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Peierls-like phase transitions in domain walls
Surface Science 606 (2012) 362–366
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Peierls-like phase transitions in domain walls Jedrzej Schmeidel, Herbert Pfnür, Christoph Tegenkamp ⁎ Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
a r t i c l e
i n f o
Article history: Received 10 August 2011 Accepted 21 October 2011 Available online 29 October 2011 Keywords: STM Domain wall Metal semiconductor interface Peierls transition
a b s t r a c t In this paper, we give an example how domain walls (DW) within p anffiffiffi adsorbed monolayer form onepffiffiffi dimensional localized electronic states. We investigated in detail the Ag 3 3 phase on Si (111), a prototype system for a low dimensional electron gas, by means of scanning tunneling microscopy. The doubling of the periodicity along the DW-direction at low temperatures (80 K) suggests a metal–insulator transition of Peierls type. The superimposed intensity modulation in the direction across the DW can be interpreted in terms of lateral quantum well states. However, the simultaneous vanishing of both features at room temperature indicates more complicated changes in band structure and/or wave functions during the transition than described by the simple Peierls model. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Grain boundaries have been intensively studied in the past. They are known to affect not only optoelectronic material properties at the meso and macroscale [1] but also to be decisive for elastic and mechanical properties [2]. The uniaxial extension of this kind of defect structure can favor directional electron [3] and even mass transport in solids [4,5], eventually promoting shunt currents and leading to failures of device structures, respectively. Microscopically, such large scale effects often start at grain boundary sites as the activation energies for transport are lower than at perfectly coordinated bulk sites. The two-dimensional analog are domain walls (DW) in adsorbed layers. On single crystals the periodic potential of the surface allows formation of commensurate or incommensurate superstructures, and the domain wall formation is the result of the combined action of adsorbate and substrate potentials. The simplest example for domain wall formation is island growth in commensurate superstructures, where the merging of the islands grown on different sublattices of the superstructure results in defect lines with particle densities deviating from the density in the islands. Particularly, rare gases physisorbed on metals or even insulating surfaces have been studied in detail in order to gain insight into the interplay of structural parameters in two dimensions [6,7,8]. In this study we concentrate on strongly metal/silicon systems. As we will show by pffiffiffi interacting pffiffiffi using Ag 3 3 superstructures grown on Si (111), the electronic structure of single grain boundaries become accessible. It is likely that such line defects may form electronic states that are split off from the two-dimensional (2D) band structure of the
⁎ Corresponding author. Fax: + 49 511 762 4877. E-mail address: [email protected] (C. Tegenkamp). 0039-6028/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2011.10.019
adsorbed layer, which then exhibit one-dimensional (1D) properties. A particularly interesting situation appears when wetting layers on semiconducting surfaces provide surface states that are modified by the adsorbed layer, but remain decoupled from the bulk states already for the 2D layer. Thus also domain wall states may be decoupled from bulk and provide a chance for studying 1D properties in this new type A good candidate for this situation seems pffiffiffi ofpsystem. ffiffiffi to p beffiffiffi the pffiffiffiAg 3 3 reconstruction on Si (111). While the perfect Ag 3 3 layer is semiconducting [9,10], already small concentrations of adatoms significantly increase the conductance and the system can be described by a nearly free electron gas. The band filling of the surface bands is crucial, since the filling factor plays a key role in stabilizing one dimensional structures, e.g. for metallic Au chains grown on vicinal Si (111) substrates [11]. Inevitably related to the low dimensional are instabilities pffiffiffi psystems ffiffiffi and phase transitions. For the 2D Ag 3 3 reconstruction on Si (111) a structural phase transitions has been observed and was interpreted in terms of a phase transition between a so-called inequivalent trimer model (IET) at low temperatures and the honeycomb chain trimer model (HCT). The assignment was supported by variable temperature STM measurements [12] and first principle calculations [13]. However, latest STM measurements suggest that the contrast of the two phases is rather induced by tip effects [14]. Metal–insulator transitions are very characteristic for quasi-1D systems. In this respect the ?(4 × 1)–(8 × 2) phase transition in In/Si (111) is the best studied system [15]. The metal–insulator transition around 130 K has been verified by surface transport [16]. pffiffiffi pffiffiffi In this paper we will focus on domain walls of the 3 ffiffiffi 3 phase pAg ffiffiffi p grown on Si (111). Although grain boundaries in Ag 3 3 structures have been identified as active scattering centers in surface transport measurements [17], only little attention has been paid to their electronic structure. Due to the fact that the length of the domain walls are comparatively short and are embedded in a semiconducting environment,
J. Schmeidel et al. / Surface Science 606 (2012) 362–366
the direct probing of the metallicity using transport measurements, is not possible. Instead, signatures of Peierls-distortions along the boundary and confinement effects in the perpendicular directions are analyzed here in detail by STM. 2. Experimental setup The experiments were performed in a UHV system working at a base pressure of 5 × 10 − 9. The system hosts a low energy electron diffraction (LEED) system in order to check the quality of the sample on a mesoscopic scale. Using a variable temperature scanning tunneling microscope (STM) the atomic structure has been investigated in detail. By heating the Si (111) sample with direct current, clean surfaces were obtained by flashing the sample to 1470 K and a well ordered (7 × 7) reconstruction was obtained after cooling the sample slowly to 1070 K. Ag was evaporated out of a molybdenum crucible using electronpbombardment. The coverage was calibrated on the basis of ffiffiffi pffiffiffi the Ag 3 3 reconstruction, which corresponds to exactly one physical monolayer [9]. 3. Results and discussion pffiffiffi pffiffiffi Ag 3 3 reconstructions obtained after deposition of around 1 ML at 770 K are shown in Fig. 1. As seen in the left part of this figure, even on the nominally flat surface, different height levels exist. They stem partly from atomic steps of the Si substrate (e.g. levels ‘2’ and ‘3’ in Fig. 1), but are also partly due to necessary restructuring during pffiffiffi pffiffiffi the transformation from Si (111)-(7 × 7) to the Ag 3 3 structure. According to the honeycomb chained triangle (HCT) model the Ag adatoms are located in this structure in threefold coordination coupled with formation of Si trimers [18,19]. The formation of Sitrimers requires removal of Si from the first Si bilayer pffiffiffi and pffiffiffi leads to the formation of hole-island pairs [20] so that Ag 3 3 patches emerge on different height levels (cf. with intensity levels ‘1’ and ‘2’). As a consequence of the bonding of one Ag atom per Si site, the
pffiffiffi pffiffiffi Fig. 1. The Ag 3 3 reconstruction on nominally flat (left) and regularly pffiffiffi stepped pffiffiffi (right) samples. The blue boxes mark domain boundaries between the Ag 3 3 island of same height. On narrow (111) terraces the domain walls grow predominantly along the 121 direction. Tunneling conditions: U = + 2 V, I = 0.5 nA, T = 80 K.
