Imaging Pauli repulsion in scanning tunneling microscopy
C. Weiss, C. Wagner, C. Kleimann, M. Rohlfing, F. S. Tautz, R. Temirov
aa r X i v : . [ c ond - m a t . m e s - h a ll ] A ug Imaging Pauli repulsion in scanning tunneling microscopy
C. Weiss,
1, 2
C. Wagner,
1, 2
C. Kleimann,
1, 2
M. Rohlfing, F. S. Tautz,
1, 2 and R. Temirov
1, 2 Institut f¨ur Bio- und Nanosysteme 3, Forschungszentrum J¨ulich, 52425 J¨ulich, Germany JARA–Fundamentals of Future Information Technology Fachbereich Physik, Universit¨at Osnabr¨uck, 49069 Osnabr¨uck, Germany (Dated: October 31, 2018)A scanning tunneling microscope (STM) has been equipped with a nanoscale force sensor andsignal transducer composed of a single D molecule that is confined in the STM junction. Theuncalibrated sensor is used to obtain ultra-high geometric image resolution of a complex organicmolecule adsorbed on a noble metal surface. By means of conductance-distance spectroscopy andcorresponding density functional calculations the mechanism of the sensor/transducer is identified.It probes the short-range Pauli repulsion and converts this signal into variations of the junctionconductance. PACS numbers: 68.37.Ef, 68.37.Ps, 67.63.Cd
Since its invention the scanning tunneling microscope(STM) has become an important tool of nanoscience, be-cause it routinely provides ˚Angstr¨om-scale image resolu-tion on various sample surfaces [1–6]. However, STMsuffers from a serious drawback—the inability to resolvecomplex chemical structure. This disadvantage arises be-cause the STM probes the local density of states (LDOS)in the vicinity of the Fermi level, while details of thechemical structure are primarily encoded in lower-lyingorbitals. Better access to chemical structure is thereforeprovided by mapping the total electron density (TED).Indeed, it has been shown recently that non-contactatomic force microscopy is able to resolve the inner struc-ture of a complex organic molecule, by imaging short-range repulsive interactions that depend on the TED[7]. Even earlier, however, it has been demonstratedthat STM acquires very similar force imaging capabilitieswhen operated in the so-called scanning tunneling hydro-gen microscopy (STHM) mode [8]—STHM images indeedclosely resemble the chemical structure formulae of theinvestigated compounds (see ref. [8] and Fig.1a). In thisletter we present an analysis of the STHM junction bymeans of dI/dV (z)-spectroscopy and density functionaltheory that allows us to explain its imaging mechanismfor the first time.The experiments were performed on PTCDA/Au(111)with a Createc low-temperature STM operated at 5-10 K in ultra-high vacuum (UHV). The electrochemi-cally etched W tips and the Au(111) surface have beenprepared using Ar + sputtering and temperature anneal-ing in UHV. The STM tips were additionally preparedby indentation into the clean gold surface. PTCDAmolecules were deposited from a quartz crucible mountedin a home-built Knudsen cell. Deposition of H or D wasperformed according to the recipe described in ref. [8].Since both H and D yield similar results, we restrictthe discussion in this letter to D .We start by summarizing the features of STHM thathave been reported before [8]. The best STHM resolu- STHM
OOOOOO a d I/ d V [ G ]0 - b V inel -V inel S T M D inelasticfeatures d I/ d V [ Ω - - D D S T M FIG. 1: (a) STM (top) and STHM image (bottom) of PTCDA(3,4,9,10-perylenetetracarboxylic-dianhydride) on Au(111):1.3 × , constant height, D , V = 316 mV (STM)and V = − G = e h = (12 . k Ω) − is the quantum of conductance. tion (as shown in Fig. 1a) is achieved in constant-heightmode with rather low tunneling bias | V | .
