Article pubs.acs.org/JPCC
Odd−Even Effects in Charge Transport through Self-Assembled Monolayer of Alkanethiolates Argo Nurbawono,†,‡ Shuanglong Liu,†,‡ Christian A. Nijhuis,‡,§ and Chun Zhang*,†,‡,§ †
Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117551 Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546 § Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543 ‡
S Supporting Information *
ABSTRACT: It has been demonstrated in experiments that charge transport through self-assembled monolayers (SAMs) of alkanethiolates shows intriguing odd−even effects when the number of methylene groups changes. Most previously reported theoretical investigations were based on semiempirical methods or largely simplified models and the quantum origin of the observed odd−even effects is still unclear. In the current study, we performed ab initio calculations for electronic and transport properties of SAM of alkanethiolates on Ag [111] surface. Extensive density functional theory (DFT) based energy minimizations of the system geometries were conducted to pinpoint the most accurate geometries amenable to experimental observations. The recently proposed dual mean field (DMF) approach that includes bias-induced nonequilibrium effects in density functionals is used to determine current−voltage characteristics. Odd−even effects are observed in both electric currents and binding energies between the SAM and the probing electrode. The significant difference between the tunneling barriers across the “top” contact of odd and even molecular junctions is revealed to be the origin of the odd−even effects in electron transport. Our calculations suggest that the odd−even effects in charge transport in the system under study occur for alkanethiolate molecules with a certain length (10 < n < 19, where n is the number of methylene groups).
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INTRODUCTION
alkanethiolates demonstrate odd−even effects in its charge mobility, with even n having larger mobility than the odd.7 Great theoretical effort has been made to understand the electronic and transport properties of SAMs.8−14 However, most of these theoretical studies especially on the transport issues were based on either semiempirical methods or largely simplified models, and the quantum origin of the experimentally observed odd−even effects in charge transport still remains unclear. To the best of our knowledge, reliable ab initio calculations based on theoretically robust quantum models for both structure optimizations and transport properties of SAM of alkanethiolates have not been done yet. In this article, we present an ab initio study for electronic and transport properties of SAM of alkanethiolates on Ag [111] substrate (see Figure 1). Extensive density functional theory
The next generation of electronic devices will very likely be built on top of molecular scale junctions.1−3 The self-assembled monolayer (SAM) of molecules has been regarded as one of the most promising building blocks for future molecular electronic devices. The alkanethiolate molecules that consist of n methylene groups (S(CH2)n−1CH3) is often used in literature in making SAM molecular junctions. Various properties of SAM of alkanethiolates have been extensively discussed in the literature.4 One of the most fascinating properties of SAM of alkanethiolates is the so-called odd−even effects in charge transport, which has been observed in various experiments. For example, the electric current through SAM of alkanethiolates with n number of methylene groups shows odd−even effects where its length dependence is significantly different between odd and even n cases.5 Current rectification by SAM of ferrocenyl-alkanethiolates also has odd−even effects with the odd n rectifying current 10 times more efficiently than the even n,6 and in an organic field effect transistor, SAM of © 2015 American Chemical Society
Received: November 20, 2014 Revised: February 13, 2015 Published: February 18, 2015 5657
DOI: 10.1021/jp5116146 J. Phys. Chem. C 2015, 119, 5657−5662
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The Journal of Physical Chemistry C
surface normal (Figure 1d) and a twist angle relative to each other (Figure 1e). We performed extensive energy minimization analyses to find the most energetically stable site for the Sterminated alkanethiolates. We found that the S atom prefers to bind between the bridge and the hollow sites, and the optimized structure is at a tilt angle around 13° and a twist angle around 50°, keeping a close agreement with the experimental spectroscopic observations.18 Inadvertently increasing the tilt angle will result in increasing energy due to steric repulsions between the two molecules. Our calculations show that 3° of change in tilt angle leads to at least 0.5 eV of energy increase, indicating that the SAM layer is stable at room temperature. In experiments, the top electrode is normally a metal probe with a passivating thin layer of highly conductive oxide that stabilizes the metal surface. One example is eutectic GaIn probe, or the so-called EGaIn method.19−22 The EGaIn probe has ∼0.7 nm of a Ga2O3 layer, which stabilizes the probe,5,6 and the bulk GaIn probe is amorphous with typically around 75 wt % of Ga. Here we model the top electrode using crystalline