visualization of electron orbitals in scanning tunneling...

ISSN 0021�3640, JETP Letters, 2014, Vol. 99, No. 12, pp. 731–741. © Pleiades Publishing, Inc., 2014.Original Russian Text © A.N. Chaika, 2014, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 99, No. 12, pp. 843–855.

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1 1. INTRODUCTION

Scanning tunneling microscopy (STM) [1, 2] isone of the most powerful techniques for atomicallyresolved studies of the surface electronic and magneticstructure [3–5], chemical analysis of surfaces at theatomic scale [6, 7], and fabrication of nanostructuresfrom individual atoms and molecules [8–12]. Scan�ning tunneling microscopy is based on the effect ofquantum tunneling of electrons through the vacuumgap separating the probe apex and the surface. Theprobe of the scanning tunneling microscope ismounted on the piezoscanner that allows positioningthe tip relative to the surface with picometer precision.At nanometer distances between the tip and sampleatoms, electrons can tunnel through the vacuum gapfrom occupied surface states to unoccupied tip statesand vice versa depending on the polarity of the biasvoltage applied between the tip and the sample(Figs. 1a and 1b).

The tunneling current I can be determined usingthe equation [15]:

, (1)

where ρt(E) and ρs(E) are densities of electron states(DOS) of the tip and the sample, respectively; V is thebias voltage, M is the tunneling matrix element, and EFis the Fermi energy.

1 The article was translated by the author.

I 4πeh

�� ρt EF eV– ε+( )ρs EF ε+( ) M2

εd

0

eV

∫=

The probability of the electron tunneling dependsexponentially on the tip�sample distance d:

, (2)

, (3)

where m is the electron mass, � is the Planck’s con�stant, and φ is the electron work function.

Estimations at typical values of the work functionsin metals and semiconductors (4–5 eV) show that tun�neling current drops by approximately one order ofmagnitude with every 1 Å increase in the tip�sampledistance. Because of the exponential dependence,most of the tunneling current flows through only twotip and surface atoms closest to each other. Change ofthe tunneling current during the tip motion across thesample allows imaging the surface atomic and elec�tronic structure with extremely high lateral and verti�cal resolution which can be about several picometers[16] and smaller than 1 pm [17], respectively. Never�theless, the questions related to the limit of the spatialresolution and physical origins of the features in highresolution STM images are still open.

If the tunneling current is collected by only oneatom at the tip apex, the limit of the spatial resolutionis determined by the electronic structure of this partic�ular atom. Usually, the sum of different atomic orbitalsproduces symmetric charge density distributionaround the tip apex atom. The approximation of thespherically symmetric tip [18, 19] is generally used insimulations of atomically resolved STM images. Whencertain orbitals of either tip [13, 20–22] or surface [23]atoms dominate in the total DOS, their direct visual�

M 2 ∝ e kd–

k 2mφ�

��=

Visualization of Electron Orbitals in Scanning Tunneling Microscopy¶

A. N. ChaikaInstitute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, 142432 Russia

Centre for Research on Adaptive Nanostructures and Nanodevices, School of Physics, Trinity College Dublin, Dublin 2, Ireland

e�mail: [email protected] May 5, 2014

Scanning tunneling microscopy (STM) is one of the main techniques for direct visualization of the surfaceelectronic structure and chemical analysis of multi�component surfaces at the atomic scale. This review isfocused on the role of the tip orbital structure and tip�surface interaction in STM imaging with picometerspatial resolution. Fabrication of STM probes with well�defined structure and selective visualization of indi�vidual electron orbitals in the STM experiments with controlled tunneling gap and probe structure are dem�onstrated.

DOI: 10.1134/S0021364014120054

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JETP LETTERS Vol. 99 No. 12 2014

CHAIKA

ization can be achieved in STM experiments with sub�ångström lateral resolution.

According to Eq. (1), tunneling current dependssymmetrically on the tip and surface DOS in theselected energy region. This is the basis of the reci�procity principle of STM [14] illustrated by Fig. 1c.Atomically resolved STM images bring the informa�tion about the orbital structure of the tip and surfaceatoms simultaneously. As a result, the convolution ofthe tip and surface electron states is not modified if thetip and surface orbitals are interchanged, as Fig. 1cillustrates.

If nonzero m electron states dominate at the tipapex, contrast inversion and asymmetric features withseveral subatomic maxima can be observed in STMexperiments [24, 25]. The subatomic features can cor�respond to direct visualization of the tip electronorbitals using the surface atomic orbitals. Interpreta�tion of the high resolution STM images can further becomplicated because of modification of the tip andsurface electronic structure at small (2.0–5.0 Å) tun�neling gaps [26–30]. According to the theoretical cal�culations performed for several tip�sample systems[13, 26, 30], the partial DOS is stronger modified form = 0 electron states which are further protruded intovacuum along the tip axis (pz, ).

This review is focused on the role of the tip elec�tronic structure and tip–sample interaction in STMexperiments with sub�ångström spatial resolution. Wediscuss the advantages of single crystalline probes withwell�defined structure for high resolution surface stud�ies and selective visualization of certain electron orbit�als in STM experiments.

