Intrusive STM imaging

An interactive scanning tunneling microscopy (STM) simulator has been designed to efficiently compute the effects of chemical and structural modifications of adsorbed species on resulting STM images. Our general approach is based on first-order perturbation theory that takes into account different tip geometries. In our intrusive STM imaging strategy, we consider small variations such as substitutions, vacancies, functionalizations, and molecular reorganizations from a reference system. First, we show that our perturbation theory approach can provide STM images that are qualitatively similar to those of a more rigorous electron scattering technique based on the Landauer-Büttiker formalism for the case of adsorbed tetracyanoethylene on a Cu(100) single crystal. Second, we demonstrate that the efficiency of Bardeen and Tersoff-Hamann approaches to generate STM images can be substantially improved by exploiting different algorithms to evaluate the tunnel current and to deal with large-scale eigenvalue problems. Following our general intrusive strategy, we have reduced the computing time to generate an STM image of a modified system by about an order of magnitude with respect to the reference image. The shape and position of the contrasts of the STM image evaluated in the context of intrusion are virtually identical to an image computed without intrusive features but within a considerably smaller computing time.

Figure 1

The sample-tip junction in the STM model, where $\mathbf{r}\equiv (x,y,z)$ denotes the position of the tip apex with respect to the sample origin, $\mathbf{R}\equiv (X,Y,Z)$ represents a point on the separation surface $\mathcal{S}$ with respect to the tip apex, and $Z\equiv (1-\mu )z$. The effects of both semi-infinite contacts are represented by their self-energies ${\Sigma }_s(E)$ and ${\Sigma }_t(E)$.

Figure 2

Optimized structural model of a TCNE (${\text{C}}_6{\text{N}}_4$) chain on a strongly reshaped Cu(100) surface. This cluster contains three TCNE molecules (green and blue) on two Cu layers (cyan). Highly buckled Cu atoms are outlined (copper). Details on the overlayers structure can be found in Ref. 86.

Figure 3

Topographic STM images of a TCNE chain on Cu(100) (a) obtained experimentally with a Pt/Ir tip ($V_0=1\text{mV},I_0=5\text{nA}$),[87] or calculated with a Pt(111) tip ($V_0=1\text{mV},I_0=15\text{nA}$) using (b) the LB approach,[86] and the (c) Bardeen and (d) TH methods.

Figure 4

Theoretical constant-height STM images at $V=-0.3$ V of (a) benzene (${\text{C}}_6{\text{H}}_6$), (b) pyridine (${\text{C}}_5{\text{H}}_5\text{N}$), (c) phenyl (${\text{C}}_6{\text{H}}_5$), (d) benzyne (${\text{C}}_6{\text{H}}_4$), and at $V=+0.3$ V of (e) phenyl computed by our TH implementation on isolated molecules. (f) Image of benzene adsorbed in the “on-top” position on Cu(100) using a Pt(111) tip and the LB approach.[57, 91]

Figure 5

Constant-height STM image ($V=0.3$ V, $z=2.8$ Å) of a 500-atom CNT (5,5) computed using the TH approximation.