Negative differential resistance in polymer molecular devices modulated with molecular length

Physics Letters A 374 (2010) 3857–3862

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Physics Letters A www.elsevier.com/locate/pla

Negative differential resistance in polymer molecular devices modulated with molecular length Yun Ren a,b , Ke-Qiu Chen a,b,∗ , Qing Wan a,b , Anlian Pan a,b , W.P. Hu c a b c

Department of Applied Physics, Hunan University, Changsha 410082, China Key Laboratory for Micro–Nano Optoelectronic Devices of Ministry of Education, Hunan University, China Key Laboratory of Organic Solids, Institute of Chemistry, Chinese Academy of Science, Beijing 100080, China

a r t i c l e

i n f o

Article history: Received 1 May 2010 Received in revised form 12 July 2010 Accepted 20 July 2010 Available online 23 July 2010 Communicated by R. Wu

a b s t r a c t We study the electronic transport properties of polymer molecular devices by applying first-principles method. The results show that the electronic transport properties depend on molecular length. Negative differential resistance can be observed and can be modulated with molecular length. © 2010 Elsevier B.V. All rights reserved.

Keywords: Negative differential resistance Molecular device First-principles

1. Introduction In recent years, molecular devices have attracted much attention. Various of molecules including organic single molecule [1–7], C 60 [8–10], conjugated polymers [11–16], cluster [17], carbon nanotubes (CNTs) [18–24], and graphene nanoribbons (GNRs) [25–30] have been extensively studied and applied in fabrication of nanometer-scale devices. Within these devices, some interesting quantum effects such as single-electron characteristic [31], Coulomb blockade [32], and molecular rectification [33–35] have been found theoretically and experimentally. In particular, negative differential resistance (NDR) behavior has been observed in different systems [10,14–16,36–38]. Polymer molecules such as oligo(phenylene ethnylene) (OPE) [14,39] and poly(para-phenylene ethynylene) (PPE) [11–13] have been extensively studied due to their well conductivity, rigidity, and available modification with thiol/thioacetate end groups. Hu et al. reported a self-assembled nanoscale photoswitch and p-type transistor based on a derivative of PPEs with thioacetate end groups (TA-PPE) [12]. And then Hu et al. have also succeed in fabricating a self-assembled polymer molecular junction based on TA-PBE about 18 nm and found that the I–V curve of this molecular junction has a highly periodic, repeatable, and identical stepwise features when the bias is larger than 3 V [13]. From previous works [40,41], it is known

*

Corresponding author at: Department of Applied Physics, Hunan University, Changsha 410082, China. Tel./fax: +86 0731 88822332. E-mail addresses: [email protected] (K.-Q. Chen), [email protected] (W.P. Hu). 0375-9601/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2010.07.040

that the conductivity is decreased with the increased length of the molecules. Then one may wonder if the well electronic transport remains for shorter PPE-based molecular junction. To answer this question, in the present work, we investigate transport properties of PPE-based molecular junctions along with the number of unit n = 3–8. Our results show that there is a small difference in current at low bias for PPE-based molecular junctions. However, an interesting NDR behavior can be observed with large peak-to-valley ratio for shorter molecular junctions, while for longer molecular junctions, the current is increased monotonously with the bias and no NDR behavior appears. 2. Model and method The molecular structures we study are illustrated in Fig. 1: PPEn molecule is connected to Au(111) electrodes through a thiol end group. Six kinds of PPE-based molecules are considered, which are formed by PPEn molecule with n = 3–8. In these structures, sulfur atom is chosen to be located at the hollow site of the gold triangle and Au–S distance along transport direction is 1.9 Å, which is typical Au–S distance with minimal total energy for the whole two-probe system. The supercell for the scattering region is defined by 4 × 4 atoms in perpendicular to the transport direction and contains two surface layers on each side of the PPE polymer molecule with shorter side chains(–OC3 H7 ) than the previous work [13]. As expected, length effect is obvious and plays an important role in electron transport. Therefore, the present work is focused on shorter main-chain with sub-8 nm (namely, 3  n  8). We use M1–M6 to describe molecular junctions with PPEn molecule

