Surface Science 605 (2011) L13–L15

Contents lists available at ScienceDirect

Surface Science

j ourna l homepage: www.e lsev ie r.com/ locate /susc

Instability of one-dimensional dangling-bond wires on H-passivated C(001), Si(001),and Ge(001) surfaces

Jun-Ho Lee, Jun-Hyung Cho ⁎Department of Physics and Research Institute for Natural Sciences, Hanyang University, 17 Haengdang-Dong, Seongdong-Ku, Seoul 133-791, Republic of Korea

⁎ Corresponding author. Tel.: +82 2 2220 0915; fax:E-mail address: chojh@hanyang.ac.kr (J.-H. Cho).

1 C. Bai, Scanning tunneling microscopy and its appliYork, 2000), and references therein.

2 P. Rodgers, Nanoscience and Technology (World Scie3 R. E. Peierls, Quantum Theory of Solids, Oxford Clas

Press, Oxford, 2001).4 H. A. Jahn and E. Teller, Proc. R. Soc. London, Ser. A5 R. Arita, Y. Suwa, K. Kuroki, and H. Aoki, Phys. Rev.6 S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950); J.

1154 (1963).7 J. W. Lyding, T.-C. Shen, J. S. Hubacek, J. R. Tucker, G

2010 (1994).8 T.-C. Shen, C. Wang, G. C. Abeln, J. R. Tucker, J. W.

Walkup, Science 268, 1590 (1995).9 M. C. Hersam, N. P. Guisinger and J. W. Lyding, J

(2000).

0039-6028/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.susc.2011.01.011

a b s t r a c t

a r t i c l e i n f o

Article history:Received 20 November 2010Accepted 6 January 2011Available online 14 January 2011

Keywords:Density functional calculationsSurface electronic phenomena

We investigate the instability of one-dimensional dangling-bond (DB) wires fabricated on the H-terminated C(001), Si(001), and Ge(001) surfaces by using density-functional theory calculations. The three DB wires arefound to show drastically different couplings between charge, spin, and lattice degrees of freedom, resultingin an insulating ground state. The C DB wire has an antiferromagnetic spin coupling between unpaired DBelectrons, caused by strong electron–electron interactions, whereas the Ge DBwire has a strong charge-latticecoupling, yielding a Peierls-like lattice distortion. For the Si DB wire, the antiferromagnetic spin ordering andthe Peierls instability are highly competing with each other. The physical origin of such disparate features inthe three DB wires can be traced to the different degree of localization of 2p, 3p, and 4p DB orbitals.

+82 2 2295 6868.

cations (Springer Verlag, New

ntific, Singapore, 2009).sics Series (Oxford University

161, 220 (1937).Lett. 88, 127202 (2002).M. Luttinger, J. Math. Phys. 4,

. C. Abeln, Appl. Phys. Lett. 64,

Lyding, Ph. Avouris and R. E.

. Vac. Sci. Technol. A18, 1349

10 T. Hitosugi, S. HKawazoe, T. Hasegaw11 S. Watanabe, Y.(1996).12 C. F. Bird and D.13 J. Y. Lee, J.-H. Ch

l rights reserved.

© 2011 Elsevier B.V. All rights reserved.

Scanning tunneling microscope (STM) has been a powerful tool notonly for investigating thephysical, chemical, and electronic properties ofsurfaces, but also to create atomic-scale structures that play animportant role in the development of a future nanotechnology.1 Atommanipulation can be achieved by a precise control of interactionsbetween the STM tip and the adsorbed atom on surfaces, therebyfabricating various nanostructures such as quantum dots and quantumwires.2 It is of crucial importance to understand the underlying physicsof such quantized low-dimensional systems for the application to novelnanoelectronic devices. Especially, the confinement of electrons in one-dimensional (1D) systems provides many exotic physical phenomenasuch as Peierls instability,3 Jahn–Teller distortion,4 spin polarization5 orthe formation of non-Fermi-liquid ground states.6

