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Coulomb blockade effects in charged Si7 clusters ona graphite substrate

F. Hagelberga,* , P. Scheierb, B. Marsenc, M. Lonfatc, K. Sattlerc

aThe Computational Center for Molecular Structure and Interactions, Department of Physics, ATM Sciences and General Science, JacksonState University, Jackson, MS 39217, USA

bInstitut fur Ionenphysik, Leopold Franzens Universita¨t Innsbruck, Technikerstr.25, A-6020 Innsbruck, AustriacDepartment of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA

Received 21 December 1999; accepted 24 February 2000

Abstract

The present work deals with the interpretation of recent high-resolution scanning tunneling microscopy (STM) measure-ments in which Si7 clusters were assembled through quasi-free growth on a clean highly oriented pyrolytic graphite (HOPG)surface. It was found that at low bias, some clusters exhibited the Coulomb blockade phenomenon, acquiring a negative chargethat blocks the tunneling current from the microscope tip to the cluster. However, upon a switch of polarity, conceivablyneutralizing the charged system, the clusters proved to be detectable within a wide range of positive and negative values of theSTM bias. We attempt to understand this effect in terms of an electronic structure change of the Si7 unit associated with atransition from a singly charged Si7 anion in a spin quartet state to a neutral Si7 cluster in a spin triplet state, performing densityfunctional computations for a Si7C54H18 cluster which simulates the combined system of the Si7 unit and the graphite layer.q 2000 Elsevier Science B.V. All rights reserved.

Keywords: silicon clusters; Deposited systems; Scanning tunneling microscopy; Coulomb blockade; Density functional theory

1. Introduction

The strong and continuing interest in the geometricand electronic properties of clusters deposited onsubstrates is for a large part motivated through the avail-ability of highly precise experimental observation meth-ods for these systems. Among these methods, scanningtunneling microscopy (STM) is of particular signifi-cance as it provides a high-resolution procedure forthe direct imaging of single clusters. The present workaims at an interpretation of recent STM findings related

to silicon clusters deposited on a highly oriented pyro-lytic graphite (HOPG) surface [1].

In this experiment, silicon clusters were producedby magnetron sputtering of pure Si. As the atomicsilicon vapor is deposited on the HOPG surface, Siatoms can conglomerate through diffusion processesfollowed by quasi free growth [2]. The coverage of thesurface was monitored and found to be much less thana monolayer, allowing for a clear distinction betweenindividual silicon clusters. As documented in Fig. 1a,an arrangement of silicon atoms could be distin-guished from the regular if slightly perturbedbackground of the HOPG atoms. Careful analysis ofthe spectroscopic data revealed that this group iscomposed of an Si3 unit and a planar Si7 unit

Journal of Molecular Structure (Theochem) 529 (2000) 149–160

0166-1280/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0166-1280(00)00542-X

www.elsevier.nl/locate/theochem

* Corresponding author. Tel.:11-601-968-7012; fax:11-601-973-3310.

E-mail address:[email protected] (F. Hagelberg).

consisting of a pentagon and an attached dimer (Fig.1b). As the bias voltage was reduced below a criticallevel of about 0.015 V, the image of the Si7 clusterdisappeared, turning into a group of black spots.However, after repeated alternation of the polarityof the bias voltage between10.015 and20.015 V,the bright image of the Si7 cluster reappeared andremained visible through a broad range of positiveand negative bias voltages. Similar behavior wasfound for a three-dimensional variant of Si7; however,in this work, we will concentrate on the planarspecies.

In what follows, we attempt to explain the detectedeffect in terms of a Coulomb blockade phenomenon.As a cluster appears bright, electrons tunnel from the