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pffiffiffi pffiffiffi valence band is filled completely. Thus the perfect Ag 3 3 reconstruction is semi-metallic [10]. In addition to the line defects associated with different heights on the surface, there are also bright lines visible in Fig. 1 (marked by boxes), which exist between island on the pffiffiffisame height. These obviously originate from stacking faults within the 3-structure, caused, e.g., by the merging of two islands during the growth pffiffiffiprocess. pffiffiffi They result in formation of domain walls (DW) between Ag 3 3 islands grown on the same Siterrace. Due to this nature, the mass density within the DW is different from the surrounding islands, leading to the formation of light or heavy domain walls, if the average particle concentration is smaller or higher than the perfectly ordered structure, respectively. This modified onedimensional (1D) particle density has direct consequences on the electronic properties of the DWs, and may lead to 1D states that pffiffiffielectronic pffiffiffi are split off from the 2D surface states of the Ag 3 3 structure. The DW itself appears both at low (80 K) and high substrate temperatures (300 K). Therefore, these DWs are different from those reported earlier [12], which were seen only at low temperatures due to formation of two inequivalent triangle (IET) domains. The domain boundaries shown directions, which seem to be energeticalin Fig. 1 appear only along 〈121〉 ly strongly favored over other possible orientations. In order to characterize these domain walls further, and especially to determine the characteristic shift vector, we zoomed-in into the DW regions. pffiffiffi pAn ffiffiffi image of such an area resolving more details within the Ag 3 3 unit cells is shown in Fig. 2. Clearly visible is the Ag
pffiffiffi pffiffiffi Fig. 2. (a) Atomically resolved Ag 3 3 structure with a domain wall running along the 121 direction. The dimerization visible along the DW will be discussed in more detail in context of Fig. 5. (b) Strongly Fourier filtered image of (a) in order to highlight theprelative ffiffiffi pffiffiffi shift of the unit cells. Please note that only the Fourier components of the Ag 3 3 structure have passed the filter. Therefore, the twofold periodicity along the DW has is not visible in this representation.
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reconstruction on both sides of the domain wall. In all cases investigated, the unit cells separated by the DW are shifted by one third of directions. Furthermore, as an imthe Ag unit length along the 〈121〉 portant finding in order to propose a reasonable pffiffiffi model, pffiffiffi the DW intersects the area, where the unit cells of both Ag 3 3 reconstructions overlap, clearly in the center. This comes out even more clearly by looking at the Fourier filtered image (Fig. 2b). Before we start to put these experimental findings into an atomic model for the DW structure, it should be emphasized that along the DW dimerization takes place. Please note, this is not obvious from the Fourier pffiffiffi filtered pffiffiffi image since higher order frequencies than that of the Ag 3 3 reconstruction were cut off. As will discuss in more detail below, the doubling is the signature for an instability typical for a metallic 1D chain. In order to propose a reasonable for these domain walls (DW), pffiffiffi model pffiffiffi the atomic structure of the Ag 3 3 unit cell has to be taken into account, which cannot be fully resolved by STM. Therefore, we try to establish a model on the basis of the HCT model and the experimental findings from above. According to the HCT model, the unit cell contains 3 Ag atoms at non-equivalent sites with respect to the Si substrate. Contrary to simplest domain wall models, where the DW would be formed pffiffiffiffiffion ffi equivalent → sublattices of the lattice gas, the shift, Δ a , by 1/3 of 3a (a =3.84 Å) direction does not correspond to a change between equivalong a 〈121〉 pffiffiffi pffiffiffi alent sublattices of the Ag 3 3 structure at the domain wall. For threefold coordinated sites, it corresponds to the change from an fcc to an hcp site, or – alternatively – to a rotation by 60∘, which is not allowed by a C3 symmetry operation. For the topmost Si trimers, e.g., this means that they are trimerized around T4 on one side of the DW, and on H3 positions on the other side [18]. For instance, the difference of the triangular structure visible in both domains in the highly Fourier filtered image (cf. with Fig. 2b) indicates this broken symmetry. However, this effect is small since all other bonding configurations within the topmost layer remain very similar after this shift. A p model ffiffiffi pof ffiffiffi the DW along the 〈121〉 direction → is shown Fig. 3, where the Ag 3 3 unit cells are shifted by Δ a along direction with respect to each other. the 〈121〉 This finding is quite surprising. It means on the one hand that the energetic differences between both types of domains must be very small. Indeed, the main difference concerns the Si-trimer structure relative to the third Si-layer, and this may be the reason why the energetic difference of these two configurations is small [21]. The energetic equivalence of hcp and fcc sites in our case clearly demonstrates that only the nearest neighbor interaction is decisive for this chemisorbed system. On the other hand, the energy of DW formation is
Fig. 3. Model of a domain wall along the 211 direction with the experimentally determined shift vector showing the (unrealistic) scenario where all Ag atoms are incorpo directions is shown. The gray rated into the DW. Only one of the three equivalent 〈121〉 (large) circles denote the Ag atoms, while the light gray (light brown) circles symbolize Si atoms in the first and second layer. Small dark gray (dark brown) circles denote Si in the third layer. The parallelograms mark the unit cells of the HCT-phases. Details of the arrangement of the Ag atoms (labels A,B,A′,B′) are explained in the text.