Ag [111] with five monolayers of bulk Ag and deposit a monolayer of GaO on its surface to mimic the effects of the oxide layer (see Figure 1b). The GaO monolayer follows the hexagonal symmetry of Ag [111] surface, and it is energetically favorable when O is closer to the Ag surface. Other possible configurations that we investigated tend to have significantly higher energies. To determine the complete structure of the SAM junction, the GaO-passivated Ag [111] probe was gradually lowered down onto the preoptimized SAMs on Ag [111] from a large distance (>5 Å). The energy starts to decrease when the molecular orbital overlap occurs and increases again when the distance becomes too short; thus, the optimum distance between the SAM and top electrode was determined by minimizing the energy. During the relaxation procedure, all atoms except for the two outermost layers of Ag [111] are fully relaxed. Generally the optimized distances between SAM and top electrode are around ∼3 Å for both odd and even n SAM, and shorter SAMs (n < 9) tend to have slightly smaller distances. Examples of the optimization procedure are shown in Figure S1 in the Supporting Information where we present the energy as a function of the distance between SAM and top electrode for different cases of n. Energy minimizations were done with the DFT-based calculations by utilizing SIESTA computational package.23 The single-ζ polarized (SZP) basis set was used in all calculations with 100 Ry mesh cutoff and 3× 3 k-point sampling in the Brillouin zone. The generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof (PBE) format24 was employed. The energy convergence criterion was set to 10−4 eV. The structure optimization was carried out until the net force on each atom is less than 0.01 eV/Å. First principles based transport calculations have been proven to be effective in understanding quantum tunneling mechanism and inspiring novel devices.25−28 In the current study, the transport calculations were performed using the so-called DMF approach we implemented in SIESTA.15 The essential point of the DMF is that the current-carrying electrons in the system experience a different mean field potential from other electrons, and the bias-induced nonequilibrium effects can be accounted for by introducing the density of current-carrying electrons into energy functionals. This theoretical basis enables exclusive
Figure 1. (a) Side view of alkanethiolates for n = 11 and n = 12. S atom is adsorbed at the bottom end of the molecule to the Ag [111] substrate. The structures are fully relaxed; notice the difference between the tip structures of odd and even. (b) Side view of the top electrode, which consists of a GaO monolayer on Ag [111]. Charge transport direction is vertically downward from the Ag-GaO probe through the SAM and to the bottom Ag substrate. The distance between the top electrode and the SAMs was obtained through energy minimization process. (c) Top view of the SAMs on Ag [111]. Each supercell contains two pairs of alkanethiolates, with tilt angle around 13° and twist angle around 50° for each pair. (d,e) Definitions of tilt and twist angles, respectively [atomic color schemes: C, black; H, white; S, yellow; Ag, gray; O, red; Ga, blue].
(DFT) based energy minimizations of the system geometries were conducted to pinpoint the most accurate geometries amenable to experimental observations. In calculating I−V characteristics, the recently proposed dual mean field (DMF) approach15,16 was employed to include the bias-induced nonequilibrium effects in density functionals. Odd−even effects in both binding energies and electric currents were found. Detailed analyses show that odd and even n alkanethiolate molecules bind with the “top” electrode in different ways, which causes a significant difference in tunneling barriers for currentcarrying electrons across the “top” contact, leading to odd− even effects in charge transport. Our calculations reveal for the first time the quantum origin of the experimentally observed different length dependence of electric current of SAM of alkanethiolates for odd and even n cases, which has potentially great implications in the future development of SAM based electronic devices.
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MODEL AND METHODS The atomic set up of the SAM alkanethiolates on Ag [111] is shown in Figure 1a for n = 11 and n = 12. A supercell contains four alkanethiolate molecules with S atom terminations at the interface with the Ag [111] substrate (Figure 1c). We do not tune the surface density of SAM molecules since the major physics presented in the article should not depend on the density. Five monolayers of bulk Ag atoms were included in the supercell. The rhombus supercell on Ag [111] hexagonal symmetry is periodic in xy plane parallel to the Ag [111] surface. The direction of the charge transport is along the z axis. As already discussed in a number of prior works,4,17,18 the SAMs make a tilt angle relative to the vertical z axis, i.e., the 5658
DOI: 10.1021/jp5116146 J. Phys. Chem. C 2015, 119, 5657−5662
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The Journal of Physical Chemistry C analysis on the current carrying electrons, which are responsible for the transport phenomenon that we are most interested in.
