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Negative differential resistance in fused thiophene trimer
Computational Materials Science 45 (2009) 889–898
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Negative differential resistance in fused thiophene trimer Sabyasachi Sen, Swapan Chakrabarti * Department of Chemistry, University of Calcutta, 92, A.P.C. Ray Road, Kolkata 700 009, India
a r t i c l e
i n f o
Article history: Received 16 April 2008 Received in revised form 6 November 2008 Accepted 12 December 2008 Available online 20 January 2009 PACS: 73.23.b 31.15.E 85.65.+h 81.07.Nb Keywords: Molecular electronics Quantum transport Nonequilibrium Green’s functions Density functional theory Negative differential resistance Molecular projected self-consistent Hamiltonian states
a b s t r a c t Current–voltage characteristics of trimer unit of cis-polyacetylene and fused thiophene trimer have been analyzed by employing nonequilibrium Green’s functions technique. In the present investigation, both the molecular systems have thiol end group and they form a self-assembled monolayer on Au (1 1 1) surface. The current–voltage characteristics of fused thiophene trimer and trimer unit of cis-polyacetylene illustrates that negative differential resistance feature gets sufficiently improved due to the addition of heteroatom sulphur to the cis conformation. The negative differential resistance feature is observed over the bias range of ±1.6 V to ±2.45 V for fused thiophene trimer and ±2.1 to ±2.45 V for trimer unit of cispolyacetylene. Manifestation of negative differential resistance feature has been explained by monitoring the shift in transmission resonance peak across the bias window with varying bias voltages. Modification of negative differential resistance feature due to addition of heteroatom (sulphur) to the cis configuration has been explained at the molecular level through an analysis of molecular projected self-consistent Hamiltonian states. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Invention of molecular and nanoelectronic components such as wires, diodes, transistors, oscillators and switches [1–8] as well as the physical understanding of their current (I)–voltage (V) properties have greatly enhanced the quest for designing novel molecular systems with unusual electronic transport properties. Electronic transport at the molecular level is influenced by quantum effects like quantum interference of electron waves, quantization of energy levels and so forth. Experimentally, unusual current–voltage behavior has been reported in scanning tunneling microscope (STM) study on 1,4 benzene-dithiolate molecule [7]. Conducting features of some small conjugated molecules like phenyl based derivatives [9] have been measured by mechanically controllable break junction experiment. Moreover, interesting physical situations like negative differential resistance (NDR), highly nonlinear current–voltage (I–V) characteristics, switching behavior have been reported in DNA [10], carbon nanotubes [11] and organic systems [12]. All these achievements and the aspiration to design modern molecular electronic devices motivate us to explore the underlying theoretical background of quantum transport processes. * Corresponding author. Tel.: +91 33 23508386; fax: +91 33 23519755. E-mail address: [email protected] (S. Chakrabarti). 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.12.010
Several attempts have been made at the theoretical level to explain the I–V characteristics of the molecular systems [2,13–18]. Quantum transport properties of materials in mesoscopic dimension are usually described by the Landauer theory [19]. It relates the transmission probability of electron with that of current. Büttiker [20] has given an extension of the Landauer theory [19] in multi-terminal molecular wire systems. A molecule or molecular chain placed between two bulk electrodes is a nonperiodic system. Under the application of finite voltage the system deviates from the equilibrium and the electrochemical potential at the molecule-electrode contact gets changed. In most of the theoretical analysis this nonequilibrium situation has been described through density functional theory (DFT) based nonequilibrium Green’s functions (NEGF) technique and in certain cases through semi empirical approach [21]. Lang [22] employed density functional theory (DFT) to predict the NDR behavior in two atomic dimers placed between two electrodes. Nonequilibrium situation in phenyldithiolate molecule bridging two gold electrodes was explained by Xue and co-workers [23]. A combination of Green’s function technique and DFT has been employed by Derosa and co-workers to explain the quantum transport in molecular system of Aun-S(p-C6H4)-S-Aun [24]. Seminario et al. [25] used DFT combined with molecular dynamics simulations to explain the conductance of thiotolane monolayer.
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One of the fascinating aspects of the modern quantum transport phenomena is NDR. In an electronic system, decrease in current due to the increase in voltage is recognized as NDR feature. The issue of NDR in molecular systems has been addressed in large number of communications. Reed and co-workers [8] reported NDR behavior in 20 -amino-4-ethynylphenyl-40 -ethynylphenyl-5´-nitro1-benzenethiolate. Chen et al [26] investigated NDR feature in molecule containing a nitroamine redox center. In their study, NDR feature was ascribed to the voltage induced redox reaction, i.e. on the change in the charge distribution in the wire and on conformational changes. NDR feature in polyphenylene-based molecular wires incorporating saturated spacers was reported by Karzazi et al. [27]. In their quantum chemical study, NDR feature was attributed to the resonant tunneling originated from shifting of the molecular energy level by external electric field. NDR feature in molecular device composed of donor and acceptor moieties was presented by Lakshmi et al. [28]. From, their two level model calculation they conjectured that the NDR behavior appears due to the bias driven electronic structure change from one class of insulating phase to another through exceedingly delocalized conducting phase. Emberly and co-workers [29] investigated NDR behavior in chain molecule. In their tight binding formalism, NDR behavior was attributed to the formation of charge density wave and consequent bond weakening. Tight binding model was also used by Léonard et al. [30] to explain the NDR feature in nanotube devices. Apart from these, several other investigations such as reduction of the acceptor moiety [31], charging effect [32–34] etc. are also quite successful in explaining the NDR behavior. Albeit, large numbers of theoretical and experimental investigations have been carried out on NDR materials [26–34], number of molecular systems having such feature is still very limited [27,35,36–38]. The experimental work of Kratochvilova and coworkers pointed out the dearth of self-assembled molecular systems in the nano device fabrication area [35]. In some of the theoretical investigations, NDR feature was attributed to specific kind of molecular systems which posses a central quantum well separated from two metallic leads by tunnel barriers [27]. Moreover,
in certain cases emergence of NDR feature depends on some added external factors like ring rotation, twisting of the ring structure leading to conformational changes [36,37] etc. Furthermore, the existence of NDR in gated molecular devices is still an unresolved issue to both the theoreticians and experimentalists [38]. All these realizations provide enough motivations to carry out further investigations and identify new materials with NDR feature. In the present theoretical work, we investigate NDR behavior in the molecular system of fused thiophene trimer and trimer unit of cis-polyacety-
Fig. 2. Current–voltage (I–V) characteristic of two probe systems of trimer unit of cis-polyacetylene and fused thiophene trimer self-assembled on Au (1 1 1) surface.
Fig. 1. (a) Structure of the two probe system of fused thiophene trimer self-assembled on Au (1 1 1) surface. Thiol ended fused thiophene trimer together with two surface gold layers in the left and right electrodes are included in the self-consistent calculation, while remainder of the gold electrodes are atoms described by employing bulk Hamiltonian parameters and self-energies on Au in the electrode region. (b) Structure of the two probe system of trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface. Thiol ended trimer unit of cis-polyacetylene together with two surface gold layers in the left and right electrodes are included in the self-consistent calculation, while remainder of the gold electrodes are atoms described by employing bulk Hamiltonian parameters and self-energies on Au in the electrode region.