2. SINGLE CRYSTALLINE TUNGSTEN PROBES FOR HIGH RESOLUTION STM

IMAGING

Because of exponential distance dependence, mostof the tunneling current is usually collected by justone, closest to the surface atom at the tip apex. This

dz

2

allows atomically resolved imaging on low�indexmetal and semiconductor surfaces even using non�ideal probes with large radii of curvature. The shapeand atomic structure of the probe are especiallyimportant for STM experiments on high�index(stepped) surfaces. According to Eqs. (1)–(3), in thecase of ideal pyramid at the tip apex up to 90% of thetunneling current can flow through the tip atom clos�est to the surface. Therefore, precise control of theapex structure can provide detailed information aboutthe electron states responsible for the STM imaging.

Electrochemically etched polycrystalline tungstenprobes are generally utilized in STM experiments [31].After chemical etching they can be cleaned and sharp�ened in ultrahigh vacuum (UHV) using high tempera�ture annealing [32] or ion sputtering [33–36]. The tipapex can also be prepared for high resolution STMimaging using the electric field applied between the tipand the sample [37–43]. This method is based ongrowth of nanotips on tungsten probes at high (~10 V)negative sample bias voltages [42]. In a number ofworks polycrystalline tungsten probes were functional�ized by molecules and atoms of light elements (car�bon, oxygen, hydrogen) [44–55]. These functional�ized probes can provide extremely high resolution inSTM experiments but they are usually not stable atsmall tunneling gaps [49] and possess unknown apexstructure.

Polycrystalline tungsten probes are preferentiallyoriented along the 〈011〉 crystallographic directions[33]. Nevertheless, the precise apex structure cannotbe granted in experiments with polycrystalline tipsbecause of formation of several nanotips at the apex[33]. Monotips with well�known orientation can befabricated using single crystalline refractory metalingots [34, 35, 37, 56]. Tungsten probes for STMexperiments presented in this review were fabricatedfrom [001]� and [111]�oriented single crystalline bars(0.5 × 0.5 × 10 mm) cut from high purity crystals usingthe spark cut. The monotips with small radii of curva�ture at the apex were obtained using electrochemical

Fig. 1. (Color online) (a, b) Schematic view of the electron tunneling (a) from occupied tip states to empty surface states and(b) from filled surface states to unoccupied tip states [13]. (c) Reciprocity principle of STM [14]. Convolution of dxz tip state and

surface electron states is equivalent to convolution of tip orbital and dxz surface orbitals.dz2d

z2

dz

2

dz

2


VISUALIZATION OF ELECTRON ORBITALS 733

etching in 2M NaOH solution with controllable cut�off adjusted by the current jump. The length of theingot immersed into the etchant was in the range of2.5–3 mm while the voltage between two electrodeswas in the range of 4.0–4.5 V. These parameters allowfabricating tungsten tips with minimal radii of curva�ture [31]. The etched tungsten tips were furthercleaned from residual oxides and sharpened in situ inthe UHV chamber of the scanning tunneling micro�scope.

Figure 2 shows the results of the transmission elec�tron microscopy (TEM) characterization of theW[001] tip apex [22]. The bright�field TEM image(Fig. 2a) proves the formation of the nanoscale pyra�mid at the tip apex after electron beam heating andcoaxial ion sputtering. The electron diffraction patterntaken from the apex (Fig. 2b) exhibits reflexes, typicalfor single crystalline tungsten. The dark�field TEMimages (Fig. 2c and 2d) taken from the diffractionspots C and D in Fig. 2b demonstrate that the tip isgrained by the {001} planes further from the apex(Fig. 2d) and has an angle of 90° at the apex that cor�

responds to the pyramid grained by the {011} planes.The split reflexes in Fig. 2b indicate the presence ofslightly misoriented single crystalline blocks at theapex. This misorientation is presumably caused by thestress applied to the apex at the final stage of the chem�ical etching and does not exceed several degrees.

3. CHANGE OF THE ELECTRON ORBITAL CONTRIBUTION AT SMALL DISTANCES

BETWEEN THE W[001] TIP AND HOPG(0001)

According to the TEM studies [22], the W[001]probe apex is stable in tunneling regime even at verysmall gaps when STM images can reveal subatomicorbital features. The stability of the tip apex allowshigher spatial resolution on the surfaces with compli�cated atomic structure [57, 58] and simplifies interpre�tation of the obtained STM data. Figure 3 demon�strates possibility to control the relative contributionof the tip electron orbitals in STM experiments withoriented single crystalline tungsten probes [13, 21, 22].Scanning tunneling microscopy images obtained with

Fig. 2. Transmission electron microscopy images of the W[001] probe after electron beam heating and co�axial ion sputtering[22]. (a) Bright�field image of the apex. (b) Diffraction pattern measured from the tip apex. (c, d) Dark�field images demonstrat�ing that apex is grained by the {011} and {001} planes.