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RESULTS AND DISCUSSION In this article, an odd−even SAM alkanethiolate pair is defined as a pair where the even n has one more methylene than the odd, such as (11,12) is one pair, while (10,11) is not. The SAM tilt angle (around 13°) causes an important odd−even difference in terms of the tip structure that the H atoms at the tips of odd SAMs are significantly more different on their vertical heights than the even ones (for example, see the tip structures of the pair (11,12) in Figure 1a). This difference does not exist if the tilt angle disappears. We expect this effect is more pronounced for SAM on Au because of their large tilt angle of around 30°.4 Because of different SAM tip structures, odd and even SAMs interact with the top electrode differently. Our calculations show that the interaction between the top AgGaO electrode and the even SAMs appears stronger than the odd ones in the same pair, which can be clearly seen from the calculated binding energies in Table 1. As a result, the tip
Figure 2. Odd−even effects at bias voltage 0.2 V. The current follows typical exponential decay of the value J versus n. The lines represent fit to the simplified form of the Simmons equation from which we determine J0 and β, for J = J0 e−βn. In this particular model, we found β even to be the same for both odd and even, while Jodd 0 < J0 . The odd−even effects always take place for n > 10 at all bias values including negative bias.
transition state from the homogeneous Simmons law to the separate odd−even series. The odd n essentially follow Jodd = 3.5× 10−5 e−1.14n throughout the whole series, and this is also reflected by the stable tip methyl conformations, which remain similar for short and long molecules. For even n there is a sudden change of J0 at n = 12, leading to a larger current prefactor, Jeven = 1.1× 10−4 e−1.14n. The exponential decay constant β = 1.14/n is the same for both odd and even (which is equivalent to β = 0.74/Å) and bias independent for −0.6 V ≤ Vb ≤ 0.6 V (see cases of other bias voltages in Figure S2 in the Supporting Information). The decay constant β we obtained is comparable to experimental values using EGaIn probe,5 HgSAM probe,8,9 and AFM probes.12,13 These experiments suggested that for SAM alkanethiolates β should take a value between 0.6/Å ≤ β ≤ 1.0/Å in small bias, and our values fall well within this range.8−10 It worth mentioning here that according to our calculations, the odd−even effects are absent for the single molecule junctions without the tilt. In order to better understand the odd−even effects shown in Figure 2, we performed the transmission analysis for all bias voltages. Figure 3 shows the transmission averaged over kx and ky as a function of single-electron energy at the bias voltage 0.2 V. Before odd−even effects take place, the transmission always drops when an extra methyl group is added as in Figure 3a, and
Table 1. Binding Energy Per Alkanethiolate Molecule between SAM and the Top Ag-GaO Electrode for 7≤ n ≤ 16; for Every Odd−Even Pair, the Binding Energy for Odd Is Always Less than Its Even Partner n
binding energy (eV)
7 8 9 10 11 12 13 14 15 16
−0.13 −1.07 −0.20 −0.31 −0.11 −0.48 −0.12 −0.47 −0.84 −1.11
structure of the even SAM is more significantly distorted by the top electrode after the junction is formed, and this is particularly noticeable for n > 8 cases due to the fact that longer SAMs are more flexible than the shorter ones. The distortions on the odd n SAMs are much less, despite the molecule−electrode distances are effectively the same as the even ones. The s−p valence interaction between the tip H atoms and the Ga layer in the electrode plays an important role in the binding between the SAM and the top electrode. The weaker binding energies of the odd SAMs originate from the more different heights among the H atoms of the tip methyl group. The difference of heights among tip H atoms of even SAMs are much less, leading to additional molecular orbital overlap with Ga and stronger binding energies. The consequences from the small difference in the conformations of the tip methyl group between the odd and even SAMs result in profound effect in the electrical characteristics of the junctions. By large, odd−even effects in charge transport in the system under study where the odd and even SAMs exhibit different n dependence may be viewed generally as the interaction effects between the SAM tip and the top electrode. As shown in Figure 2 the current at 0.2 V clearly shows odd−even effects for n > 10, and for n < 9, they behave in the typical Simmons law behavior,29 J = J0 e−βn, i.e., without odd−even effects. The pair (9,10) particularly appears as a
Figure 3. (a) Average transmissions as functions of single-electron energy at bias 0.2 V for n ≤ 10 and (b) for n > 10. The transmission is averaged over kx and ky. 5659
DOI: 10.1021/jp5116146 J. Phys. Chem. C 2015, 119, 5657−5662
