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Page 1: Reinterpretation of the scanning tunneling microscopy ...

PHYSICAL REVIEW B 15 SEPTEMBER 1999-IVOLUME 60, NUMBER 11

Reinterpretation of the scanning tunneling microscopy images of Si„100…-„231… dimers

Kenji Hata,* Satoshi Yasuda, and Hidemi Shigekawa*Institute of Applied Physics and CREST, Japan Science and Technology Corporation (JST), University of Tsukuba,

Tennodai 1-1-1, Tsukuba 305-8573, Japan~Received 4 May 1998; revised manuscript received 1 April 1999!

We revisit and refine the interpretation of the scanning tunneling microscopy~STM! images of the Si~100!dimers, based on results from an extensive set of STM observations carried out at low temperature~80 K! andtotal-energy calculations of Si~100! surfaces. The interpretation addresses some unresolved questions andbrings much experimental and theoretical research into unanimous agreement. We show that tunneling fromsurface resonances and bulk states seriously contributes to the STM images within usual tunneling conditions.In the empty state, tunneling from these states overwhelms tunneling from the localizedp* surface state,which STM is generally believed to observe.@S0163-1829~99!05935-4#

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I. INTRODUCTION

Even though the dimer of Si~100! is one of the mostsimple surface reconstructions, it has turned out to bsource of neverending controversy. A great deal of reseahas been devoted to elucidate its atomic configuration, ocal properties, and electronic structure.1–6 In particular, scan-ning tunneling microscopy~STM! has considerably contributed to enlighten our understandings.1–6 Generally, it isinterpreted that STM observes the surface states localizethe dangling bonds of the dimers.1,2 Interpretation of theSTM images of the dimers from this standpoint seems tosimple and in accordance with what is expected fromgeneral laws of chemical bonding.1 However a careful analysis of the existing data reveals that our understanding iscomplete, and in the following we point out two problemwhich require further consideration.

The first question is concerned with the interpretationthe filled-state STM images obtained at room temperatureto now. Previous room-temperature STM studies shdimers as bean-shaped protrusions which have a maximat the center of the Si-Si dimer bond in the filled states.1,2 Wenominate them as bean-type dimers in the following. In ctrast, when the empty states are probed, two round shprotrusions are resolved,2 which we refer to as protrusiontype dimers. These STM images are easily explained bysuming symmetric dimers,1 though it is now well establishedthat dimers are buckled.3 Indeed at temperatures below;200K ~low temperatures!, a majority of the dimers is observed ia buckled configuration.3 Buckling induces a charge transfefrom the lower to upper atom of the dimer, and the filledpand emptyp* surface states are localized at the danglbonds of the upper and lower atoms of the buckled dimrespectively. Generally, it is assumed that thep andp* sur-face states1,2 are observed in the STM images as dimers.order to interpret the apparent symmetric dimers observeSTM at room temperature within the framework of buckldimers, the concept of flip-flop motion was introduced: bucled dimers are flip-flopping far faster than the scanningSTM, thus dimers appear in an apparent symmetric confiration. In this scheme, STM images obtained at room teperature must reflect the average of STM images of the bu

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led dimers at low temperature in the two possibconfigurations. It is easy to interpret the empty-state imaat room temperature: the two protrusions observed in(231) unit cell are both thep* surface state localized at thlower atom of the buckled dimer in the two possible configrations. On the other hand, it is puzzling why similprotrusion-type dimers are not observed in the filled stinstead of the bean-shaped dimers. Indeed, in Fig. 1 we sgray scale images of the simulated spatial distribution offlip-flopped filledp and emptyp* surface states calculateby first-principle methods. Methodology of the first-principcalculations is presented in Sec. III C. Flip-flop motion wsimulated by adding the electronic structure of the surfstates in the two possible configurations of the buckdimer. It is a surprise to notice that the images of the flfloppedp andp* surface states are very similar with a smnode in between the dimer. A similar result has beentained by Owenet al., where they simulated STM images othe flip-flopping buckled dimers following Tersoff and Hamman’s formalism. Their simulation shows a protrusion-tySTM image of the dimers in the filled states@Fig. 2~a! in Ref.7#.

