Dynamics and Energetics of Reconstruction at the Si(100) Surface

Article pubs.acs.org/JPCC

Dynamics and Energetics of Reconstruction at the Si(100) Surface Chun-Sheng Guo,*,†,‡ Klaus Hermann,‡ and Yong Zhao†,§ †

Key Laboratory of Advanced Technology of Materials (Ministry of Education), Superconductivity and New Energy R&D Center, Southwest Jiaotong University, Chengdu, P. R. China ‡ Department of Inorganic Chemistry, Fritz-Haber-Institut der MPG, Faradayweg 4-6, D-14195 Berlin, Germany § School of Materials Science and Engineering, University of New South Wales, Sydney, 2052 NSW, Australia ABSTRACT: In experiments the reconstructed Si(100) surface shows silicon dimers pointing along the [011] direction. However, the origin of the dimer formation is still unclear. Our theoretical studies on dynamics and energetics show that the reconstruction process depends crucially on the initial local surface morphology: starting from different local tilting scenarios various reconstruction domains can appear as a result of thermal excitation. Molecular dynamics simulations show that c(4 × 2) and asymmetric p(2 × 1) reconstructions can appear quite easily while p(2 × 2) domains are less likely to be found even though they are energetically favorable. The latter is consistent with experimental findings of p(2 × 2) domains being observed quite rarely. The simulations show further that spontaneous dimer-flipping in asymmetric p(2 × 1) domains is possible at about 100 K and driven by the stress within the aligned atoms below the tilted dimers. This can result in a transition to c(4 × 2) reconstruction which is consistent with this reconstruction dominating in experiments above 80 K.

1. INTRODUCTION Geometric and electronic properties of the Si(100) surface have been intensively studied in the past decades due to its importance for many silicon devices grown on this surface.1−11 11 Different reconstruction patterns have been observed for Si(100) surfaces where, historically, the first was identified by low-energy electron diffraction (LEED) to yield a p(2 × 1) pattern.1 Later, c(4 × 2) reconstruction was also found in LEED experiments.2 The symmetric p(2 × 1) reconstruction, called s-p(2 × 1) in the following, is described by parallel buckled Si dimers of the topmost layer and was first observed by scanning tunneling microscopy (STM) at room temperature (RT).3 Today, the c(4 × 2) reconstruction is widely accepted as the ground state geometry of the Si(100) surface, and it is the dominant component observed in low-temperature STM experiments at 120 K.4 However, for temperatures below 40 K domains with also asymmetric p(2 × 1) reconstruction, called a-p(2 × 1) in the following, as well as p(2 × 2) and c(4 × 2) reconstructed domains were observed to coexist in STM experiments.5−7 Theoretical studies showed that the p(2 × 2) reconstruction of the Si(100) surface is energetically close to c(4 × 2) with an energy difference of only about 0.002 eV/dimer, and it is lower by 0.02 eV/dimer compared with a-p(2 × 1) reconstruction.8 However, the p(2 × 2) reconstruction has been observed later in experiments at very low temperatures,7,9 and the amount of p(2 × 2) domains was found to be much smaller than that of the other reconstructions. The frequently observed s-p(2 × 1) is suggested by theory to be unstable and assumed as a time average of p(2 × 2) and c(4 × 2) reconstructions.8,10 However, recent STM measurements near 7 K suggest that the apparent s-p(2 × 1) pattern is just a fake image of the c(4 × 2) © XXXX American Chemical Society

reconstruction measured at high bias voltage, because the surface contribution of Si 3px surface states can hybridize with the 3pz states in the STM junction.11 Questions as to the structure and dynamics of the apparently simple Si(100) surface still remain unclear, such as why is the p(2 × 2) reconstruction found more rarely than the other reconstructions in experiments although it is energetically favorable? Why does the a-p(2 × 1) reconstruction disappear and leave only one dominant reconstruction pattern, c(4 × 2), at elevated temperature whereas a-p(2 × 1), p(2 × 2), and c(4 × 2) domains coexist at very low temperature? What is the basic mechanism of the apparent s-p(2 × 1) reconstruction at room temperature? These questions will be addressed in the present work. In section 2, we introduce the models and discuss details of the computational methods. Section 3 presents results and discussion. Finally, Section 4 summarizes our conclusions.