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lene. In the entire study, we employ nonequilibrium Green’s functions (NEGF) technique combined with DFT [2,39,40]. 2. Computational procedure Geometry optimization of thiol ended trimer unit of cis-polyacetylene and fused thiophene trimer have been implemented in GAUSSIAN 03 program [41] using B3LYP [42,43] type exchangecorrelation functional and 6-31+G(d, p) basis set. Optimized structures form a self-assembled monolayer on Au (1 1 1) surface with thiol endgroup. In the optimized structure, estimated C–S (thiol 0 endgroup) distance is 1.76 Å and measured S–Au distance is 2.39 Å A. In the present investigation, quantum transport properties are evaluated by using the formalism of Brandbyge et al. [44]. Within this method the electronic current has been calculated by considering the Kohn–Sham wave function as an authentic single-particle wave function. As a result even with the use of commonly used exchange-correlation functionals the nonequilibrium situation of electrons due to a current flow has been satisfactorily described [44]. Earlier, Stokbro et al. [39] reported that zero bias transmission spectrum of Di-thiol-benzene did not change appreciably due to a change in DFT functional from local density approximation (LDA) to generalized-gradient approximation (GGA). Furthermore, use of the GGA functional in electronic transport calculation takes enormous computational time. Considering these facts, we perform all the calculations at the LDA level of theory using double zeta polarized basis function. Within LDA, we choose Perdew–Zunger parametrization [45] of the correlation energy of a nonspinpolarized homogenous electron gas as calculated by Ceperly–Alder technique [46]. Besides exchange-correlation potential, Hartree potential and pseudopotential are the other effective DFT potentials used in the calculations. For the core electrons, norm conserving Troullier-Martins pseudopotentials have been used [47]. In our study, 5 d electrons of Au are treated explicitly as valence electrons within DZP basis set. In the present study, the area of interest is two semi-infinite electrodes (L and R) coupled via the contact (C) region (molecule
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or molecular chain in a particular calculation; here trimer unit of cis-polyacetylene and fused thiophene trimer). The atoms in two semi-infinite electrodes (L and R) are the parts of semi-infinite bulk electrodes, which interact with the atoms of contact (C) region. The Hamiltonian along with density matrix is assumed to converge to bulk values in the region of semi-infinite bulk electrodes. The Hamiltonian, density matrix and overlap matrix differ from their bulk values only in the C, C–L and C–R region. Thus, the system under investigation resembles finite L–C–R element of the infinite system. The density matrix is achieved from a series of Green’s function matrices. In the present calculation the Green’s function matrix is obtained by inverting the finite matrix corresponding to L–C–R part.
Fig. 4. Zero bias transmission spectra of two probe systems of trimer unit of cispolyacetylene and fused thiophene trimer self-assembled on Au (1 1 1) surface.
Fig. 3. Differential conductance against voltage (dI/dV V) curve of two probe systems of trimer unit of cis-polyacetylene and fused thiophene trimer selfassembled on Au (1 1 1) surface.
Fig. 5. Zero bias DOS of two probe systems of trimer unit of cis-polyacetylene and fused thiophene trimer self-assembled on Au (1 1 1) surface.
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Following nonequilibrium Green’s function formalism the current (I) through the system becomes
Z 2e 1 de½nF ðe lL Þ nF ðe lR Þ h 1 Tr½CL ðeÞGðeÞCR ðeÞGðeÞ;
IðVÞ ¼
IðVÞ ¼ ð1Þ
where G is the retarded Green’s function of the coupled system, CR ðeÞ ¼ i½RR ðeÞ RyR ðeÞ=2 and CL ðeÞ ¼ i½RL ðeÞ RyL ðeÞ=2. RL and RR are the self-energies signifying the coupling of the L and R regions to the rest of the semi-infinite electrodes. V is the applied bias with eV ¼ lL lR . Here, lL and lR are the electrochemical potential of the left and right electrode, respectively. If left to right transmission amplitude matrix t(e) is expressed as
tðeÞ ¼ ½CR ðeÞ1=2 GðeÞ½CL ðeÞ1=2 ;
Eq. (1) is seen to be equivalent to the Landauer–Büttiker formula [48] for the conductance. By using Eq. (2) one can write Eq. (1) as
ð2Þ
2e h
Z
1
1
de½nF ðe lL Þ nF ðe lR Þ Tr½t y tðeÞ;
ð3Þ
Using the aforesaid methodology the current–voltage (I–V) characteristics have been evaluated through ATK 2.0.4 [49] computational technique. In the present investigation, semi-infinite left and right electrodes are represented by two Au (1 1 1)–(3 3) surface. For the evaluation of I–V characteristics, 1 1 500 k-point sampling has been employed in the entire two probe calculation. Apart from this, we also estimated zero bias quantum transport properties of fused thiophene trimer at 4 4 500 k-point sampling and 6 6 500 k-point sampling and finally compared those results with that of the 1 1 500 k-point sampling. It has been
Fig. 6. Transmission spectra of two probe systems of fused thiophene trimer and trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, at the positive bias voltage of 0.0 V, 0.4 V, 0.8 V, 1.2 V and 1.4 V, respectively. Shaded region indicates the bias window. A positive bias corresponds to electron current from left to right electrode.
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noticed that k-point sampling has little impact on the transmission spectra of the chosen system. More over to justify our findings as not due to an artifact of analysis we calculated the band structure of the electrode with 1 1 500 k-point sampling and found that continuity of the energy band across the fermi level is restored (see Supporting information).
3. Results and discussion In the present study, the model system chosen are trimer units of cis-polyacetylene and fused thiophene trimer. Two probe configurations of fused thiophene trimer and its prisitine analog, selfassembled on Au (1 1 1) surface with thiol end group are depicted
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in Fig. 1a and b, respectively. Cis- and trans-polyacetylene are two conformations of polyacetylene. Of the two conformations, trans-polyacetylene is thermodynamically stable and it has been observed that in presence of heteroatoms (sulphur, nitrogen, oxygen, carbonyl group, C@C(CN)2 and so forth) cis isomer gets transformed into thermally stable fused five membered ring. Such a configuration is not uncommon. Experimental justifications of these structures have been provided by Lambert and co-workers [50,51]. In the present study, fused thiophene trimer is obtained by adding heteroatom sulphur to the cis structure. Quantum transport calculations are carried out on both trimer unit of cis-polyacetylene and fused thiophene trimer. In the present study, we primarily focus on the quantum transport properties of trimer unit of cis-polyacetylene. Thereafter, we
Fig. 7. Transmission spectra of two probe systems of fused thiophene trimer and trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, at the positive bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V, respectively. Shaded region indicates the bias window. A positive bias corresponds to electron current from left to right electrode.