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Fig. 1. (a) The molecular structure of PPE polymer molecule with a thiol end group but different number of units n (namely, different lengths); (b) schematic illustration of the molecular device based on the PPE polymer molecule with n = 3, other PPE-based devices are the same as above. In our models, two layers of Au atoms are chosen as left/right surface atoms in the scattering region. Note that the P 1, P 2, . . . , Pn, Pn + 1 and Pn + 2 for PPEn molecule are referred to subsystems.

with n = 3–8. The structures have been optimized and quantum transport properties have been calculated by an ab initio code package Atomistix Toolkit (ATK) [42–44]. The program ATK is based on the nonequilibrium Green’s functions in combination with the density-functional theory and can deal with electronic structure of molecules, crystals, as well as surfaces. It is known that this method’s premise is to divide the whole two-probe system into three parts: left electrode, a center scattering region, and right electrode. Taken into account the screen effect between electrodes and central molecule, a portion of electrodes are included in the scattering region. In our calculations, local-density approximation for exchange-correlation potential is used, each atomic core for all atoms is respected by norm-conserving Troullier–Martins pseudopotential [45], the valence electrons wave function is expanded by a SIESTA localized basis set [43], the Brillouin zone has been sampled with (4, 4, 100) points within the Monkhorst–Pack kpoint sampling scheme, and a real-space grid with a mesh cutoff energy is 150 Ry. The calculational process for ATK program is briefly described as follows: At first, self-energies of left and right electrodes are obtained as given a self-consistent potential depending on bias. Then the electron density can be obtained from the Green’s function of the center scattering region. Next, the Hamiltonian making use of evaluating Green’s function can be provided. Through self-consistent iterative scheme, the electron density can be finally computed. Once the electron density for the system is known, in principle, all physical quantities can be achieved such as transmission coefficient, density of state (DOS), projected density of state (PDOS), molecular orbitals, molecular projected selfconsistent Hamiltonian (MPSH), and current, etc. The transmission coefficient T ( E , V b ) is presented as





T ( E , V b ) = Tr Im Σ L ( E )G R ( E )Σ R ( E )G A ( E )

(1)

where G R ( A ) is the retarded (advanced) Green’s function of the center scattering region. According to the Landauer–Büttiker formula [46], the expression of current is given

I (V b ) =

2e h

μr T ( E , V b ) dE , μl

(2)

where μl/r are electrochemical potentials of the left and right electrodes. With the applied bias potential V b , the difference in the chemical potentials is given by eV b , and we use μl ( V b ) = μl (0) − eV b /2 and μr ( V b ) = μr (0) + eV b /2. The energy region of the transmission spectrum that contributes to the current is referred to as the bias window. 3. Results and discussion I–V characteristic curves for the PPE-based molecular devices with different molecular lengths are described in Fig. 2. For M1– M4, the characteristics of I–V curves are approximately similar to each other except a small difference in magnitude of current. It is found from Fig. 2 that the current through molecular junction is initially very small but it increases slowly with the increases of bias at positive bias until 0.7 V. Then, a rapid increase in current appears, and the maximal current is up to 17 μA at 0.98 V. However, ranging from 0.98 V to 1.05 V, it is observed that the current decreases rapidly with the augment of bias and its minimal current is reduced to 1 μA at 1.05 V. As we known, the decrease in current with an increasing bias shows an NDR behavior. For M1– M4, the NDR behavior appears in bias region [0.98, 1.05] V with peak-to-valley ratio being 13.83, 20.46, 19.79, and 9.21, respectively, which is higher than those found in some other systems [10,25,47]. When the bias is larger than 1.5 V, the current is increased with bias. The current is asymmetric at positive and negative biases, which is accord with the experimental observation [13]. The asymmetric behavior has been also observed in some other systems, even for some symmetric molecules [48–50]. The possible reasons are asymmetric contacts between molecule and electrodes, asymmetric molecule, or different electrode surface. In the present work, the asymmetric I–V behavior is due to the fact that the optimized system has become asymmetric. It is noted that an NDR behavior occurs at negative bias with the peak-tovalley ratio being 6.95 for M1, 2.73 for M2, 3.02 for M3, and 1.91 for M4. Additionally, the corresponding bias regions where the NDR appears are [−1.6, −1.4] V, [−1.8, −1.4] V, [−1.8, −1.4] V, and [−2.0, −1.2] V for M1–M4, respectively. From Fig. 2, it is also found that the NDR vanishes for longer PPE-based molecular junc-

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Fig. 2. I–V characteristics curves of all PPE-based molecular devices. Here, M1–M6 correspond to the molecular junctions based on PPEn molecule with n = 3–8, respectively.