2. THEORETICAL DETAILS We performed total energy and molecular dynamics (MD) calculations using the SIESTA12,13 computer code which is based on density functional theory (DFT) and localized linearcombination-of-numerical-atomic-orbital (LCAO) basis sets for the description of valence electrons in addition to normconserving nonlocal pseudopotentials adopted for the atomic core. The pseudopotentials are constructed using the Trouiller and Martins scheme to describe the valence electron interaction Received: September 9, 2014 Revised: October 8, 2014

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dx.doi.org/10.1021/jp509095t | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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with the atomic core.14 The nonlocal components of the pseudopotential are expressed by the fully separable scheme of Kleinman and Bylander.15 To explore geometry details of the different reconstructions, the local density approximation (LDA) exchange-correlation16 is employed together with double-ζ-plus-polarization (DZP) basis sets in both optimization calculations and molecular dynamics (MD) simulations. The geometric equilibrium structures are obtained with repeated slab models which are periodic along the [011] and [01̅1] directions with a two-dimensional 4 × 6 supercell, allowing for 2 × 6 [011] oriented dimers (see Figure 1). The

those obtained earlier.8,17,18 As an example, the bond length between the two atoms in a Si dimer of the a-p(2 × 1) reconstructed surface is found to yield 2.30 Å which is quite close to 2.26 Å reported earlier.8 The deviations in the optimized geometry are explained by the use of larger basis sets and energy cutoffs in the present work, while the same exchange-correlation functional as before, LDA, is applied.8,18 Figure 2 shows the different geometric structure of a Si dimer

Figure 1. Side (a) and top (b) view of a 4 × 6 slab of the Si(100) surface with a-p(2 × 1) dimer reconstruction on the surface. Up/down dimer atoms are shown by red/blue balls, and the first and second Si bulk layer atoms are marked in green and dark while those of the lower bulk are shown in lighter gray. Saturator hydrogen at the bottom is represented by white balls. This color scheme will be adopted throughout the paper.

Figure 2. Side and top views of geometric structures of surface dimers with two bulk layer underneath taken from the a-p(2 × 1), p(2 × 2), and c(4 × 2). All bond lengths and angles are average values. Distances are given in Å units.

three-dimensional unit cell of this slab contains 168 Si atoms, 7 Si layers with 24 atoms each. Further, an additional layer of 48 H atoms is arranged at the bottom of the slab to saturate dangling bonds of the Si atoms at the lower boundary. The vacuum thickness between adjacent slabs along [001] is set at 15 Å. Conjugate gradient optimizations are performed to fully relax the slab structure until a force tolerance of 0.01 eV/Å is reached. This model is also used to study the buckling of paired atoms in the dimer layer dependent on various initial scenarios, see section 3.1. The optimized a-p(2 × 1), p(2 × 2), and c(4 × 2) reconstructions obtained with this model serve also as starting points of MD simulations based on classical equations of motion to describe surface dimer flipping, see section 3.2. The integration is performed in time steps of 2 fs, and 3000 time steps are collected for subsequent statistical analyses. In all calculations, the H atoms and their binding Si layer at the slab bottom are fixed. In Figure 1 this model is shown with an a-p(2 × 1) reconstruction with a color scheme used throughout this paper. In the following, we denote the complete set of dimer atoms as a dimer layer, while the Si layer underneath is considered as the first Si bulk layer and the next as the second. In order to obtain some statistical information on buckling at the initial steps starting from the unreconstructed Si(100) surface, see section 3.1, we considered also a larger model in our MD simulations. This consists of a two-dimensional 8 × 8 supercell of the bulk-terminated Si(100) surface such that 4 × 8 [011] oriented dimers can buckle. It is composed of 448 Si atoms, 7 Si layers with 64 atoms each, and additional layer of 128 H atoms at the bottom to saturate dangling bonds of the Si atoms at the lower boundary.

