Self-assembly of a two-dimensional molecular layer in a nonhomogeneous electric field: Kinetic Monte Carlo simulations

Behavior of mobile adsorbed species can be affected by the presence of a strong non-homogeneous electric field. Such a field exists in the proximity of a biased tip of the scanning tunneling microscope. Depending on the electronic properties of the adsorbate and the polarity of the electric field, self-assembly of ordered structures on the surface can be facilitated or prevented. We use a kinetic Monte Carlo model to investigate the effect of the electric field on the assembly of planar molecules on weakly interacting surfaces. Using phthalocyanine molecules as a model system, we study mechanisms behind the results of our previous experimental study of electric-field controlled switching of molecular arrays. The complex interplay between intermolecular and field-molecule interactions is illustrated by detailed phase diagrams at various surface coverages.

Figure 1

The CuPc molecule occupies exactly 15 sites of the model surface. Closest sites where another molecule with the same orientation can be placed without overlap are marked by “CP” (close-packing sites).

Figure 2

Map of pair potential energy for identically oriented CuPc molecules during the simulation. The map was calculated with $E_{\mathrm{ol}}=0.1\mathrm{eV}$ (overlap energy) and $E_{\mathrm{cp}}=-25$ meV (close-packing energy).

Figure 3

Potential energy of a static dipole perpendicular to the surface as a function of lateral distance from the STM tip apex. Solid line: Real potential calculated for a dipole moment of 0.35 eÅ, parabolic tip with a radius of 50 nm, tip bias of 3 V, and tip-sample distance of 1 nm. Dashed line: Approximation by a triangular potential well with a width of 49.2 nm.

Figure 4

Self-assembly of molecules without an external electric field ($E_{\mathrm{es}}=0$). Negative values of $E_{\mathrm{cp}}$ represent an attractive interaction, while positive values correspond to a repulsive interaction. Dark areas signify that an ordered structure is formed, while white areas represent a disordered 2D gas phase. Values with an asterisk denote NCP structures.

Figure 5

(a) Large islands formed at 0.6 ML with $E_{\mathrm{cp}}=-0.1$ eV. $F_{\max }=2.89.$ (b) Smaller islands formed at 0.6 ML with $E_{\mathrm{cp}}=-0.2$ eV. $F_{\max }=1.58$. (c) Hexagonal structure formed at 0.8 ML with $E_{\mathrm{cp}}=+0.05$ eV. The unit cell consists of 19 lattice points. (d) Oblique structure formed at 0.9 ML with $E_{\mathrm{cp}}=+0.05$ eV. The unit cell consists of 16 lattice points. Insets show details of the molecular packing.

Figure 6

Ordering of molecules depending on coverage and the depth of the potential well $E_{\mathrm{esd}}$. (a) Weak attractive interaction ($E_{\mathrm{cp}}=-25$ meV). (b) No interaction ($E_{\mathrm{cp}}=0$). (c) Weak repulsive interaction ($E_{\mathrm{cp}}=+25$ meV). Dark areas correspond to ordered structures (asterisk denotes an NCP structure under the STM tip).

Figure 7

Simulated images of the molecular arrangement under the STM tip before and after a voltage pulse. (a) Initial configuration of molecules under the STM tip ($E_{\mathrm{esd}}=-0.1$ eV, 0.6 ML). (b) Domain rotation. (c) Domain shift. (d) No change. Top half of images (b)–(d) are the average occupancy before the voltage pulse, bottom half after the voltage pulse. The white arrows mark the boundary between the two halves.

Figure 8

Simulated voltage pulse under the STM tip: Probabilities of domain rotation, shift, and no change depending on the value of $E_p$ (depth of the potential well during pulse).

Figure 9

The stable molecular island during a simulated voltage pulse. Each white dot marks the center of a molecule which didn't move since the beginning of the pulse. Images are labeled by the value of $E_p$ (depth of the potential well during pulse). For $E_p\ge -0.03$ eV, the island always disintegrates.