Fig. 3. The transmission coefficients as a function of the electron energy E in [−2, 2] eV for M1–M6. Note that each transmission coefficient is shifted upper by step-height 0.7 ranging from M1 to M6.

tions such as M5–M6. The currents for both cases are enhanced with the increase of bias, but the asymmetric I–V characteristic remains. Moreover, the current of M5 is larger than that of M6, which means length effect has an important influence on electron transport. From these investigations, it is expected that there is a smaller current in the previous work for about 18 nm PPE-based molecular junction [13]. Note that the value of the current is influenced by microscopic details of the system. It is also expected that electron–phonon interaction plays a vital role in electron trans-

port, especially for long molecular junction [51]. Thus we think that both length effect and the phonon scattering effect are the main physical origins of the smaller current (at the level of p A) in the previous work [13]. To see more clearly the transport behavior at low bias, the transmission coefficients as a function of incident electron energy E at zero bias for M1–M6 are given in Fig. 3. A wide transmission gap appears around the Fermi level in the energy range about [−1, 0.1] eV. Some transmission peaks are regularly distributed in

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Fig. 4. The transmission coefficients and the projected density of states (PDOS) as a function of the electron energy E in [−1, 1] eV in each subsystem at 0.98 V for M1.

the energy range [0.1, 2] eV and [−1.7, −1] eV. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are located beside the Fermi level, and correspond to two peaks beside the Fermi level very well. Furthermore, other molecular orbitals in energy range [−2, 2] eV correspond to each transmission peak in Fig. 3. Moreover, with an increase of the length of PPE molecule, more resonant transmission peaks and molecular orbitals appear in these transmission regions, which may be beneficial to electronic transport especially at high bias. It can also be found that the LUMO orbital makes main contribution to the current at low bias. If we further decompose all atoms in the scattering region into some subsystems for PPE-based molecular junction: Au atoms in left surface layers, sulfur atom as left anchor atom, P 1, P 2, . . . , P n, P n + 1, P n + 2, sulfur atom as right anchor atom, Au atoms in right surface layers as shown in Fig. 1(a). Here, we take M1 as an example, nine subsystems are considered. To better understand the physical properties, we also give transmission coefficients as well as the PDOS in these subsystems at 0.98 V in the energy range [−1, 1] eV in Fig. 4. The LUMO ( 1 eV) has been far away from the Fermi level. However, the HOMO approaches the Fermi level with the increase of the bias and mainly determines its electronic transport properties at low bias. In energy region [−1, 1] eV, all three transmission peaks are located below the Fermi level, and the HOMO is just corresponding to the first transmission peak below the Fermi level, which is in favor of electronic transport. It is easily found that almost all states in energy region [−1, −0.5] eV are localized at P 3 from the PDOS as presented in Fig. 4. This is to say, these states are scattered at P 3 and cannot been traveled through P 3. Simultaneously, most states in [0.05, 1] eV are localized at Au and sulfur atom layers, but it is hardly found on P 1– P 5. In the energy region [−0.5, 0] eV, a broad transmission region with three transmission peaks are produced as a result of the perfect delocalized molecular orbitals such as HOMO-2, HOMO-1 and HOMO.

In order to further understand the NDR behavior and length effect for PPE-based molecular devices, the transmission spectra as a function of electron energy E at different biases for M4 and M5 are given in Fig. 5(a), (b). As seen from Fig. 5(a), there are several molecular orbitals falling into bias window and forming some resonant transmission peaks with the increase of bias. As a result, electrons can be easily transported between two electrodes through these transport channels. In particular, when the bias is increased to 0.98 V, four molecular orbitals HOMO-3, HOMO-2, HOMO-1 and HOMO are completely corresponding to broad and big resonant transmission peaks, which means a strong coupling between central molecule and electrodes as reported by Geng et al. [4]. However, the current is decreased quickly and an NDR behavior appears while the bias continue to rise until 1.05 V. This can be understood. From Fig. 5(a), we can see that HOMO is of a big right shift, and other three molecular orbitals HOMO-3, HOMO-2, and HOMO-1 are of slight left shift. This leads to HOMO-1 and HOMO being almost fully suppressed, and only HOMO-3 and HOMO-2 remains excellent delocalization. However, as shown in Fig. 5(b), the total number of molecular orbitals of M5 is more than those of M4 in Fig. 5(a), but fewer molecular orbitals lie in the bias window. In particular, the HOMO is shifted towards the Fermi level but the LUMO is basically unchanged at positive bias. When the bias is increased to 0.4 V, the LUMO starts to make contribution to electronic transport. Until 1.2 V, the LUMO + 1 together with LUMO commonly have contribution to the current. Thus, the current is increased quickly when the bias is over 0.8 V. One may wonder why such great differences between M1–M4 and M5–M6 are shown? Compared M5 with M4 at ±1.2 V in Fig. 5, we can find that for M5 fewer and small transmission peaks are responsible for its small transport properties owing to the weaker coupling between molecule and electrodes induced by the length effect. Therefore, length of molecular junction has an important influence on I–V characteristics.

