Thermal amplitudes of surface atoms on Si(111) 2×1 and Si(001) 2×1

Ol, Alerhand; Joannopoulos, J. D.; Ej, Mele

doi:10.1103/physrevb.39.12622

Cited by 22 publications

(16 citation statements)

References 24 publications

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“…In the above analysis both dimer atoms have the same isotropic vibration amplitude of ((w 2 >) 1/2 =0.12 A, a value found in other experiments [22] and matching theoretical calculations [23]. As demonstrated in a previous study [22], we can measure (u 2 ) from a systematic study of F versus temperature.…”

Section: Fe^p = E^( R 2+ri )/2 E -Mqhu 2 >Cos[^q _ Ar]mentioning

confidence: 67%

“…This result is both surprising and puzzling since previous experiment and theory indicate that vibration amplitudes should increase with increasing temperature, thereby decreasing F. In terms of the static model above, for F004 to increase the displacement Az must decrease significantly. Using (u 2 ) =0.042 A 2 at 500 °C, estimated from both theory [23] and experiment [22], Az=0.44 A at 500°C versus 0.55 A at room temperature. Using only this simple static model, this decrease in Az may indicate a phase transition at elevated temperatures from an asymmetric to symmetric (2x1) surface.…”

Section: Fe^p = E^( R 2+ri )/2 E -Mqhu 2 >Cos[^q _ Ar]mentioning

confidence: 99%

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Direct measurement of the asymmetric dimer buckling of Ge on Si(001)

1993

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The asymmetric or symmetric nature of the dimer adatom arrangement on reconstructed Si and Ge(001) surfaces is still controversial. There has not been a direct quantitative determination of the asymmetry. Using x-ray standing waves we have directly measured the asymmetry of Ge dimers on the Si(001) surface as 0.55 ±0.02 A. Our results unequivocally rule out the possibility of symmetric dimers. At elevated temperatures the dimer asymmetry decreases, raising the possibility of a high temperature asymmetric to symmetric phase transition on the (001) surfaces. PACS numbers: 68.55.Ce, 68.35.Bs, 81.10.Bk Since the earliest low-energy electron diffraction [l] (LEED) studies the detailed nature of the dimer adatom arrangement on the technologically important Si (001) surface has been studied intensively by all manner of surface probes [2][3][4][5] and techniques [6,7]. These studies have in turn stimulated sophisticated theoretical efforts [8-10] using ab initio total energy and molecular dynamics approaches [11,12] to locate the surface dimer positions and subsurface distortions. In spite of these efforts, ambiguities persist regarding the symmetric or asymmetric nature of surface dimers, particularly at room temperature.Scanning-tunneling-microscopy (STM) observations provide direct, though qualitative, information on the buckling of dimers on the Si(00l) surface. In earlier work, room temperature results showed [7] that roughly half the dimers were asymmetric, that is, the two dimer atoms were at different heights with respect to the surface. A recent low temperature STM study by Wolkow [13] shows that at room temperature asymmetric dimers are present near defects while a large part of the surface is covered with apparently symmetric dimers (both atoms at the same height). On cooling to low temperature (120 K) an increase of dimers in the asymmetric configuration is observed. It has been suggested that any symmetric appearance of dimers [13] is due to a rapid switching [14] of the dimer orientation in the up and down direction.On the experimental side, two questions need clarification: (a) What is the magnitude of the dimer asymmetry, if any, and (b) are the dimers at room temperature asymmetric or symmetric? In this Letter we describe a direct quantitative x-ray standing wave (XSW) measurement of the surface dimer displacement and asymmetry on the well-known Si(001)/Ge (2x1) reconstructed surface [15] at room temperature and, to our knowledge, we present the first characterization of the dimers at high temperatures. With suitable preparation, a monolayer of Ge atoms deposited by molecular beam epitaxy at high temperature onto a clean UHV Si(001) surface substitutes for the topmost Si adatoms, forming Ge dimers [16]. Although a Ge-substituted dimer surface is not a replica of either the bare Si(001) or Ge(001) surfaces, theoretical calculations [8,9,11,17] suggest that the adatom stability of both Si and Ge(001) surfaces is similar. Substituting Ge for the Si dimer atoms at the (001) surface does not perturb the obs...

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Section: Fe^p = E^( R 2+ri )/2 E -Mqhu 2 >Cos[^q _ Ar]mentioning

confidence: 67%

Section: Fe^p = E^( R 2+ri )/2 E -Mqhu 2 >Cos[^q _ Ar]mentioning

confidence: 99%

Direct measurement of the asymmetric dimer buckling of Ge on Si(001)

1993

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“…Figure 2 shows the x- To determine the Ga ad-dimer (L), we separate the measured coherent fraction into three factors fcH = CaHDH [16], where C is the Ga ordered fraction, aH is the Ga geometrical factor, and DH is the Ga Debye-Wailer factor. For the symmetric dimer cases illustrated in »g 1 a22o = Icos(m'L/2~22o)l By making the simplified assumption that the Ga thermal vibration amplitude is isotropic and equal to the value found for the Si(100) surface [18] ((u2)'/2 = 0.12 A), we can estimate that D400 = 0.86 and D220 = 0.93 for the Ga atoms. This D~oo value along with the measured value of f, 4po gives the measured value of the ordered fraction C = f,4pp/D~~= 0.63~0.06, since a400 = 1 for symmetric ad-dimers.…”

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confidence: 90%

Resolving the Ga Ad-Dimer Location and Orientation on the Si(100) Surface

et al. 1994

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Quantitative x-ray standing wave measurements of the Ga ad-dimer bond length, orientation, and location for the Si(100)-(2 x 2):Ga surface combined with first-principles molecular cluster calculations on four different ad-dimer models lead to the conclusion that Ga atoms form ad-dimers which are aligned parallel to the underlying Si dimers and lie in between Si dimer rows at the valley bridge site.

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“…Thermal amplitudes of silicon surface atoms with different surface orientations have been studied to show the anisotropic properties of vibrational amplitudes along different directions. 4 An ab initio study of silicon thin films has shown that the mechanical properties vary with the film thickness. 5 Using the local harmonic model, an augmented continuum theory has been proposed for the size dependence of the coefficient of thermal expansion of nanostructures.…”

Section: Introductionmentioning

confidence: 99%

Size and surface orientation effects on thermal expansion coefficient of one-dimensional silicon nanostructures

Zhao

Aluru

2009

Journal of Applied Physics

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We perform classical molecular dynamics simulations based on the Tersoff interatomic potential to investigate the size and surface orientation dependence of lattice constant and thermal expansion coefficient of one-dimensional silicon nanostructures. Three different surface orientations of silicon are considered, i.e., Si͑110͒, Si͑111͒, and Si͑100͒ with 2 ϫ 1 reconstruction. For each surface orientation, we investigate nanostructures with thicknesses ranging from 0.3 to 5.0 nm. We compute the vibrational amplitude of surface atoms, lattice constant, and thermal expansion coefficient as a function of size and temperature, and compare them for different surface orientations. An analytical expression is developed to compute the variation of the thermal expansion coefficient with size of the nanostructure.

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Thermal amplitudes of surface atoms on Si(111) 2×1 and Si(001) 2×1

Cited by 22 publications

References 24 publications

Direct measurement of the asymmetric dimer buckling of Ge on Si(001)

Direct measurement of the asymmetric dimer buckling of Ge on Si(001)

Resolving the Ga Ad-Dimer Location and Orientation on the Si(100) Surface

Size and surface orientation effects on thermal expansion coefficient of one-dimensional silicon nanostructures

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