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the W[001] probes on highly oriented pyrolytic graph�ite (HOPG) surface (Fig. 3b) qualitatively reproducethe shapes of the electron d orbitals with differentmomentum projections ( , dxz, and dxy). The sub�

atomic resolution achieved in the experiments [13, 22]corresponds to direct visualization of the tungsten tipatom d orbitals using atomic orbitals of the graphitesurface in accordance with the reciprocity principle ofSTM [14], as Fig. 3a illustrates. The gap resistancedependences of the HOPG(0001) STM images mea�sured with several W[001] probes [13] demonstratethat subatomic orbital features can be resolved only atsmall tunneling gaps (Fig. 3d). At small currents (largetip�sample distances) typical HOPG(0001) STMimages with hexagonal symmetry are resolved. Thismay correspond to imaging one of two non�equivalentsurface atoms [59] or the hollow sites [60]. Withincreasing current (decreasing distance) symmetric

dz

2

atomic features transform into asymmetric ones withtwo, three, and four subatomic maxima. The effect wasreproducibly observed in a series of experiments withdifferent W[001] probes sharpened in UHV using thesame procedure. The electron microscopy studiesrevealed that the W[001] tip was not substantiallymodified after STM experiments with subatomic reso�lution [22] confirming the pyramidal model of theW[001] tip shown in Fig. 3a. The transformation of thesubatomic features was reproducibly observed in verynarrow intervals of the gap resistances (tip–sampledistances). In accordance with Eqs. (1)–(3), anincrease in the tunneling current from 2.7 to 9.1 nA atfixed bias voltage (Fig. 3d) corresponds to change ofthe tip–sample distance in the range of 0.2–0.3 Å.This result emphasizes exceptional importance of pre�cise control of the tunneling gap resistance for improv�ing spatial resolution and selective imaging of the elec�

Fig. 3. (Color online) (a) Schematic model of a W[001] probe interacting with a graphite (0001) surface. (b) 1.7 × 1.7 Å2 STMimages of the tungsten tip atom electron orbitals measured using carbon atomic orbitals of HOPG(0001) at V = –0.1 V, I = 0.7nA (left panel), V = –35 mV, I = 7.2 nA (central panel), V = –0.1 V, I = 1.8 nA (right panel). (c) Partial DOS associated with dorbitals of the W[001] tip atom at different tip–surface distances (indicated on each panel). Reprinted from [21] with permissionfrom Elsevier. (d) Gap resistance dependence of 7 × 7 Å2 STM images of a graphite surface measured with the W[001] probe atfixed sample bias voltage V = –35 mV (currents are indicated on each frame). Reproduced from [13] with permission from EPLand IOP Publishing.

dz

2



tron states with different symmetry using STM. Notethat transformation of symmetric atomic features intoasymmetric ones was not observed in our STM exper�iments with [111]�oriented tungsten probes. This canbe related to different electronic structure of theW[001] and W[111] probes interacting with the graph�ite surface.

Similar subatomic features with two�, three�, andfour�fold symmetry were observed in unique non�con�tact atomic force microscopy (AFM) experiments[61]. The subatomic features were explained by directvisualization of the orbital structures of [011]�, [111]�,and [001]�oriented apexes formed on the polycrystal�line tungsten probe during the AFM experiments. TheSTM images measured with stable single crystallineW[001] probes (Fig. 3d) demonstrate that the observedtransformation of the subatomic features is related tomodification of the tungsten tip atom electronic struc�ture with decreasing tip�surface distance rather thanmodification of the crystallographic orientation of theapex as suggested in [61].

For explanation of the fine electronic structureeffects in the W[001] tip�HOPG(0001) system, the

density functional theory (DFT) calculations of theelectronic structure of the interacting tip and surfaceatoms [13, 21] were carried out using the VASP(Vienna Ab�initio Simulation Package) software [62].The calculations revealed drastic reduction of the par�tial DOS associated with the most extended along thetip axis orbital near EF at tunneling gaps d < 2.5 Å

because of its stronger overlap with the electron orbit�als of the surface carbon atoms. Figure 3c shows theresult of the partial DOS calculations for three differ�ent tunneling gaps [21]. At larger tip�sample distancesand small bias voltages applied in the STM experi�ments (Fig. 3d), the spatial resolution is determined bya set of the electron d�states with different symmetry atthe apex atom. An improvement of the spatial resolu�tion can be anticipated at distances d = 2.5–4.0 Åsince at these distances the orbital dominates in the

tip DOS near EF. At smaller distances (2.2–2.5 Å), thespatial resolution in the experiments can be defined bythe nonzero m tip electron states (dxz and dxy) havinglarger DOS near EF at these tunneling gaps. Theseconclusions are in agreement with the results indepen�

dz

2

dz

2

Fig. 4. (Color online) (a–c) Isosurface of the change in electron density for the interacting (a) He–W[011], (b) He–W[111], and(c) He–W[001] systems. The helium atom is positioned directly below the apex atom, with the tip–sample distance d = 4.0 Å forthe W[011] tip and d = 3.5 Å for the W[111] and W[001] tips. (d–f) Constant�height slices through the DOS corresponding to thesystems shown on panels (a–c). The positions of the tungsten tip atoms in the first two layers are drawn as black circles. Repro�duced from [28] with permission from IOP Publishing.