dominant in this case, and any other type of domain wall seems to be energetically highly unfavorable, in particular those that involve domains on equivalent sublattices. In particular, the domain wall model shown in Fig. 3 is the only one compatible with the positions of the domain wall relative to the Si trimers appearing as dark spots in Fig. 2. Only the atom density within the DW cannot be determined by STM since atomic details within the DW cannot be resolved. Furthermore, the atom density within the wall depends on p the Ag excess concentration ffiffiffi overall pffiffiffi with respect to the perfect Ag 3 3 structure. Depending on the exact coverage the model comprises even amphoelectric properties of the 1d structure. Because of the shifting of the unit cells deduced from the STM images, the center of the DW comprises a superposition of (AB…) and (A′B′…) chains as sketched schematically in Fig. 3. In the case of the unrealistic scenario that all Ag atoms are present (AA ′BB′A…), the unit cell along the DW would contain 5 Ag atoms in total. Thus, based on a simple band filling picture, the (AA′BB′A…) and (ABA…) configurations are expected to be semi-metallic, while the (AA′BA…) and (AA…) configurations should reveal metallic bands with filling factors close to one half. The latter configurations would correspond to heavy and light domain walls, respectively. In order to elucidate the nature of the DWs in more detail and to support the structural models from above, high resolution STM images were taken at different tunneling conditions and substrate temperatures. As an example, Fig. 4a shows a DW taken at −1 V at a tunneling current of 0.5 nA. As can be seen, at low temperatures (80 K) bright spots within the grain boundary appear. Moreover, at +2 V bias voltage the rearrangement of the atoms within DW is accompanied by intense shoulders (Fig. 4b). Interestingly, both the spatial variation of the intensity and the doubling vanishes at room temperature (Fig. 4c). As we will show in the following, the variation of the
Fig. 4. STM images (9:2 6:4 nm2 ) of the domain wall (DW) for different tunneling conditions and temperatures: a) 0.5 nA, − 1 V, 80 K, b) 0.25 nA, + 2 V, 80 K, c) 0.5 nA, + 2 V, 300 K. At 80 K the twofold reconstruction along the domain wall is clearly visible, which vanishes at 300 K. Line scans taken along the center of the boundary are presented in Fig. 5a.
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intensity along the directions perpendicular to the domain wall, is strongly dependent on the bias voltage, in contrast to the intensity modulation along the boundary. Thus, the former effect is an electronic effect, while the latter is caused by a reconstruction within the domain wall. Nonetheless, both effects are coupled with each other and, as it turns out, this coupling is important in order to see phase transitions in embedded 1d structures. The change in the periodicity along the DW comes out more clearly by taking line scans, as shown for different tunneling conditions in Fig. 5. At low temperatures pffiffiffi the pffiffiffiperiodicity seen is different from the lattice vector of the Ag 3 3 structure. The detailed analysis revealspaffiffiffispacing of 1.33 nm, which is exactly twice the periodicity of the 3-reconstruction shown in Fig. 3a. The reconstruction along the boundary is not dependent on the tunneling conditions. The corrugation of the chain structure varies between 0.8 Å at 1 V bias voltage and 0.5 Å at 1:5 V. Both for occupied and unoccupied states the twofold periodicity is seen. Therefore, the reconstruction is induced by a real lattice distortion rather than by hybridization effects of atomic orbitals. This lattice distortion vanishes at room temperature. The peak-to-peak separation pffiffiffi ispnow ffiffiffi 6.7 Å and matches perfectly with the periodicity of the Ag 3 3 reconstruction. Although we cannot directly measure the opening of a band gap within the already existing gap of Si by STM, the interpretation of the data is fully compatible with a Peierls-driven distortion, i.e. a metal–insulator transition due to an enhanced electron–phonon coupling along the chain, as sketched schematically in Fig. 5b [22]. Relying onp this ffiffiffi simple model, the doubling of the periodicity with respect to the 3 reconstruction means that the surface bands are semi-filled, in qualitative agreement with our geometric model of the domain wall (see Fig. 3). Assuming that the 1d system can be described also by a nearly free electron gas (NFEG), similar to the 2D pffiffiffi system pffiffiffi [10], the doubling of the periodicity with respect to the Ag p3ffiffiffi 3 reconstruction, corresponds to a Fermi vector kF ¼ π= 2 3a ¼ 0:24 Å (a = 3.84 Å), which implies an electron concentration of n1d ¼ 2kF =π ¼ 1:5 107 cm1 . The excess Ag atoms at the grain boundary should therefore be responsible for about 0.58 electrons per Si-site. It should be noted, however, that the perfect 1d scenario of the domain wall is only seen at low temperatures where the appearance of the signatures of the metallic 1d state is closely related to the confinement in the perpendicular direction. This more complicated situation invalidates the simple electron counting rules just applied, which require rigid bands (see below). Therefore, quantitative
Fig. 5. a) Line scans taken along the grain boundary. The scans are shifted for better visibility. In contrast to the measurement taken atp 300 the line scans taken at 80 K reffiffiffi K, pffiffiffi veal a twofold periodicity with respect to the Ag 3 3 reconstruction. This finding is not dependent on the bias voltage. b) Illustration of a Peierls-driven metal–insulator transition: Below TP the doubling within the chain is associated with a gap opening for half-filled bands. Above TP the chain switches back into a metallic state.