STM tip at least into the lowest unoccupied molecularorbital (LUMO) of the cluster. At zero or extremelysmall bias voltage, a tunneling current will beobserved only if the overlap between the LUMO ofthe cluster and the electronic states of the HOPGsubstrate is sufficiently large, implying a finite prob-ability for the transfer of electrons absorbed by thecluster to the substrate. Thus, a requirement for a“conducting” state of a planar cluster attached to aflat HOPG surface is that the LUMO exhibitsa substantial population of pz orbitals whose orienta-tion is perpendicular to the planes of both the clusterand the substrate. If, in contrast, the LUMO predomi-nantly consists of px/py orbitals, the cluster will adopta “blocking” state, which is due to the fact that thetunneling electron is trapped on the cluster whichthereby becomes negatively charged. Electrostaticrepulsion then blocks the transfer of any additionalelectrons from the STM tip and the tunneling currentis interrupted. This situation is likely to prevail untilthe cluster is neutralized, as could have occurred inthe STM measurement through the reversal of the biasvoltage. Conceivably, this neutralization is associatedwith a change of the electronic structure of theLUMO. On grounds of these considerations, theelementary mechanism of the observed effect appearsto be a transition between two different electronicstates of the planar Si7 cluster, the first involving a“blocking” and the second a “conducting” LUMO.For confirmation of this model, theory is challengedto answer three basic questions: (a) Can one isolate aplanar Si7 unit which bears resemblance with the oneexperimentally detected? (b) Can one identify twoelectronic configurations of this unit which satisfythe criteria of “blocking” vs. “conducting” states?(c) Can one explain the transition between thesestates, as observed in measurement?

2. Method

The computational investigations were started byisolating planar Si7 species in the gas phase throughgeometry optimization. Different charge and spin

F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 529 (2000) 149–160150

Fig. 1. (a) STM image of planar Si7 in “conducting” state. (b) Modelof planar Si7.

Fig. 2. (a) Initial geometry used in the geometry optimization of Si7 in spin singlet, triplet and quintet configuration. (b,c) DFT(B3LYP)equilibrium geometries for planar Si7 in spin triplet configuration.

F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 529 (2000) 149–160 151

states were investigated, more specifically neutral Si7

in spin singlet, triplet and quintet configurations(S� 0, 1, 2), as well as singly charged Si7 anions inspin doublet and quartet configurations (S� 1/2, 3/2).The quantum chemical procedure employed in thiseffort was the density functional theory (DFT) utiliz-ing the Becke three parameter hybrid method inconjunction with the correlation functional of Lee,Yang and Parr (B3LYP) [3]. In all cases, a gaussianbasis set of composition 6-31Gp was used, which hasbeen demonstrated in the past to be an adequatechoice for the treatment of silicon clusters [4].

In a second series of investigations, we analyzedplanar Si7 deposited on a graphite layer. We basedthis part of our work on an extension of the graphitesurface pseudocluster model outlined in Ref. [5].More specifically, the substrate was represented by aone-layer cluster consisting of 54 carbon atoms termi-nated 18 hydrogen atoms. To investigate the influenceof the graphite surface on the Si7 system, we attachedSi7 to various sites of the C54H18 cluster and subjectedthe combined system to a DFT (B3LYP) treatment.Subsequently, we selected the site of lowest energyand made allowance for geometric rearrangementof the Si atoms. In this way, neutral deposited Si7

was studied inS� 0; 1 and 2 spin configurationas well as Si7

2 with S� 1=2 and 3/2. The size ofthe investigated Si7C54H18 cluster makes a compu-tation using the 6-31Gp basis set prohibitivelytime consuming. Therefore, a 3-21Gp basis setwas employed which has been shown elsewhere[6] to yield very satisfactory approximations tothe 6-31Gp results as far as small silicon clustersare concerned. All computations reported herewere carried out on the CRAY C916 of theMississippi Center of Computational Research atUniversity of Mississippi using the program“Gaussian 98” [7].

3. Results and discussion

In this section, we will first comment on Si7 clustersin the gas phase and then turn to planar Si7 clustersdeposited on a HOPG surface. Planar Si7 species oftriplet and quintet spin configuration were foundthrough geometry optimization, without imposingany dimensional or symmetry constraints on thesystems. Fig. 2b and c displays the equilibrium struc-tures emerging from our B3LYP treatment forS� 1and S� 2; while Fig. 2a shows the initial geometryused, i.e. a regular Si5 pentagon and a Si dimerattached in radial direction to one of the Si5 constitu-ents. Table 1 contains the Si7 Binding Energies forS� 0; 1 and 2, where energies for two differentgeometric variants obtained forS� 1 are listed.From our computation, theS� 1 cases are highestin binding energy, corresponding to maximum stabi-lity among the species compared. Planar Si7 turns outto have sizable electron affinities. Thus, we arrive at avalue of 2.85 eV for theS� 2 and 2.77 eV for theS�1 configuration by comparing them with an Si7

2 spinquartet�S� 3=2� and a spin doublet�S� 1=2�; respec-tively, as obtained by DFT(B3LYP) analysis. Itshould be noted that, within the experimental uncer-tainty of the STM measurement, all bond distancesfound for planar Si7 in S� 1 and theS� 2 conditionswere compatible with those determined from theexperiment.

