Structural Regulation of Mechanical Gating in Molecular Junctions

In contrast to silicon-based transistors, single-molecule junctions can be gated by simple mechanical means. Specifically, charge can be transferred between the junction’s electrodes and its molecular bridge when the interelectrode distance is modified, leading to variations in the electronic transport properties of the junction. While this effect has been studied extensively, the influence of the molecular orientation on mechanical gating has not been addressed, despite its potential influence on the gating effectiveness. Here, we show that the same molecular junction can experience either clear mechanical gating or none, depending on the molecular orientation in the junctions. The effect is found in silver–ferrocene–silver break junctions and analyzed in view of ab initio and transport calculations, where the influence of the molecular orbital geometry on charge transfer to or from the molecule is revealed. The molecular orientation is thus a new degree of freedom that can be used to optimize mechanically gated molecular junctions.


Experimental methods and conductance characterization of Ag and Ag-ferrocene junction.
A mechanically controllable break junction set up is used to form molecular junction. A Ag wire (99.997%, 0.1 mm, Alfa Aesar) with a notch at its middle is fixed on top of a flexible substrate (1mm thick phosphor bonze covered by 100µm Kapton foil). This structure is placed in a vacuum chamber that is cooled by liquid helium to ~ 4.2K. Using a three-point bending mechanism, the substrate is pushed and bent. This process stretches the wire notch, resulting a gradual reduction in its cross section down to the atomic scale. Fine bending of the substrate is achieved by a piezo electric actuator (PI P-882 PICMA) which is driven by a 24-bit DAQ card (PCI 4461 -National Instruments), followed by a piezo driver (SVR 150/1, Piezomechanik). Sufficient bending of the substrate results wire breaking into two wire segments with freshly exposed atomic tips that are formed in an ultraclean cryogenic environment. These sharp wire segments serve as electrodes. Molecular junctions are prepared by continuously breaking and reforming a metallic atomic contact between the electrode tips, while sublimating ferrocene molecules (99.5%, Alpha Aesar, further purified in situ) from a locally heated molecular source towards the atomic contact. Direct current (d.c.) conductance is measured when the junction is gradually pulled apart to form conductance versus distance traces. A constant 500 mV from the DAQ card is supplied to a divider by 10 (to improve signal to noise ratio) and the resulted 50 mv bias is applied across the junction. The resulted current output from the junction is amplified by a I/V preamplifier (Femto DLPCA-200), and the amplified signal is recorded by the same DAQ card. The d.c. conductance of the junction is thus the measured current divided by the applied voltage (50 mV). Inter-electrode displacement is estimated based on the dependence of the tunneling current on the electrode separation, following a standard process 1 . Differential conductance spectra (dI/dV versus V) is recorded using a standard lock-in technique. A reference sine signal from a lock-in amplifier (SR830) with a peak to peak voltage of 10 mv and a frequency of ~3.333 kHz is added to a d.c. voltage and the total voltage is divided by 10 to improve signal to noise ratio. The response alternating current (a.c.) is probed by a lock-in amplifier (SR830) and recorded by the DAQ card The differential conductance spectra are obtained by dividing the alternating current signal (dI) with the applied alternating voltage bias (dV), as a function of a swiped d.c. voltage bias (V).
The d.c. conductance of the junction (current/voltage) is recorded during repeated junction stretching as a function of relative interelectrode displacement. First, a bare Ag junction was characterized. Figure S1a presents in blue examples for conductance traces as a function of interelectrode displacement. During the elongation of the Ag junction, the conductance decreases in steps when the contact diameter is reduced.
The last conductance plateau at ~1 G 0 (G 0 =2 ℎ ⁄ , is the conductance quantum, where is the electron charge and ℎ is the Plank's constant) provides the conductance of a single atom contact between the Ag electrode tips 2 . After the insertion of ferrocene molecules, tilted plateaus below the ~1 G 0 step are clearly seen ( Figure S1a, red traces). To statistically characterize the most probable conductance features, conductance histograms ( Figure S1b) are constructed from 5,000 and 10,000 consecutive conductancedisplacement traces for Ag junctions before (blue) and after (red) the introduction of ferrocene, respectively.
While the conductance histogram for bare Ag junctions reveals a peak at ~1 G 0 (Inset of Figure S1b) that is associated with the most probable conductance of single Ag atom contacts, after the introduction of ferrocene an additional conductance peak beneath the 1G 0 peak is observed. Gaussian fitting of the corresponding peak, shown by a black dash dot line in Figure S1b yields a most probable conductance value of (7.25 ± 0.06) 10 -3 G 0 for Ag-ferrocene molecular junctions. The error corresponds to 2SD or 2 standard deviations of the fitted Gaussian.