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dently obtained in [63, 64] which confirmed the asym�metric electronic structure of the W[001] probe atsmall distances between the tip and graphite surfaceatoms. The suppression of further protruded along thetip axis pz and orbitals of the probe and surface

atoms at small (d < 4.0 Å) tunneling gaps were theoret�ically predicted for several interacting tip–sample sys�tems [26, 28, 30, 65].

The modification of the electronic structure oftungsten probes with different crystallographic orien�tations of the apex at small tip�surface distances wasstudied theoretically in [28, 63, 64]. Figure 4 illustratesthe asymmetric charge density distribution around theW[011] and W[001] tip atoms interacting with ahelium atom at d < 2.5 Å [28]. The theoretical calcu�lations (Fig. 4), predict the subatomic features withtwo and four maxima at small tunneling gaps for the[011]� and [001]�oriented tungsten probes. At thesame time, the charge density distribution around theW[111] tip atom is symmetric even at very small dis�tances between the interacting atoms (Fig. 4e) anddoes not produce three subatomic maxima as assumedin [61]. Theoretical calculations [28] also revealed thatatomic structure of the W[001] probe is stable even atvery small distances between the tip and helium atoms(~1.5 Å) while the W[011] and W[111] probes are sub�stantially relaxed at small distances and, most proba�bly, cannot provide stable STM imaging at tunnelinggaps below 2.25 and 2.5 Å, respectively. These resultsprove that selective imaging of the electron d�stateswith different symmetry can take place only atextremely small tip�sample distances (d < 2.5 Å) anddemonstrate the advantages of single crystalline tung�sten probes with different crystallographic orienta�tions. It can be assumed that W[001] probes can bemore suitable for the scanning tunneling spectroscopy(STS) experiments demanding higher apex stability. Atthe same time, W[111] probes can provide higher spa�

dz

2

tial resolution in STM experiments on complex sur�faces and should not produce subatomic featuresrelated to the tip apex atom.

4. VISUALIZATION OF THE CARBON BONDS IN QUASI�FREESTANDING GRAPHENE

ON SiC(001)

The examples of high resolution STM studies ofcomplex surfaces using a single crystalline W[111]probe can be found in [14, 66]. Figure 5 demonstratesthe picometer lateral resolution achieved with theW[111] probe during STM studies of the trilayergraphene grown on cubic�SiC(001) surface. The topmonolayer of graphene on SiC(001) consists of nan�odomains connected to each other through thedomain boundaries [14, 66]. The STM images mea�sured in the middle of domains demonstrate theatomic scale rippling (Fig. 5a) typical for freestandingsingle layer graphene [67]. The lateral and verticaldimensions of the observed ripples are 3–5 nm and1 Å, respectively, that is in good agreement with thetheoretical calculations [67]. The spatial resolutionachieved during the STM experiments with theW[111] tip on allows direct imaging of the nanoscalerippling of the graphene surface and visualization ofthe random picoscale distortions of the carbon bondlengths in the honeycomb lattice. This is illustrated onFig. 5b by the STM image measured on top of a ripple.This small surface region can be considered as flat thatis supported by the same contrast of different carbon�carbon bonds in the randomly distorted honeycomblattice (Fig. 5b). One of the distorted hexagons isshown in Fig. 5c for clarity. The lengths of the sides ofa hexagon differ from the value known for ideal two�dimensional graphene lattice (142 pm) on 1–16 pm.The observed distortions are in a good agreement withthe theory [67]. The picometer lateral resolutionobtained in STM studies of the graphene/SiC(001)

Fig. 5. (Color online) Scanning tunneling microscopy images of graphene synthesized on cubic�SiC(001) measured with singlecrystalline W[111] tip. The images demonstrate random distortions typical for quasi�freestanding graphene. The STM imageswere measured at (a) V = 22 mV and I = 70 pA and (b, c) V = 22 mV and I = 65 pA.



system is comparable with the spatial resolutionachieved in recent non�contact AFM experiments[68].

5. ATOMIC RESOLUTION IN STM EXPERIMENTS WITH SINGLE�CRYSTAL

DIAMOND PROBES

Taking into account the reciprocity principle(Fig. 1c), the experiments with single crystallineW[001] probes on HOPG(0001) (Fig. 3) demonstratethe possibility to improve the spatial resolution usingSTM probes with carbon atom at the tip apex. In thiscase, STM images will be obtained using more local�ized carbon s and p orbitals at the apex. This situationwas realized in the experiments with polycrystallinetungsten probes functionalized by molecules consist�ing of carbon, oxygen and hydrogen atoms [44–55].Despite the sub�ångström lateral resolution achieved[49], these probes are usually not stable at small tun�neling gaps. Enhanced tip stability and control of thetip electronic structure can be achieved in STM exper�iments with single�crystal, conductive diamondprobes [69]. The boron�doped diamond probes can beutilized both for STM and STS experiments demand�ing high apex stability. Note that heavily boron�dopeddiamond crystals can possess superconductive proper�ties [70] that assume possible applications in low�tem�perature studies of superconducting nanostructures.