All planar species investigated are substantiallylower in binding energy than the three-dimensionalground state of Si7 (see Fig. 3) which has beenthoroughly studied by several authors [4,8]. Fromthe B3LYP analysis, we find a binding energy differ-ence of DE � 2:96 eV between the spin singletground state and the planar geometry discussedabove in the spin triplet configuration. The fact thatthe strongly preferred ground state structure is notobserved in the STM measurement may be ascribedto the mechanism of cluster generation in this experi-ment. Individual Si atoms join each other to a formcluster unit as they move in a diffusion-like process onthe graphite surface, which favors the emergence ofplanar silicon clusters. Using the pseudocluster modelemployed in this work to obtain a more detailedunderstanding of this formation, we calculated thedistribution of expectation values of the electrostaticpotential produced by the C54H18 layer in different


Table 1Binding energies for planar Si7 clusters inS� 1 andS� 2 config-uration

Spin Binding energy (eV)

S� 0 16.26S� 1 (1.variant) 19.07S� 1 (2.variant) 19.28S� 2 17.53


Fig. 3. Si7 in D5h ground state geometry.

Fig. 4. Electrostatic potential produced by C54H18 in the plane of the substrate (a) and in a plane of vertical distance 3 A˚ from the substrate (b).


Fig. 5. Representation of the three sites studied for Si adsorbed to the C54H18 cluster—edge site (a), particle site (b), hole site (c), the threeequilibrium positions for Si resulting from geometry optimizations of the three sites: E� edge site; P� particle site; H� hole site (d).


Fig. 5. (continued)

vertical distances from this unit. Fig. 4a and b shows acomparison between the electrostatic potential in theC54H18 plane and at a vertical distance of 3 A˚ from thisplane which we found close to the equilibriumdistance between the substrate and the cluster, aswill be described later in this section. Obviously, thevery marked differences between electrostatic poten-tial values in the C54H18 plane, reflecting the periodi-city of the system, have weakened considerably as onemoves to the indicated distance from the plane.Between both sites, the variation in the electrostaticpotential changes fromDV � 190:5 eV to DV �0:04 eV: Under the aspect of this result, the influenceof the substrate on the geometry of a deposited clusterappears to be small at the examined distance from thelayer. This assumption, however, has to be tested by acloser inspection of the adsorption of Si atoms to thesubstrate.

We selected three different test sites on the C54H18

pseudocluster for the attachment of a Si atom, asshown in Fig. 5a–c. In the first geometric variant, Siis placed above a center of a C6 hexagon (“hole site”,shown in Fig. 5c. The Si position in the secondgeometric variant is above the midpoint of a C–Cbond (“edge site”, Fig. 5a) and in the third, above aC atom (“particle site”, Fig. 5b). For all three sites, ageometry optimization of the whole system wasperformed; the final positions of the adsorbed Siatom are displayed in Fig. 5d. While the hole siteremains unchanged in the optimization process, theoptimized Si positions for both edge site and particlesite differ characteristically from the respective initialpositions, both being somewhat shifted from theiroriginal places towards the center of the C6 hexagon.The vertical distances of the Si atoms from the C54H18

layer range from 2.0 A˚ (edge site) to 3.2 A˚ (hole site).Table 2 summarizes the binding energies for the threecases. From this comparison, the hole site emerges asthe least favored one, being lower in binding energy

by approximately 1 eV than the two other alternativeswhich turn out to be nearly degenerate. It should benoted, however, that in the present approach, the parti-cle site results with slightly higher binding energythan the edge site. In both of these variants, theadsorbed Si atom exhibits bonding interactions withselected pz-orbitals of the C54H18 layer while no suchbonding is observed in case of the hole site.