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deviations must be expected. On the other hand, confinement along the DW, as seen for instance for Cu wires of finite length [23] plays no role in our case. The intensity variation in STM as a function of bias voltage and temperature, mentioned above, occurs simultaneously in both directions. In contrast to the corrugation seen along the defect line, the corrugation is much larger in the direction across the DW, and depends sensitively on the bias voltages. As we will show in the following, this finding can be rationalized by confinement of the 1d metallic chain structure in its perpendicular direction. A sequence of images of the DW for positive and negative bias conditions at a tunneling current of 0.25 nA is shown in Fig. 6a. Qualitatively, scans taken at 0.1 nA and at 0.5 nA tunneling current show the same features, indicating that the spatial distribution of the intensity in the vicinity does not depend on the tip-sample distance. From line scans taken along the dashed lines shown in Fig. 6a, which intersect a maximum in the chain structure, it is obvious that particularly for positive bias voltages the pffiffiffi p ffiffiffi domain walls appear more intense than the surrounding Ag 3 3. The corrugation amplitude is more than 1 Å. While one maximum is seen at +1 V and 1.5 V, at + 2 V even two maxima become apparent. At + 2.5 V again the line defect is imaged as a trench. Generally, unoccupied states are spatially more extended. Therefore, effects of confinement can be observed more easily with these states. The line scans were taken in constant current mode. Consequently, the intensity reflects only indirectly the density of states. Although dI/dV measurements with high bias resolution have not been performed, it turns out that the intensity variation can be explained by the confinement of the electron gas and formation of electronic subbands, in analogy to Pt/Ge (100) [24,25], e.g. if we identify the large single peak at +1 V and the double peak structure at + 2 V with resonances of the n = 1 and n = 2 states, we obtain within the model of a
Fig. 6. a) Sequence of STM images (12 6 nm2 ) for different bias voltages. STM images were taken at T = 80 K, I = 0.25 nA. b) The dashed lines are guides to the eye inporder ffiffiffi pto ffiffiffi elucidate the bias dependent intensity modulation with respect to the Ag 3 3 reconstruction.
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parabolic (infinitely high) potential well an effective width of the well to be around 1 nm. This matches qualitatively with the width of the trench. Of course this is only a rough estimate, but it rationalizes the pronounced variation of the intensity distribution. For a quantitative treatment of the quantum well states (QWS) high resolution dI/dV mappings are necessary. QWS of higher order have not been found. These states are obviously not any more confined by the potential of the DW. However, the energy of the n = 2 state is, despite its comparatively high energy, still confined, although the unoccupied states pffiffiffi of pffiffiffithe domain boundary are in resonance with those of the Ag 3 3 structure. It is important to note that confinement with clear resonances takes place only in the low-temperature Peierls state, similarly to Pt chains on Ge (100) [24,25], whereas at room temperature no resonances are observed, but only an increased intensity at the DW, reflecting the higher DOS within the domain wall. This first of all implies that the rigid band model shown in Fig. 5b is too simple, since localization in the low-temperature phase can only be explained by a shift of bands and/or a change in symmetry of the wave functions involved. Apparently, only within the Peierls state of the chain, the confinement effect is enabled since pffiffiffi the pffiffiffi1d bands cannot hybridize with the band structure of the Ag 3 3 reconstruction. 4. Summary Temperature and bias voltage dependent STM measurements have revealed that localized 1D electronic properties can be obtained pffiffiffi pffiffiffi at domain boundaries in the monolayer of silver forming a Ag 3 3 structure. The peculiar properties found here may be related to the special kind of broken symmetry of the domain walls under investigation, which involve also the substrate-overlayer-symmetry coupled with the change of positions of Si trimers around T4 to H3 positions. Typical 1D properties are found, including in particular the period doubling along the DW at low temperatures. While the qualitative behavior can be explained within the framework of a Peierls distortion, the 1D properties, i.e. the confinement of electronic states in the direction perpendicular to the DW seems to be strongly coupled with this phase transition. This reflects electronic changes coupled with the phase transition that are not described within the simple Peierls
model, but are a combined effect of the existing 3D lateral interactions. Obviously, also the symmetry of the wave functions is an important parameter in order to conserve 1d electronic properties of embedded 1d structures. Acknowledgment We thank gratefully the Deutsche Forschungsgemeinschaft for financial support. References [1] Y.A. Vlasov, V.N. Astratov, A.V. Baryshev, A.A. Kaplyanskii, O.Z. Karimov, M.F. Limonov, Phys. Rev. E 61 (2000) 5784. [2] J. Karch, R. Birringer, H. Gleiter, Nature 330 (1987) 556. [3] J. Rivnay, L.H. Jimison, J.E. Northrup, M.F. Toney, R. Noriega, S. Lu, T.J. Marks, A. Facchetti, A. Salleo, Nat. Mat. 8 (2009) 952. [4] K. Kemmochi, K.I. Hirano, Thin Solid Films 25 (1975) 353. [5] J.E. Sanchez Jr., O. Kraft, E. Arzt, Appl. Phys. Lett. 61 (1992) 3121. [6] C. Ramseyer, C. Girardet, J. Chem. Phys. 103 (1995) 5767. [7] L.W. Bruch, R.D. Diehl, J.A. Venables, Rev. Mod. Phys. 79 (2007) 1381. [8] C. Schwennike, J. Schimmelpfennig, H. Pfnür, Phys. Rev. B 