The second problem is the mismatch between the typsurface bias used to observe the surface in the past andenergy window where thep andp* surface states are locaized. A survey of previous STM observations of the Si~100!

FIG. 1. Cross sections of the electronic and atomic structurethe simulated flip-flopped buckled dimers.~a! Simulated filledpsurface state and~b! p* empty surface state. Cross sections wetaken along a plane which includes the buckled dimer. The smblack and large gray circles represent the position of the upperlower atom of the buckled dimer, respectively. The electronic strture was calculated by first-principles methods and the flip-flop mtion was simulated by adding the two possible configurations.

8164 ©1999 The American Physical Society

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PRB 60 8165REINTERPRETATION OF THE SCANNING TUNNELING . . .

surface reveals that most of the STM images are of the fistates taken with a surface bias as large as22 V.1–5 How-ever, the typical bias of22 V is out of the range of wherethep surface state is located. We can see this by considethe surface band gap and the width of the surface staTypical I -V curves of the dimers show a surface band gap;0.5 V with the Fermi level located in the midgap.4 Thesurface band gap of;0.5 V is also supported from otheexperiments.8 Theoretical9 and photoemission10,11 studiesshow that the bandwidths of thep andp* states are 0.6–0.8V each. When combined with the surface band gap of;0.5V, this means that thep and p* surface states are roughlocalized in the range of;61 V from the Fermi level. In atypical STM image taken at22 V, a significant part of thetunneling current must come from states other than thefacep andp* states.

In this paper, we provide results from an extensive seSTM observations at room and low temperature~80 K!, andpresent a refined interpretation of the STM images of dimIn our interpretation, at typical tunneling conditions usedthe past, a serious part of the tunneling current comes fstates other than thep andp* surface states. The new intepretation addresses the aforementioned unresolved quesand brings results of much experimental and theoreticalsearch into unanimous agreement.

II. EXPERIMENT

Defects are the major reason why high biases~;22 V!were used in the past. It is believed that surfaces of Si~001!inevitably contain a significant density of defects. When oattempts to lower the bias, these defects become very bbecause many defects are metallic, making it difficult to oserve the dimers clearly. We have overcome this problemfabricating a surface with very low defect density. After tsample was prebaked at;700 °C for one night, it wasflashed to 1200 °C for several seconds. The pressurekept below 131028 Pa during flashing~in most timesaround 531029 Pa). We found that keeping this extremegood vacuum pressure during flashing is crucial to havsurface with low defect density.12 By this procedure, a cleanSi~100! surface with a small ratio of defects lower than 0.2was repeatedly made on any provided sample.N-type Sisamples phosphorus-doped with a conductivity of 0.1V cmwere used. TunnelingI -V measurements of the surface shothat the Fermi level is at the upper edge of the conducband, which agrees with then-type doping, and a width othe surface band gap was;0.5 V.

III. RESULTS AND DISCUSSION

A. STM results at room temperature

Surfaces free from defects make observation of the dimpossible at any desired surface bias. Figure 2~a! shows anSTM image of the filled state probed with a low surface bjust below the surface band gap~20.6 V! at room tempera-ture. Not a bean-type but a protrusion-type dimer is oserved. We could observe the protrusion-type dimers infilled states at low surface biases with the same frequencin the empty state. The protrusions are observed at the slocation where the empty-state protrusions are observed,

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we attribute them to be observing thep surface state locatedat the dangling bond of the upper atom of the dimer. Evtime the bias is increased, the dimers would gradually revto the bean type at;21 V as shown in Fig. 2~b!, in areversible fashion. This indicates that the protrusion-tydimers observed here are not induced by some peculiarsurface interaction.