Additional experimental data.
Each set contains data measured for a single junction at different interelectrode distances. Figure S2. Current-voltage curves, differential conductance spectra, and TVS plots for type 1.  In view of the calculations in Figure 3, main text, the differential conductance is expected to be similar for parallel and perpendicular ferrocene junctions in a wide range around zero bias voltage. Figure 2 in the main text and Figures S2 and S3 in the Supplementary Information reveal that the measured differential conductance of types 1 and 2 are similar as well. We therefore do not distinguish between the two configurations based on the conductance of the junction. The molecular junctions are first prepared, and the identification is done a posteriori by repeated dI/dV vs. V measurements for different interelectrode separations. Note that the molecular junctions are prepared by breaking an atomic contact between the electrodes in the presence of adsorbed molecules or by bringing together the electrode tips of an already broken junction to arbitrarily capture a molecule between the two electrodes. In both cases, we do not observe a preference for the realization of type 1 or 2. We therefore arbitrarily obtain both types.

Structures and structural relaxation
Prior the transport calculation, possible molecule's binding conformations to the electrodes were studied through molecule's structure optimization by the quasi-Newton-Raphson method 9 . All the examined structures were non-periodic clusters composed of the ferrocene molecule and an attached pair of Ag electrodes with a pyramidal shape, as schematically depicted in the insets of Figure 2 and in Figure S5. The Ag electrodes were cut out of a face-centered Ag crystal along the (100) direction considering a bulk lattice parameter 10 . They consist of an apex atom and a set of atomic layers with a growing number of atoms. During relaxation, we kept the Ag atomic positions fixed. The sequence of pyramids was necessary to study of the conductance's convergence when the size of the pyramidal electrode tips increases. Due to computational demands, the structure optimization was performed for clusters with three-layered leads and the molecule coordinates were pre-relaxed in the gas phase.
The infinite electrodes were accounted for by self-energy operators applied to the Ag pyramids following Ref. 13. At a given voltage V, the electric current is given by the expression where the factor 2 accounts for spin degeneracy, , is the transmission function and , denotes the Fermi-Dirac distributions of the left (L) and right (R) electrodes. We assumed that the external bias voltage causes a symmetric shift of the left and right chemical potentials, , where µ stands for the equilibrium chemical potential. Further, we adopted the zero-temperature form of , ; this approximation is valid as long the transmission function , varies slowly within the energy range ∈ , , , , where is the working temperature multiplied by the Boltzmann constant.
Considering the expression , , , it follows that the current and its derivative are given by where the Fermi energy equals the chemical potential at T = 0. We neglected the explicit voltage dependence in the transmission, which can quantitatively, and sometimes qualitatively change the differential conductance. The bias voltage can lead to non-equilibrium Stark effect of the resonances 11 . This effect can simply be understood as orbital modifications due to the presence of an effective electric field induced by the voltage V. Consequently, the coupling of an orbital to the two electrodes is more asymmetric at 0 than at V = 0 and the heights of the corresponding transmission peaks diminish. Therefore, the theoretical differential conductance of type-1 conformation could overemphasize the resonance heights and the inclusion of non-equilibrium Stark effect would diminish them, making them more consistent with the experimental data.