and the first bulk layer atoms underneath obtained by the optimizations of the a-p(2 × 1), p(2 × 2), and c(4 × 2) for a horizontal (left) and perpendicular view (right). For the a-p(2 × 1) reconstruction the tilting angle is found to be 14.5° with a bond length between the dimer atoms of 2.30 Å, while separation of the upper and lower dimer atoms (red and blue balls) from nearest atoms in the first bulk layer amounts to 2.39 and 2.33 Å, respectively. For the p(2 × 2) and c(4 × 2) reconstructed Si(100) surfaces, the tilting angles are found to yield 17.2° and 17.3° with dimer bond lengths of 2.39 and 2.43 Å, respectively. The structure within the dimer layer has been fully studied, while only few theoretical investigations paid attention to the geometric structure of the first Si bulk layer which may also participate in the surface reconstruction. As shown in the righthand side of Figure 2, including also information on the first Si bulk layer (atoms in green), the geometry of the first bulk layer of a-p(2 × 1) reconstruction is identical with that in the bulk, 3.85 Å between one pair of atoms bonding to a dimer atom; in contrast, for p(2 × 2) and c(4 × 2) interatomic distances between atoms in pairs binding to the lower dimer atom differ by 0.44 and 0.47 Å from that bonding to the upper dimer atom in the [011̅ ] direction, respectively. The explanation of these structural differences is obvious: Si atoms in the first bulk layer below the parallel tilted dimers of the a-p(2 × 1) reconstruction are forced to be aligned by the rigid boundary constraint of the crystal bulk whereas they can relax below the alternately tilted dimers of the p(2 × 2) and c(4 × 2). Their geometry differences compared with the first bulk layer are consistent with the energy differences: the calculated total energies of the p(2 × 2) and c(4 × 2) reconstruction are quite similar9 with

3. RESULTS AND DISCUSSION 3.1. Initial Geometry-Dependent Reconstructions. Overall, the results obtained in our simulation are close to B



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the [011] direction and arranged along [01̅1]. This leads to disordered buckling where adjacent dimers in the neighboring dimer row along [01̅1] tend to tilt parallel to each other resembling an a-p(2 × 1)-like reconstruction. Finally, structure (d) starts with two adjacent parallel dimers tilted wrt. the [011] direction and arranged along [011]. This results also in disordered tilting characterized as a mixture of a-p(2 × 1) and p(2 × 2) reconstructions. Obviously, an initially tilted Si dimer will preferably induce oppositely tilted dimers in its neighborhood along [01̅1] rows, resulting in alternate tilt along [01̅1]. The dynamical process can be understood as steric repulsion between adjacent dimers which is enhanced by the lateral relaxation of Si atoms of the first bulk layer, see Figure 4a, b: The first bulk layer atoms below the initial dimers deform in response to the dimer tilt and afterward drive neighboring dimers to buckle in the opposite orientation. The dependence of dimer formation on the initial dimers along [011] is more complex: Two adjacent dimers oppositely tilted, see model (a), induce an opposite dimer tilt along the [011] direction, while parallel tilted dimers, separated by an unreconstructed Si pair (model (b)) or adjacent (model (c)), induce parallel dimer tilt along [011]. These results can be also understood by the deformation and dynamics within the two bulk layers, as shown in Figure 4. The adjacent atoms bonding to the down/up dimer atom move further/closer from each other in the bulk first layer, respectively. In model (a), the two initial dimers are adjacent and oppositely tilted, leading to strong and localized deformation in the first bulk layer, so that atoms in the second bulk layer move parallel to those in the first bulk layer. Consequently, the deformed geometry in the first bulk layer results in dimer tilt to the opposite orientation wrt. [011]. In model (b) and (c), the deformation of the first bulk layer induced by the initial dimers is rather small and the atoms in the second bulk layer remain in their original positions. Two atoms in the first bulk layer rotate slightly around the second bulk layer atom (shown by a black dot) to which they bind. This induces a parallel tilt wrt. [011] relating to a-p(2 × 1) and p(2 × 2) reconstructions. In model (d), atoms in the first bulk layer prefer to align along the [011] direction under parallel initial dimers. This leads to a-p(2 × 1) reconstruction with the initial dimers. However, tilted atoms in the first bulk layer are more favorable energetically (like those in p(2 × 2) and c(4 × 2)) than aligned ones without further constraints, and alternate tilt appears far away from the initial dimers. At the very beginning of dimer formation at an unreconstructed Si (100) surface, atoms in random pairs are expected to move close to each other and buckle into dimers. To explore these initial dynamics of dimer formation, we performed MD simulations starting from an 8 × 8 unreconstructed surface at 10, 80, and 160 K (additional calculations near the three temperatures were performed for statistical reasons). The speed of the surface atoms at a finite temperature follows the Boltzmann distribution, which is close to the pseudorandom speed distribution used in the MD simulations. Therefore, the surface morphologies in the MD runs can unravel the dimer formation process although the conclusion could be rough due to the small model used. In these MD runs around 30% of the surface atoms become tilted dimers within the first 150 fs. These dimers buckled initially are randomly ordered but can be classified within 4 × 4 domains according to models (a)−(d). The corresponding results are collected in Table 1. Apparently, the data based on two tilted