48 (1993) 8928. [9] Y. Nakajima, S. Takeda, T. Nagao, S. Hasegawa, X. Tong, Phys. Rev. B 56 (1997) 6782. [10] J.N. Crain, M.C. Gallagher, J.L. McChesney, M. Bissen, F.J. Himpsel, Phys. Rev. B 72 (2005) 045312. [11] J.N. Crain, et al., Phys. Rev. B 69 (2004) 125401. [12] N. Sato, T. Nagao, S. Hasegawa, Surf. Sci. 442 (1999) 65. [13] H. Aizawa, M. Tsukada, N. Sato, S. Hasegawa, Surf. Sci. 429 (1999) L509. [14] H.M. Zhang, J.B. Gustafsson, L.S.O. Johansson, J. Physics: Conf. Series 61 (2006) 1336. [15] S. Wippermann, W.G. Schmidt, Phys. Rev. Lett. 105 (2010) 126102. [16] T. Tanikawa, I. Matsuda, T. Kanagawa, S. Hasegawa, Phys. Rev. Lett. 93 (2004) 016801. [17] I. Matsuda, C. Liu, T. Hirahara, M. Ueno, T. Tanikawa, T. Kanagawa, R. Hobara, S. Yamazaki, S. Hasegawa, K. Kobayashi, Phys. Rev. Lett. 99 (2007) 146805. [18] K.J. Wan, X.F. Lin, J. Nogami, Phys. Rev. B 47 (1993) 13700. [19] Y.G. Ding, C.T. Chan, K.M. Ho, Phys. Rev. Lett. 67 (1991) 1454. [20] A. Shibata, K. Takayanagi, Jpn. J. Appl. Phys. 32 (1993) 1385. [21] W. Chen, Corresponding DFT calculations of both HTC models are underway (2012). [22] R. Peierls, Oxford University Press. 1967 [23] S. Fölsch, P. Hyldgaard, R. Koch, K.H. Ploog, Phys. Rev. Lett. 92 (2004) 056803. [24] A. van Houselt, N. Oncel, B. Poelsema, H.J.W. Zandvliet, Nano Lett. 6 (2006) 1439. [25] N. Oncel, A. van Houselt, J. Huijben, A.-S. Hallbäck, O. Gurlu, H.J.W. Zandvliet, B. Poelsema, Phys. Rev. Lett. 95 (2005) 116801.
Contents lists available at SciVerse ScienceDirect
Surface Science journal homepage: www.elsevier.com/locate/susc
Peierls-like phase transitions in domain walls Jedrzej Schmeidel, Herbert Pfnür, Christoph Tegenkamp ⁎ Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
a r t i c l e
i n f o
Article history: Received 10 August 2011 Accepted 21 October 2011 Available online 29 October 2011 Keywords: STM Domain wall Metal semiconductor interface Peierls transition
a b s t r a c t In this paper, we give an example how domain walls (DW) within p anffiffiffi adsorbed monolayer form onepffiffiffi dimensional localized electronic states. We investigated in detail the Ag 3 3 phase on Si (111), a prototype system for a low dimensional electron gas, by means of scanning tunneling microscopy. The doubling of the periodicity along the DW-direction at low temperatures (80 K) suggests a metal–insulator transition of Peierls type. The superimposed intensity modulation in the direction across the DW can be interpreted in terms of lateral quantum well states. However, the simultaneous vanishing of both features at room temperature indicates more complicated changes in band structure and/or wave functions during the transition than described by the simple Peierls model. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Grain boundaries have been intensively studied in the past. They are known to affect not only optoelectronic material properties at the meso and macroscale [1] but also to be decisive for elastic and mechanical properties [2]. The uniaxial extension of this kind of defect structure can favor directional electron [3] and even mass transport in solids [4,5], eventually promoting shunt currents and leading to failures of device structures, respectively. Microscopically, such large scale effects often start at grain boundary sites as the activation energies for transport are lower than at perfectly coordinated bulk sites. The two-dimensional analog are domain walls (DW) in adsorbed layers. On single crystals the periodic potential of the surface allows formation of commensurate or incommensurate superstructures, and the domain wall formation is the result of the combined action of adsorbate and substrate potentials. The simplest example for domain wall formation is island growth in commensurate superstructures, where the merging of the islands grown on different sublattices of the superstructure results in defect lines with particle densities deviating from the density in the islands. Particularly, rare gases physisorbed on metals or even insulating surfaces have been studied in detail in order to gain insight into the interplay of structural parameters in two dimensions [6,7,8]. In this study we concentrate on strongly metal/silicon systems. As we will show by pffiffiffi interacting pffiffiffi using Ag 3 3 superstructures grown on Si (111), the electronic structure of single grain boundaries become accessible. It is likely that such line defects may form electronic states that are split off from the two-dimensional (2D) band structure of the
⁎ Corresponding author. Fax: + 49 511 762 4877. E-mail address: [email protected] (C. Tegenkamp). 0039-6028/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2011.10.019
adsorbed layer, which then exhibit one-dimensional (1D) properties. A particularly interesting situation appears when wetting layers on semiconducting surfaces provide surface states that are modified by the adsorbed layer, but remain decoupled from the bulk states already for the 2D layer. Thus also domain wall states may be decoupled from bulk and provide a chance for studying 1D properties in this new type A good candidate for this situation seems pffiffiffi ofpsystem. ffiffiffi to p beffiffiffi the pffiffiffiAg 3 3 reconstruction on Si (111). While the perfect Ag 3 3 layer is semiconducting [9,10], already small concentrations of adatoms significantly increase the conductance and the system can be described by a nearly free electron gas. The band filling of the surface bands is crucial, since the filling factor plays a key role in stabilizing one dimensional structures, e.g. for metallic Au chains grown on vicinal Si (111) substrates [11]. Inevitably related to the low dimensional are instabilities pffiffiffi psystems ffiffiffi and phase transitions. For the 2D Ag 3 3 reconstruction on Si (111) a structural phase transitions has been observed and was interpreted in terms of a phase transition between a so-called inequivalent trimer model (IET) at low temperatures and the honeycomb chain trimer model (HCT). The assignment was supported by variable temperature STM measurements [12] and first principle calculations [13]. However, latest STM measurements suggest that the contrast of the two phases is rather induced by tip effects [14]. Metal–insulator transitions are very characteristic for quasi-1D systems. In this respect the ?