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investigate the modifications in quantum transport properties due to the addition of heteroatom (sulphur) to the cis isomer. Fig. 2 illustrates the I–V characteristic of both the molecular systems. In the I–V characteristic curve, external voltage has been varied from 2.8 V to +2.8 V. From Fig. 2, we observe that initially current through both the molecular structures increases with the increase in external voltage both for positive bias and negative bias. This feature is observed up to the bias voltage of ±1.4 V in case of fused thiophene trimer and ±2.0 V for trimer unit of cis-polyacetylene. Beyond these voltages (±1.4 V for fused thiophene trimer and ±2.0 V for trimer unit of cis-polyacetylene) current through both the molecular systems diminishes with the increase in external bias voltage. The reduction in current due to the enhancement in external bias voltage is the manifestation of NDR. This feature is
prominent up to the bias voltage of ±2.45 V in both the molecular systems. Fig. 2 also reveals that above ±2.5 V current through both the molecular structures again increases with the increase in external bias voltage. Therefore, NDR feature disappears beyond the external bias voltage of ±2.5 V. All these observations are further verified by plotting differential conductance (dI/dV) against V and is presented in Fig. 3. From, Figs. 2 and 3 we also notice that reduction in current is relatively larger in case of fused thiophene trimer than its pristine analog. In this context, it is worth mentioning that NDR behavior in polyacetylene system (trans-polyacetylene) has been already reported by Emberly et al. [29] In this study, we discuss the NDR feature in cis configuration and relevant modifications due to the addition of heteroatom (sulphur) to the cis geometry.
Fig. 8. Transmission spectra of two probe systems of fused thiophene trimer and trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, at the negative bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V, respectively. Shaded region indicates the bias window. A negative bias corresponds to electron current from right to left electrode.
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It is also evident from Fig. 3 that in either sample dI/dV against V graph is not perfectly symmetric about zero voltage. Experimental studies like the work of Reichert and co-workers [52] have already established that contact asymmetry can result in asymmetric I–V relationship even in a perfectly symmetric molecule. Theoretical work of Zahid et al. [53] also reported an asymmetric I–V in case of a spatially symmetric molecule [9,10-bis((20 -para-mercaptophenyl)-ethinyl)-anthracene]. They concluded that unequal coupling of the molecules with the surface atoms of the electrodes is responsible for asymmetric I–V relation. In general, asymmetric I–V in a symmetric molecule may be resulted by several factors such as the inclusion of additional atom, different electrode surface etc. In present study, observed asymmetry in I–V relationship (Fig. 3) is attributed to the small asymmetry in the optimized structures of the molecular systems (see Supporting information). In the two probe configurations presented in Fig. 1 flow of current from left to right electrode corresponds to positive bias and that from right to left electrode corresponds to negative bias. Albeit, the asymmetry in molecular structures is not evident from Fig. 1, a closure inspection at the co-ordinates of the molecules, surface atoms and electrodes (presented in the Supporting information) reveals that slight asymmetry is present in both the optimized
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structures. Consequently, current through both the molecular systems will be dissimilar in either direction. In order to provide an explanation of the observed NDR behavior, we mention the work of Zhou et al. [2]. In their DFT/NEGF study, NDR feature of HCOO–C6H4–(CH2)n sandwiched between two aluminum electrodes was explained by observing the shift in transmission resonance peaks across the bias window with varying bias voltages. According to Landauer–Büttiker formula the current (I) is directly dependent on transmission amplitude. Consequently, extent of transmission spectra within the bias window will determine the amount of current passing through a particular molecular system. In the present investigation, we utilize this idea and following the work of Zhou et al. [2], shift in transmission spectra across the bias window was monitored at different bias voltages. At the outset, we compare the zero bias transmission spectra of both the molecular systems (Fig. 4). From Fig. 4, we notice that the zero bias transmission spectra of both the molecular systems are quite comparable excepting the additional transmission peak around 1.6 eV in case of trimer unit of cis-polyacetylene. In addition to this we also analyze the zero bias density of states (DOS) of both the molecular systems. Fig. 5 demonstrates the related comparison. Similar to the transmission spectra, DOS plots of both
Fig. 9. Molecular projected self-consistent Hamiltonian (MPSH) states of the two probe system of fused thiophene trimer self-assembled on Au (1 1 1) surface, contributing to the bias window at the bias voltage of 0.0 V, 2.0 V, 2.4 V and 2.6 V, respectively. A positive bias corresponds to electron current from left to right electrode.
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the molecular systems are quite analogous except for the additional peak at 1.6 eV in case of trimer unit of cis-polyacetylene. Transmission spectra corresponding to the bias voltage of 0.0 V, 0.4 V, 0.8 V, 1.2 V and 1.4 V are presented in Fig. 6. It is evident from Fig. 6 that in both the molecular systems, transmission spectra contributing to the bias window gradually increases with the increase in external bias voltage. As a consequence of this, current through both the molecular systems increases. A comparison of transmission spectra obtained at the bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V reveals a regular reduction in transmission resonance peak within the bias window (Fig. 7). Consequently, current through both the molecular systems diminishes. This feature (NDR feature) is apparent over the bias range of 1.6 V to 2.45 V in case of fused thiophene trimer and 2.1 V to 2.45 V for trimer unit of cis-polyacetylene. From Fig. 7, we also notice that at 2.6 V, some other transmission resonance peaks enter into the bias window and current through both the molecular systems again starts to increase. This is an indication of removal of the NDR behavior. In Fig. 7, resonance peak at 1.3 eV results in an overall increase in current at the positive bias voltage of 2.6 V. Moreover, from Fig. 7 we also notice that at higher positive bias voltages, additional transmission peak of trimer unit of cis-polyacetylene enters into the bias window. Consequently, reduction in current will be relatively lesser in case of trimer unit of cis-polyacetylene. Fig. 8 depicts transmission spectra corresponding to negative bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V, respectively. Similar to positive bias variation, transmission resonance peak contributing to the bias window gradually decreases with the increase in negative bias voltage. This results in a decrease in current through both the molecular systems. Hence NDR behavior is observed both in positive as well as in negative bias. At 2.6 V, some additional transmission peaks enter into the bias window
and current through both the molecular systems again increases. This indicates a removal of NDR character. We present a molecular origin of the observed variation in transmission spectra (Figs. 6–8) through an analysis of molecular projected self-consistent Hamiltonian (MPSH) states [39,54,55]. MPSH states are the eigenstates of the molecular system placed in two probe environment. These eigenstates are attained by digonalizing the molecular projected self-consistent Hamiltonian (MPSH) matrix. The matrix is obtained by projecting the self-consistent Hamiltonian of the molecular junction onto the molecule. The finite MPSH matrix is expressed as,
2
H L þ RL
6 Vy 4 L 0
VL
0
3
HC
VR
V yR
7 5;
HR þ RR
ð4Þ
where HL, HR and HC are Hamiltonian matrices in the left electrode (L), right electrode (R) and contact region (C), respectively. Likewise, VL and VR are the interaction potential between the L–C and L–R regions, respectively. In a recent work, Staykov et al. [54] employed MPSH analysis to explain the electrical rectifying nature of a single-molecule nanowire of type donor-p-bridge-acceptor. Explanation of NDR feature through MPSH analysis has been already made by Sen et al [55]. It is well known from these studies that MPSH states delocalized between two electrodes contribute to the transmission spectra and MPSH states localized on the electrodes do not make any contribution to transmission spectra. Primarily, we analyze the MPSH states of fused thiophene trimer. Fig. 9 depicts the related MPSH states. It is quite evident from Fig. 9 that MPSH states 240, 237, 228, 227, 224 shows complete delocalization at zero bias voltage and the same is localized at 2.0 V, 2.4 V and 2.6 V. As a result these MPSH
Fig. 10. Molecular projected self-consistent Hamiltonian (MPSH) states of the two probe system of trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, contributing to the bias window at the bias voltage of 0.0 V, 2.3 V, 2.4 V and 2.6 V respectively. A positive bias corresponds to electron current from left to right electrode.