Recently, a variant of hydrogen resist STM nanolithographytechnique, termed feedback controlled lithography,7,8,9 was used to

generate 1D arrays of individual dangling bonds (DBs) by the selectiveremoval of H atoms from an H-passivated Si(001) surface along oneside of an Si dimer row.10 This technique can be extended to fabricatethe same 1D arrays on the H-passivated C(001) and Ge(001) surfaces.Such fabricated DB wires have a single DB per atom, offering quasi-1Dmetallic systems with a half-filled DB state, crossing the Fermi level.As stated by Peierls in the 1950s,3 those quasi-1D metals may beunstable against metal-insulator transition, where electrons and holesnear the Fermi level often couple strongly with a lattice vibration,thereby resulting in formations of a charge density wave (CDW) andan electron band gap at the Fermi level.11 However, it was recentlyproposed12,13 that the Si DB wire exhibits the preference of theantiferromagnetic (AF) ordering rather than the Peierls instability.

In this work, using first-principles density-functional calculations,we demonstrate that the three DB wires fabricated on the H-passivated C(001), Si(001), and Ge(001) surfaces undergo a metal-insulator transition, driven by drastically different couplings betweencharge, spin, and lattice degrees of freedom. We find that in the C DBwire [see Fig. 1(a)], the strong electron–electron interactions give riseto the preference of the AF spin coupling between unpaired DBelectrons, while in the Si DB wire, the stability of the AF spin orderingis weakened but still favored over the Peierls model. However, the GeDB wire is found to show a significant preference for the Peierlsinstability [see Fig. 1(b)] that exhibits alternating up and down

eike, T. Onogi, T. Hashizume, S. Watanabe, Z.-Q. Li, K. Ohno, Y.a, and K. Kitazawa, Phys. Rev. Lett. 82, 4034 (1999).A. Ono, T. Hashizume, and Y. Wada, Phys. Rev. B 54, R17308

R. Bowler, Surf. Sci. 531, L351 (2003).o and Z. Zhang, Phys. Rev. B 80, 155329 (2009).

a b

Fig. 1.Optimized structure of the DBwires on H-terminated (a) C(001) and (b) Ge(001)surfaces. For distinction, the atoms composing the DB wires are drawnwith dark colors.The side view of the Ge DB wire is also given in the inset of (b).

0

50

B)

AFFM

NM

L14 J.-H. Lee, J.-H. Cho / Surface Science 605 (2011) L13–L15SURFACESCIEN

CE

LETTERS

vertical displacements of the Ge atoms composing the DB wire,accompanying a charge transfer from the down to the up Ge atom. Ouranalysis shows that the on-site electron−electron interactionsdecrease in strength as the sequence of CNSiNGe DB wires due tothe different degree of localization of 2p, 3p, and 4p DB orbitals, whilethe strength of electron-lattice coupling decreases as the reversedsequence.

The total-energy and force calculations were performed usingnon spin-polarized or spin-polarized density functional theory14

within the generalized-gradient approximation.15 The C (Si, Ge, andH) atom is described by ultrasoft16 (norm-conserving17) pseudo-potentials. The surface was modeled by a periodic slab geometry.The slab for the C DB wire consists of twelve C atomic layers, wherethe upper and bottom sides are passivated by one H atomic layerto have an inversion symmetry. However, the slab for the Si orGe DB wire contains six atomic layers plus one passivating Hatomic layer, where the bottom side is terminated by two Hatoms per Si or Ge atom. We simulated the DB wires of infinitelength by using a 4×1 or 4×2 unit cell that includes two dimerrows perpendicular to the wire direction. The electronic wavefunctions were expanded in a plane-wave basis set with a cutoffof 25 Ry. The k-space integration was done with sixteen (eight)points in the surface Brillouin zone of the 4×1 (4×2) unit cell.The present calculational scheme has been successfully appliedfor the adsorption of various molecules on the C(001), Si(001), andGe(001)surfaces.18

We first determine the atomic structures of the C, Si, and Ge DBwires within the nonmagnetic (NM), ferromagnetic (FM), and AFconfigurations. Here, the NM configuration is based on the Peierlsmodel where the surface atoms composing the DB wire are displacedup and down alternatively.11 To obtain the energy gains caused byPeierls distortion andmagnetic orderings, we calculate the energies ofthe NM, FM, and AF configurations relative to the non-distorted NMconfiguration (designated as NM0) where each atom composing theDB wire is constrained to have an identical height. The results for thethree DB wires are plotted in Fig. 2. We find that for the C and Si DB