(4 × 1)–(8 × 2) phase transition in In/Si (111) is the best studied system [15]. The metal–insulator transition around 130 K has been verified by surface transport [16]. pffiffiffi pffiffiffi In this paper we will focus on domain walls of the 3 ffiffiffi 3 phase pAg ffiffiffi p grown on Si (111). Although grain boundaries in Ag 3 3 structures have been identified as active scattering centers in surface transport measurements [17], only little attention has been paid to their electronic structure. Due to the fact that the length of the domain walls are comparatively short and are embedded in a semiconducting environment,
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the direct probing of the metallicity using transport measurements, is not possible. Instead, signatures of Peierls-distortions along the boundary and confinement effects in the perpendicular directions are analyzed here in detail by STM. 2. Experimental setup The experiments were performed in a UHV system working at a base pressure of 5 × 10 − 9. The system hosts a low energy electron diffraction (LEED) system in order to check the quality of the sample on a mesoscopic scale. Using a variable temperature scanning tunneling microscope (STM) the atomic structure has been investigated in detail. By heating the Si (111) sample with direct current, clean surfaces were obtained by flashing the sample to 1470 K and a well ordered (7 × 7) reconstruction was obtained after cooling the sample slowly to 1070 K. Ag was evaporated out of a molybdenum crucible using electronpbombardment. The coverage was calibrated on the basis of ffiffiffi pffiffiffi the Ag 3 3 reconstruction, which corresponds to exactly one physical monolayer [9]. 3. Results and discussion pffiffiffi pffiffiffi Ag 3 3 reconstructions obtained after deposition of around 1 ML at 770 K are shown in Fig. 1. As seen in the left part of this figure, even on the nominally flat surface, different height levels exist. They stem partly from atomic steps of the Si substrate (e.g. levels ‘2’ and ‘3’ in Fig. 1), but are also partly due to necessary restructuring during pffiffiffi pffiffiffi the transformation from Si (111)-(7 × 7) to the Ag 3 3 structure. According to the honeycomb chained triangle (HCT) model the Ag adatoms are located in this structure in threefold coordination coupled with formation of Si trimers [18,19]. The formation of Sitrimers requires removal of Si from the first Si bilayer pffiffiffi and pffiffiffi leads to the formation of hole-island pairs [20] so that Ag 3 3 patches emerge on different height levels (cf. with intensity levels ‘1’ and ‘2’). As a consequence of the bonding of one Ag atom per Si site, the
pffiffiffi pffiffiffi Fig. 1. The Ag 3 3 reconstruction on nominally flat (left) and regularly pffiffiffi stepped pffiffiffi (right) samples. The blue boxes mark domain boundaries between the Ag 3 3 island of same height. On narrow (111) terraces the domain walls grow predominantly along the 121 direction. Tunneling conditions: U = + 2 V, I = 0.5 nA, T = 80 K.
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pffiffiffi pffiffiffi valence band is filled completely. Thus the perfect Ag 3 3 reconstruction is semi-metallic [10]. In addition to the line defects associated with different heights on the surface, there are also bright lines visible in Fig. 1 (marked by boxes), which exist between island on the pffiffiffisame height. These obviously originate from stacking faults within the 3-structure, caused, e.g., by the merging of two islands during the growth pffiffiffiprocess. pffiffiffi They result in formation of domain walls (DW) between Ag 3 3 islands grown on the same Siterrace. Due to this nature, the mass density within the DW is different from the surrounding islands, leading to the formation of light or heavy domain walls, if the average particle concentration is smaller or higher than the perfectly ordered structure, respectively. This modified onedimensional (1D) particle density has direct consequences on the electronic properties of the DWs, and may lead to 1D states that pffiffiffielectronic pffiffiffi are split off from the 2D surface states of the Ag 3 3 structure. The DW itself appears both at low (80 K) and high substrate temperatures (300 K). Therefore, these DWs are different from those reported earlier [12], which were seen only at low temperatures due to formation of two inequivalent triangle (IET) domains. The domain boundaries shown directions, which seem to be energeticalin Fig. 1 appear only along 〈121〉 ly strongly favored over other possible orientations. In order to characterize these domain walls further, and especially to determine the characteristic shift vector, we zoomed-in into the DW regions. pffiffiffi pAn ffiffiffi image of such an area resolving more details within the Ag 3 3 unit cells is shown in Fig. 2. Clearly visible is the Ag
pffiffiffi pffiffiffi Fig. 2. (a) Atomically resolved Ag 3 3 structure with a domain wall running along the 121 direction. The dimerization visible along the DW will be discussed in more detail in context of Fig. 5. (b) Strongly Fourier filtered image of (a) in order to highlight theprelative ffiffiffi pffiffiffi shift of the unit cells. Please note that only the Fourier components of the Ag 3 3 structure have passed the filter. Therefore, the twofold periodicity along the DW has is not visible in this representation.
