Critical roles of metal-molecule contacts in electron transport through molecular-wire junctions

We study the variation of electron transmission through Au-S-benzene-S-Au junctions and related systems as a function of the structure of the Au:S contacts. For junctions with semi-infinite flat Au(111) electrodes, the highly coordinated in-hollow and bridge positions are connected with broad transmission peaks around the Fermi level, due to a broad range of transmission angles from transverse motion, resulting in high conductivity and weak dependence on geometrical variations. In contrast, for (unstable) S adsorption on-top of an Au atom, or in the hollow of a 3-Au-atom island, the transmission peaks narrow up due to suppression of large transmission angles. Such more one-dimensional situations may describe more common types of contacts and junctions, resulting in large variations in conductivity and sensitivity to bonding sites, tilting, and gating. In particular, if S is adsorbed in an Au vacancy, sharp spectral features appear near the Fermi level due to essential changes of the level structure and hybridization in the contacts, admitting order-of-magnitude variations of the conductivity. Possibly such a system, can it be fabricated, will show extremely strong nonlinear effects and might work as uni- or bi-directional voltage-controlled two-terminal switches and nonlinear mixing elements. Finally, density-functional theory based transport calculations seem relevant, being capable of describing a wide range of transmission peak structures and conductivities. Prediction and interpretation of experimental results probably require more precise modeling of realistic experimental situations.

Figure 1

The four molecules considered in this work, connected to two Au(111) surfaces via thiolate or thiol bonds. From left to right: DTB, DTBd, DMtB, and DTBO. The S-S distances are [H-terminated/sandwiched between Au(111) electrodes] $6.40∕6.37\mathrm{A}$, $6.85∕6.89\mathrm{A}$, $8.14∕7.997\mathrm{A}$, and $6.25∕6.23\mathrm{A}$, respectively (without termination, S-B-S is $6.15\mathrm{A}$ and $\mathrm{S}\text{−}\mathrm{C}{\mathrm{H}}_2\text{−}\mathrm{B}\text{−}\mathrm{C}{\mathrm{H}}_2\text{−}\mathrm{S}$ is $6.19\mathrm{A}$).

Figure 2

(Color online) Au-S-benzene-S-Au junctions with three types of contacts. Left: S in the hollow of a three-Au atom island (point contact). Middle: S in hcp (three-fold hollow) site of relaxed Au(111). Right: S in an Au vacancy. The distances are in angstroms. The distances between the first surface layers of electrodes are given in Table .

Figure 3

(Color online) Definition of adsorption sites. [3d(fcc) denotes a site on top of a gold atom in the third layer; 2d (hcp) denotes a site on top of a gold atom in the second layer.]

Figure 4

(Color online) Charge redistribution for the bond formation. Top row. Left: DTB on three adatoms at hcp; right: on flat surface hcp. Bottom row. Left: DTB in vacancy; right: DTBd at hcp. Isosurfaces enclosure the regions with maximum charge redistribution and contain 40% of the displaced (solid) or removed (facet) charge. The distances are in angstroms. The inset shows the view of the surface layer with S atom in vacancy. The notation M and M is discussed in the text.

Figure 5

(Color online) Charge redistribution for the bond formation. DTBO at hcp and in vacancy. Isosurfaces enclosure the regions with maximum charge redistribution and contain 40% of the displaced (solid) or removed (facet) charge. The distances are in angstroms. The inset shows the view of the surface layer with S atom in vacancy.

Figure 6

Adsorption-site dependence of the transmission $T(E,V_b=0)$ for Au-DTB-Au on flat, relaxed Au(111). Full line: hcp site (three-fold hollow); dashed line: fcc site; dashed-dotted line: bridge site; dotted line: on-top site, not stable, forces on sulfur atom parallel to the gold surface were constrained. Much of the sharp line structures in this and subsequent figures is due to nonconvergence of the matching procedure of the extended molecule in the bulk electrodes; see also Sec. 7.

Figure 7

(Color online) Adsorption-site dependence of the total transmission $T(E,V_b=0)$ and transmission eigenchannels for DTB in the presence of defects. Top panel: hcp three-fold hollow on an island of three adatoms (point contact); second panel: hcp site (three-fold hollow) (flat surface for reference); third panel: hcp site near a vacancy; fourth panel: fcc-bridge site near a vacancy, (meta)stable; fifth panel: one S atom at flat hcp site, one S atom buried in vacancy; sixth panel: both S atoms buried in Au vacancies.

Figure 8

(Color online) Total transmission $T(E,V_b=0)$ and transmission eigenchannels for DTBd: Top panel: sulfur adsorbed at hcp$–$hcp; middle panel: in-vacancy$–$hcp; bottom panel: in-vacancy$–$in-vacancy.

Figure 9

(Color online) Zero-bias transmission spectrum $T(E,V_b=0)$ for DTBO; sulfur adsorbed at top: hcp$–$hcp; middle: vacancy$–$hcp; bottom: vacancy$–$vacancy.

Figure 10

(Color online) Left: total transmission $T(E,V_b=0)$ eigenchannels for DMtB, semi-log scale. Right: corresponding setup.

Figure 11

Schematic quantum well picture illustrating the M-S-mol-S-M system without $(V_b=0)$ bias voltage (left) and with $(V_b\ne 0)$ bias voltage (right).

Figure 12

Bias voltage dependence of the transmission spectrum $T(E,V_b)$ of DTB adsorbed between hcp sites between flat gold surfaces—Ref. 38 (previously unpublished). A self-consistent calculation has been employed for each bias voltage. The bias window $V_b=({\mu }_R-{\mu }_L)∕e$ is inside the shaded triangular region. Courtesy of K. Stokbro, 2004.

Figure 13

(Color online) Bias voltage dependence of the transmission spectrum of $T(E,V_b)$ of DTB adsorbed at the on-top site between flat Au(111) surfaces. The transmission of DTB at the hcp site is shown for reference.

Figure 14

(Color online) Zero-bias transmission spectra of $\mathrm{Au}\text{−}\mathrm{S}\text{−}{\left(\mathrm{C}\mathrm{H}\right)}_n\text{−}\mathrm{S}\text{−}\mathrm{Au}$ for $n=1,2,3$. DTBd corresponds to $n=2$. Note that the issue of chemical stability (for $n=1,3$) is not addressed (and anyway dependent on the environment).

Figure 15

(Color online) Bias voltage dependence of the transmission spectrum $T(E,V_b)$ of DTBd adsorbed in vacancy sites. The second transmission channel is shown in red. Arrow marks the higher transmission peak following the left electrode potential.

Figure 16

(Color online) Bias voltage dependence of the transmission spectrum $T(E,V_b)$ of DTBO adsorbed at vacancy hcp sites.

Figure 17

(Color online) Bias voltage dependence of the transmission spectrum $T(E,V_b)$ of DTBO adsorbed at vacancy$–$vacancy sites.

Figure 18

(Color online) Transmission $T(E,V_b=0)$ for DTB with $3\times 3$ (thick line; left Fano resonance) and $1\times 1$ (thin line; right Fano resonance) electrodes. Inset: DTB with $3\times 3$ electrodes, the difference between the curves is that the benzene ring has been rotated by $90\mathrm{deg}$.