Imaging asymmetric Coulomb blockade phenomena across metallic nanoislands

Abstract

Coulomb blockade (CB) arises in nanoscale systems with ultra-small capacitance, where discrete charging effects dictate electron transport, enabling wide-ranging applications based on single-electron transistors. Despite established electrostatic control of charge states in quantum dots and nanoislands, a rigorous quantitative link between junction parameters and the CB spectrum remains elusive. Here, using scanning tunneling spectroscopy, we investigate the spatial variation of CB in indium nanoislands on semiconducting black phosphorus. We observe spatially dispersive charging resonances whose trajectories exhibit a finite shift of the symmetry axis in bias as well as a pronounced asymmetric curvature. By comparing the experimental results with calculations based on orthodox theory, we show that these features originate from work function differences in the junctions, underscoring the importance of junction-specific electrostatics in nanoscale charge transport.

Figures (11)

• Figure 1: Coulomb blockade in an STM-defined DBTJ. (a) Schematic illustration of the STM measurement geometry, showing In nanoislands formed on a BP substrate. (b) Equivalent circuit model of the DBTJ, where $C_\mathrm{TI} \,(C_\mathrm{IS})$ and $R_\mathrm{TI} \,(R_\mathrm{IS})$ denote the capacitance and resistance between the In island and the tip (substrate), respectively. (c) Normalized differential conductance $(\mathrm{d}I/\mathrm{d}V)/(I/V)$ spectrum measured on the In nanoisland (blue), together with a simulated spectrum (gray) based on orthodox Coulomb blockade theory. Parameters of the simulation: $C_\mathrm{IS} = 6.74\,\mathrm{aF}$, $R_\mathrm{IS} = 15.0\,\mathrm{M\Omega}$, $C_\mathrm{TI} = 0.92\,\mathrm{aF}$, $R_\mathrm{TI} = 2.4\,\mathrm{G\Omega}$, and $Q_0 = 1.305\,e$. The Coulomb energy $\Delta_\mathrm{TI}$, corresponding to the peak spacing, is determined from the average separation between adjacent conductance peaks. Measurement conditions: $V_\mathrm{set} = 0.6~\mathrm{V}, I_\mathrm{set}= 250~\mathrm{pA}, V_\mathrm{mod}=10~\mathrm{mV}$
• Figure 2: Spatially resolved Coulomb blockade spectra. (a), Normalized differential conductance $(\mathrm{d}I/\mathrm{d}V)/(I/V)$ spectra acquired at different lateral positions across an In nanoisland, as indicated by the colored markers in (b). The horizontal bars denote the extracted Coulomb peak spacings $\Delta_\mathrm{TI}$. Setup conditions: $V_\mathrm{set} = 0.6~\mathrm{V}, I_\mathrm{set}= 250~\mathrm{pA}, V_\mathrm{mod}=10~\mathrm{mV}$. (b) and (c) Differential conductance maps of an island at different bias voltages, showing concentric conductance modulations around the nanoisland. Scale bar, $10~\mathrm{nm}$. Setup conditions: $V_\mathrm{set}= -0.4 ~{\rm V}\ \mathrm{and} -0.8~{\rm V}$ respectively, $I_\mathrm{set}= 100~\mathrm{pA}, V_\mathrm{mod}=10~\mathrm{mV}$.
• Figure 3: Spatially dispersive Coulomb peaks in an In nanoisland. (a) Spatially resolved normalized $(\mathrm{d}I/\mathrm{d}V)/(I/V)$ spectra acquired across an In nanoisland. The curved features correspond to CB peaks whose energies vary with lateral position. Setup conditions: $V_\mathrm{set} = 0.6~\mathrm{V}, I_\mathrm{set}= 250~\mathrm{pA}, V_\mathrm{mod}=10~\mathrm{mV}$. (b) Orthodox theory-based simulation with the work-function differences, $\delta\phi_\mathrm{TI} = 0.25~\mathrm{eV}$ and $\delta\phi_\mathrm{IS} = -0.3784~\mathrm{eV}$, chosen within the range of the reference values to achieve the best agreement with the experimental data SI. The background signals of in- and outside the island are from averaged data of each region in (a). The white dots mark the CB peak positions extracted from the measured spectra in (a). Parameters of simulation: $C_\mathrm{IS} = 6.74\,\mathrm{aF}$, $R_\mathrm{IS} = 15.0\,\mathrm{M\Omega}$, $C_\mathrm{TI} = 0.8\text{--}1.0\,\mathrm{aF}$, $R_\mathrm{TI} = 2.4\,\mathrm{G\Omega}$.
• Figure 4: Coulomb blockade asymmetry from work function differences. (a)--(c) Simulated $\mathrm{d}I/\mathrm{d}V$ spectra as a function of $C_\mathrm{TI}$ with varying work function differences: (a), no work function difference, (b), between tip and island ($\delta\phi_\mathrm{TI} = 0.3\,\mathrm{eV}$) and (c), between island and substrate ($\delta\phi_\mathrm{IS} = -0.007\,\mathrm{eV}$). The white arrows in (b) and (c) show the amount of the shift due to the $\delta \phi _\mathrm{TI}$ and $\delta\phi_\mathrm{IS}$ respectively, compared to the (a) (no work function difference). The yellow dotted lines in (a--c) represent the dispersion axis. In (b), the axis is shifted by amount of $\delta \phi _\mathrm{TI}$, compared to the axis of (a) marked as shaded dotted line. The white dotted curves in (c) mark the CB curvatures of (a). Parameters of simulation: $C_\mathrm{IS} = 6.74\,\mathrm{aF}$, $R_\mathrm{IS} = 15.0\,\mathrm{M\Omega}$, $C_\mathrm{TI} = 4.5\text{--}10.5\,\mathrm{aF}$, $R_\mathrm{TI} = 2.4\,\mathrm{G\Omega}$.
• Figure S1: Atomic structures of In islands and BP substrate. (a) Schematic representation of black phosphorus (BP) atomic structure showing zigzag-shaped chains puckered out-of-plane. The zigzag (ZZ) and armchair (AC) directions are indicated. (b) Differential topography of In islands on BP, showing various islands, adatoms which do not form islands, and vacancy defects of BP. Triangular islands align one edge with the ZZ direction. Scale bar, $10~\mathrm{nm}$. (c) Magnified view of (b) clearly showing the BP lattice orientation and island alignment. Stripes on islands are moiré patterns resulting from In-BP lattice mismatch.