10 mV. Theappearance of STHM imaging after D dosing coincideswith the emergence of non-linear differential conductancespectra G ( V ) ≡ dI/dV ( V ) close to zero bias. In par-ticular, inelastic features appear (in Fig. 1b at ± V inel )[8–11]. In some cases, as in Fig. 1b, a pronounced zerobias anomaly has also been observed [8]. Imaging in thepresence of D can be switched reversibly between theSTM and STHM modes by changing the applied bias V [8]: If | eV | exceeds | eV inel | , the junction images in theconventional STM (or LDOS) mode. If, however, | eV | is sufficiently smaller than | eV inel | , the junction operatesin the STHM mode, yielding images with ultra-high ge-ometric resolution. The nature of the inelastic featureshas been investigated in detail in nanojunctions contain-ing H [8–12]. They are assigned to transitions betweentwo structurally different states of the junction. However,the precise nature of the associated two-level system isstill debated [9–11].Understanding the structure of the STHM junctionis vital for identifying the imaging mechanism. Basedon the conductance values in our experiments ( > × − G ) we conclude that the tip-surface separationmust be smaller than 1 nm [13]. At such distancesthe junction can accommodate only a single monolayerof D [14, 15]. Clearly, the deuterium-induced imagingmode requires the presence of D just below the tunnel-ing tip apex. Given the high resolution that is achievedin STHM, which in Fig. 1a is of the order 50 pm, at mostone D molecule can be in the active area of the junction.Therefore we can model the junction in the STHM mode,i.e. at | V | < | V inel | , by a single D molecule physisorbed[17] between the tip apex and the sample surface. For | V | > | V inel | , the D molecule is displaced away fromthe tip apex, as proven by the recurrence of conventionalSTM imaging in conjunction with the occurrence of astructural transition at | V inel | .Switching the bias between | V | < | V inel | and | V | > | V inel | we can study the properties of a given junction,and in particular the differential conductance G as a func-tion of tip-surface distance z , in presence and absenceof the confined D molecule, without any other struc-tural changes of the junction. Fig. 2a displays the re-sults of G ( z )-spectroscopy for the empty junction (curvemeasured with | V | > | V inel | and labelled G vac ) and forthe junction with D (curve measured with | V | < | V inel | and labelled G D ). G vac increases exponentially withdecreasing z , as expected for vacuum tunneling. In con-trast, G D behaves non-exponentially. Two opposingtendencies are observed: For intermediate z , G D ex-ceeds G vac , while for smaller tip-surface distances thesituation reverses. Based on the data in Fig. 2a, we candefine three characteristic regimes.At the shortest distances recorded in Fig. 2a (regime3) G D exhibits increased noise and conductance jumps.Such conductance changes usually occur when the tun-neling junction undergoes structural modifications due tothe tip contacting the sample surface. Notably, the dis-continuities in G D occur at tip-surface distances where G vac still behaves strictly exponentially, i.e. the emptyjunction is still out of contact. Hence, the contactin question must occur via the confined D molecule.Clearly, the associated structural changes will occur inthe softest part of the junction, i.e. the D molecule,which eventually is squeezed out of the junction. Indeed,images measured at the onset of regime 3 (images 5 and6 in Fig. 2c) show a sudden loss of STHM resolution.Having identified regime 3 with the squeezing of theD molecule out of the junction, we can associate thepreceding regime 2 with the gradual compression of the FIG. 2: (a) dIdV ( z ) spectra recorded at fixed bias, measuredwith D on PTCDA/Au(111) ( z -axis scale given by scale bar). G = e h is the quantum of conductance. G D (magenta): V = − G vac (black): V = −