Figure 6 illustrates the high spatial resolutionobtained with the [111]�oriented single�crystal dia�mond probe and its advantages compared to theW[001] tip utilized in earlier STM experiments [19,20, 57, 58]. The images measured with the diamondand tungsten probes (Figs. 6a and 6b) reveal true hon�eycomb lattice of the graphite surface with both α andβ atoms resolved. However, the hollow sites are sub�stantially deeper on STM images measured with thediamond probe, as cross�sections of the STM imagesdemonstrate (Figs. 6c and 6d). This is related to differ�ent spatial distribution of the tungsten and carbonatomic orbitals which are responsible for the STMimaging in each particular case. The comparison ofthe cross�sections in Figs. 6c and 6d shows that con�ductive diamond probes can provide higher lateral andvertical resolution than traditional d�metal probes. Onboth cross�sections one can see non�equivalence ofthe α and β atoms of the graphite surface (with andwithout nearest neighbors in the second layer). Theindividual atoms in honeycombs are better resolved inthe image measured with the diamond probe. Theresults of the DFT calculations [69] revealed that non�equivalence of the surface atoms in STM experimentswith the diamond probe at tip�sample distances d >3.0 Å corresponds to the different DOS on the α andβ atoms. Figure 6f demonstrates that DOS on theFermi level is approximately 25% larger for the βatoms. This is in agreement with the observed heightdifference between non�equivalent surface atoms in

the cross�sections shown in Figs. 6c and 6d (0.1–0.2 Å). Figures 6g and 6h show the charge density mapcalculated for the graphite (0001) surface at the tip�sample distance of 4.5 Å and STM image measuredusing the diamond probe, respectively. Good agree�ment between the theoretical and experimental imagesproves that high resolution HOPG(0001) STM imag�ing with the boron�doped diamond probes can beachieved at distances in the range of 3.5–4.5 Å. Atthese distances the electronic structure of the tip andsurface atoms are not substantially modified by thetip�sample interaction (Fig. 7). This allows STMimaging of the surface electronic structure unper�turbed by the tip�sample interaction (Fig. 6h).

Calculations of the partial DOS associated with theelectron orbitals of the diamond probe and graphitesurface atoms at different tunneling gaps (Fig. 7) showthat electronic structure of the interacting atoms ismodified at tip�sample distances d < 3.0 Å. The over�lapping of the tip and surface atomic orbitals leads todecrease in the partial DOS associated with the pzorbital of the graphite surface atoms when the dia�mond tip atom is positioned directly above the surfaceatom (Fig. 7a, right panel). The suppression of the pzorbital of a surface atom at small tunneling gaps (d <2.5 Å) is in qualitative agreement with the results of thetheoretical calculations performed for the adatom ofthe Si(111)7 × 7 surface interacting with the tungstentip atom [30]. If the diamond tip atom is positionedabove the hollow site (left panels in Figs. 7a and 7b),the overlapping of the tip and surface atomic orbitalsdoes not take place even at small distances. Therefore,the change of the partial DOS of the tip and surfaceatoms is minor even at very small tunneling gaps (d =1.5 Å in Fig. 7). According to DFT calculations [69],the electronic structure of the diamond probe isdefined by the carbon p states with domination of thepx and py orbitals. Scanning tunneling microscopyimages in Figs. 6a and 6h can correspond to imaging ofthe surface pz orbitals by the px, y orbitals of the dia�mond tip atom. The STM experiments and DFT cal�culations demonstrate the advantages of the probeshaving p orbitals at the tip atom compared to the tra�ditional metallic probes with d orbitals at the apex.The p orbitals of light elements can provide higher spa�tial resolution and allow atomically resolved STMimaging at larger tip�sample distances without modifi�cation of the surface electronic structure. Note that inexperiments with the single�crystal diamond probe[69] d orbitals definitely could not be responsible forthe high resolution imaging that cannot be excluded inSTM experiments with the tungsten probes function�alized by molecules and light element atoms [44–55].

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Fig. 6. (Color online) (a, b) 18 × 9 Å STM images of HOPG(0001) measured using (a) single�crystal diamond probe at V =⎯50 mV, I = 0.1 nA and (b) W[001] probe at V = –0.4 V, I = 0.18 nA. (c, d) Cross�sections (c) 1–2 and (d) 3–4 of the images inpanels (a) and (b), respectively. (e, f) Total DOS associated with the α and β atoms of the graphite (0001) surface. (g) Calculatedelectron density distribution map in the energy range [EF–0.2 eV; EF] and (h) STM image measured with the diamond probe atV = –50 mV, I = 0.8 nA. Reproduced from [69] with permission from IOP Publishing.



