Theory of Rectification in Tour Wires: The Role of Electrode Coupling

We report first-principles studies of electronic transport and rectification in molecular wires attached to gold electrodes. Our ab initio calculation gives an accurate description of the voltage drop as well as the broadening and alignment of the molecular levels in the metal-molecule-metal complex. We find that the operation range and rectification in such strongly chemisorbed molecules is limited by the width of the transmission resonances and their proximity to the Fermi level.

Figure 1

(a) Geometry of molecule $A$ connected to two Au(111) surfaces. Isosurface of induced density and contour plot of induced potential at $e{V}_b={\mu }_L-{\mu }_R=-1\mathrm{e}\mathrm{V}$. In the contour plot, red (blue) represents low (high) electrostatic potental and high (low) effective potential. For the isosurface, blue represents accumulation of positive charge (holes) and gray represents negative charge (electrons). (b) Similar to (a) but for molecule $B$ at $d=2.7\AA$.

Figure 2

(a) Transmission spectra, $T(E,V_b)$, (thin lines, shifted vertically for clarity), bias window (thick black lines), and equilibrium transmission (dashed line) for molecule $A$. Equilibrium conductance: $G={10}^{-2}{G}_0$. Transmission peaks correspond to $T\approx 1$. (b) Similar to (a) but for molecule $B$ at $d=2.7\AA$. Equilibrium conductance: $G={10}^{-4}{G}_0$. Transmission peaks correspond to $T\approx {10}^{-2}$. (c) Current-voltage characteristics of molecule $A$ and molecule $B$. (d) Black squares: Rectification at $V_b=\pm 1\mathrm{V}$ and total current at $V_b=1\mathrm{V}$ as a function of separation distance $d$. White squares: Rectification obtained from a simple model, introduced below.

Figure 3

(a) Simple model of rectification. The HOMO sits $\delta E_M$ below ${\mu }_L$ and is shifted by $\pm \eta e{V}_b$ in positive/negative bias polarities. (b) Rectification as a function of applied voltage $e{V}_b$ for $\delta E_M=5$ and for different values of $\eta$. (c) Maximum rectification as a function of $\delta ϵ$ for different values of $\eta$.