Interpretation of differential conductance curves in break junction experiments.
In the examined molecular junctions, the two resonances seen in the differential conductance curves (dI/dV vs. V) above and below zero voltage (see Figure 2c, Figure S2c,d, and the wide peaks in Figure 3c) shift towards zero voltage in response to junction squeezing. However, as explained below, we conclude that both HOMO and LUMO are shifted downwards together (i.e., gating effect) with no significant changes in the HOMO -LUMO gap, as illustrated in Figure 3a.  . The HOMO (red) and LUMO (blue) are located 1eV below and above the Fermi energy. Since the voltage drops equally across the junction, when a voltage of 2V is applied to the junction the quasi Fermi levels of the electrodes are aligned with both HOMO and LUMO, at -eV and eV. As a result, both HOMO and LUMO contribute to the resonance peaks seen in the differential conductance at eV. Bottom Panel: Cartoon of energy scheme and differential conductance curve for asymmetric electrode-molecule coupling as in traditional STM experiments (molecule coupling to the tip is much smaller that its coupling to the substrate, Γ ≪ Γ ). Also, here the HOMO (red) and LUMO (blue) are located eV below and a above the Fermi energy. When a voltage of V is applied to the junction the quasi Fermi level of the tip is aligned with either the HOMO or LUMO, since the voltage drops on the vacuum gap between the tip and the molecule. As a result, either the HOMO or LUMO contribute to the resonance peaks seen in the differential conductance at eV. (b) Same as (a), but with HOMO and LUMO located 1.5eV below and 0.5eV above the Fermi energy, respectively. The voltage range required to probe the levels varies accordingly.  Figure S6a. In case of a similar HOMO and LUMO distance from the Fermi energy, the dI/dV curve shows a resonance in the differential conductance curve with a shape that is an outcome of both HOMO and LUMO shapes. In Figure S6, we do not illustrate the resonance shapes but the orange curve in Figure 3c, provides a calculated example (sharp HOMO peaks on top of a wide LUMO peak). The observed resonance appears at a voltage that is given by the energy of the HOMO and LUMO multiplied by 2. This factor is a consequence of the voltage division between the two metal-molecule interfaces, where the alignment of the quasi Fermi energy with either the HOMO or LUMO takes place at an applied voltage (times e) equal to twice the level's energy: Ve=2E. Note that a similar scaling is observed in Figures 3a and   3c, and the description here is given mathematically by Eq. (3) in Supporting Information Section 4.
In the opposite limit, where the electrode-molecule coupling of the two electrodes is highly asymmetric as in traditional STM experiments, the situation is very different as illustrated in Figure S6 bottom panel. Here, an applied voltage across the junction falls mainly on the insulating gap between the electrode tip and the molecule (in Figure S6, we assume that all the voltage drops on the tip-molecule interface for simplicity).
As described in the figure, depending on the voltage sigh either the HOMO or LUMO are probed in the dI/dV curve separately, leading to a resonance in the differential conductance curve located at a voltage corresponding (in eV) to the HOMO or LUMO energy with a shape that is the outcome of the shape of each energy level individually.
We will now examine an energy level shift and how it is reflected in dI/dV curves for symmetric coupling between the electrode and molecule. As seen in Figure 3a, a shift of both HOMO and LUMO to a lower energy (i.e., a gating effect with no significant change in the HOMO-LUMO gap), is translated in the dI/dV curves in Figure 3c to a shift of the LUMO wide resonance towards zero voltage and a shift of the HOMO narrow resonance to a higher voltage in an absolute value. The dI/dV response to the HOMO and LUMO shift to a lower energy is schematically illustrated in Figure S6b for a symmetric (top) and asymmetric (bottom) coupling. In the actual measurements (Figure 2a), we do not clearly probe the very sharp resonances but the wide dI/dV resonance reveals the expected downwards shift and peak widening seen in the calculations (Figure 3c) in response to junction squeezing.

DFT analysis of the physical mechanism driving the gating effect.
The gating mechanism observed in our DFT calculations is based on two physical principles. First, as the junction compresses, the confinement of the molecular orbitals is augmented. Second, there is a selfconsistent rearrangement of the charge density in the junction. Here, we provide insights into both phenomena based on ab-initio calculations. Figure S7 shows the relative change of bond lengths upon compression. At ~10Å, compression occurs between the apex and the nearest ring (on both sides). Below 9Å this distance (Apex-C, orange data) reduced and compression now takes place mainly between the rings, i.e. the height of the ferrocene reduces (purple data). Interestingly, in the very squeezed limit, the vertical compression of the molecule is compensated by an increase of the C-C distance, and henceforth widening of the rings. Figure S7: Relative changes of various bond lengths upon stretching, the reference values d max are taken at 10.3Å. The average length of the 10 carbon bonds is denoted by C-C; the average distance of the two rings is C 5 -C 5 ; the average distance from the apex to the 5 nearest carbons is denoted by Apex-C. Figure S8 shows that changes in charge due to compression mainly takes place at the molecule's rings, while the charge on the iron center is almost intact. We also analyze the charge transfer from the density of states (DOS) projected onto the atomic species of the junction for two apex distances in Figures S9 a and b. Unlike the transmission function, the DOS can be understood as an energy-resolved occupation number.
For both apex distances, the DOS around the Fermi energy has the form of Lorentzian-like HOMO and LUMO peaks, superimposed on a background that weakly increases with energy. The junction compression leads to a HOMO and LUMO shift downwards. Namely, change is transferred to the molecule and occupies more states. As seen in Figure S8, this excess charge is mainly accumulated on the carbon rings.