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Fig. 11. Comparison of Molecular projected self-consistent Hamiltonian (MPSH) states contributing to the additional transmission peak in two probe system of trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface (at 1.61 eV at the bias voltage of 0.0 V, at 1.42 eV at the bias voltage of 2.3 V, at 1.38 eV at the bias voltage of 2.4 V and at 1.39 eV at the bias voltage of 2.6 V) and corresponding MPSH states in the two probe system of fused thiophene trimer self-assembled on Au (1 1 1) surface. A positive bias corresponds to electron current from left to right electrode.
states will results in transmission peak only at zero bias voltage. Hence, current through fused thiophene trimer will diminish at the bias voltage of 2.0 V, 2.4 V. Albeit MPSH states 240, 237, 228, 227, 224 are localized at 2.6 V, contribution from the MPSH state 215 results in slight increase in current and removal of NDR character. MPSH states of trimer unit of cis-polyacetylene are presented in Fig. 10. Similar to fused thiophene trimer some of the MPSH states (229, 222 and 219) are delocalized only at zero bias voltage. As consequence of this, relevant transmission peaks will be present only at zero bias voltage not at 2.3 V and 2.4 V. This in turn causes a reduction in current at 2.3 V and 2.4 V. At 2.6 V delocalization is only noticed at the MPSH state 214, and current through the molecular system again starts increase. At this stage is inevitable to investigate why NDR feature in trimer unit of cis-polyacetylene gets improved if heteroatom (S) is added to the cis conformation. This feature may be ascribed to the additional transmission peak of trimer unit of cis-polyacetylene. Related MPSH analysis is presented in Fig. 11. It is evident from Fig. 11 that albeit MPSH states corresponding to the additional transmission peak of trimer unit cis-polyacetylene show complete delocalization and MPSH states in fused thiophene trimer are localized. Consequently, within the NDR region the reduction in current will be relatively lesser in case of trimer unit cispolyacetylene. It is also interesting to note that prior to NDR region
current through fused thiophene trimer is relatively larger than its pristine analog. This feature is particularly noticeable at 1.2 V and 1.4 V (Fig. 2). Transmission spectra presented in Fig. 6 illustrates that additional transmission peak of trimer unit cis-polyacetylene does not enter into the bias window at these bias voltages. Furthermore, an examination of MPSH states contributing to the bias window at these voltages manifests that MPSH states of are more delocalized in case of fused thiophene trimer. Hence due to above two factors current through fused thiophene trimer would be relatively larger at 1.2 V and 1.4 V. It is worth mentioning that in an earlier work [55] we investigated the NDR feature in fused furan trimer. A comparison of the results of the present analysis and that obtained with fused furan trimer illustrates that in the present study NDR feature is present over a wider range of bias voltages (±1.6 V to ±2.45 V) and in either case I–V relationship is slightly asymmetric. 4. Conclusions In the present work we report NDR behavior in trimer unit of cis-polyacetylene and modification of its NDR feature due to the addition of heteroatom (sulphur) to the cis configuration. In the investigation we estimated transport properties through nonequilibrium Green’s function technique. In fused thiophene trimer NDR feature is prominent over the bias range of ±1.6 V to ±2.45 V and in
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trimer unit of cis-polyacetylene the same is noticed over the bias range of ±2.1 to ±2.45 V. We present an explanation of the observed NDR character by monitoring the shift in transmission resonance peak across the bias window against varying bias voltages. Finally, a molecular origin of the NDR character has been provided through an analysis of MPSH states contributing to the bias window at different bias voltages. Acknowledgements At the very outset we would like to convey our special thanks to Atomistix Inc. for allowing us to use ATK 2.0.4 for electronic transport calculations. The financial support from DST, Govt. of India (Under FIST Program) to purchase the GAUSSIAN 03 program is gratefully acknowledged. S. Sen acknowledges Prof. A. Guha, Director, JIS College of Engineering. S. Sen would also like to thank P. Seal for providing necessary helps in computational purpose. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.commatsci.2008.12.010. References [1] C.W. Bauschlicher Jr., J.W. Lawson, Phys. Rev. B 75 (2007) 115406–115411. [2] Y.-h. Zhou, X.-h. Zheng, Y. Xu, Z.Y. Zeng, J. Chem. Phys. 125 (2006) 244701– 244705. [3] J. Koch, M.E. Raikh, F. von Oppen, Phys. Rev. Lett. 96 (2006) 056803–056806. [4] C. Zhang, M.-H. Du, H.-P. Cheng, X.-G. Zhang, A.E. Roitberg, J.L. Krause, Phys. Rev. Lett. 92 (2004) 158301–158304. [5] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, New York, 1996. [6] R.H. Mathews, J.P. Sage, T.C.L.G. Sollner, S.D. Calawa, C.-L. Chen, L.J. Mahoney, P.A. Maki, K.M. Molvar, Proc. IEEE 87 (1999) 596–605. [7] M.A. Reed, C. Zhou, C.J. Muller, T.P. Burgin, J.M. Tour, Science 278 (1997) 252– 254. [8] M.A. Reed, J. Chen, A.M. Rawlett, D.W. Price, J.M. Tour, Appl. Phys. Lett. 78 (2001) 3735–3737. [9] A. Halbritter, Sz. Csonka, G. Mihály, E. Jurdik, O. Yu Kolesnychenko, O.I. Shklyarevskii, S. Speller, H. van Kempen, Phys. Rev. B 68 (2003) 035417– 035423. [10] S. Roche, Sequence dependent DNA-mediated conduction, Phys. Rev. Lett. 91 (2003) 108101–108104. [11] A.N. Andriotis, M. Menon, D. Srivastava, L. Chernozatonskii, Phys. Rev. Lett. 87 (2001) 066802–066805. [12] E.G. Emberly, G. Kirczenow, Phys. Rev. Lett. 91 (2003) 188301–188304. [13] M. Di Ventra, S.T. Pantelides, N.D. Lang, Phys. Rev. Lett. 84 (2000) 979–982.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Negative differential resistance in fused thiophene trimer Sabyasachi Sen, Swapan Chakrabarti * Department of Chemistry, University of Calcutta, 92, A.P.C. Ray Road, Kolkata 700 009, India
a r t i c l e
i n f o
Article history: Received 16 April 2008 Received in revised form 6 November 2008 Accepted 12 December 2008 Available online 20 January 2009 PACS: 73.23.b 31.15.E 85.65.+h 81.07.Nb Keywords: Molecular electronics Quantum transport Nonequilibrium Green’s functions Density functional theory Negative differential resistance Molecular projected self-consistent Hamiltonian states