The observations related to the system SiC54H18

may be used for the definition of a plausible initialgeometry for the optimization of the combined systemSi7C54H18. In the light of these findings, it appears thatthe atoms of a planar silicon cluster attached to theC54H18 substrate will preferentially occupy particle oredge sites and avoid hole sites. Inspecting the geome-try of the C54 array, one notices that a Si7 structuresimilar to the experimentally detected one, namely adistorted Si7 pentagon joined to a Si dimer with bonddistances ranging approximately from 2.4 to 2.8 A˚ ,can be realized by arranging the Si atom accordingto the geometric model shown in Fig. 6a, where all Siatoms initially occupy particle sites and have the samedistance from the C54H18 layer. We analyzed theresulting Si7 cluster, performing single point calcula-tions in both spin triplet and quintet configurations onthis unit by use of a 6-31Gp basis set in conjunctionwith the B3LYP method. Examining the nature of theLUMO of the beta system for this planar Si7 cluster inspin quintet configuration, we find that it predomi-nantly occupies atomic orbitals of px /py character,i.e. those oriented in the plane of the molecule. Thisimplies that upon absorption of one electron, the unitwill display “blocking” behavior, since the overlapbetween the added electron and any substrate willvanish. However, the molecular orbital followingthe LUMO in the beta system is composed of pz

atomic orbitals which can overlap with the corre-sponding pz orbitals of the substrate and thus act asa “conducting” unit. Investigation of the spin tripletconfiguration reveals the same succession of molecu-lar orbitals. However, in the spin triplet case, it is thebeta HOMO that displays blocking behavior, whilethe conducting orbital is the LUMO of the system.Thus, an added electron can overlap with electronicstates of the substrate, which makes the system as awhole conducting.

Analogous observations were made for thegeometry optimized planar Si7 clusters. Thus, our


Table 2Parameters for the investigated Si sites of SiC54H18

Site Binding energy (eV) Vertical distance of Sifrom C54H18 (A)

Particle site 682.91 2.37Edge site 682.87 2.00Hole site 682.02 3.21

results suggest that an isolated planar Si7 unit in spinquintet configuration �S� 2� if adsorbed on asubstrate and subjected to STM analysis might exhibitblocking behavior, as an electron transferred from themicroscope tip to the cluster will occupy the LUMOof the Si7 system. We tested this hypothesis by attach-ing a planar Si7 unit, as presented in Fig. 6a stabilizedin S� 2 condition to a C54H18 unit and allowed fornuclear relaxation of the whole system. In this, as in

all further geometry optimizations performed, onlysmall deviations from planarity in the per cent rangewere found for the two system components, i.e Si7 andC54H18. We determined a value of 3.2 A˚ as the averagevertical distance of the Si atoms from the substrate. Asrevealed by the investigation of the molecular orbitalsof Si7C54H18, the (beta-) LUMO of this systemconsists predominantly of px/py atomic orbitals ofthe Si constituents, in close analogy to the respective


Fig. 6. (a) The structural model used as initial geometry in the first set of geometry optimizations of Si7 1 C54H18 (see text for details). (b,c)Geometric structure of (Si7C54H18)

2 for S� 1=2 obtained from relaxation of the structure displayed in (a). (d) Geometric structure of(Si7C54H18)

2 for S� 1=2 obtained in the second set of geometry optimizations of Si7 1 C54H18 (see text for details).


Fig. 6. (continued)

free Si7 unit. Any additional electron absorbed bySi7C54H18 �S� 2� will occupy the LUMO and therebychange the spin quintet into a spin quartet�S� 3=2�configuration. We confirmed this by computation ofthe (Si7C54H18)

2 system. It was found that the HOMOof this S� 3=2 system is a spin alpha state, beinghigher in energy than the beta HOMO by a smallbut non-negligible energy difference of 0.1 eV. Thisimplies that the loss of one electron from the unit islikely to occur from the alpha system, leaving the unitin a spin triplet�S� 1� configuration. In this case,electron absorption from the STM will give rise to aspin doublet state�S� 1=2� for the system as a whole.We identified this state by performing a calculationfor (Si7C54H18)

2 with S� 1=2; the resulting geometrybeing shown in Fig. 6b and c. Analyzing the HOMOof the beta system for this unit, we found it predomi-nantly composed of Si(pz) atomic orbitals, thus satis-fying the necessary requirement for a conductingstate.