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The Journal of Physical Chemistry C this also happens for shorter pair (5,6). When odd−even effects take place, the features and magnitude of the transmissions for each SAMs in a pair are almost identical as shown in Figure 3b for 11 ≤ n ≤ 16. The current−voltage (I−V) curves are similar for positive and negative biases as shown in Figure 4. In Figure
Figure 5. xy-plane averaged mean-field potential for current-carrying electrons along z axis: (a) for n = 7,8, and (b) for n = 11,12. In panel a, z < 14 Å is the bottom substrate and the SAMs start from z = 14 Å onward to the right. The top Ag-GaO electrode starts at z = 41 Å (for n = 7) or z = 43 Å (for n = 8). In panel b, the top electrode starts at z = 50 Å (for n = 11) or z = 52 Å (for n = 12). In panel a, the height of the tunneling barriers across the top contact are approximately the same for both odd and even, while in panel b the barrier for even n is lower by 1.34 eV. Figure 4. Electric current versus bias voltage for odd and even n. (a) For n ≤ 10, the current does not follow odd−even effect, and in fact, the current for n = 10 is larger than n = 9 , which indicates a transition region. (b) For n > 10, the current follows odd−even effect. Also notice that the currents for negative bias are slightly lower than positive bias due to asymmetry along the z axis.
and in effect increases the conductivity of the junction. The reduction of the tunneling barrier in even n compensates the longer tunneling length through one extra methyl group in even n, leading to similar electric currents between n = 11 and n = 12. This also explains why in an odd−even pair the electric current for the odd number is smaller than the even one. For comparison, the averaged mean field potentials for the “transition states” (n = 9 and n = 10) are shown in Figure S3 in the Supporting Information. Our calculations clearly suggest that in the Simmons law J = J0 e−βn, the prefactor J0 is determined by the electron tunneling through the potential barrier across the top contact (defined by the SAM−top contact van der Waals interface), which causes the odd−even effects for n > 10, and the parameter β describes the dependence on the molecular length (n) that is the same for odd and even cases. The tunneling-eigenchannel analysis is helpful in understanding how electron transport proceeds through the whole junction. In DMF method, the tunneling eigenchannels are computed from diagonalizing the transmission matrix of the current-carrying electrons. We show the isosurfaces of the dominant tunneling eigenchannels for various SAMs at bias 0.2 V in Figure 6a. For comparison, the isosurface of the valence σz band right below the Fermi energy of an infinite alkanethiolate chain is shown in Figure 6b. The shape of the tunneling eigenchannel in the SAMs obviously resemble the σz band of an infinite chain (see the band structure of the infinite chain in Figure S4 in Supporting Information), suggesting the electron transport across the junction through the highest valence band of the molecule. Further orbital analysis shows that the eigenchannel is made of 80% C pz and some other contributions from s and d orbitals. The different tip effects on tunneling between odd and even cases can also be seen. In addition we show the DMF correction to the mean-field potential for current-carrying electrons for n = 7 in Figure 7 defined as δV = Vn − Ve, where Ve and Vn are effective meanfield potentials for equilibrium and current-carrying electrons, respectively. In this case we have a large band gap system with
4b the I−V curves for SAMs (n > 10) in an odd−even pair appear almost identical. We did structure optimizations up to n = 19, but only performed transport calculations up to n = 16 because for longer molecules the electric currents are too low (≤10−12 A) so that very high computational accuracy in nonequilibrium contour integral is needed to produce meaningful results, which is beyond the computer power we have. While the odd−even difference in the tip structures remains very similar for the pair (17,18), it is reasonable to believe that the odd−even effects in transport may still persist for pair (17,18). However, the phenomena may disappear for n > 18 since flexural distortions and excessive twisting in tips start to occur during the structural optimizations for both odd and even molecules. To see how the different tip structures of odd and even molecules affect the electron transport, we plot in Figure 5 the variation of averaged mean field potential for current-carrying electrons along the z axis. The potential is averaged across the xy plane and shown in Figure 5a for the pair (7,8) and Figure 5b for (11,12). It is obvious that there is no difference in the potential along the odd and even SAMs except at the top contact (the interface between the tip methyl-GaO monolayer), and this is further clear evidence that the odd−even effects are predominantly tip effects. For the pair (7,8), the height and width of potential barriers across the top contact are also similar, indicating the fact that for shorter molecules n < 9, the electric current is governed by the length of molecule n where no odd−even effects are present. For the pair (11,12), due to the stronger binding with the top electrode, the tip structure of the even one (n = 12) is distorted, which greatly decreases the tunneling barrier across the top contact (1.34 eV lower than the odd one), giving subsequent advantage to the tunneling process 5660
