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Shot noise of 1,4-benzenedithiol single-molecule junctions Mohammad Amin Karimi, Safa Golrokh Bahoosh, Markus Herz, Ryoma Hayakawa, Fabian Pauly, and Elke Scheer Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b04848 • Publication Date (Web): 09 Feb 2016 Downloaded from http://pubs.acs.org on February 14, 2016

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Shot noise of 1,4-benzenedithiol single-molecule junctions M. A. Karimi1, S. G. Bahoosh1, M. Herz1, R. Hayakawa 1,2, F. Pauly1, E. Scheer1* 1 2

Department of Physics, University of Konstanz, 78457 Konstanz, Germany

International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan *

Corresponding author: [email protected]

KEYWORDS: single-molecule junction, charge transport, low temperature, inelastic electron tunneling spectroscopy, shot noise, density functional theory

ABSTRACT We report measurements of the shot noise on single-molecule Au-1,4-benzenedithiol (BDT)-Au junctions, fabricated with the mechanically controllable break junction (MCBJ) technique at 4.2 K in a wide range of conductance values from 10-2 to 0.24 conductance quanta. We introduce a simple measurement scheme using a current-amplifier and a spectrum analyzer, and that does not imply special requirements regarding the electrical leads. The experimental findings provide evidence that the current is carried by a single conduction channel throughout the whole conductance range. This observation suggests that the number of channels is limited by the Authiol bonds and that contributions due to direct tunneling from the Au to the π system of the aromatic ring are negligible also for high conductance. The results are supported by quantum transport calculations using density functional theory (DFT). 1

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The determination of the quantum mechanical transport channels and their transmission probabilities requires additional information beyond the linear conductance.1, 2 So far, the two best established methods include the analysis of the superconducting subharmonic gap structure3, 4

and the investigation of the shot noise.5-12 While the first one has been mainly used for atomic

contacts1 and for the high-conductance molecule C60,13 the shot noise analysis has been applied to atomic contacts5-8 as well as to single-molecule junctions.9-12. However most of the experiments on single molecules concentrate on a rather narrow transmission range or study highly conductive molecules with a conductance very close to 1 G0, where G0 = 2e2/h is the conductance quantum, e=|e| is the elementary charge and h is Planck’s constant. Shot noise results from the discrete nature of the electronic charge. For a system that has N conduction channels with the transmission probabilities τn and at finite temperature T, the total current noise power can be expressed as14, 15:

= 2G coth 1 − + 4k . 1 2 Here V is the applied bias potential, and kBT is the thermal energy. For kBT ≤ eV it reduces to SI= 2e ˂ I > F. In the expression, ˂ I > is the time-averaged current and F is the Fano factor, which is given by # =

∑ 1 − . 2 ∑

From equation (2) it is clear that for a perfect transmission of electrons all shot noise is suppressed, because there are no fluctuations in the occupation numbers of left and right moving

2


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electrons. Several experiments on atomic-scale junctions showed this suppression at low temperatures5, 6, 16-18 and also at ambient conditions.7, 19 There is a longstanding puzzle regarding “the” conductance value of an Au-BDT-Au contact, because both, the theoretical predictions as well as the experimental findings are wide spread.2025

In a previous work we suggested that the conductance may vary over three orders of magnit-

ude upon changing the junction geometry26. In particular we showed that also the high-conductance state of Au-BDT-Au junctions can be distinguished from mere Au-Au contacts because we clearly detected the vibrational modes of BDT in the IET spectra.26 From the successful fitting with the single-level model26-28 and the sign of the IET peaks we concluded that these junctions were single-molecule junctions, but unambiguous clarification requires the determination of the number of conduction channels. Therefore we refine here the procedure of ref. 26. Here we report measurements of shot noise on Au-1,4-benzenedithiol (BDT)-Au junctions at low (G ≈ 10-2 G0) and at high (G > 0.1 G0) conductance states, acquired at 4.2 K using a versatile setup, which enables us to determine noise in a broad range of conductance values without the necessity of double wiring and performing cross-correlation5, 6, 16-18 and without going to high frequency measurements.7, 19 In brief, the measurement scheme relies on careful calibration of all unavoidable noise contributions29. The current through the contact is first amplified using a transimpedance amplifier. This signal is fed to a spectrum analyzer that measures the noise spectrum between 1 and 100 kHz. The signal shows contributions of 1/f noise at low frequencies and rolls off above roughly 90 kHz. We limit the frequency range to the white part of the spectrum to determine the shot noise and the thermal noise. We repeat the measurement for different bias voltages. The shot noise is then calculated by subtracting the thermal noise SI(V = 0).

