Simulating STM transport in alkanes from first principles

Simulations of scanning tunneling microscopy (STM) measurements for molecules on surfaces are traditionally based on a perturbative approach, most typically employing the Tersoff-Hamann method. This assumes that the STM tip is far from the sample so that the two do not interact with each other. However, when the tip gets close to the molecule to perform measurements, its electrostatic interplay with the substrate may generate nontrivial potential distribution, charge transfer, and forces, all of which may alter the electronic and physical structure of the molecule. These effects are investigated with the ab initio quantum transport code SMEAGOL, combining the nonequilibrium Green’s-function formalism with density functional theory. In particular, we investigate alkanethiol molecules terminated with either ${\text{CH}}_3$ or ${\text{CF}}_3$ end-groups on gold surfaces for which recent experimental data are available. We discuss the effects connected to the interaction between the STM tip and the molecule, as well as the asymmetric charge transfer between the molecule and the electrodes.

Figure 1

Schematic diagram of a metal-molecule-metal junction. A scattering region (the part of the system enclosed by the dashed box) is sandwiched between two current/voltage probes kept at the chemical potentials ${\mu }_1$ and ${\mu }_2$, respectively. The electrodes are modeled as being periodic in the direction of transport. A number of layers of the electrodes are included in the scattering region to allow the charge density to converge to the bulk value.

Figure 2

(Color online) Decanethiol molecule with (a) ${\text{CH}}_3$ and (b) ${\text{CF}}_3$ end-group. Color code: $\text{C}=\text{black}$, $\text{S}=\text{dark gray}$ (brown online), $\text{H}=\text{light gray}$ (blue online), and $\text{F}=\text{dark gray}$ (purple online).

Figure 3

(Color online) Orbital-resolved DOS for the isolated decanethiol molecule. Panels (a) and (b) are for the ${\text{CH}}_3$ termination, while panels (c) and (d) are for the ${\text{CF}}_3$. In panels (b) and (d) only the DOS corresponding to $\pi$ orbitals perpendicular to the molecule axis are displayed.

Figure 4

(Color online) Local density of states for the isolated decanethiol molecule terminated with the ${\text{CH}}_3$ group showing: (a) the HOMO-1 state, (b) the HOMO, and (c) the LUMO. The local DOS for the molecule terminated with the ${\text{CF}}_3$ group is similar and it is not displayed here. Color code: $\text{C}=\text{black}$, $\text{S}=\text{dark gray}$ (brown online), $\text{H}=\text{light gray}$ (blue online), and $\text{F}=\text{dark gray}$ (purple online).

Figure 5

(Color online) Real (positive $k$) and complex (negative $k$) bandstructures for a ${\text{C}}_2{\text{H}}_4$ polymer infinite chain: (a) calculations obtained by including basis functions into the vacuum region; (b) calculations obtained with basis functions positioned only over the molecule. Note in both cases the semicircular complex band joining the molecular HOMO and LUMO. Moreover, when basis functions are included into the vacuum paraboliclike bands associated to free-electron-like states appear in the band gap. The $k$ vector is measured in units of $\pi /c$, where $c=2.5\text{Å}$ is the supercell lattice vector in the $z$ direction.

Figure 6

(Color online) Simulation cell used in the transport calculations: a ${\text{CF}}_3$-terminated decanethiol molecule is attached to gold surface and probed with a Au STM tip. The case of the ${\text{CH}}_3$-terminated molecule is similar and it is not displayed here. Color code: $\text{Au}=\text{gray}$ (yellow online), $\text{C}=\text{black}$, $\text{S}=\text{dark gray}$ (brown online), $\text{H}=\text{light gray}$ (blue online), and $\text{F}=\text{dark gray}$ (purple online).

Figure 7

(Color online) $I\text{−}V$ curves for ${\text{CH}}_3$-terminated decanethiol attached to a gold surface for different distances between the C atom in the ${\text{CH}}_3$ group and the probing tip. Changing this distance by $0.1\text{Å}$ causes the size of the current to change by approximately one order of magnitude at 1 V. Panel (b) is a zoom of panel (a) in the current range between $\left[-30,20\right]\text{pA}$.