6. CHEMICAL CONTRAST IN STM EXPERIMENTS ON THE GaTe ( ) SURFACE

Figures 8a–8c show STM images of the

GaTe( ) surface (Fig. 8d) measured using a singlecrystalline W[001] probe [58]. The images presentedin Figs. 8a and 8b demonstrate preferential visualiza�tion of the electronic features corresponding to the tel�lurium and gallium surface atoms, respectively. TheSTM image in Fig. 8c reveals more complicated pat�tern corresponding to the visualization of the elec�tronic features from both surface sublattices. Theimages in Figs. 8a–8c were obtained at almost thesame sample bias voltage. Theoretical calculations

[58] showed that DOS of the GaTe( ) surface in the

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energy interval relevant to the STM experiments ismostly defined by the Te 5p electron states. Therefore,the images with preferential visualization of either tel�lurium or gallium sublattices cannot be explained bythe surface electronic structure without considerationof the tip–sample interaction. It can be suggested that

chemical contrast in STM images of the GaTe( )surface is related to modification of the surface elec�tronic structure at small tunneling gaps. With decreas�ing tip�sample distances the p orbitals of the

GaTe( ) surface atoms can be selectively sup�pressed as it was observed for the pz orbitals of theSi(111)7 × 7 [30] and graphite (Fig. 7) surface atomsinteracting with the tips and for the orbital of the

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dz

2

Fig. 8. (Color online) (a–c) 3 × 3 nm2 STM images of the GaTe( ) surface measured with a W[001] tip at (a) V = –1 V and

I = 120 pA, (b) V = –1 V and I = 50 pA, and (c) V = –0.9 V and I = 50 pA. (d) Schematic model of the GaTe( ) surface [30].

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Fig. 7. (Color online) Partial DOS of (a) the β atom of a graphite (0001) surface closest to the diamond tip and (b) the tip apexatom at different tunneling gaps and lateral positions of the tip (left panels) above the hollow site and (right panels) above theβ atom. Reproduced from [69] with permission from IOP Publishing.

pxpypz

pxpypz

pxpypz

pxpypz

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W[001] tip atom interacting with the graphite surface(Fig. 3). Because of different spatial distribution of theGa 4p and Te 5p orbitals, their modification can takeplace at different tunneling gaps. The overlapping ofthe surface and tip atomic orbitals can decrease therelative contribution of the Te 5p orbitals at small tun�neling gaps stipulating the chemical selective STM

imaging of the GaTe( ) surface (Figs. 8a and 8b).

7. CONCLUSIONS

Visualization of individual atomic orbitals corre�sponds to the limit of spatial resolution in STM exper�iments. During the last few years several studies dem�onstrating the direct visualization of either tip or elec�tron orbitals of surface atoms have been published. Anexample of the direct orbital imaging is presented inFig. 3. The subatomic features observed in theseexperiments are related to modification of the elec�tronic structure of the tungsten tip atom interactingwith the carbon atom of the graphite surface. Theoret�ical calculations demonstrate the suppression of thefurther protruded tip orbitals at small tunneling gapsbecause of the overlapping of the tip and sample wave�functions. Taking into account the reciprocity princi�ple of STM, similar results can be obtained duringinvestigations of the d�metal surfaces using the probespossessing symmetric charge density distributionaround the tip atom even at small distances. Theresults obtained with the [111]�oriented single�crystaldiamond and tungsten probes demonstrate the feasi�bility of STM imaging with picometer lateral resolu�tion without subatomic effects of the tip electronicstructure. The picometer spatial resolution can beachieved using such probes even on surfaces with com�plicated atomic structure. The results presented in thisreview demonstrate the importance of precise controlof the tunneling gap and the probe structure for selec�tive visualization of the electron orbitals in STMexperiments. Detailed knowledge of the role of tip�sample distance and interaction between tip and sur�face atoms can provide explanation of the selectiveorbital imaging observed at the same sample bias volt�ages and contribute to development of the surfacechemical analysis at the atomic scale.

I am grateful to S.N. Molotkov, S.I. Bozhko,S.S. Nazin, V.N. Semenov, A.M. Ionov, V.Yu. Aristov,N.N. Orlova, M.G. Lazarev, S.A. Krasnikov, S. Mur�phy, O. Lübben, B.E. Murphy, K. Radican, I.V. Shvets,L.V. Yashina, and A.A. Volykhov for collaboration andfruitful discussions. This work was supported by theRussian Foundation for Basic Research (projectnos. 11�02�01256 and 14�02�01234) and by the7th European Framework Programme (Marie Curiegrant). Scanning tunneling microscopy images wereprocessed using the WSxM software [71].

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REFERENCES

1. G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Appl.Phys. Lett. 40, 178 (1982).

2. G. Binnig and H. Rohrer, Helv. Phys. Acta 55, 726(1982).

3. G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys.Rev. Lett. 49, 57 (1982).

4. R. Wiesendanger, H.�J. Güntherodt, G. Güntherodt,R. J. Gambino, and R. Ruf, Phys. Rev. Lett. 65, 247(1990).

5. R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009).6. R. M. Feenstra, J. A. Stroscio, J. Tersoff, and A. P. Fein,

Phys. Rev. Lett. 58, 1192 (1987).7. M. Schmid, H. Stadler, and P. Varga, Phys. Rev. Lett.

70, 1441 (1993).8. D. M. Eigler and E. K. Schweizer, Nature 344, 524

(1990).9. M. F. Crommie, C. P. Lutz, and D. M. Eigler, Science

262, 218 (1993).10. A. A. Khajetoorians, J. Wiebe, B. Chilian, and R. Wie�

sendanger, Science 332, 1062 (2012).11. A. A. Khajetoorians, J. Wiebe, B. Chilian, S. Lounis,

S. Blügel, and R. Wiesendanger, Nature Phys. 8, 497(2012).

12. S. A. Krasnikov, O. Lübben, B. E. Murphy, S. I. Boz�hko, A. N. Chaika, N. N. Sergeeva, B. Bulfin, andI. V. Shvets, Nano Res. 6, 929 (2013).