differences of only 0.003 eV/dimer, while the energy of the ap(2 × 1) reconstruction is higher by 0.02 eV/dimer. It implies the structure of the first bulk layer can be a determining factor of their stabilities, as will be discussed in section 3.2. The energetic differences are so small that coexisting domains of the three reconstruction types can be expected at a Si(100) surface. This contrasts with the experimental result that the p(2 × 2) reconstruction is only rarely observed7,9 and the a-p(2 × 1) reconstruction at low temperature disappears which leaves a dominant c(4 × 2) reconstruction at temperatures between 80 and 200 K.4 To explain these findings we performed MD simulations starting from a clean unreconstructed Si(100) surface. These simulations show Si atoms in pairs moving close to each other and buckling into dimers which can be explained as saturating dangling surface bonds. During this process, it is observed that dimers buckled in initially have a powerful influence over the followed reconstruction: atoms in the bulk layers (especially in the first bulk layer) are displaced due to stress induced by the tilt dimers and afterward dominate the tilt orientations of the buckling dimer around them. To examine further details, we start from a 4 × 6 supercell of the unreconstructed Si(100) surface with two adjacent tilted dimers and optimize the complete surface without constraints. The results of the final buckling structures are shown in Figure 3 (only atoms of the

Figure 3. Perspective view of initial (left) and optimized structures (right) resulting from differently buckled and arranged Si dimer pairs at the Si(100) surface, (a) adjacent dimers with opposite tilt, (b) dimers with parallel tilt separated by an unreconstructed Si pair, (c) adjacent dimers with parallel tilt, and (d) dimers with parallel tilt at larger separation, see text.

dimer and the first two bulk layers are shown). Structure (a) starts with two adjacent dimers oppositely tilted wrt. [011] and arranged along the [01̅1] direction. After optimization a perfect c(4 × 2) reconstruction is produced. Structure (b) starts with two parallel dimers tilted wrt. [011] and arranged along the [01̅1] direction where the tilted dimers are separated by an unreconstructed Si pair. This results in a perfect p(2 × 2) reconstruction with an alternating dimer tilt along [01̅1]. Structure (c) starts with two adjacent parallel dimers tilted wrt. C



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Figure 4. Dynamics in the first bulk layer (right) starting with differently buckled and arranged Si dimer pairs (left) in top view. Model (a)−(d) (left) are also shown in Figure 3 in side view. Arrows indicate the corresponding movement directions. The color coding of the atom balls is that of Figure 1, and the triangles mark the atoms in the first bulk layer bonding to the tilted dimers.