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The measurements are performed using the MCBJ technique, by gently breaking an atomicscale contact between gold wires. After identifying a stable contact, the current-voltage characteristics (I-Vs), the differential conductance (dI/dV), the IET spectrum (d2I/dV2/(dI/dV)), and the shot noise SI from the contact are measured. The details of the measurement setup, sample fabrication and junction assembly are described in the Supporting Information (SI). The I-Vs and dI/dVs are determined before and after the noise measurements to make sure that the contact was stable during the measurement period (see SI). We found the highest probability for stable contacts in the high-conductance range of around G ≈ 0.2 to 0.24 G0. In the low conductance range stable contacts were found mostly around G ≈ 0.01 G0. In order to extract the Fano factor from the excess noise, we follow a procedure presented by Kumar et al.30 for Au atomic contacts. To simplify the fitting, two dimensionless, voltagedependent parameters are introduced:

% =

− 0 3 0

( =

e e coth 4 2 2

Using these definitions, expression (1) is reduced to a linear relationship: % = *( − 1+# 5

The first system, which we investigated, was the well-studied gold contact that serves as a reference system. We found good agreement for it with literature (see SI). Figure 1 (a) shows the I-V for a contact with a conductance of 0.23 G0. The single-level fit to the I-V yields an energy level of E0= 0.25 eV and the coupling constants of ГR = 0.076 eV and ГL= 0.067 eV (corresponding to a slight asymmetry α = ГL/ГR = 0.88) in agreement with the 4


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earlier findings and demonstrating that the molecule is bound to the electrodes almost symmetrically. Further support that charges flow through the molecule was obtained by studying the IET spectra. The vibrational modes of the molecule are detected by their effect on the current through the molecular junction. In the off-resonant situation τn « 1 and for a rather symmetrical coupling to both electrodes α ≈ 1, the excitation of a molecular vibration by the charge carriers gives rise to a peak in the d2I/dV2.31, 32 For the theoretical description of the IET spectra, the optimization of the geometry as well as accurate evaluations of the vibrational modes and of the electron-vibration (EV) coupling constants are necessary. These quantities can be calculated using a combination of DFT and NEGF33, 34. For the quantum transport calculations in this work, we apply the quantum chemistry package TURBOMOLE 6.5.35 The DFT calculations to obtain self-consistent electronic structures and optimized geometries are performed with the exchange-correlation functional PBE.36 We utilize the def-SV(P) basis set,37 which is of split-valence quality with polarization functions on all non-hydrogen atoms. Elastic charge transport is determined as described in ref. 38, while the inelastic interactions due to the EV coupling are treated at the level of the so-called lowestorder expansion (LOE).34 In Fig. 1 (b) we show an experimental (black line) IET spectrum and a theoretical one (red line). The character of those modes, which are responsible for the peaks in the spectra, is indicated. The assignment of the vibrational modes according to previous experimental results and our theoretical calculations is summarized in Table S1 in the SI. We calculated the IET spectra for different configurations and binding positions and find slight variations of both the positions and the amplitudes of the peaks. While this is in qualitative agreement with the experimentally observed variations of the IET spectra, they are much less than found in the 5


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experiment. As discussed further in the SI, this may be due to an insufficient sampling of the configurational space or effects not accounted for theoretically, such as a strong energy dependence of the transmission function due to conductance fluctuations.