14 P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham,Phys. Rev. 140, A1133 (1965).15 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).16 D. Vanderbilt, Phys. Rev. B 41, 7892 (1990); K. Laasonen, A. Pasquarello, R. Car, C.Lee, and D. Vanderbilt, Phys. Rev. B 47, 10142 (1993).17 N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991).18 J.-H. Cho, L. Kleinman, K.-J. Jin and K.S. Kim, Phys. Rev. B (2002) 66, 113306, J.-H.Cho and L. Kleinman, Phys. Rev. B (2003) 68, 195413, J.-H. Choi and J.-H. Cho, Phys.Rev. Lett. (2007) 98, 246101; 102, 166102 (2009).

wires, the AF configuration is more stable than the NM and FM ones,whereas for the Ge DB wire, the NM configuration with a Peierlsdistortion is the most stable. Note that the AF configuration has anundistorted structure [see Fig. 1(a)], indicating the absence of spin-Peierls instability.

As shown in Fig. 2, the energy gain arising from a Peierls distortionis 46 and 116 meV/DB for the Si and Ge DB wires, respectively.However, the C DB wire does not show a Peierls distortion, indicatingthat the electronic energy gain obtained by the charge redistributioncannot prevail over the larger elastic energy cost of a lattice distortion.On the other hand, the energy gain caused by the AF spin ordering is132, 53, and 35 meV/DB for the C, Si, and Ge DB wires, respectively.We note that the FM configuration is less stable than the AF one by 31,58, and 70 meV/DB for the C, Si, and Ge DB wires, respectively (seeFig. 2). Thus, we can say that the C DB wire significantly favors the AFspin coupling between DB electrons, while the Ge DBwire exhibits thePeierls instability driven by a strong electron-lattice coupling.However, for the Si DB wire, the AF spin ordering is only 7 meVmore favored over the Peierls instability, indicating that the electron–electron and electron–lattice interactions are highly competing witheach other.

Fig. 3 shows the electronic band structures for the NM (or NM0)and AF configurations of the C, Si, and Ge DB wires. In the NM0

configuration, a surface band due to the DB electrons is found to crossthe Fermi level at an almost midpoint of the symmetry line ΓJ, yieldinga half-filled band [see the S state in Fig. 3(a)]. This half-filled DB statehas band widths of 1.04, 0.75, and 0.63 eV for the C, Si, and Ge DBwires, respectively. It is noticeable that the AF spin ordering splits thehalf-filled DB band into two subbands (S1 and S2) where the indirectband gap (Egap) is as large as 1.37, 0.55, and 0.43 eV for the C, Si, andGe DB wires, respectively. On the other hand, the Peierls instabilityopens Egap=0.32 and 0.62 eV for the Si and Ge DB wires, respectively.Thus, for the C and Si DB wires, the electronic energy gain due to theAF energy gap is greater than that of the Peierls gap (zero in the C DBwire), whereas for the Ge DB wire, the former is smaller than thelatter. These different features of the electronic band structuresbetween the AF and NM configurations give rise to an AF ground statefor the C and Si DB wires and a NM ground state for the Ge DB wire.

It is noteworthy that the different degree of localization of 2p, 3p,and 4pDB orbitals should influence the strength of electron–electronand electron–lattice interactions in the three DB wires. In the case ofthe C DB wire, the highly localized 2p orbital enhances moreeffectively the electron–electron interactions, giving rise to thepreference of the AF spin ordering. However, in the Ge DB wire, therather delocalized 4p orbital is likely to facilitate the electron-latticecoupling, producing the Peierls instability. The different degree oflocalization of DB orbitals can be seen from their charge and spin

-150

-100

-50

C Si

ΔE(m

eV/D

Ge

Fig. 2. Calculated energies (per dangling bond) of the NM, FM, and AF configurationsrelative to the NM0 configuration for the C, Si, and Ge DB wires.

a

b

c

Γ J Γ J

Γ J Γ J

Γ J Γ J

-1

0

1

Ene

rgy

(eV

)