Figure 8

(Color online) Orbital-resolved DOS for the decanethiol molecule attached to the gold surface. Panels (a) and (b) are for the ${\text{CH}}_3$ termination, while panels (c) and (d) are for the ${\text{CF}}_3$. In panels (b) and (d) only the DOS corresponding to $\pi$ orbitals perpendicular to the molecule axis are displayed for C and S, while in panel (d) all the fluorine $\pi$ orbitals are shown. The HOMO-LUMO gap is large, although the HOMO is about 1 eV below $E_{\text{F}}$.

Figure 9

(Color online) Local DOS isosurface for the ${\text{CH}}_3$-terminated decanethiol molecule on the Au (111) surface: (a) the HOMO-1 level, (b) the HOMO level, and (c) the LUMO level. Note how the HOMO is localized around the thiol end-group and it is not expected to conduct efficiently. Color code: $\text{Au}=\text{gray}$ (yellow online), $\text{C}=\text{black}$, $\text{S}=\text{dark gray}$ (brown online), and $\text{H}=\text{light gray}$ (blue online).

Figure 10

(Color online) Local DOS isosurface for the ${\text{CF}}_3$-terminated decanethiol molecule on the Au (111) surface: (a) the HOMO-1 level, (b) the HOMO level, and (c) the LUMO level. Note how the HOMO is localized around the thiol end-group and it is not expected to conduct efficiently. Color code: $\text{Au}=\text{gray}$ (yellow online), $\text{C}=\text{black}$, $\text{S}=\text{dark gray}$ (brown online), $\text{H}=\text{light gray}$ (blue online), and $\text{F}=\text{dark gray}$ (purple online).

Figure 11

Transmission coefficients at zero bias for decanethiol attached to gold surface and terminated with (a) ${\text{CH}}_3$ and (b) ${\text{CF}}_3$ end-group. Note the gap in the transmission of about 5 eV on either side of the Fermi level.

Figure 12

(Color online) (a) $I\text{−}V$ curve and (b) differential conductance for decanethiol molecules terminated with both ${\text{CH}}_3$ and ${\text{CF}}_3$ groups. Note the bias asymmetry, with the conductance at negative bias being two to three times larger than that for positive bias. The conductance is lower for the ${\text{CF}}_3$-terminated molecule than that of the ${\text{CH}}_3$-terminated.

Figure 13

(a) Schematic energy-level diagram of the STM geometry. Since the molecule is more strongly coupled to the surface than to the tip its occupation is determined by the surface chemical potential; i.e., it will charge for negative bias and decharge for positive. Such a charging mechanism produces a shift of the occupied molecular level toward higher (lower) energy for negative (positive) bias. (b) Cartoon showing the electrostatic interaction between tip and molecule ${\text{CF}}_3$ end-group. In this case there is an electric-dipole forming, so that the molecule will be attracted or repulsed by the STM tip, depending on the bias polarity.

Figure 14

(Color online) Transmission coefficients as a function of energy for different biases for ${\text{CH}}_3$-terminated decanethiol. Note how the resonances in the transmission coefficients due to the occupied states move up in energy closer to the bias window at negative bias, and move away from the bias window for positive bias. The vertical lines mark the bias window.

Figure 15

(Color online) Transmission coefficients as a function of energy for different biases for ${\text{CF}}_3$-terminated decanethiol. Note how the resonances in the transmission coefficients due to the occupied states move up in energy closer to the bias window at negative bias and move away from the bias window for positive bias. The vertical lines mark the bias window.

Figure 16

Mulliken populations for decanethiol molecule terminate with (a) ${\text{CH}}_3$ and (b) ${\text{CF}}_3$ groups and attached to the gold surface. Note how in both cases the occupation of the molecule drops as the bias increases from negative to positive.

Figure 17

(Color online) Net occupation of the atoms as the function of position along the axis of the molecule.

Figure 18

Schematic illustration showing the tilting angle of the molecule over the Au surface and the rotation due to the interaction with the STM tip.

Figure 19

(Color online) $I\text{−}V$ curves and differential conductance as a function of bias obtained both with and without considering the effects of the electrostatic-induced rotation of the molecule. Panels (a) and (b) show the $I\text{−}V$ and $dI/dV$ curves for the ${\text{CH}}_3$ termination, and (c) and (d) show the same for the ${\text{CF}}_3$ case.