Figure 1. (a) Experimental I-V of an Au-BDT-Au junction with a conductance of 0.23 G0 (black symbols) fitted with the single level model (solid red line). (b) Experimental (black) IET spectrum for the same junction and theoretical (red) one for a configuration with stretching length d = 6.4 Å and G = 0.26 G0 for in TT configuration, calculated for T = 4.2 K and an AC modulation of 5 mV as used in the experiment. Pronounced peaks at the voltages corresponding to the known vibrational modes of Au-BDT-Au junctions confirm the presence of the BDT molecule between two Au leads. Next the excess noise was measured for the same contact as studied in Fig. 1. In Fig. 2 (a) and (b) we plot the noise in two different ways according to eq. (1) and (5). The red lines are calculated according to these equations, assuming a single channel with transmission τ1 = 0.23. As visible, this assumption yields an excellent agreement with the experimental findings. We tentatively calculated the noise for several channels with the same total transmission. All combinations of transmissions with more than one channel lead to a noise higher than compatible 6


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with the experimental observation. To exemplify, the green and blue lines in Fig. 2 (b) are calculated shot noise curves for contributions of two and three channels with equal transmission. The results support our claims that also the highly transmissive Au-BDT-Au contacts exhibit a single transport channel.

Figure 2. (a) Shot noise as a function of the bias voltage applied across the Au-BDT-Au junction. The zero bias conductance for this junction is 0.23 G0. The red line is the fit to eq. (1), yielding τ1 = 0.23. (b) The excess noise, plotted for the reduced parameters X and Y. The red line is the fit to the data and gives a Fano factor of F = 0.77 for a transmission probability of τ1 = 0.23. The green line is the calculated excess noise for two channels with the same transmission probabilities of τ1 = τ2 = 0.115 and the blue line is those for three channels with τ1 = τ2 = τ3 = 0.0766. We repeated the experiment for several contacts with conductance G > 0.01 G0. The IET spectra and noise measurements for four further contacts are presented in the SI. In all cases the observed noise is best described by a single channel, but contributions of additional channels with transmissions in the order of 10% of the dominating one cannot be fully excluded because of the finite measurement resolution. For decreasing conductance the Fano factor increases to 1, 7


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corresponding to the full shot noise, and a disentanglement of several channels is not possible, although the measurement scheme itself works well for conductance values in the range of 0.01 < G/G0 < 0.1. In order to inspect the experimental results, we compare with transport calculations performed for Au-BDT-Au contacts upon stretching. There are comprehensive experimental and theoretical studies on Pt-benzene-Pt contacts.11,

39, 40

Moreover, the transport through BDT junctions has

also been widely examined theoretically.41-46 Prior computational work studying the evolution of the stretching process was done either based on DFT methods21, 22, 47 or by means of combined molecular dynamics-Monte Carlo (MD-MC) simulations.48 However, in these works on AuBDT-Au junctions, the number of open conduction channels was not determined. Theoretically, it is well established that the conductance of single-molecule Au-BDT-Au junctions depends sensitively on the Au–S binding geometry at the molecule-electrode contacts.41, 43 The fact that the sulfur can bind to almost any position on the Au electrodes41 is believed to be the reason for the large spread of conductance values in single-molecule junction experiments.49 In order to sample part of the space of possible geometries that are realized in our MCBJ experiments, we have set up two kinds of molecular junctions. Using Au pyramids oriented along the (111) direction, we consider either atomically sharp tips with a single metal atom at their tip or where the tip atom is removed. Putting a BDT molecule close to the point where the tips touch, a molecular junction is formed. An adiabatic trajectory for a stretching process is simulated by separating the metal electrodes symmetrically in each step by 0.4 Å, followed by a subsequent geometry optimization. Our Au pyramids consist of 20 or 19 atoms at each side, of which the outermost two gold layers are kept fixed in the optimization step, while the rest of the

