Figure 1

(a) Experimental constant-distance (black) and constant-current (dark gray) $dI/dV$ spectra together with displacement curve $\Delta z\left(V\right)$ (light gray) atop a single ${\text{C}}_{60}$ molecule on Au(111). The tunnel gap for constant-distance spectroscopy was set at 2.5 V and 1 nA, while 1 nA was used for the constant-current spectrum. (b) Calculated constant-distance (black) and constant-current (dark gray) $dI/dV$ spectra and $\Delta z\left(V\right)$ (light gray). For the calculations an initial tip-sample distance of 0.6 nm was used. The apparent barrier height $\varphi =7.8\text{eV}$ was determined from experimental current-versus-distance data.Reuse & Permissions

Figure 2

Local density of states of a ${\text{C}}_{60}$ molecule on Au(111) extracted from $dI/dV$ spectra at constant distance (dots) using Eq. (4) and at constant current for the indicated initial tip-sample distances (solid lines) using Eq. (6). The dashed line shows the result of dividing constant-current $dI/dV$ data only by the transmission factor [Eq. (6) without second term, $z_0=0.8\text{nm}$, see also Ref. 14]. An apparent barrier height $\varphi =7.8\text{eV}$ was used for the normalization.Reuse & Permissions

Figure 3

(a) Constant-distance (black) and constant-current (gray) spectra of $dI/dV$ of the occupied Cu(111) surface state along with the tip displacement curve (light gray), $\Delta z$. The feedback parameters prior to spectroscopy were set to $-0.6\text{V}$ and 1 nA. Inset: simulation of constant-distance and constant-current spectra for a sample LDOS according to Eq. (7) with parameters $E_0=-445\text{meV}$, $\Gamma =24\text{meV}$, $\varphi =4\text{eV}$, and $z_0=0.5\text{nm}$. (b) Extracted sample LDOS, ${\varrho }_{\text{s}}$, from constant-distance and constant-current spectra shown in (a) using Eqs. (4, 6).Reuse & Permissions

Figure 4

Calculated constant-distance (black) and constant-current (gray) spectrum together with tip displacement characteristics (light gray) for a model LDOS of an unoccupied surface state [Eq. (7)]. The dashed line indicates the middle of the step-like onset $\left(E_0=1.35\text{eV}\right)$, which coincides with the inflection point of the displacement curve.Reuse & Permissions

Figure 5

(Color online) (a) Constant-current (1 nA) spectrum of $dI/dV$ acquired at the center of a Ag dimer adsorbed on Ag(111). The arrow marks the voltage, at which maps of $dI/dV$ are taken. (b) Constant-current and (c) constant-distance map of $dI/dV$ recorded at 3.5 V, 1 nA over a $3\text{nm}\times 3\text{nm}$ area. Dashed circles indicate the positions of the dimer atoms. (d) Spatial map of normalized constant-current $dI/dV$ for the Ag dimer shown in (b) and (c), which was extracted by using Eq. (6) for each image point. An apparent barrier height $\varphi =5\text{eV}$ and a tip-sample distance $z_0=0.5\text{nm}$ were used for the simulations.Reuse & Permissions