each stage, starting from equilibrium structures, 3000 time steps are collected for subsequent statistical analyses. At low temperature, 40 K, dimers only vibrate in these models and no dimer flipping occurs. When the MD temperature is increased to 100 K, dimer-flipping is observed at the a-p(2 × 1) surface and yields a higher-order reconstruction. As the MD temperature increases to 160 K, we find the initial a-p(2 × 1) changing to a (4 × 2) reconstructed surface except for few domains of a-p(2 × 1) remaining which reveals the phase transition. In contrast, p(2 × 2) and c(4 × 2) remained unchanged even when MD temperatures rise to 300 K. The phase transition can be directly pictured by examining the evolution of the vibrations of three adjacent dimers within six a-p(2 × 1) dimers along the [011̅ ] direction, as shown Figure 5a, where δz is the height difference between the up and down dimer atoms. Curve α represents the vibration of a dimer without flipping while curves β and γ show dimers next to it being flipped. Clearly, the identically tilted dimers of the starting structure change to alternating dimers after the MD runs for about 1.5 ps. In detail, δz shows positions of the three neighboring dimers which are vibrating around the 0.6 Å, associated with an a-p(2 × 1) reconstruction, within the first 0.4 ps. In the next 1 ps, dimer β and γ flip (δz becomes negative) and |δz| shifts to 0.7 Å associated with that of c(4 × 2). The arrows in Figure 5a denote the occurrence of dimer flipping once the δz value is less than about 0.2 Å. The flipped dimers are preserved over the next 4 ps (only 2 ps dynamics is shown in Figure 5), suggesting a stable c(4 × 2) phase at this temperature. Aligned atoms in the first bulk layer below the tilted dimers are less favorable energetically than tilted ones like those in p(2 × 2) and c(4 × 2), which results in the instability of the a-p(2 × 1) reconstruction. The spontaneous dimer-flipping of a-p(2 × 1) at low temperatures must originate from the stress release within the first bulk layer. This can be shown by following vibration evolution of a flipped dimer and its four neighboring atoms of the first bulk layer. As shown in Figure 5b, Dab (distance between adjacent atom a and b labeled in the figure) and Dcd are identical in the beginning and δx(a, b) and δx(c, d) are both zero, according to the geometry of an a-p(2 × 1) reconstruction. In the first 0.4 ps curve β shows an a-p(2 × 1) dimer with δz vibrating near 0.6 Å (cp. Figure 5a) while δx(a, b) and δx(c, d) both vibrate near 0.0 Å. When simultaneous flipping of dimer β occurs distance Dab becomes larger than Dcd,

Table 1. Starting from an Unreconstructed Si(100) Surface, Percentages of Dimers Which Buckled in the First 150 fs of the MD Time Roughly Classified According to Models (a)− (d) within 4 × 4 Domains at Different Temperatures model

10 K

80 K

160 K

a b c d

∼40−45% ∼5% ∼30−40% ∼10−15%

∼50−60% ∼5% ∼20−30% ∼5%

∼50−60% ∼5% ∼20−30% ∼5%

dimers in 4 × 4 domains are far from a complete consideration of reconstruction dependence on the initial surface scenarios. Nevertheless, the approximate results provide already some meaningful information: most of the dimers formed in the first 150 fs could be assigned to model (a) and (c) while only few to model (b) or (d). This suggests that the p(2 × 2) reconstruction is difficult to obtain on the Si(100) surface at all temperatures which is consistent with the experimental findings that p(2 × 2) has been observed only rarely7,9 although it is energetically favorable. On the other hand, our simulations also imply the buckling strongly depends on neighboring environments. Therefore, one can imagine surface defects should strongly affect the buckling of the adjacent dimers, which means the results collected in Table 1 will be dramatically changed near the surface defects, and consequently various domains of reconstructions are usually found near the defects. 3.2. Spontaneous Dimer Flipping in a-p(2 × 1) above 100 K. The results shown above suggest a probability of a-p(2 × 1) reconstructed domains appearing at different temperatures. This agrees with STM observations at very low temperatures,5−7 but is not compatible with the experimental results at temperatures of 80 K when c(4 × 2) becomes the dominant reconstruction.4 A possible issue related to the disappearance of a-p(2 × 1) is its instability associated with the energy barrier of a dimer flipping. It has been proposed that the energy involved in flipping an isolated dimer is around 0.09 eV.19 However, experimental results imply that a phase transition from an a-p(2 × 1) to a c(4 × 2) reconstruction could occur around 120 K (0.01 eV in thermal energy), much lower than the theoretical energy barrier. To explain these findings we performed MD simulations with ideal a-p(2 × 1), p(2 × 2), and c(4 × 2) models at 40, 100, 160, and 300 K. At D