The empty-state STM images show a more complicadependence on bias. When the surface bias is above11.4 V,regions between the dimer rows are observed. This is hlighted in Fig. 2~c!, where the bias was switched from a lo~0.6 V! to a high bias~1.5 V! in the intermediate of scanningImmediately it is apparent that the bright rows observedlow ~0.6 V! and high biases~1.5 V! are completely out ofphase. We attribute the bright rows observed at low biasethe dimers, since they are in-phase with the dimer rowsserved in the filled state. This means that regions betweendimers are observed at high biases. The phase shift occua bias around 1.4 V. The phase shift was reporpreviously1 and was interpreted as an extension of the noof the antibonding state of a symmetric dimer with biwhich was lately supported by theoretical studies.13 How-ever, as mentioned before, dimers are buckled, and thep*surface state of buckled dimers is calculated not to shsuch an extension with bias.13 Considering these points, winterpret that at high biases, the main part of the tunnelcurrent comes from states localized between the dimer rooverwhelming tunneling from thep* surface state.

Results obtained at room temperature are summariProtrusion-type dimers are observed both in the emptyfilled states at low biases. On the other hand, at high biabean-type dimers are observed in the filled states whileregion between the dimer rows is observed in the emstates. We interpret the results as the following.~i! At lowbiases, STM observes thep or p* surface states. Theprotrusion-type dimers are observed as a result of theflop motion of the buckled dimers. The range of surfaceases~21 V to ;11.4 V! where the protrusion-type dimersobserved is in good accordance with the energy windwhere thep andp* bands are localized.~ii ! At high biases,

FIG. 2. STM images of dimers at room temperature.~a! Lowbias filled state~20.6 V!. ~b! The bias was gradually decreasefrom 20.9 to 21.7 V. The bean⇔protrusion transition of thedimers occurred around;21 V. The reason why the bean-shapedimers are not clearly visible at high biases might be becauseimage was taken simultaneously with the protrusion-type dimobserved at low biases, which show stronger contrast than the btype dimers.~c! Empty-state image. The surface bias was switchfrom a low ~10.6 V! to a high~11.5 V! bias in the middle.

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8166 PRB 60KENJI HATA, SATOSHI YASUDA, AND HIDEMI SHIGEKAWA

tunneling from other states starts to participate in, and inempty states overwhelm, tunneling from thep* surfacestate. The spatial distribution of the other states is localibetween the Si-Si dimer bond in the filled states and betwthe dimer rows in the empty states, respectively. The nSTM images and interpretation presented here addresstwo problems mentioned in the Introduction. Moreovmany experimental results—the widths of thep and p*bands, surface band gap obtained fromI -V curves, and thevoltage dependence of the STM images—come into scoincidence within the familiar notion of flip-flopping buckled dimers.

B. STM results at low temperature „80 K…

In order to reinforce our assertions, an extensive seSTM observations was carried out at a low temperature~80K! where the flip-flop motion of dimers is frozen. We shothat the low-temperature STM images of the dimers unamously coincide with the complementary room-temperatresults further supporting our interpretation.

First we provide results of the observation of the fillstates. Figure 3 shows some typical filled-state STM imaof the dimers with different biases ranging from20.8 to22.0 V to show the dependence of the STM images on sface bias. STM images taken at low bias~;21.0 V! showclear zigzag chains forming ac(432) phase,3 which weinterpret to reflect tunneling from thep surface state localized at the upper atom of the dimer. The upper atom ofdimers and the dimer rows are aligned in an antiferromnetic order providing the observedc(432) phase. Based onthis understanding, the locations of the upper atoms ofdimers are assigned as black circles in the STM image taat 20.8 V. As the bias is increased, thec(432) zigzagcomponent fades and instead a (231) component emergeand grows in intensity as shown in the STM images taken

FIG. 3. STM images~1 nA! of the filled states of the dimers asurface biases ranging from20.8 to 22.0 V at 80 K. Scale434 nm.