In an effort to quantify further the differencebetween the two states characterized as “blocking”and “conducting”, we carried out computations ofthe overlap density between the atomic orbitals ofthe Si atoms and the pz orbitals of the C54H18 layerfor both (Si7C54H18)

2 in S� 1=2 andS� 3=2 condi-tions. Thus, the scalar product

OV�C;Si� �X

aifi�C�uX

bjc j�Si�D E

was evaluated for both cases, wheref i(C) denotes thepz orbitals of C atoms,ai the HOMO molecular orbitalcoefficients for pz orbitals of C atoms,c j(Si) theatomic orbitals of Si atoms,bj the HOMO molecularorbital coefficients for atomic orbitals of Si atoms.

The ratio of the overlap integrals OV(C,Si) for(Si7C54H18)

2 in S� 1=2 and S� 3=2 condition wasfound to be 11.3, making the overlap of the Si atomicorbitals with the pz orbitals of the C atoms in spindoublet configuration one order of magnitude higherthan in spin quartet configuration. Estimating theprobabilities for transition of an electron attached tothe Si7 unit into an atomic state of the substrate by thesquare of OV(C,Si), such a transition appears by abouta factor of hundred more likely to occur for the spindoublet than the spin quartet system. These resultslend quantitative support to the intuitively plausiblehypothesis that the occupation of predominantly pz

orbitals in the Si states of the beta HOMO, as obtainedfor theS� 1=2 system, leads to sizably higher overlapbetween the electrons of Si and C constituents than incase of theS� 3=2 system, corresponding to conduct-ing behavior in the former and blocking behavior inthe latter case.

In an additional series of computations, the opti-mized planar Si7 clusters in spin triplet and quintetconfiguration were attached at various sites of theSi7C54H18 substrate. The investigation then followedthe lines described in the foregoing paragraphs.Although this second set of computations resulted insomewhat different relaxed Si7 structures (see Fig. 6dfor the geometry resulting forS� 1=2�; the sameconclusions with respect to the assignment of spinquartet (doublet) character of the system to a blocking(conducting) situation could be drawn. In keepingwith the observations made on single Si atomsadsorbed to Si7C54H18, it was found for all cases inves-tigated that the Si7 constituents do not occupy anyhole sites and are instead attached to positions closeto particle and edge sites.

4. Conclusion

In high-resolution STM experiments, Si7 clusterswere assembled through quasi-free growth on aclean HOPG substrate. It was found that at low biassome of the clusters identified exhibited the Coulombblockade phenomenon, acquiring a negativelycharged state which interrupts the tunneling currentfrom the microscope tip to the cluster. Upon a switchof polarity, however, conceivably neutralizing theanionic systems, the respective clusters became visi-ble again and proved to be detectable within a widerange of positive and negative values of the STM bias.

In an attempt to explain the experimental effect foran observed planar Si7 species, we studied possibleelectronic structure changes of this unit as inducedby charging and subsequent discharging of the cluster.Several equilibrium geometries with non-zero spin,namely S� 1 and S� 2 were isolated in the gasphase using the B3LYP method based on densityfunctional theory. In order to simulate a Si7 clusteradsorbed on a graphite surface, a Si7C54H18 pseu-docluster model was adopted. In the framework ofthis approach, it could be shown that an initial high


spin state�S� 2� of planar Si7 on graphite is likely totransform itself into a lower spin state�S� 1� in theprocess of gain and loss of one electron. Furthermore,it has been demonstrated for theS� 2 case, that theLUMO orbital of the neutral species is characterizedby a strongly reduced overlap of the Si7 atomic orbi-tals with the pz orbitals of the substrate atoms, so thatthe absorption of an electron by the Si7 cluster canresult in Coulomb blockade. ForS� 1; in contrast,a markedly enhanced overlap is found for the LUMO,in accordance with experimental observation.

From our computational analysis, it seems, there-fore, that the detected transition from “blocking” to“conducting” behavior of Si7 clusters adsorbed on aHOPG surface finds a natural interpretation in theframework of a spin cascade model. The sequenceof bias reduction and reversal may turn an initialS�2 state with a non-conducting LUMO, leading toCoulomb blockade, into anS� 1 state with aLUMO that establishes sufficient overlap betweenthe cluster and the substrate to allow for the flow oftunneling current. In continuation of the researchpresented here, we are currently analyzing an experi-mentally detected three-dimensional Si7 geometryalong the lines described in this work.

Acknowledgements

The support given to this work by the NationalScience Foundation through the CREST program(HRD-9805465) is gratefully acknowledged. One of

us (PS) is indebted to the APART program of theAustrian Academy of Sciences.

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