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reconstruction on both sides of the domain wall. In all cases investigated, the unit cells separated by the DW are shifted by one third of directions. Furthermore, as an imthe Ag unit length along the 〈121〉 portant finding in order to propose a reasonable pffiffiffi model, pffiffiffi the DW intersects the area, where the unit cells of both Ag 3 3 reconstructions overlap, clearly in the center. This comes out even more clearly by looking at the Fourier filtered image (Fig. 2b). Before we start to put these experimental findings into an atomic model for the DW structure, it should be emphasized that along the DW dimerization takes place. Please note, this is not obvious from the Fourier pffiffiffi filtered pffiffiffi image since higher order frequencies than that of the Ag 3 3 reconstruction were cut off. As will discuss in more detail below, the doubling is the signature for an instability typical for a metallic 1D chain. In order to propose a reasonable for these domain walls (DW), pffiffiffi model pffiffiffi the atomic structure of the Ag 3 3 unit cell has to be taken into account, which cannot be fully resolved by STM. Therefore, we try to establish a model on the basis of the HCT model and the experimental findings from above. According to the HCT model, the unit cell contains 3 Ag atoms at non-equivalent sites with respect to the Si substrate. Contrary to simplest domain wall models, where the DW would be formed pffiffiffiffiffion ffi equivalent → sublattices of the lattice gas, the shift, Δ a , by 1/3 of 3a (a =3.84 Å) direction does not correspond to a change between equivalong a 〈121〉 pffiffiffi pffiffiffi alent sublattices of the Ag 3 3 structure at the domain wall. For threefold coordinated sites, it corresponds to the change from an fcc to an hcp site, or – alternatively – to a rotation by 60∘, which is not allowed by a C3 symmetry operation. For the topmost Si trimers, e.g., this means that they are trimerized around T4 on one side of the DW, and on H3 positions on the other side [18]. For instance, the difference of the triangular structure visible in both domains in the highly Fourier filtered image (cf. with Fig. 2b) indicates this broken symmetry. However, this effect is small since all other bonding configurations within the topmost layer remain very similar after this shift. A p model ffiffiffi pof ffiffiffi the DW along the 〈121〉 direction → is shown Fig. 3, where the Ag 3 3 unit cells are shifted by Δ a along direction with respect to each other. the 〈121〉 This finding is quite surprising. It means on the one hand that the energetic differences between both types of domains must be very small. Indeed, the main difference concerns the Si-trimer structure relative to the third Si-layer, and this may be the reason why the energetic difference of these two configurations is small [21]. The energetic equivalence of hcp and fcc sites in our case clearly demonstrates that only the nearest neighbor interaction is decisive for this chemisorbed system. On the other hand, the energy of DW formation is
Fig. 3. Model of a domain wall along the 211 direction with the experimentally determined shift vector showing the (unrealistic) scenario where all Ag atoms are incorpo directions is shown. The gray rated into the DW. Only one of the three equivalent 〈121〉 (large) circles denote the Ag atoms, while the light gray (light brown) circles symbolize Si atoms in the first and second layer. Small dark gray (dark brown) circles denote Si in the third layer. The parallelograms mark the unit cells of the HCT-phases. Details of the arrangement of the Ag atoms (labels A,B,A′,B′) are explained in the text.
dominant in this case, and any other type of domain wall seems to be energetically highly unfavorable, in particular those that involve domains on equivalent sublattices. In particular, the domain wall model shown in Fig. 3 is the only one compatible with the positions of the domain wall relative to the Si trimers appearing as dark spots in Fig. 2. Only the atom density within the DW cannot be determined by STM since atomic details within the DW cannot be resolved. Furthermore, the atom density within the wall depends on p the Ag excess concentration ffiffiffi overall pffiffiffi with respect to the perfect Ag 3 3 structure. Depending on the exact coverage the model comprises even amphoelectric properties of the 1d structure. Because of the shifting of the unit cells deduced from the STM images, the center of the DW comprises a superposition of (AB…) and (A′B′…) chains as sketched schematically in Fig. 3. In the case of the unrealistic scenario that all Ag atoms are present (AA ′BB′A…), the unit cell along the DW would contain 5 Ag atoms in total. Thus, based on a simple band filling picture, the (AA′BB′A…) and (ABA…) configurations are expected to be semi-metallic, while the (AA′BA…) and (AA…) configurations should reveal metallic bands with filling factors close to one half. The latter configurations would correspond to heavy and light domain walls, respectively. In order to elucidate the nature of the DWs in more detail and to support the structural models from above, high resolution STM images were taken at different tunneling conditions and substrate temperatures. As an example, Fig. 4a shows a DW taken at −1 V at a tunneling current of 0.5 nA. As can be seen, at low temperatures (80 K) bright spots within the grain boundary appear. Moreover, at +2 V bias voltage the rearrangement of the atoms within DW is accompanied by intense shoulders (Fig. 4b). Interestingly, both the spatial variation of the intensity and the doubling vanishes at room temperature (Fig. 4c). As we will show in the following, the variation of the
Fig. 4. STM images (9:2 6:4 nm2 ) of the domain wall (DW) for different tunneling conditions and temperatures: a) 0.5 nA, − 1 V, 80 K, b) 0.25 nA, + 2 V, 80 K, c) 0.5 nA, + 2 V, 300 K. At 80 K the twofold reconstruction along the domain wall is clearly visible, which vanishes at 300 K. Line scans taken along the center of the boundary are presented in Fig. 5a.