-1

0

1

Ene

rgy

(eV

)

-1

0

1

Ene

rgy

(eV

)

AFNM0

S

S1

S2

NM AF

AFNM

S1

S2

S1

S2

S1

S2

S1

S2

Fig. 3. Calculated band structures for the (a) C, (b) Si, and (c) Ge DBwires within the NMandAF configurations. The energy zero represents the Fermi level. The direction of ΓJ line isalong theDBwire. The solid lines represent the subbands due to theDBelectrons. In theAFconfiguration, the subbands of themajority andminority spins are equal to eachother. Thecharge or spin characters of subbands at the J point are also given. The plots are drawn inthe vertical plane containing themaximummagnitude of charge or spin density. In the AFconfiguration, the solid (dotted) line represents the majority (minority) spin density. Thefirst contour line and the line spacings are the same as 0.005 electrons/bohr3.

L15J.-H. Lee, J.-H. Cho / Surface Science 605 (2011) L13–L15

SURFACESCIENCE

LETTERS

characters in Fig. 3. It is notable that the NM configuration of the Siand Ge DB wires shows a charge transfer from the down to the upatoms, representing a CDW formation. On the other hand, the AFconfiguration of the three DB wires involves an opposite spinorientation between adjacent dangling bonds, as shown in Fig. 3.

To examine how the on-site electron–electron interactions varyamong the three DB wires, we evaluate the Hubbard correlationenergy U by using the constrained DFT calculations.19 Here, wesimulate one minority-electron transfer from the S1 state to the S2state in the AF configuration and calculate the change in the totalenergy. We obtain U=3.45, 1.71, and 1.36 eV for the C, Si, and Ge DBwires, respectively. This sequence of U corresponds to that of thelocalization degree of 2pN3pN4p DB orbitals. We note that the valuesof U are significantly larger than the electron hopping parametert=1.04, 0.75, and 0.63 eV, which are estimated from the bandwidthof the corresponding NM0 configuration. Thus, it is most likely that therelatively larger ratio of U/t=3.32 (2.28) in the C (Si) DB wire givesrise to the preference of the AF spin ordering rather than a CDWformation.

The physics of the C, Si, and Ge DB wires could be described by theso-called Peierls–Hubbard (PH)20 Hamiltonian. In the U→∞ limit, thePH model can be converted to the Heisenberg spin-Peierls21,22 model,which becomes the Heisenberg Hamiltonian if the spin-Peierls effectswere ignored. Noting that the C DB wire has a larger value of Uwithout the spin-Peierls effects, its AF spin ordering may be welldescribed by the Heisenberg Hamiltonian. On the other hand, if theeffect of U were ignored, the PH model becomes the Peierls modelwhich describes properly the Peierls-like distortion in the Ge DB wire.The detailed model analysis will be done in our future work.

In summary, we demonstrated drastically different features ofelectron–electron and electron–lattice interactions in 1D DB wiresfabricated on the H-terminated C(001), Si(001), and Ge(001)surfaces, caused by the different degree of localization of 2p, 3p, and4p DB orbitals. We found that the C DB wire prefers the AF spinordering due to strong electron–electron interactions, the Ge DB wireshows a Peierls-like lattice distortion with a strong charge-latticecoupling, whereas the Si DB wire shows a high competition betweenthe electron–electron and electron–lattice interactions. These dispa-rate electronic properties of the C, Si, and Ge DB wires might be apromising perspective for the design of nanoelectronic devices forstorages and processing of quantum information on the three typicalsemiconductor surfaces.

Acknowledgement

This work was supported by the National Research Foundation ofKorea (NRF) grant funded by the Korean Government (KRF-314-2008-1-C00095 and KRF-2009-0073123).

19 V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. T. Czyżyk and G. A. Sawatzky, Phys.Rev. B 48, 16929 (1993).20 D. K. Campbell, J. T. Gammel, and E. Y. Loh, Jr., Phys. Rev. B 42, 475 (1990).21 E. Pytte, Phys. Rev. B 10, 4637 (1974).22 W. Barford and R. J. Bursill, Phys. Rev. Lett. 95, 137207 (2005).