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high biases above21.5 V. At 22 V, the STM image re-sembles ac(432) zigzag component overlapped with(231) component. In order to investigate this fading effemore quantitatively, average cross sections of the dimerthe STM images taken at high~22.0 V! and low ~20.8 V!biases are shown in Figs. 4~a! and 4~b!, respectively. Crosssections are taken at the locations displayed as dashed bin Fig. 3. In addition, we display the cross section of telectronic structure of thep surface state calculated by firsprinciple methods in Fig. 4~c! for comparison. We registereFig. 4~c! against Figs. 4~a! and 4~b! by attributing the globalminimum of the cross sections to the middle of the dimrows where the lower atoms of the dimers are at the adjacBy comparing Figs. 4~b! and 4~c!, we can understand thaSTM is not observing the atoms of the dimers and the crugation in the STM images reflects the global corrugationthe electronic structure with some diminished spatial resotion. From Fig. 4~b!, it is apparent that there exists two typeof minima aligned alternatively in the cross sections. MinimA and B defined in Fig. 4 are both located in the middbetween the dimers, though they are different becauseupper~lower! atoms are located at the immediate adjacenminimumA (B). This difference is due to the34 periodic-ity of the reconstruction in this direction and gradually dcreases as the bias is increased as shown in Fig. 4~a!. Wedefine the height difference between the two minimaA andB

FIG. 4. Average cross section of the filled-state STM imagtaken at~a! a high bias~22.0 V! and ~b! a low bias~20.8 V!. ~c!Cross section of the electronic structure of the filledp surface state.Two types of minima indicated byA and B in the cross sectionsexist aligned alternatively. HD is defined as the height differenbetweenA andB, and Corr as the average corrugation of the dime~d! Dependence of HD/Corr on surface bias. Also HD vs surfabias is displayed in the inset.

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PRB 60 8167REINTERPRETATION OF THE SCANNING TUNNELING . . .

as HD, and the average corrugation of the dimers as Coshown in Figs. 4~a! and 4~b!. HD divided by the corrugationof the dimers~Corr! is assumed to serve as an indicatorthe strength of thec(432) zigzag component versus th(231) component. The dependence of HD/Corr on the sface bias is plotted in Fig. 4~d!. Also HD versus surface biais displayed in the inset of Fig. 4~d!. HD/Corr remains con-stant below21.4 V and gradually decreases with increasbiases. It should be noted that even at biases as high a22V, HD/Corr does not drop to zero, thus the remainic(432) zigzag component should have been observedreported as buckled dimers in previous studies.3,14–16We in-terpret the experimental results as the following.~i! Tunnel-ing from thep surface state is observed at low biases nthe Fermi edge.~ii ! A decrease of thec(432) zigzag com-ponent at high bias reflects an opening of a new tunnechannel from other states which are mainly localized intween the Si-Si dimer bond and have an almost (231) pe-riodicity. ~iii ! As the bias is increased, tunneling from othstates becomes important and thec(432) zigzag componenfades. Tunneling from the other states at high biases shbe the cause of the protrusion⇔bean-type transitions of thappearance of the dimers observed in the filled states at rtemperature.

Next, we shift to the observations of the empty stateslow temperature. Figure 5 shows an STM image at low teperature~80 K! where the bias was switched from a low~0.6V! to a high bias~1.5 V! in the intermediate. Again, thephase shift is observed, and areas between the dimerare observed at the high bias. Dimers appear different inSTM images taken at low and high biases. At the low biSTM images show rows of zigzag chains in ac(432)phase,3 which reflects tunneling from thep* surface statelocalized at the lower atom of the dimer. In contrast, athigh bias, a bright row similar to that observed at room teperature is obtained, though a bright and dark (231) unit

FIG. 5. An STM image~1 nA! of the empty states at 80 K.~a!The bias was switched from a low~0.6 V! to a high~1.5 V! bias inthe middle.