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junction is fully relaxed. The steps are repeated until the junction breaks, and conductance values resolved into contributions from individual conduction channels are determined. The evolution of the Au-BDT-Au structure and its total energy in the junction breaking process as a function of lead-lead separation d is presented in Fig. 3 (a) and (b) for the case of atomically sharp tips. A selected number of simulation snapshots are shown, and the complete process can be found in the SI. Starting from an Au-Au contact with the molecule wired in parallel, the BDT moves into the contact as the tips are being retracted. While the orientation of the BDT molecule typically changes abruptly whenever bonds break, as the S atoms slide along the electrodes, see e.g. the distances of d = 2.4 and 5.2 Å, it varies continuously in elastic stages, when forces build up and energies increase. The contact breaks at d = 8.8 Å between an S and Au atom and not at an Au-Au bond, as might have been expected.50,51 This is presumably due to the high symmetry of the chosen Au electrodes and the limited number of flexible metal atoms. The variation of the conductance, resolved in terms of conduction channels, is shown in Fig. 3 (c). It decreases rather monotonically upon stretching in the elastic stages, while it jumps to higher values after plastic deformations, see d = 3.2 and 5.6 Å. This confirms that the conductance depends sensitively on the contact configuration, i.e. the binding sites of the sulfur anchors on the gold, the molecule’s orientation, and the separation between the electrodes. The most remarkable feature is that a single conduction channel dominates the transport for most of the electrode separations. As soon as electrode separations are larger than d > 1.6 Å, corresponding to a conductance of G < 0.3 G0, the ratio G2/G1 is below 10%, i.e. below the measurement resolution. For smaller distances, a gold-dominated transmission channel arises, bypassing the molecule. Left-incoming transmission eigenchannel wavefunctions for selected stretching stages in Fig. 3 (c), evaluated at EF, corroborate these statements. 9


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Figure 3. (a) Junction geometries at selected stages of the stretching process. The displacement d of the left and right electrodes is counted from our initial configuration. (b) Total energy and (c) total conductance as well as those of the first three conduction channels for Au-BDT-Au junctions as a function of d. The insets of (c) show the first two left-incoming transmission eigenchannel wavefunctions, evaluated at the Fermi energy, for the contacts at d = 0.8 and 6.4 Å.

At distances of d = 3.6 and 6.4 Å, we find local energy minima with conductance values of G = 0.307 G0 (with, omitting the energy argument EF, τ1 = 0.302, τ2 = 4.1·10-3, τ3 = 5.8·10-4) and G = 0.267 G0 (τ1 = 0.267, τ2 = 2.7·10-4, τ3 = 1.6·10-4), respectively. In the latter case, the molecule is contacted to the two tip atoms only, i.e., it is bonded in a top-top (TT) configuration. According to our DFT calculations this configuration is a possible candidate for the most stable junctions, found in the high-conductance range of around G ≈ 0.2 to 0.24 G0. The fact that electronic 10


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transport in Au-BDT-Au junctions is due to a single channel is further supported by the simulations for blunt tips, discussed in the SI. For all conductance values computed, which lie in the range from 0 to 0.6 G0, only a single channel contributes. In conclusion, we studied the transport properties of Au-BDT-Au junctions including conductance, IET spectra and shot noise measurements. Shot noise measurements have been obtained by a simplified and versatile measurement scheme and are used for revealing the number of transport channels in this particular system, i.e. for a hydrocarbon-based molecule with only partially transmitted channels. The agreement between the experimental results and the DFT calculations supports the formation of a stable high-conductance Au-BDT-Au junction with one channel, as suggested before by studies of the nonlinear conductance. This underlines the important role of BDT as a fruit-fly molecule for studying novel concepts of quantum transport through molecules as well as a broad range, single channel conductor. Acknowledgment. We thank Oren Tal, Ran Vardimon, Jan van Ruitenbeek, Youngsang Kim, Wolfgang Belzig, and Marius Bürkle for stimulating discussions. We gratefully acknowledge financial support by the German Research Foundation (DFG) through Collaborative Research Center (SFB) 767, and the Carl-Zeiss Foundation. This work was supported by the bwHPC program through the computational resources bwUniCluster and the JUSTUS HPC facility. Supporting Information Available. Details on experimental procedures and theoretical methods. This material is available free of charge via the internet at http://pubs.acs.org. Note: The authors declare no competing financial interest.

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Shot Noise of 1,4-Benzenedithiol Single-Molecule ... - ACS Publications

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