, the polarizability of a halogen atom increases in the order of F < Cl < Br, bromine shows large polarizability between the halogen atoms . These data also reflected the experimentally determined relative permittivity values of 4.3 for indigo and 6.2 for Tyrian purple calculated from the geometric capacitance at high frequency (>1.0 MHz) . Moreover, the indigoid-based nanodevices exhibited ambipolar operation with the electron (μ e ) and hole (μ h ) mobilities from 10−2 to 0.2 cm2(V × s)−1. In a more recent study, higher mobilities in Tyrian purple were also reported with the μ e and μ h values of 0.4 cm2(V × s)−1 . However, the analyzed SET nanodevices are different from any conventional OFET, which only controls the charge density between the electrodes but on the single-electron transport through the energy modifications of molecular orbitals [32, 33].
Charging energy E N–1 –E N of different charge states of indigo and Tyrian purple molecules in the SET environment
Charging energy (eV)
From these diagrams, it is clear that the non-linear dependence of E(q, V G ) on V G is not detectable because the diagrams only depend on the ΔE values between the charge states. The excitation energy for indigo is greater than for Tyrian purple, but this energy term of the second electron is smaller than for the first one in both modeled systems. Overall, in terms of stability, mobility, low operating voltage, and ON/OFF ratio, the indigoid OFET nanodevices are among the best reported in the literature .
SETs have been proposed as a future alternative to modern Si-based electronics. The use of single molecules, or nanoscale collections of single molecules, as electronic components is the ultimate goal for conventional electronics in order to minimize electrical circuits, replacing bulk materials. Some SETs were successfully realized within individual carbon nanotubes, organic molecules, and self-assembled gold nanoparticles in an experiment [35–37]. The other example of promising SETs based on graphene is being heavily investigated in research labs, because this material promises a band gap tunable by electrostatic gates . For this reason, we have developed the in silico model of the indigoid-based SET nanodevices using the optimized DFT methodology. This theoretical approach was able to correctly predict the main electronic properties of the natural dye molecules weakly coupled to gold electrodes. The improved electron transport characteristics were determined for Tyrian purple SET system, operating in the incoherent transport regime and describing by sequential tunneling of single electrons and sequential transport mechanism, such as Coulomb blockade, rather than coherent, ballistic tunneling. As the best available organic semiconductors, indigoids demonstrate the potential for sustainable electronics based on the biodegradable and biocompatible materials. Concerning the aforementioned experimental data, our simulation results inspire confidence that indigoid-based SET devices will work and be competitive to normal transistors soon or more in the far future.
The authors are grateful to the BMBF (Bundesministerium für Bildung und Forschung) for their partial support of this work by providing the BMBF01 grant to Jens-Albert Broscheit. This publication was funded by the German Research Foundation (DFG) and the University of Wuerzburg in the funding program Open Access Publishing.
SS conceived of the study, participated in its design and coordination, performed the DFT calculations and analysis of results, and drafted the manuscript. NR, CF, and JB conceived of the study and participated in its design and coordination, and analysis of results. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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