Nanomechanical modulation of single-electron tunneling through molecular-assembled metallic nanoparticles

We present a microscopic study of single-electron tunneling in nanomechanical double-barrier tunneling junctions formed using a vibrating scanning nanoprobe and a metallic nanoparticle connected to a metallic substrate through a molecular bridge. We analyze the motion of single electrons on and off the nanoparticle through the tunneling current, the displacement current, and the charging-induced electrostatic force on the vibrating nanoprobe. We demonstrate the mechanical single-electron turnstile effect by applying the theory to a gold nanoparticle connected to the gold substrate through an alkane dithiol molecular bridge and probed by a vibrating platinum tip.

Figure 1

(Color online) (a) Schematic illustration of the nanomechanical double-barrier tunnel junctions formed using a vibrating platinum tip and a gold metallic nanoparticle connected to the gold substrate through an alkane dithiol molecular bridge with 12 alkane units (AK12). The platinum tip is modeled as a 4-atom pyramid sitting on top of the semi-infinite substrate. (b) The equivalent circuit model of the system. Note that the substrate junction capacitance $\left(C_S\right)$ and resistance $\left(R_S\right)$ are fixed, while the tip junction capacitance $\left(C_T\right)$ and resistance $\left(R_T\right)$ are time dependent due to the tip vibration. The tip-substrate capacitance $\left(C_0\right)$ is also time dependent.

Figure 2

(Color online) (a) The molecular junction and tip junction resistance as a function of the junction length. The tip junction resistance increases exponentially with tip-nanoparticle distance as the tip remains weakly coupled to the nanoparticle during the tip vibration cycle. (b) The static current-voltage $\left(I\text{−}V\right)$ and excess island charge-voltage $\left(n\text{−}V\right)$ characteristics of the double-barrier tunnel junctions for a $10\text{−}\mathrm{nm}$-diameter nanoparticle at tip-nanoparticle distance of $3.0\mathrm{\AA }$ (dotted line), $6.0\mathrm{\AA }$ (solid line), and $9.0\mathrm{\AA }$ (dashed line) for temperatures of $T=\mathrm{5,150}\mathrm{K}$, respectively. The inset shows the magnified view of $I\text{−}V$ characteristics at $6.0\mathrm{\AA }$ and $9.0\mathrm{\AA }$. Note that at $x=6.0\mathrm{\AA }$, we already have $R_T⪢R_S$, so the $n\text{−}V$ characteristics remains approximately the same as $x$ increases further.

Figure 3

(a) The time-averaged tunneling $I\text{−}V$ characteristics (solid line) and the instantaneous tunneling $I\text{−}V$ characteristics at $x=3.0\mathrm{\AA }$ (dotted line) at three tip vibrating frequencies of $f=1,10,100\mathrm{MHz}$. The tunnel currents are virtually independent of the tip vibrating frequency. (b) The time-averaged $n\text{−}V$ characteristics (solid line), the instantaneous $n\text{−}V$ characteristics at $x=3.0\mathrm{\AA }$ (dotted line) and $x=9.0\mathrm{\AA }$ (dashed line), respectively. The instantaneous values are the values obtained at the moments when the tip moves to $x=3.0\mathrm{\AA }$ or $9.0\mathrm{\AA }$

Figure 4

Upper figures show the average number of shuttled electron per cycle of tip vibration, middle figures show the average displacement current, and lower figures show the average electrostatic force on the metallic tip as a function of tip-substrate bias voltage at tip vibrating frequencies of $f=1,10,100\mathrm{MHz}$. In the middle figures, we have shown both the capacitive part (solid line) and “Coulomb blockade” part (dotted line) of the displacement current. The capacitive part increases linearly with voltage and tip vibrating frequency. But the Coulomb blockade part oscillates with increasing voltage. In the lower figures, we have shown both the capacitive part $F_{\mathit{Cap}}$ (solid line) and discrete-electron part $F_{CB}$ (dotted line) of the electrostatic force on the tip. Note that the stepwise increase in the shuttled electrons in the upper figures correlates with the steplike increase in discrete-electron force $F_{CB}$ in the lower figures.