a b s t r a c t Current–voltage characteristics of trimer unit of cis-polyacetylene and fused thiophene trimer have been analyzed by employing nonequilibrium Green’s functions technique. In the present investigation, both the molecular systems have thiol end group and they form a self-assembled monolayer on Au (1 1 1) surface. The current–voltage characteristics of fused thiophene trimer and trimer unit of cis-polyacetylene illustrates that negative differential resistance feature gets sufficiently improved due to the addition of heteroatom sulphur to the cis conformation. The negative differential resistance feature is observed over the bias range of ±1.6 V to ±2.45 V for fused thiophene trimer and ±2.1 to ±2.45 V for trimer unit of cispolyacetylene. Manifestation of negative differential resistance feature has been explained by monitoring the shift in transmission resonance peak across the bias window with varying bias voltages. Modification of negative differential resistance feature due to addition of heteroatom (sulphur) to the cis configuration has been explained at the molecular level through an analysis of molecular projected self-consistent Hamiltonian states. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Invention of molecular and nanoelectronic components such as wires, diodes, transistors, oscillators and switches [1–8] as well as the physical understanding of their current (I)–voltage (V) properties have greatly enhanced the quest for designing novel molecular systems with unusual electronic transport properties. Electronic transport at the molecular level is influenced by quantum effects like quantum interference of electron waves, quantization of energy levels and so forth. Experimentally, unusual current–voltage behavior has been reported in scanning tunneling microscope (STM) study on 1,4 benzene-dithiolate molecule [7]. Conducting features of some small conjugated molecules like phenyl based derivatives [9] have been measured by mechanically controllable break junction experiment. Moreover, interesting physical situations like negative differential resistance (NDR), highly nonlinear current–voltage (I–V) characteristics, switching behavior have been reported in DNA [10], carbon nanotubes [11] and organic systems [12]. All these achievements and the aspiration to design modern molecular electronic devices motivate us to explore the underlying theoretical background of quantum transport processes. * Corresponding author. Tel.: +91 33 23508386; fax: +91 33 23519755. E-mail address: [email protected] (S. Chakrabarti). 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.12.010
Several attempts have been made at the theoretical level to explain the I–V characteristics of the molecular systems [2,13–18]. Quantum transport properties of materials in mesoscopic dimension are usually described by the Landauer theory [19]. It relates the transmission probability of electron with that of current. Büttiker [20] has given an extension of the Landauer theory [19] in multi-terminal molecular wire systems. A molecule or molecular chain placed between two bulk electrodes is a nonperiodic system. Under the application of finite voltage the system deviates from the equilibrium and the electrochemical potential at the molecule-electrode contact gets changed. In most of the theoretical analysis this nonequilibrium situation has been described through density functional theory (DFT) based nonequilibrium Green’s functions (NEGF) technique and in certain cases through semi empirical approach [21]. Lang [22] employed density functional theory (DFT) to predict the NDR behavior in two atomic dimers placed between two electrodes. Nonequilibrium situation in phenyldithiolate molecule bridging two gold electrodes was explained by Xue and co-workers [23]. A combination of Green’s function technique and DFT has been employed by Derosa and co-workers to explain the quantum transport in molecular system of Aun-S(p-C6H4)-S-Aun [24]. Seminario et al. [25] used DFT combined with molecular dynamics simulations to explain the conductance of thiotolane monolayer.
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One of the fascinating aspects of the modern quantum transport phenomena is NDR. In an electronic system, decrease in current due to the increase in voltage is recognized as NDR feature. The issue of NDR in molecular systems has been addressed in large number of communications. Reed and co-workers [8] reported NDR behavior in 20 -amino-4-ethynylphenyl-40 -ethynylphenyl-5´-nitro1-benzenethiolate. Chen et al [26] investigated NDR feature in molecule containing a nitroamine redox center. In their study, NDR feature was ascribed to the voltage induced redox reaction, i.e. on the change in the charge distribution in the wire and on conformational changes. NDR feature in polyphenylene-based molecular wires incorporating saturated spacers was reported by Karzazi et al. [27]. In their quantum chemical study, NDR feature was attributed to the resonant tunneling originated from shifting of the molecular energy level by external electric field. NDR feature in molecular device composed of donor and acceptor moieties was presented by Lakshmi et al. [28]. From, their two level model calculation they conjectured that the NDR behavior appears due to the bias driven electronic structure change from one class of insulating phase to another through exceedingly delocalized conducting phase. Emberly and co-workers [29] investigated NDR behavior in chain molecule. In their tight binding formalism, NDR behavior was attributed to the formation of charge density wave and consequent bond weakening. Tight binding model was also used by Léonard et al. [30] to explain the NDR feature in nanotube devices. Apart from these, several other investigations such as reduction of the acceptor moiety [31], charging effect [32–34] etc. are also quite successful in explaining the NDR behavior. Albeit, large numbers of theoretical and experimental investigations have been carried out on NDR materials [26–34], number of molecular systems having such feature is still very limited [27,35,36–38]. The experimental work of Kratochvilova and coworkers pointed out the dearth of self-assembled molecular systems in the nano device fabrication area [35]. In some of the theoretical investigations, NDR feature was attributed to specific kind of molecular systems which posses a central quantum well separated from two metallic leads by tunnel barriers [27]. Moreover,
in certain cases emergence of NDR feature depends on some added external factors like ring rotation, twisting of the ring structure leading to conformational changes [36,37] etc. Furthermore, the existence of NDR in gated molecular devices is still an unresolved issue to both the theoreticians and experimentalists [38]. All these realizations provide enough motivations to carry out further investigations and identify new materials with NDR feature. In the present theoretical work, we investigate NDR behavior in the molecular system of fused thiophene trimer and trimer unit of cis-polyacety-
Fig. 2. Current–voltage (I–V) characteristic of two probe systems of trimer unit of cis-polyacetylene and fused thiophene trimer self-assembled on Au (1 1 1) surface.
Fig. 1. (a) Structure of the two probe system of fused thiophene trimer self-assembled on Au (1 1 1) surface. Thiol ended fused thiophene trimer together with two surface gold layers in the left and right electrodes are included in the self-consistent calculation, while remainder of the gold electrodes are atoms described by employing bulk Hamiltonian parameters and self-energies on Au in the electrode region. (b) Structure of the two probe system of trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface. Thiol ended trimer unit of cis-polyacetylene together with two surface gold layers in the left and right electrodes are included in the self-consistent calculation, while remainder of the gold electrodes are atoms described by employing bulk Hamiltonian parameters and self-energies on Au in the electrode region.