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4. CONCLUSION In this study we have performed energetics and dynamics calculations for dimer formation and dimer flipping at the Si(100) surface using density-functional theory methods. Dimer formation starting from an unreconstructed Si(100) surface is a process where a few atoms in pairs buckle initially due to thermal excitation or local defects and strongly influence the subsequent reconstruction. This is due to stress originating from atoms below the tilted dimers: the neighboring atoms binding to an up/down dimer atom move closer to/further from each other, respectively. This suggests that the reconstruction process depends crucially on the initial local surface morphology. Local tilting scenarios of two tilted dimers induced by thermal excitation indicate that p(2 × 2) reconstruction appears only rarely in experiment compared with a-p(2 × 1) or c(4 × 2) although it is energetically favorable. Above 120 K, c(4 × 2) is the dominant reconstruction observed in experiments which suggests the a-p(2 × 1) is unstable at these temperatures. Our MD simulations suggest that the energy required for flipping a dimer at the a-p(2 × 1) reconstructed surface is only 0.01 eV. Stress due to unfavorably aligned atoms in the bulk layers below the tilted dimers is explained as the origin of phase transition at the rather low temperature. In contrast, dimer flipping at a c(4 × 2) reconstructed surface at 300 K was not found in our MD simulations in contrast to STM results. Together with recent experimental findings,11 this may suggest that the c(4 × 2) reconstruction is still the dominant reconstruction at room temperature.

Figure 5. (a) Vibrational motions of three neighboring dimers at an ap(2 × 1) surface. δz denotes the height difference between the two atoms in a dimer. Curve α presents the fluctuation of the unflipped dimer while curves β and γ represent the flipping dimers next to it. Arrows denote the occurrence of the dimers flipping once the δz is less than about 0.2 Å. (b) Vibrational motion of the flipping dimer β and four atoms bonding to it in the first bulk layer. δx(a, b) is defined as δx(a, b) = Dab − 3.8 Å, where Dab is distance between adjacent atom a and b.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

shown by positive δx(a, b) and negative δx(c, d) around 0.65 ps. After that, δx(a, b) vibrates around 0.2 Å while δx(c, d) vibrates around −0.2 Å characterizing a c(4 × 2) reconstructed surface. Interestingly, Si atoms of first bulk layer vibrate only slightly normal to the Si(100) surface plane and remain essentially in this plane during the dimer flipping. Obviously the above results suggest that at very low temperatures atoms vibrate little and the stress is frozen. With rising temperature the higher thermal energy leads to stronger vibration and the energy barrier for dimer flipping is overcome enabling subsequent dimer flipping. The energy barrier for dimer flipping was calculated in the present study within an isolated dimer model19 which excludes the influence of the environment and the calculated value of 0.09 eV overestimates the real barrier substantially. Therefore, we estimate a real energy barrier of dimer flipping at a-p(2 × 1) surface of 0.01 eV because spontaneous dimer flipping occurs around MD temperature 100 K. Since the s-p(2 × 1) reconstruction was observed at room temperature by STM measurements8,10 and interpreted as a dimer-flipping behavior, one could estimate the energy barrier of a dimer flip at the c(4 × 2) or p(2 × 2) reconstructed surfaces to be as low as 0.03 eV. However, in our MD simulations only little dimer flipping at temperatures of 300 K was observed. This confirms the recent understanding, based on STM measurements at high bias voltage, that the s-p(2 × 1) reconstruction is a c(4 × 2) reconstruction in reality.11 Our MD results suggest that the c(4 × 2) reconstruction dominates even at room temperature.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported financially by the National Natural Science Foundation of China (Grant No. 51302231) and the Fundamental Research Funds for the Central Universities (Grants SWJTU2682013RC02, SWJTU11ZT31, 2682013CX004). Further, we thank the Fritz Haber Institute Berlin (Germany) for computational support and discussions.

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REFERENCES

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Dynamics and Energetics of Reconstruction at the Si(100) Surface

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