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align alternatively along the dimer-row direction. Thbrighter units are registered against thec(432) regionscanned with low bias, from which we attribute the lowatom of the dimer to a circle as shown in Fig. 5. It shows tthe brighter unit corresponds to the location of the upatom of the dimer. This cannot be explained by an extensof the wave function of thep* state localized at the loweatom with bias, but means that tunneling from other stabecomes important at high biases. In order to investigatedetails of the phase shift with bias, we have carried out Sobservations of the dimers on a defect-freec(432) buckleddimer domain scanned with different biases ranging fromto 2.1 V with an increase rate of 0.1 V as shown in Fig.Also a set of cross sections of the STM images of Figalong the dimers are displayed in Fig. 7. In the lower sectof Fig. 7, the cross section of the calculated electronic strture of thep* surface state is displayed for clarity. Registwas done in the same fashion employed to display Fig. 4~c!.The same phase shift presented in Fig. 5 is evident. Atbiases below 1.4 V, two types of minima in the cross stions are clearly observable, which reflects thec(432) zig-zag component, likewise the case of the observations offilled states. We interpret that tunneling from thep* surfacestate localized at the lower atom of the dimer is observedthese low biases. As the bias increases and approaches 1the corrugations of the dimers gradually decrease, whshould reflect an opening of tunneling channels from otstates. It is a surprise to observe an almost flat STM imagthe transition bias of 1.4 V. As the bias is increased ab

FIG. 6. STM images of the empty states at surface biases ring from 0.8 to 1.9 V at 80 K. Tunneling current 0.6 nA. Sca535 nm.

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8168 PRB 60KENJI HATA, SATOSHI YASUDA, AND HIDEMI SHIGEKAWA

1.4 V, a new corrugation emerges which is out of phase wthat observed at low biases. The new corrugation observehigh biases is characterized by two types of maxima aligalternatively forming a34 periodicity in contrast to the twotypes of minima observed at low biases. Again, the lotemperature results are fully consistent with the rootemperature observations.

Subsequently, we register the filled-state STM imagagainst the empty-state images taken at low biases to emsize their similarity and to show that band bending doesaffect our interpretation. Figure 8 shows an STM imagethe dimers at low temperature~80 K! where the bias wasswitched from positive to negative in the intermediatescanning at the location indicated by the black line. Henthe upper half is an empty-state image while the lower haan image of the filled state both taken at low biases. Silarity between the dimers in the STM images of the emand filled states is striking, which agrees with the protrusitype image of dimers obtained at room temperature boththe empty and filled states at low biases. Moreover, whamore important is that the opposite side of the dimer is

FIG. 7. Cross section of STM images of Fig. 6 along the dimeThe inset in the bottom shows the cross section of the electrstructure of thep* surface state.

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served in the empty and filled states. This is emphasizedmatching ac(432) phased stick and ball pattern to thc(432) zigzag component of the STM image. Obviousthe stick and ball patterns observed in the empty and fistates are out of phase, giving other evidence that thep andp* surface states localized at the opposite side of the diare observed in the STM images taken at low biases. F

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FIG. 8. An STM image~1 nA! showing both the filled andempty states at 80 K. The bias was switched from positive~10.6 V!to negative~20.8 V! in the intermediate of scanning at the locatioof the black line. The stick and ball schematics are assigned toc(432) zigzag components of the STM image, which reflect tuneling from thep* andp surface states.

FIG. 9. Spatial distribution of the electronic density of statesthe buckled dimers within62 V of the Fermi energy except thepandp* bands.~a! Filled states.~b! Empty states.D andU indicatethe lower and upper atoms of the buckled dimer, respectively.

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PRB 60 8169REINTERPRETATION OF THE SCANNING TUNNELING . . .

thermore, we can definitely state that the filled-state Simages taken at low bias are really observing the filled stanot the empty states. This is important because it excluthe possibility that the appearance of protrusion dimersserved at room temperature in the filled states at low biasedue to observing the empty states at negative surface biaa result of band bending.