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lene. In the entire study, we employ nonequilibrium Green’s functions (NEGF) technique combined with DFT [2,39,40]. 2. Computational procedure Geometry optimization of thiol ended trimer unit of cis-polyacetylene and fused thiophene trimer have been implemented in GAUSSIAN 03 program [41] using B3LYP [42,43] type exchangecorrelation functional and 6-31+G(d, p) basis set. Optimized structures form a self-assembled monolayer on Au (1 1 1) surface with thiol endgroup. In the optimized structure, estimated C–S (thiol 0 endgroup) distance is 1.76 Å and measured S–Au distance is 2.39 Å A. In the present investigation, quantum transport properties are evaluated by using the formalism of Brandbyge et al. [44]. Within this method the electronic current has been calculated by considering the Kohn–Sham wave function as an authentic single-particle wave function. As a result even with the use of commonly used exchange-correlation functionals the nonequilibrium situation of electrons due to a current flow has been satisfactorily described [44]. Earlier, Stokbro et al. [39] reported that zero bias transmission spectrum of Di-thiol-benzene did not change appreciably due to a change in DFT functional from local density approximation (LDA) to generalized-gradient approximation (GGA). Furthermore, use of the GGA functional in electronic transport calculation takes enormous computational time. Considering these facts, we perform all the calculations at the LDA level of theory using double zeta polarized basis function. Within LDA, we choose Perdew–Zunger parametrization [45] of the correlation energy of a nonspinpolarized homogenous electron gas as calculated by Ceperly–Alder technique [46]. Besides exchange-correlation potential, Hartree potential and pseudopotential are the other effective DFT potentials used in the calculations. For the core electrons, norm conserving Troullier-Martins pseudopotentials have been used [47]. In our study, 5 d electrons of Au are treated explicitly as valence electrons within DZP basis set. In the present study, the area of interest is two semi-infinite electrodes (L and R) coupled via the contact (C) region (molecule
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or molecular chain in a particular calculation; here trimer unit of cis-polyacetylene and fused thiophene trimer). The atoms in two semi-infinite electrodes (L and R) are the parts of semi-infinite bulk electrodes, which interact with the atoms of contact (C) region. The Hamiltonian along with density matrix is assumed to converge to bulk values in the region of semi-infinite bulk electrodes. The Hamiltonian, density matrix and overlap matrix differ from their bulk values only in the C, C–L and C–R region. Thus, the system under investigation resembles finite L–C–R element of the infinite system. The density matrix is achieved from a series of Green’s function matrices. In the present calculation the Green’s function matrix is obtained by inverting the finite matrix corresponding to L–C–R part.
Fig. 4. Zero bias transmission spectra of two probe systems of trimer unit of cispolyacetylene and fused thiophene trimer self-assembled on Au (1 1 1) surface.
Fig. 3. Differential conductance against voltage (dI/dV V) curve of two probe systems of trimer unit of cis-polyacetylene and fused thiophene trimer selfassembled on Au (1 1 1) surface.
Fig. 5. Zero bias DOS of two probe systems of trimer unit of cis-polyacetylene and fused thiophene trimer self-assembled on Au (1 1 1) surface.
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Following nonequilibrium Green’s function formalism the current (I) through the system becomes
Z 2e 1 de½nF ðe lL Þ nF ðe lR Þ h 1 Tr½CL ðeÞGðeÞCR ðeÞGðeÞ;
IðVÞ ¼
IðVÞ ¼ ð1Þ
where G is the retarded Green’s function of the coupled system, CR ðeÞ ¼ i½RR ðeÞ RyR ðeÞ=2 and CL ðeÞ ¼ i½RL ðeÞ RyL ðeÞ=2. RL and RR are the self-energies signifying the coupling of the L and R regions to the rest of the semi-infinite electrodes. V is the applied bias with eV ¼ lL lR . Here, lL and lR are the electrochemical potential of the left and right electrode, respectively. If left to right transmission amplitude matrix t(e) is expressed as
tðeÞ ¼ ½CR ðeÞ1=2 GðeÞ½CL ðeÞ1=2 ;
Eq. (1) is seen to be equivalent to the Landauer–Büttiker formula [48] for the conductance. By using Eq. (2) one can write Eq. (1) as
ð2Þ
2e h
Z
1
1
de½nF ðe lL Þ nF ðe lR Þ Tr½t y tðeÞ;
ð3Þ
Using the aforesaid methodology the current–voltage (I–V) characteristics have been evaluated through ATK 2.0.4 [49] computational technique. In the present investigation, semi-infinite left and right electrodes are represented by two Au (1 1 1)–(3 3) surface. For the evaluation of I–V characteristics, 1 1 500 k-point sampling has been employed in the entire two probe calculation. Apart from this, we also estimated zero bias quantum transport properties of fused thiophene trimer at 4 4 500 k-point sampling and 6 6 500 k-point sampling and finally compared those results with that of the 1 1 500 k-point sampling. It has been
Fig. 6. Transmission spectra of two probe systems of fused thiophene trimer and trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, at the positive bias voltage of 0.0 V, 0.4 V, 0.8 V, 1.2 V and 1.4 V, respectively. Shaded region indicates the bias window. A positive bias corresponds to electron current from left to right electrode.
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noticed that k-point sampling has little impact on the transmission spectra of the chosen system. More over to justify our findings as not due to an artifact of analysis we calculated the band structure of the electrode with 1 1 500 k-point sampling and found that continuity of the energy band across the fermi level is restored (see Supporting information).
3. Results and discussion In the present study, the model system chosen are trimer units of cis-polyacetylene and fused thiophene trimer. Two probe configurations of fused thiophene trimer and its prisitine analog, selfassembled on Au (1 1 1) surface with thiol end group are depicted
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in Fig. 1a and b, respectively. Cis- and trans-polyacetylene are two conformations of polyacetylene. Of the two conformations, trans-polyacetylene is thermodynamically stable and it has been observed that in presence of heteroatoms (sulphur, nitrogen, oxygen, carbonyl group, C@C(CN)2 and so forth) cis isomer gets transformed into thermally stable fused five membered ring. Such a configuration is not uncommon. Experimental justifications of these structures have been provided by Lambert and co-workers [50,51]. In the present study, fused thiophene trimer is obtained by adding heteroatom sulphur to the cis structure. Quantum transport calculations are carried out on both trimer unit of cis-polyacetylene and fused thiophene trimer. In the present study, we primarily focus on the quantum transport properties of trimer unit of cis-polyacetylene. Thereafter, we
Fig. 7. Transmission spectra of two probe systems of fused thiophene trimer and trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, at the positive bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V, respectively. Shaded region indicates the bias window. A positive bias corresponds to electron current from left to right electrode.