13. A. N. Chaika, S. S. Nazin, V. N. Semenov, S. I. Boz�hko, O. Lübben, S. A. Krasnikov, K. Radican, andI. V. Shvets, Eur. Phys. Lett. 92, 46003 (2010).

14. C. J. Chen, J. Vac. Sci. Technol. A 6, 319 (1988).15. C. J. Chen, Introduction to Scanning Tunneling Micros�

copy (Oxford Univ. Press, New York, 2008).16. A. N. Chaika, O. V. Molodtsova, A. A. Zakharov,

D. Marchenko, J. Sanchez�Barriga, A. Varykhalov,I. V. Shvets, and V. Yu. Aristov, Nano Res. 6, 562(2013).

17. H. Gawronski, M. Mehlhorn, and K. Morgenstern,Science 319, 930 (2008).

18. J. Tersoff and D. R. Hamann, Phys. Rev. Lett. 50, 1998(1983).

19. J. Tersoff and D. R. Hamann, Phys. Rev. B 31, 805(1985).

20. A. N. Chaika, V. N. Semenov, S. S. Nazin, S. I. Boz�hko, S. Murphy, K. Radican, and I. V. Shvets, Phys.Rev. Lett. 98, 206101 (2007).

21. A. N. Chaika, S. S. Nazin, V. N. Semenov, N. N. Or�lova, S. I. Bozhko, O. Lübben, S. A. Krasnikov, K. Rad�ican, and I. V. Shvets, Appl. Surf. Sci. 267, 219 (2013).

22. A. N. Chaika, N. N. Orlova, V. N. Semenov, E. Yu. Post�nova, S. A. Krasnikov, M. G. Lazarev, S. V. Chekmazov,V. Yu. Aristov, V. G. Glebovsky, S. I. Bozhko, andI. V. Shvets, Sci. Rep. 4, 3742 (2014).

23. A. N. Chaika, S. S. Nazin, and S. I. Bozhko, Surf. Sci.602, 2078 (2008).

24. C. J. Chen, Phys. Rev. Lett. 69, 1656 (1992).25. W. Sacks, Phys. Rev. B 61, 7656 (2000).26. M. Polok, D. V. Fedorov, A. Bagrets, P. Zahn, and

I. Mertig, Phys. Rev. B 83, 245426 (2011).



27. H. Choi, R. C. Longo, M. Huang, J. N. Randall,R. M. Wallace, and K. Cho, Nanotechnology 24,105201 (2013).

28. C. A. Wright and S. D. Solares, J. Phys. D: Appl. Phys.46, 155307 (2013).

29. W. A. Hofer, Prog. Surf. Sci. 71, 147 (2003).30. P. Jelinek, M. Shvec, P. Pou, R. Perez, and V. Chab,

Phys. Rev. Lett. 101, 176101 (2008).31. J. P. Ibe, P. P. Bey, S. L. Brandow, R. A. Brizzolara,

N. A. Burnham, D. P. DiLella, K. P. Lee, C. R. K. Mar�rian, and R. J. Colton, J. Vac. Sci. Technol. 8, 3570(1990).

32. Z. Q. Yu, C. M. Wang, Y. Du, S. Thevuthasan, andI. Lyubinetsky, Ultramicroscopy 108, 873 (2008).

33. D. K. Biegelsen, F. A. Ponce, J. C. Tramontana, andS. M. Koch, Appl. Phys. Lett. 50, 696 (1987).

34. D. K. Biegelsen, F. A. Ponce, and J. C. Tramontana,Appl. Phys. Lett. 54, 1223 (1989).

35. S. Morishita and F. Okuyama, J. Vac. Sci. Technol. A 9,167 (1991).

36. K. N. Eltsov, V. M. Shevlyuga, V. Y. Yurov, A. V. Kvit,and M. S. Kogan, Phys. Low�Dim. Struct. 9–10, 7(1996).

37. H.�W. Fink, IBM J. Res. Develop. 30, 460 (1986).38. J. A. Stroscio, R. M. Feenstra, and P. A. Fein, Phys.

Rev. Lett. 58, 1668 (1987).39. H. Neddermeyer and M. Drechsler, J. Microsc. 152,

459 (1988).40. J. Wintterlin, J. Wiechers, H. Brune, T. Gritsch,

H. Hofer, and R. J. Behm, Phys. Rev. Lett. 62, 59(1989).

41. C. J. Chen, J. Vac. Sci. Technol. A 9, 44 (1991).42. S. Heike, T. Hashizume, and Y. Wada, J. Vac. Sci. Tech�

nol. B 14, 1522 (1996).43. A. Castellanos�Gomez, G. Rubio�Bollinger, M. Gar�

nica, S. Barja, A. L. Vazquez de Parga, R. Miranda, andN. Agrait, Ultramicroscopy 122, 1 (2012).