Variation of the tip-surface distance with bias is anothpossible explanation for the dependence of the STM imaon bias. All of the STM images in Figs. 3 and 6 were takat a constant current, thus an increase in bias means acrease in the tunneling barrier height and the tip-surfacetance. Generally, an increase in the tip-surface distancesults in a decrease of resolution, which one might suspecbe the cause of the protrustion⇔bean ~room-temperature!,zigzag⇔bean transitions~low temperature! of the appear-ance of the dimers observed in the filled states. Howeverthis mechanism the phase shift observed in the empty scannot be explained. Furthermore, STM images taken atstant barrier height (13109 V) also show an identical transition shown in Figs. 3 and 6 at the same bias in the safashion. Strictly speaking, constant barrier height doesmean a constant tip-surface distance. Since the feedbacSTM is regulated to keep the tunneling current constantparticular bias, it is difficult to scan the surface with the satip-surface distance at different biases. Considering thfactors, we have compared STM images taken with a labarrier height~far from the surface! at low biases~21 V, 100pA! and with a small barrier height~close to the surface! athigh biases~22 V, 64 nA!. The STM images were basicallthe same, though somewhat of an increase of the zigzagchain component was observed at high bias. We did notserve complete zigzag chained dimers at high biases, thurule out the variation of tip-surface distance as the mcause of the dependence of STM images on bias.

C. Theoretical calculations

STM observations consistently show that tunneling frostates other than thep and p* surface states becomes important at high biases. In this section we briefly discusspossible states observed at high biases. As thep andp* arethe only localized surface states of the buckled dimers,have to consider the more extended surface resonancesthe bulk continuum states. We refer to the calculations cried out by Krugeret al.,17,18 where they have employedself-scattering theoretical method based on first principwhich is suited to calculate surface resonances extendilong range into the bulk. In their calculations, the back bo(B1) and dimer bond (D1 ,Di* ) states were shown to lieclose to thep andp* surface states in energy~look at Fig. 5in Ref. 18!. We assign them as the states observed by Sat high voltages.

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In order to give a rough idea of the spatial distributionsthese states, the spatial distribution of overlapped bawithin 62 V of the Fermi energy in the filled and emptstates, except thep andp* bands, was calculated. Standarformalism of first-principle calculations was employed witthe local-density approximation and plane-wave-based nlocal pseudopotentials with a cutoff energy of 10 Ry. Calclations were carried out on ac(432) supercell containing aslab of silicon ten layers thick geometrically optimized bRamstad9 with a vacuum region of five layers thickness.must be noted that the supercell technique is not suitedtreat surface resonances which extend into the bulk. Henin this paper, the aim of our calculation is to roughly esmate whether or not the spatial distribution of bands locanear to the Fermi energy, except thep and p* bands, issimilar to what was observed in the STM images at hibiases. Figure 9 shows the spatial distribution of states nthe Fermi energy except thep and p* bands. A strong in-tensity in the middle of the Si-Si dimer bond in the fillestates@Fig. 9~a!# is observed, while they are localized mainlbetween the dimer rows in the empty states@Fig. 9~b!#, incoincidence with the STM observations. In order to givemore detailed analysis, we have to calculate the surface renances with a more proper method or use a very deep cewhich the effect of the thickness of the cell becomes neggible. Also we have to simulate the STM images by combing the calculated electronic structures with the tunneliprobabilities. Matching STM images and theoretical calcutions would be an interesting subject for future work.

IV. CONCLUSIONS

This study has two important implications for future STMstudies on Si~100!. First, careful attention must be paid wheone observes the empty states and attempts to investigatelocations of absorbates; if the surface is probed at high biaunintentionally one would make an erroneous attributioAlso, it is important to use a low surface bias when obseing the filled states, particularly when studying absorbatessome extreme cases we have observed a surface which mics a perfect surface at22 V, but shows many defects at21V. These defects might influence the sites of adsorptionthe electronic characteristics. If the absorbates only influethe p and p* states, they might be even invisible at higbiases.

ACKNOWLEDGMENTS

This work was supported by the Shigekawa ProjectTARA, University of Tsukuba. The support of a Grant-inAid for Scientific Research from the Ministry of EducationScience and Culture of Japan is also acknowledged.

a,

*Electronic address: [email protected],[email protected] Wide Web: http://dora.ims.tsukuba.ac.jp

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