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investigate the modifications in quantum transport properties due to the addition of heteroatom (sulphur) to the cis isomer. Fig. 2 illustrates the I–V characteristic of both the molecular systems. In the I–V characteristic curve, external voltage has been varied from 2.8 V to +2.8 V. From Fig. 2, we observe that initially current through both the molecular structures increases with the increase in external voltage both for positive bias and negative bias. This feature is observed up to the bias voltage of ±1.4 V in case of fused thiophene trimer and ±2.0 V for trimer unit of cis-polyacetylene. Beyond these voltages (±1.4 V for fused thiophene trimer and ±2.0 V for trimer unit of cis-polyacetylene) current through both the molecular systems diminishes with the increase in external bias voltage. The reduction in current due to the enhancement in external bias voltage is the manifestation of NDR. This feature is
prominent up to the bias voltage of ±2.45 V in both the molecular systems. Fig. 2 also reveals that above ±2.5 V current through both the molecular structures again increases with the increase in external bias voltage. Therefore, NDR feature disappears beyond the external bias voltage of ±2.5 V. All these observations are further verified by plotting differential conductance (dI/dV) against V and is presented in Fig. 3. From, Figs. 2 and 3 we also notice that reduction in current is relatively larger in case of fused thiophene trimer than its pristine analog. In this context, it is worth mentioning that NDR behavior in polyacetylene system (trans-polyacetylene) has been already reported by Emberly et al. [29] In this study, we discuss the NDR feature in cis configuration and relevant modifications due to the addition of heteroatom (sulphur) to the cis geometry.
Fig. 8. Transmission spectra of two probe systems of fused thiophene trimer and trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, at the negative bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V, respectively. Shaded region indicates the bias window. A negative bias corresponds to electron current from right to left electrode.
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It is also evident from Fig. 3 that in either sample dI/dV against V graph is not perfectly symmetric about zero voltage. Experimental studies like the work of Reichert and co-workers [52] have already established that contact asymmetry can result in asymmetric I–V relationship even in a perfectly symmetric molecule. Theoretical work of Zahid et al. [53] also reported an asymmetric I–V in case of a spatially symmetric molecule [9,10-bis((20 -para-mercaptophenyl)-ethinyl)-anthracene]. They concluded that unequal coupling of the molecules with the surface atoms of the electrodes is responsible for asymmetric I–V relation. In general, asymmetric I–V in a symmetric molecule may be resulted by several factors such as the inclusion of additional atom, different electrode surface etc. In present study, observed asymmetry in I–V relationship (Fig. 3) is attributed to the small asymmetry in the optimized structures of the molecular systems (see Supporting information). In the two probe configurations presented in Fig. 1 flow of current from left to right electrode corresponds to positive bias and that from right to left electrode corresponds to negative bias. Albeit, the asymmetry in molecular structures is not evident from Fig. 1, a closure inspection at the co-ordinates of the molecules, surface atoms and electrodes (presented in the Supporting information) reveals that slight asymmetry is present in both the optimized
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structures. Consequently, current through both the molecular systems will be dissimilar in either direction. In order to provide an explanation of the observed NDR behavior, we mention the work of Zhou et al. [2]. In their DFT/NEGF study, NDR feature of HCOO–C6H4–(CH2)n sandwiched between two aluminum electrodes was explained by observing the shift in transmission resonance peaks across the bias window with varying bias voltages. According to Landauer–Büttiker formula the current (I) is directly dependent on transmission amplitude. Consequently, extent of transmission spectra within the bias window will determine the amount of current passing through a particular molecular system. In the present investigation, we utilize this idea and following the work of Zhou et al. [2], shift in transmission spectra across the bias window was monitored at different bias voltages. At the outset, we compare the zero bias transmission spectra of both the molecular systems (Fig. 4). From Fig. 4, we notice that the zero bias transmission spectra of both the molecular systems are quite comparable excepting the additional transmission peak around 1.6 eV in case of trimer unit of cis-polyacetylene. In addition to this we also analyze the zero bias density of states (DOS) of both the molecular systems. Fig. 5 demonstrates the related comparison. Similar to the transmission spectra, DOS plots of both
Fig. 9. Molecular projected self-consistent Hamiltonian (MPSH) states of the two probe system of fused thiophene trimer self-assembled on Au (1 1 1) surface, contributing to the bias window at the bias voltage of 0.0 V, 2.0 V, 2.4 V and 2.6 V, respectively. A positive bias corresponds to electron current from left to right electrode.
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the molecular systems are quite analogous except for the additional peak at 1.6 eV in case of trimer unit of cis-polyacetylene. Transmission spectra corresponding to the bias voltage of 0.0 V, 0.4 V, 0.8 V, 1.2 V and 1.4 V are presented in Fig. 6. It is evident from Fig. 6 that in both the molecular systems, transmission spectra contributing to the bias window gradually increases with the increase in external bias voltage. As a consequence of this, current through both the molecular systems increases. A comparison of transmission spectra obtained at the bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V reveals a regular reduction in transmission resonance peak within the bias window (Fig. 7). Consequently, current through both the molecular systems diminishes. This feature (NDR feature) is apparent over the bias range of 1.6 V to 2.45 V in case of fused thiophene trimer and 2.1 V to 2.45 V for trimer unit of cis-polyacetylene. From Fig. 7, we also notice that at 2.6 V, some other transmission resonance peaks enter into the bias window and current through both the molecular systems again starts to increase. This is an indication of removal of the NDR behavior. In Fig. 7, resonance peak at 1.3 eV results in an overall increase in current at the positive bias voltage of 2.6 V. Moreover, from Fig. 7 we also notice that at higher positive bias voltages, additional transmission peak of trimer unit of cis-polyacetylene enters into the bias window. Consequently, reduction in current will be relatively lesser in case of trimer unit of cis-polyacetylene. Fig. 8 depicts transmission spectra corresponding to negative bias voltage of 1.6 V, 2.2 V, 2.3 V, 2.4 V and 2.6 V, respectively. Similar to positive bias variation, transmission resonance peak contributing to the bias window gradually decreases with the increase in negative bias voltage. This results in a decrease in current through both the molecular systems. Hence NDR behavior is observed both in positive as well as in negative bias. At 2.6 V, some additional transmission peaks enter into the bias window
and current through both the molecular systems again increases. This indicates a removal of NDR character. We present a molecular origin of the observed variation in transmission spectra (Figs. 6–8) through an analysis of molecular projected self-consistent Hamiltonian (MPSH) states [39,54,55]. MPSH states are the eigenstates of the molecular system placed in two probe environment. These eigenstates are attained by digonalizing the molecular projected self-consistent Hamiltonian (MPSH) matrix. The matrix is obtained by projecting the self-consistent Hamiltonian of the molecular junction onto the molecule. The finite MPSH matrix is expressed as,
2
H L þ RL
6 Vy 4 L 0
VL
0
3
HC
VR
V yR
7 5;
HR þ RR
ð4Þ
where HL, HR and HC are Hamiltonian matrices in the left electrode (L), right electrode (R) and contact region (C), respectively. Likewise, VL and VR are the interaction potential between the L–C and L–R regions, respectively. In a recent work, Staykov et al. [54] employed MPSH analysis to explain the electrical rectifying nature of a single-molecule nanowire of type donor-p-bridge-acceptor. Explanation of NDR feature through MPSH analysis has been already made by Sen et al [55]. It is well known from these studies that MPSH states delocalized between two electrodes contribute to the transmission spectra and MPSH states localized on the electrodes do not make any contribution to transmission spectra. Primarily, we analyze the MPSH states of fused thiophene trimer. Fig. 9 depicts the related MPSH states. It is quite evident from Fig. 9 that MPSH states 240, 237, 228, 227, 224 shows complete delocalization at zero bias voltage and the same is localized at 2.0 V, 2.4 V and 2.6 V. As a result these MPSH
Fig. 10. Molecular projected self-consistent Hamiltonian (MPSH) states of the two probe system of trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface, contributing to the bias window at the bias voltage of 0.0 V, 2.3 V, 2.4 V and 2.6 V respectively. A positive bias corresponds to electron current from left to right electrode.