44. H. Dai, J. H. Hafner, A. G. Rinzler, D. T. Colbert, andR. E. Smalley, Nature 384, 147 (1996).

45. K. F. Kelly, D. Sarkar, G. D. Hale, S. J. Oldenburg, andN. J. Halas, Science 273, 1371 (1996).

46. J. Repp, G. Meyer, S. M. Stojkovic, A. Gourdon, andC. Joachim, Phys. Rev. Lett. 94, 026803 (2005).

47. Z. T. Deng, H. Lin, W. Ji, L. Gao, X. Lin, Z. H. Cheng,X. B. He, J. L. Lu, D. X. Shi, W. A. Hofer, andH.�J. Gao, Phys. Rev. Lett. 96, 156102 (2006).

48. R. Temirov, S. Soubatch, O. Neucheva, A. C. Lassise,and F. S. Tautz, New J. Phys. 10, 053012 (2008).

49. C. Weiss, C. Wagner, C. Kleimann, M. Rohlfing,F. S. Tautz, and R. Temirov, Phys. Rev. Lett. 105,086103 (2010).

50. L. Gross, N. Moll, F. Mohn, A. Curioni, G. Meyer,F. Hanke, and M. Persson, Phys. Rev. Lett. 107, 086101(2011).

51. Z. Cheng, S. Du, W. Guo, L. Gao, Z. Deng, N. Jiang,H. Guo, H. Tang, and H.�J. Gao, Nano Res. 4, 523(2011).

52. J. I. Martinez, E. Abad, C. Gonzalez, F. Flores, andJ. Ortega, Phys. Rev. Lett. 108, 246102 (2012).

53. F. Mohn, L. Gross, N. Moll, and G. Meyer, NatureNano. 7, 227 (2012).

54. C. Chiutu, A. M. Sweetman, A. J. Lakin, A. Stannard,S. Jarvis, L. Kantorovich, J. L. Dunn, and P. Moriarty,Phys. Rev. Lett. 108, 268302 (2012).

55. A. J. Lakin, C. Chiutu, A. M. Sweetman, P. Moriarty,and J. L. Dunn, Phys. Rev. B 88, 035447 (2013).

56. H.�W. Fink, W. Stocker, and H. Schmid, J. Vac. Sci.Technol. B 8, 1323 (1990).

57. A. N. Chaika, V. N. Semenov, V. G. Glebovskiy, andS. I. Bozhko, Appl. Phys. Lett. 95, 173107 (2009).

58. L. V. Yashina, R. Püttner, A. A. Volykhov, P. Stojanov,J. Riley, S. Yu. Vassiliev, A. N. Chaika, S. N. Dedyulin,M. E. Tamm, D. V. Vyalikh, and A. I. Belogorokhov,Phys. Rev. B 85, 075409 (2012).

59. M.�H. Whangbo, W. Liang, J. Ren, S. N. Magonov, andA. J. Wawkuschewski, J. Phys. Chem. 98, 7602 (1994).

60. M. Ondracek, P. Pou, V. Rozsival, C. Gonzalez,P. Jelinek, and R. Perez, Phys. Rev. Lett. 106, 176101(2011).

61. S. Hembacher, F. J. Giessibl, and J. Mannhart, Science305, 380 (2004).

62. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169(1996).

63. C. A. Wright and S. D. Solares, Nano. Lett. 11, 5026(2011).

64. C. A. Wright and S. D. Solares, Appl. Phys. Lett. 100,163104 (2012).

65. M. Ternes, C. Gonzalez, C. P. Lutz, P. Hapala,F. J. Giessibl, P. Jelinek, and A. J. Heinrich, Phys. Rev.Lett. 106, 016802 (2011).

66. A. N. Chaika, O. V. Molodtsova, A. A. Zakharov,D. Marchenko, J. Sanchez�Barriga, A. Varykhalov,S. V. Babenkov, M. Portail, M. Zielinski, B. E. Murphy,S. A. Krasnikov, O. Lübben, I. V. Shvets, and V. Y. Aris�tov, Nanotechnology 25, 135605 (2014).

67. A. Fasolino, J. H. Los, and M. I. Katsnelson, NatureMater. 6, 858 (2007).

68. L. Gross, F. Mohn, N. Moll, B. Schuler, A. Criado,E. Guitian, D. Pena, A. Gourdon, and G. Meyer, Sci�ence 337, 1326 (2012).

69. V. Grushko, O. Lübben, A. N. Chaika, N. Novikov,E. Mitskevich, A. Chepugov, O. Lysenko, B. E. Mur�phy, S. A. Krasnikov, and I. V. Shvets, Nanotechnology25, 025706 (2014).

70. E. A. Ekimov, V. A. Sidorov, E. D. Bauer, N. N. Mel’nik,N. J. Curro, J. D. Thompson, and S. M. Stishov, Nature428, 542 (2004).

71. I. Horcas, R. Fernandez, J. M. Gomez�Rodriguez,J. Colchero, J. Gomez�Herrero, and A. M. Baro, Rev.Sci. Instrum. 78, 013705 (2007).

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