130 mV. All spectrarecorded from the same stabilization point. (b) R G ( z ) curves(cf. text) measured at positions ~r (blue) and ~r (red) markedin the lower inset. The ratio G vac ( ~r ) /G vac ( ~r ) is shown ingreen. (c) STHM images (1 . × . , constant height, V = − at dif-ferent z indicated by black triangles in panel b. junction that eventually causes this squeeze-out. Toquantify the effect of D on the junction conductancein regimes 1 and 2, we define the conductance ratio R G ( z ) ≡ G D ( z ) /G vac ( z ). As can be seen in Fig. 2a, R G ( z ) can be larger or smaller than 1, depending onthe value of z . Fig. 2b (red, blue) shows that in regime2, where the best STHM resolution is recorded (images3 to 5 in Fig. 2c), R G ( z ) curves measured at differentlateral positions above the PTCDA molecule each dis-play a distinct slope. At the same time G vac curves donot vary appreciably from point to point above PTCDA(Fig. 2b, green), which is consistent with the blurred andfeatureless STM images that are recorded with the emptyjunction at | V | > | V inel | (Fig. 1a). The R G ( z ) curves inFig. 2b hence show that the STHM contrast in Fig. 1a z' [Å] s-typep-type n ( E z ´) / t, D F , n ( E ) t, v a c F z' z´ eq D modeltip FIG. 3: DFT-LDA simulated n t , D ( E F , z ′ ) /n t , vac ( E F ) vs.D -tip distance z ′ for s - (black) and p -type (red) orbitals atthe Au atom below the deuterium molecule. n t , D ( E F , z ′ ) isthe LDOS of the model tip at the Fermi level at given D -tipdistance z ′ and n t , vac ( E F ) is LDOS at the Fermi level of thebare tip electrode. Equilibrium distance z ′ eq is indicated bythe vertical line. For details of the simulation, cf. ref. [18]. can be ascribed to the effect of D on the junction con-ductance which becomes pronounced in a narrow rangeof z -values in regime 2 . We therefore need to study thenature of regime 2 in more detail.To investigate the influence of D on the tunnellingconductance of an STHM junction in regime 2, we havecarried out a density functional theory (DFT) calcula-tion in which we systematically varied the distance z ′ between D and an Au(111) surface (Fig. 3 inset) [18].This surface was chosen to model the tip electrode in ourSTHM experiments. We calculate the model tip DOSat the Fermi level, n t , D ( E F , z ′ ), as the LDOS at themetal atom located directly underneath the D . Divid-ing n t , D ( E F , z ′ ) by n t , vac ( E F ), the LDOS of the baretip without D , we find that the tip DOS decays sub-stantially with decreasing z ′ (Fig. 3). The origin of thisbehavior is the Pauli exclusion principle: To minimizeoverlap between the closed shell of D and the metal elec-trons, both of their wave functions must rearrange locally,which depletes the metal’s local DOS in the vicinity ofthe Fermi level [15, 19, 20], while the associated energycost leads to a repulsive force between D and the metal(Pauli repulsion).In the limit of low tunneling bias Tersoff-Hamann the-ory of STM predicts G ∝ n t , D ( E F , z ′ ) n s ( E F , ~r t ), where n s is the sample LDOS at tip position ~r t [21]. Ac-cordingly, G and R G must decrease proportionally to n t , D ( E F , z ′ ) as D approaches the tip. DFT resultsshown in Fig. 3 suggest that the rate of tip DOS decreaseshould be in the range from 0.2 to 1 ˚A − . At the sametime experimental data from Fig. 2b show rates between1.1 and 1.5 ˚A − . To be able to compare both resultswe additionally have to divide experimental values bythe factor dz ′ dz accounting for the differences between the scales z and z ′ . dz ′ dz must be in the range between ≃ the z -variation of R G ( z ) in regime 2 can be explained as an effect of Pauli repul-sion in the STHM junction .This result holds the key for understanding the con-trast formation in STHM. To demonstrate this, we firstdiscuss the STHM contrast above an inherently simpleobject, namely Au adatoms on Au(111), before turningto the more complex PTCDA molecule with its inter-nal structure. Fig. 4 (bottom panel) shows the experi-mental image of an Au adatom dimer. The image hasbeen recorded at constant height, nearly zero bias volt-age (2 mV), and with a junction containing D , i.e. underSTHM conditions. We observe two well-separated struc-tures, each of which corresponds to one of the adatoms.In comparison to the flat sample surface, the adatoms ap-pear bright, i.e. with a large G ( ~r t ), because the sampleLDOS n s ( ≃ E F , ~r t ) at tip positions close to the adatoms,e.g. at ~r t2 , is increased with respect to the one at ~r t1 , dueto a reduced effective tip-sample distance (cf. the toppanel of Fig. 4). So far this is not different from conven-tional constant height imaging in STM. However, in thecenter of each