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Fig. 11. Comparison of Molecular projected self-consistent Hamiltonian (MPSH) states contributing to the additional transmission peak in two probe system of trimer unit of cis-polyacetylene self-assembled on Au (1 1 1) surface (at 1.61 eV at the bias voltage of 0.0 V, at 1.42 eV at the bias voltage of 2.3 V, at 1.38 eV at the bias voltage of 2.4 V and at 1.39 eV at the bias voltage of 2.6 V) and corresponding MPSH states in the two probe system of fused thiophene trimer self-assembled on Au (1 1 1) surface. A positive bias corresponds to electron current from left to right electrode.
states will results in transmission peak only at zero bias voltage. Hence, current through fused thiophene trimer will diminish at the bias voltage of 2.0 V, 2.4 V. Albeit MPSH states 240, 237, 228, 227, 224 are localized at 2.6 V, contribution from the MPSH state 215 results in slight increase in current and removal of NDR character. MPSH states of trimer unit of cis-polyacetylene are presented in Fig. 10. Similar to fused thiophene trimer some of the MPSH states (229, 222 and 219) are delocalized only at zero bias voltage. As consequence of this, relevant transmission peaks will be present only at zero bias voltage not at 2.3 V and 2.4 V. This in turn causes a reduction in current at 2.3 V and 2.4 V. At 2.6 V delocalization is only noticed at the MPSH state 214, and current through the molecular system again starts increase. At this stage is inevitable to investigate why NDR feature in trimer unit of cis-polyacetylene gets improved if heteroatom (S) is added to the cis conformation. This feature may be ascribed to the additional transmission peak of trimer unit of cis-polyacetylene. Related MPSH analysis is presented in Fig. 11. It is evident from Fig. 11 that albeit MPSH states corresponding to the additional transmission peak of trimer unit cis-polyacetylene show complete delocalization and MPSH states in fused thiophene trimer are localized. Consequently, within the NDR region the reduction in current will be relatively lesser in case of trimer unit cispolyacetylene. It is also interesting to note that prior to NDR region
current through fused thiophene trimer is relatively larger than its pristine analog. This feature is particularly noticeable at 1.2 V and 1.4 V (Fig. 2). Transmission spectra presented in Fig. 6 illustrates that additional transmission peak of trimer unit cis-polyacetylene does not enter into the bias window at these bias voltages. Furthermore, an examination of MPSH states contributing to the bias window at these voltages manifests that MPSH states of are more delocalized in case of fused thiophene trimer. Hence due to above two factors current through fused thiophene trimer would be relatively larger at 1.2 V and 1.4 V. It is worth mentioning that in an earlier work [55] we investigated the NDR feature in fused furan trimer. A comparison of the results of the present analysis and that obtained with fused furan trimer illustrates that in the present study NDR feature is present over a wider range of bias voltages (±1.6 V to ±2.45 V) and in either case I–V relationship is slightly asymmetric. 4. Conclusions In the present work we report NDR behavior in trimer unit of cis-polyacetylene and modification of its NDR feature due to the addition of heteroatom (sulphur) to the cis configuration. In the investigation we estimated transport properties through nonequilibrium Green’s function technique. In fused thiophene trimer NDR feature is prominent over the bias range of ±1.6 V to ±2.45 V and in
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trimer unit of cis-polyacetylene the same is noticed over the bias range of ±2.1 to ±2.45 V. We present an explanation of the observed NDR character by monitoring the shift in transmission resonance peak across the bias window against varying bias voltages. Finally, a molecular origin of the NDR character has been provided through an analysis of MPSH states contributing to the bias window at different bias voltages. Acknowledgements At the very outset we would like to convey our special thanks to Atomistix Inc. for allowing us to use ATK 2.0.4 for electronic transport calculations. The financial support from DST, Govt. of India (Under FIST Program) to purchase the GAUSSIAN 03 program is gratefully acknowledged. S. Sen acknowledges Prof. A. Guha, Director, JIS College of Engineering. S. Sen would also like to thank P. Seal for providing necessary helps in computational purpose. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.commatsci.2008.12.010. References [1] C.W. Bauschlicher Jr., J.W. Lawson, Phys. Rev. B 75 (2007) 115406–115411. [2] Y.-h. Zhou, X.-h. Zheng, Y. Xu, Z.Y. Zeng, J. Chem. Phys. 125 (2006) 244701– 244705. [3] J. Koch, M.E. Raikh, F. von Oppen, Phys. Rev. Lett. 96 (2006) 056803–056806. [4] C. Zhang, M.-H. Du, H.-P. Cheng, X.-G. Zhang, A.E. Roitberg, J.L. Krause, Phys. Rev. Lett. 92 (2004) 158301–158304. [5] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, New York, 1996. [6] R.H. Mathews, J.P. Sage, T.C.L.G. Sollner, S.D. Calawa, C.-L. Chen, L.J. Mahoney, P.A. Maki, K.M. Molvar, Proc. IEEE 87 (1999) 596–605. [7] M.A. Reed, C. Zhou, C.J. Muller, T.P. Burgin, J.M. Tour, Science 278 (1997) 252– 254. [8] M.A. Reed, J. Chen, A.M. Rawlett, D.W. Price, J.M. Tour, Appl. Phys. Lett. 78 (2001) 3735–3737. [9] A. Halbritter, Sz. Csonka, G. Mihály, E. Jurdik, O. Yu Kolesnychenko, O.I. Shklyarevskii, S. Speller, H. van Kempen, Phys. Rev. B 68 (2003) 035417– 035423. [10] S. Roche, Sequence dependent DNA-mediated conduction, Phys. Rev. Lett. 91 (2003) 108101–108104. [11] A.N. Andriotis, M. Menon, D. Srivastava, L. Chernozatonskii, Phys. Rev. Lett. 87 (2001) 066802–066805. [12] E.G. Emberly, G. Kirczenow, Phys. Rev. Lett. 91 (2003) 188301–188304. [13] M. Di Ventra, S.T. Pantelides, N.D. Lang, Phys. Rev. Lett. 84 (2000) 979–982.
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