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intensity along the directions perpendicular to the domain wall, is strongly dependent on the bias voltage, in contrast to the intensity modulation along the boundary. Thus, the former effect is an electronic effect, while the latter is caused by a reconstruction within the domain wall. Nonetheless, both effects are coupled with each other and, as it turns out, this coupling is important in order to see phase transitions in embedded 1d structures. The change in the periodicity along the DW comes out more clearly by taking line scans, as shown for different tunneling conditions in Fig. 5. At low temperatures pffiffiffi the pffiffiffiperiodicity seen is different from the lattice vector of the Ag 3 3 structure. The detailed analysis revealspaffiffiffispacing of 1.33 nm, which is exactly twice the periodicity of the 3-reconstruction shown in Fig. 3a. The reconstruction along the boundary is not dependent on the tunneling conditions. The corrugation of the chain structure varies between 0.8 Å at 1 V bias voltage and 0.5 Å at 1:5 V. Both for occupied and unoccupied states the twofold periodicity is seen. Therefore, the reconstruction is induced by a real lattice distortion rather than by hybridization effects of atomic orbitals. This lattice distortion vanishes at room temperature. The peak-to-peak separation pffiffiffi ispnow ffiffiffi 6.7 Å and matches perfectly with the periodicity of the Ag 3 3 reconstruction. Although we cannot directly measure the opening of a band gap within the already existing gap of Si by STM, the interpretation of the data is fully compatible with a Peierls-driven distortion, i.e. a metal–insulator transition due to an enhanced electron–phonon coupling along the chain, as sketched schematically in Fig. 5b [22]. Relying onp this ffiffiffi simple model, the doubling of the periodicity with respect to the 3 reconstruction means that the surface bands are semi-filled, in qualitative agreement with our geometric model of the domain wall (see Fig. 3). Assuming that the 1d system can be described also by a nearly free electron gas (NFEG), similar to the 2D pffiffiffi system pffiffiffi [10], the doubling of the periodicity with respect to the Ag p3ffiffiffi 3 reconstruction, corresponds to a Fermi vector kF ¼ π= 2 3a ¼ 0:24 Å (a = 3.84 Å), which implies an electron concentration of n1d ¼ 2kF =π ¼ 1:5 107 cm1 . The excess Ag atoms at the grain boundary should therefore be responsible for about 0.58 electrons per Si-site. It should be noted, however, that the perfect 1d scenario of the domain wall is only seen at low temperatures where the appearance of the signatures of the metallic 1d state is closely related to the confinement in the perpendicular direction. This more complicated situation invalidates the simple electron counting rules just applied, which require rigid bands (see below). Therefore, quantitative
Fig. 5. a) Line scans taken along the grain boundary. The scans are shifted for better visibility. In contrast to the measurement taken atp 300 the line scans taken at 80 K reffiffiffi K, pffiffiffi veal a twofold periodicity with respect to the Ag 3 3 reconstruction. This finding is not dependent on the bias voltage. b) Illustration of a Peierls-driven metal–insulator transition: Below TP the doubling within the chain is associated with a gap opening for half-filled bands. Above TP the chain switches back into a metallic state.
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deviations must be expected. On the other hand, confinement along the DW, as seen for instance for Cu wires of finite length [23] plays no role in our case. The intensity variation in STM as a function of bias voltage and temperature, mentioned above, occurs simultaneously in both directions. In contrast to the corrugation seen along the defect line, the corrugation is much larger in the direction across the DW, and depends sensitively on the bias voltages. As we will show in the following, this finding can be rationalized by confinement of the 1d metallic chain structure in its perpendicular direction. A sequence of images of the DW for positive and negative bias conditions at a tunneling current of 0.25 nA is shown in Fig. 6a. Qualitatively, scans taken at 0.1 nA and at 0.5 nA tunneling current show the same features, indicating that the spatial distribution of the intensity in the vicinity does not depend on the tip-sample distance. From line scans taken along the dashed lines shown in Fig. 6a, which intersect a maximum in the chain structure, it is obvious that particularly for positive bias voltages the pffiffiffi p ffiffiffi domain walls appear more intense than the surrounding Ag 3 3. The corrugation amplitude is more than 1 Å. While one maximum is seen at +1 V and 1.5 V, at + 2 V even two maxima become apparent. At + 2.5 V again the line defect is imaged as a trench. Generally, unoccupied states are spatially more extended. Therefore, effects of confinement can be observed more easily with these states. The line scans were taken in constant current mode. Consequently, the intensity reflects only indirectly the density of states. Although dI/dV measurements with high bias resolution have not been performed, it turns out that the intensity variation can be explained by the confinement of the electron gas and formation of electronic subbands, in analogy to Pt/Ge (100) [24,25], e.g. if we identify the large single peak at +1 V and the double peak structure at + 2 V with resonances of the n = 1 and n = 2 states, we obtain within the model of a
Fig. 6. a) Sequence of STM images (12 6 nm2 ) for different bias voltages. STM images were taken at T = 80 K, I = 0.25 nA. b) The dashed lines are guides to the eye inporder ffiffiffi pto ffiffiffi elucidate the bias dependent intensity modulation with respect to the Ag 3 3 reconstruction.
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parabolic (infinitely high) potential well an effective width of the well to be around 1 nm. This matches qualitatively with the width of the trench. Of course this is only a rough estimate, but it rationalizes the pronounced variation of the intensity distribution. For a quantitative treatment of the quantum well states (QWS) high resolution dI/dV mappings are necessary. QWS of higher order have not been found. These states are obviously not any more confined by the potential of the DW. However, the energy of the n = 2 state is, despite its comparatively high energy, still confined, although the unoccupied states pffiffiffi of pffiffiffithe domain boundary are in resonance with those of the Ag 3 3 structure. It is important to note that confinement with clear resonances takes place only in the low-temperature Peierls state, similarly to Pt chains on Ge (100) [24,25], whereas at room temperature no resonances are observed, but only an increased intensity at the DW, reflecting the higher DOS within the domain wall. This first of all implies that the rigid band model shown in Fig. 5b is too simple, since localization in the low-temperature phase can only be explained by a shift of bands and/or a change in symmetry of the wave functions involved. Apparently, only within the Peierls state of the chain, the confinement effect is enabled since pffiffiffi the pffiffiffi1d bands cannot hybridize with the band structure of the Ag 3 3 reconstruction. 4. Summary Temperature and bias voltage dependent STM measurements have revealed that localized 1D electronic properties can be obtained pffiffiffi pffiffiffi at domain boundaries in the monolayer of silver forming a Ag 3 3 structure. The peculiar properties found here may be related to the special kind of broken symmetry of the domain walls under investigation, which involve also the substrate-overlayer-symmetry coupled with the change of positions of Si trimers around T4 to H3 positions. Typical 1D properties are found, including in particular the period doubling along the DW at low temperatures. While the qualitative behavior can be explained within the framework of a Peierls distortion, the 1D properties, i.e. the confinement of electronic states in the direction perpendicular to the DW seems to be strongly coupled with this phase transition. This reflects electronic changes coupled with the phase transition that are not described within the simple Peierls
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