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CONCLUSIONS Primary aspects of the odd−even phenomena observed in tunnel junctions with SAM of alkanethiolates on Ag [111] were studied using ab initio calculations based on DFT energy minimization and DMF transport approach. The fact that the atomically different top electrode used in this theoretical model still demonstrates the odd−even effects with results comparable with experiments suggests that the odd−even effects are robust phenomena that are not due to a particular choice of top electrodes. Compared with odd SAM in the same pair, the even one binds with the top electrode stronger, which causes more significant conformational distortions at the tip. The significant reduction of the tunneling barrier of even n SAMs for 10 < n < 19 across the top contact caused by the tip distortion is found to be the quantum origin of the odd−even effects in charge transport in the system under study. Shorter SAMs (n < 10) do not show this effect because they are too rigid, and the tunneling barriers in the same pair are comparable. While long SAMs (n > 18) generally have the problem of too much flexural distortion for both odd and even cases, they may not show odd−even phenomena either. In summary, our calculations explained for the first time the odd−even effects in charge transport through the SAM alkanethiolates with a full quantum model. We believe the conclusions of the article have great implications for the future development of SAM based electronic devices.
Figure 6. (a) Isosurfaces of tunneling eigenchannels at bias voltage 0.2 V, for n = 7, 8, 11, and 12, respectively. For odd n, the eigenchannels resemble infinite alkanethiolates where the charge transport is facilitated by the σz-bond of C pz oribitals. However, for the even n the last methylene appears like an impurity state compared to the rest of the channel. Also there is no qualitative changes in the isosurface between n = 7 and n = 11, and all odd n follow monotonous Simmons law. This is in contrast to the even n where the tip conformations change significantly between n = 8 and n = 12; thus, n = 8 does not follow the Simmons law for even n. (b) Density of states (DOS) of an infinite alkanethiolate, with the highest occupied valence band denoted as σz. This band is the origin of the conducting eigenchannels shown in panel a. The calculated energy band gap of the infinite chain is around 9.7 eV, comparable to experimentally obtained values,30 and the Fermi level is the green dashed line [atomic color schemes: C, black; H, white; S, yellow; Ag, gray; O, red; Ga, blue].
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ASSOCIATED CONTENT
S Supporting Information *
Examples of the structure optimization, odd−even effects at different bias voltages, and the isosurface of potential profiles. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research is supported by the Ministry of Education (Singapore) and NUS academic research funds (Grant No.: R144-000-325-112 and R-144-000-344-112). C.A.N. thanks the support from the Singapore National Research Foundation (NRF Award No. NRF-RF2010-03). Computations were performed at the Graphene Research Centre and the Centre for Computational Science and Engineering at NUS.
Figure 7. Isosurface of DMF correction to the mean field potential defined as the difference between equilibrium potential and nonequilibrium potential, i.e., δV = Vn − Ve, for n = 7 at bias voltage 0.2 V. Nonequilibrium corrections to the potential are mainly at the contact region between GaO monolayer and the alkanethiolate tips, which are qualitatively the same for odd and even. Similar illustration for n = 8 can be found in the Supporting Information [atomic color schemes: C, black; H, white; S, yellow; Ag, gray; O, red; Ga, blue].
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very small current, and thus, DMF corrections are in general small; nevertheless, as shown in the figure they can be important around the contact regions where tunneling starts from the upper probe to the molecule. The DMF correction for n = 8 is shown in Figure S5 in the Supporting Information. As a final remark, the upper Ag-GaO probe used in the present work is different from any experiments using SAM alkanethiolates that we found in the literature, yet the odd−even effects are clearly demonstrated with straightforward explanations, and the β value we obtained is comparable to experimental ones. The tip effects are therefore crucial for the tunneling process, and they are genuine, robust properties of the SAM alkanethiolates.
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