of the adatoms (i.e. at ~r t ≃ ~r t3 ) a dark areais observed in Fig. 4. In contradiction to conventionalSTM [23], Fig. 4 clearly implies that G ( ~r t3 ) < G ( ~r t2 ).The reason for this deviation from the normal STM be-havior can be found in the presence of D in the junc-tion, and in particular in its trajectory, which is displayedschematically in Fig. 4 (top): As the tip moves from ~r t2 to ~r t3 , the D molecule will have to move to a new verticalequilibrium position closer to the tip (smaller z ′ ) becauseat that position the stronger Pauli repulsion from theadatom is balanced by a stronger Pauli repulsion fromthe tip. In conjunction with Fig. 3, this must lead to asharp reduction in n t ( ≃ E F ). According to Fig. 4 thisreduction overcompensates the rise in n s ( ≃ E F , ~r t ) [22]and leads to the dark areas in the centers of the adatoms.The analysis of the adatom image thus shows that theSTHM contrast can be understood as an ( x, y ) -map ofthe short-range Pauli repulsion from the sample surfaceacting on the D molecule in the STHM junction, super-imposed over the conventional LDOS contrast .With this knowledge, we can finally analyze the STHMcontrast generation above PTCDA. As in the case of thedimer, the D molecule follows the tip and probes lat-eral variations of the Pauli repulsion from the adsorbedPTCDA. For example, when the tip moves from a posi-tion above the center of a C ring to a position directlyabove a carbon atom, the D molecule in the junctionwill—similarly to the trajectory shown in Fig. 4—moveto a higher equilibrium position closer to the tip, be-cause of the increased TED above the carbon atom. As
10 Å z z´ constantheight
DOSdepletion r t1 r t3 r t2 tip apex atom D FIG. 4: (a)(b) STHM image of a Au dimer on Au(111) (con-stant height, V =2 mV, D ) (bottom panel) and schematicsketch of contrast generation. Cf. text for details. in the case of the adatoms discussed above, this leadsto a reduced n t ( ≃ E F ) and therefore lower conductance.In the STHM image the carbon atoms of PTCDA (andby a similar argument the σ -bonds between the carbons)therefore appear darker than the ”empty” spaces insidethe C and C O rings of the PTCDA backbone, just asobserved in the image of Fig. 1a.In conclusion, we arrive at the following model ofSTHM imaging: A single D molecule is physisorbed inthe STM junction, such that it is confined directly un-derneath the tip apex. This molecule is the crucial el-ement in the STHM imaging process, as it probes theshort-range Pauli repulsion from the surface (sensor ac-tion) and transforms this force signal into variations ofthe tunneling conductance (transducer action), the latteragain via Pauli repulsion. Because of its nanoscale size,the sensor is insensitive to long-range forces. Clearly, thesensor/transducer modulates the tunneling conductanceon top of the normal LDOS contrast. As long as thePauli-induced conductance modulation is larger than theLDOS-induced change of the background conductanceitself, the image will be dominated by the STHM con-trast. We note that the described functionality shouldalso work with other closed-shell particles besides hy-drogen and deuterium [24]. Comparing STHM to con-ventional STM, direct tunneling between tip and samplesurface still forms the basis of imaging in STHM. How-ever, in STHM a compliant element that is sensitive to alaterally varying sample property other than the LDOSis added to the tunneling junction, where it modulatesthe tunneling current that is used for imaging. Financial support from the Helmholtz Gemeinschaft isgratefully acknowledged, as are helpful discussions withJ. Kroha (Bonn), S. Bl¨ugel and N. Atodiresei (J¨ulich). [1] C.J. Chen, Oxford University Press, (1993)[2] C.D. MacPherson, Phys. Rev. Lett.
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15 ˚Atowards and away from the surface. For each configura-tion, the LDOS was calculated by projecting the quan-tum mechanical states on the local orbitals ( s , p z , d z ) ofthe Au atom directly below the D . The d z -orbital doesnot yield a significant contribution. Note that DFT doesnot consider the masses of the nuclei (unless dynamics ofthe nuclei is considered), i.e. in DFT there is no differencebetween H and D .[19] N.D. Lang, Phys. Rev. Lett.
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