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Fig. 5. (a) and (b) correspond to the transmission coefficients as a function of the electron energy E at different biases for M4 and M5, respectively. The region between the green thick solid lines is referred to the bias window; the short thick black line, dark green line, and red solid lines are referred to the HOMO, the LUMO, other molecular orbitals in energy region [−1.5, 1.5] eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

Fig. 6. Upper: the molecularly projected self-consistent Hamiltonian (MPSH) of HOMO-3, HOMO-2, HOMO-1, HOMO, and LUMO for M4 at 0.98 V (left) and 1.05 V (right); lower: the MPSH of HOMO and LUMO as well as LUMO + 1 for M5 at 1.0 V and 1.2 V.

To elucidate the NDR mechanism and length effect more clearly, the MPSHs of HOMO-3, HOMO-2, HOMO-1, HOMO, and LUMO for M4 at bias 0.98 V and 1.05 V are given in Fig. 6. Wherein, the former four molecular orbitals are all within bias window. At 0.98 V, molecular orbitals within bias window HOMO-3, HOMO-2, HOMO-1 and HOMO are delocalized and make large contribution to the current. Although the LUMO far away from the Fermi level is delocalized, but it hardly makes any contribution to current at low bias since there is insufficient incident energy to transport electron between two electrodes. However, when the bias is larger than 1.05 V, the HOMO near the Fermi level has great changes induced by the weak coupling between left surface Au atoms and P 1– P 5 subsystems as well as sulfur atoms, which is responsible for the decrease in current, and the NDR behavior. As expected, all molecular orbitals around the Fermi level within bias window are important to electronic transport especially at low bias. For M5, it is found that only HOMO and LUMO fall into bias window at 1.0 V. Moreover, the coupling between PPE molecule and left surface atoms turns to be weaker for HOMO, which means the HOMO is suppressed and leads to a lower transport behavior between two electrodes through PPE molecule. Likewise, the LUMO is also suppressed because of its weak coupling between PPE molecule and right surface atoms. Although HOMO and LUMO are within bias window, there is only a little contribution to the current as a result of weak coupling between molecule and electrodes. Thus, only small current through the molecular junction even if the bias reaches 1.0 V. While the bias is over 1.2 V, even though HOMO and LUMO are hardly changed, another molecular orbital LUMO + 1 comes into the bias window and exhibits a good delocalization, and leads to a rapidly increase in current for M5. We can ob-

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serve that the main chain of PPE molecule mainly determines the whole electronic transport properties, but side chains have a small influence on electronic transport from the given MPSH states in Fig. 6. 4. Conclusions In summary, by applying the nonequilibrium Green’s functions together with the density-functional theory, we have investigated the PPE-based molecular junctions with various lengths below 8 nm. The NDR behavior can be observed in sub-6 nm molecular junctions and the maximal peak-to-valley ratio reaches 20, which may be useful in molecular switches and molecular memories. For longer molecular junctions (> 6 nm), it is found that length effect has a remarkable influence on electronic transport, which is different from the cases below 6 nm. As expected, the current is smaller and increased slowly with bias in longer molecular junction. Based on the analysis of the projected density of states in combination with transmission coefficient as well as molecular projected self-consistent Hamiltonian, it is found that the frontier molecular orbitals being suppressed at some special locations of molecular junction and energy values within bias window is responsible for the NDR behavior. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 60871065), by the Ministry of Science and Technology of China (No. 2006CB605105), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 200805320011), and by Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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