Quantitative determination of a nano-object's atom density without atomic resolution

We outline a possibility to determine the adatom density of individual nano-objects via measurement of their electronic structure. For this aim, the nonlinear shift of image potential states measured on individual Cu nanoclusters on Ag(100) by low-temperature scanning tunneling spectroscopy is carefully analyzed. The quantitative analysis is confirmed by density-functional theory calculations. A peak width analysis furthermore reveals whether the clusters are purely metallic or alloyed.

Figure 1

Topography, electronic structure, and confinement effect: (a) Topography image of a small (3.0 ${\mathrm{nm}}^2)$ and a large island (16.1 ${\mathrm{nm}}^2)$ $(I=44$ pA, $V=0.2$ V). (b) Spatially resolved $dz/dV$ intensity at a 6.1 V bias voltage $(I=44$ pA, $V=6.1$ V). (c) 2D representation of the confinement effect correction function for an island of 20 ${\mathrm{nm}}^2$.

Figure 2

Voltage dependence of $dz/dV$ along a line across the (a) large and (b) small islands in Fig. 1 as indicated there by the solid and dashed lines, respectively.

Figure 3

Dependence of 2nd S-IPS on the island size $A$ with respect to the terrace value. (a) Relative line width ${\overline{\Gamma }}_{\mathrm{rest}}$. (b) Energy shift as measured $(\Delta E_{\mathrm{meas}}$, red squares) and without the confinement effect $({\overline{\Delta E}}_{\mathrm{rest}}$, black circles). Black line is the expected energy shift for the quantum size confinement deduced from a simple particle-in-a-box model for square-shaped boxes $\Delta E_{\mathrm{box}}=\frac{{\pi }^2{\hslash }^2}{2m^{*}}\frac{n_x^2+n_y^2}{A}$ with an effective mass parameter $m^{*}=m_e$ with $m_e$ the electron mass and $n_x=n_y=1$. (c) Zoom into the remaining energy shift $\left({\overline{\Delta E}}_{\mathrm{rest}}\right)$ for the smallest islands after the confinement subtraction (black circles, left axis) and island atom density as deduced from density-functional theory (DFT) calculations [17, 27] (gray (blue) diamonds, right axis). Error bar on the $y$ axis reflects the energy spread across individual islands. Insets: Island structure as calculated by the DFT for Cu islands with 25 and 49 atoms on the left and on the right, respectively.

Figure 4

Differential conductivity $dI/dV$ spectra on two islands of different size: (a) Topography image of a small (2.6 ${\mathrm{nm}}^2)$ and a large island (24.8 ${\mathrm{nm}}^2)$ $(I=44$ pA, $V=0.2$ V). (b) Normalized $dI/dV$ spectra recorded at points marked in (a). (c) Energy shifts $\Delta E_{\mathrm{meas}}$ of the 2nd image potential state with respect to the average value on the terrace (gray/blue triangles, left axis), and $\Delta E_{\mathrm{rest}}$ corrected by the step effect (black circles, left axis); gray curve (right axis) depicts the island height vs position $x$ along the black line in (a). The dashed gray/blue line shows the energy correction function employed.