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Manganese Nanostructures on Si(100)(2 × 1) Surfaces: Temperature-Driven Transition from Wires to Silicides C. A. Nolph, K. R. Simov, H. Liu, and P. Reinke* Department of Materials Science and Engineering, UniVersity of Virginia, 395 McCormick Road, CharlottesVille, Virginia 22904, United States ReceiVed: June 18, 2010; ReVised Manuscript ReceiVed: October 4, 2010
The Si(100)(2 × 1) surface serves as a template for the formation of Mn wires at room temperature, which are the starting point for the annealing experiments discussed here. The evolution of the Mn surface structures as a function of annealing temperature was observed with scanning tunneling microscopy for the temperature range between 115 and 600 °C and establishes a surface phase diagram for the Mn-Si(100)(2 × 1) system. The stability of the Mn nanowires is limited; they break up below 115 °C (the lowest annealing temperature studied), and ultrasmall clusters are formed. These clusters are initially positioned on the terraces but migrate to the step edges at around 250 °C, which sets the limit for the Mn surface diffusion length. At around 300 °C the Mn adatoms move into subsurface sites, and the empty and filled states images strongly indicate that Mn acts as an acceptor in this near-surface region. A further increase in temperature leads to the formation of large crystallites (several tens of nanometers), which exhibit the characteristic shape associated with Mn silicides. The modification of the Si surface with temperature is characterized by the dramatic increase in the defect population (defect density and size and step edge roughness). The condensation of dimer vacancies begins around 200 °C and progresses to the formation of long dimer vacancy lines at elevated temperatures. The step edge roughness and the step edge formation energies were calculated for SA and SB steps, and their modulation with annealing temperature illustrates the impact of Mn on the defect and kink stabilities. These data will be used to perform a thermodynamic and kinetic modeling of defect population in the presence of Mn at moderate substrate temperatures. This study presents a surface phase diagram, which includes the evolution of the Mn nanostructures and the modification of the Si surface. The identification of near-surface layers of Mn acceptors is particularly relevant for the design of basic building blocks for future Si-based spintronics. Introduction The seamless combination of spin- and charged-based electronics is one of the most intriguing and challenging materials science problems in spintronics. In order to effectively use the charge and the spin of the electron in a common device, a new set of basic device building blocks needs to be designed, which includes contacts for the injection of spin-polarized currents and synthesis of magnetically doped semiconductor layers.1-7 For GaAs and Ge, the formation of dilute magnetic semiconductors through Mn doping has been confirmed,2,8-10 but the magnetism in Mn-doped Si is still discussed controversially. Several theoretical studies predict a net magnetic moment for specific Mn surface structures on the Si(100)(2 × 1) surface and a ferromagnetic coupling in delta-doped Mn layers embedded in a Si matrix. The hybridization between Mn and the Si p band is thought to lead to a coupling between the Mn magnetic moments, and the magnetism of these layers is therefore controlled by the specific bonding geometry of Mn and the Si lattice.11-13 These intriguing predictions have not yet been confirmed experimentally owing to the difficulties in the synthesis of specific surface structures and bonding configurations. The experimental realization and control of Mn surface structures on Si(100)(2 × 1) is the goal of our present study. The experiments presented here are based on previous work on the formation of monatomic Mn wires on the reconstructed Si(100) surface at room temperature.14 Specifically, we investigated the transformation of these Mn surface structures during
annealing at temperatures between 100 and about 400 °C, closing the gap to the temperature range beyond 400 °C, which has been studied previously and is dominated by the formation of large silicide crystallites. The annealing of Mn wires, which are formed from the room temperature deposition of Mn on Si(100), triggers a substantial rearrangement of the Mn surface structures. It progresses from Mn wires to Mn clusters, then to subsurface bonding, and subsequently the formation of larger crystallites. At the same time, the Si surface undergoes considerable structural changes and a large number of dimer vacancies (DVs) and dimer vacancy lines (DVLs) are formed at relatively low temperatures. The transition between the different surface structures is observed with scanning tunneling microscopy (STM). Experimental Section The sample preparation and characterization were performed in an Omicron Nanotechnology Variable Temperature SPM system, with a base pressure of 8 × 10-11 mbar. The Si samples (B-doped: 1.2 × 1017-1.5 × 1017 cm-3) were annealed for an extended period at about 550 °C and then repeatedly flashed to high temperature by direct current heating, followed by a cooldown period (1 h) to room temperature. This treatment routinely creates a surface with areal defect densities of less than 5%, which are suitable for the formation of Mn wires.14 All STM images were obtained in constant current mode with a sample bias of -1.5 V (filled states) and +1.5 V (empty states) and a
10.1021/jp105620d 2010 American Chemical Society Published on Web 10/29/2010
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feedback current of 0.03 nA. Electrochemically etched W wire was used as a tip material. Image analysis was performed using ImageJ15 and WSxM16 software packages. Mn was evaporated from a Mo crucible using a home-built electron beam evaporation source; the deposition rate was calibrated prior to each experiment with a quartz crystal monitor placed at the sample position, and a flux of 0.0025 nm/s was maintained throughout the deposition. The Mn coverage (ΘMn) was obtained from STM image analysis after deposition and determined to be in the submonolayer regime between 0.04 and 0.4 ML. The Mn was deposited at room temperature, and the sample was then annealed by direct current heating at temperatures between 100 and 600 °C for 5 min (a new sample was used for each temperature). The annealing temperature is reached within a few seconds of adjusting the heating current. The temperature calibration for small Si samples (10 × 2 × 0.5 mm) in this intermediate-temperature regime is notoriously difficult: the sample size is too small and the annealing temperature too low for a reliable pyrometric measurement, and contact with a thermocouple greatly diminishes the quality of the surface due to the presence of transition metal contaminants. The temperature was therefore calibrated by establishing the relation between temperature and heating power with a sacrificial sample contacted with a K-type thermocouple. The accuracy of this method depends on the contact resistance between sample and sample holder, and six different samples were used for calibration and to establish the confidence range of the measurement. The following samples were prepared: (1) Tanneal ) 115 ( 28 °C, ΘMn ) 0.04 ML; (2) Tanneal ) 268 ( 30 °C, ΘMn ) 0.14 ML; (3) Tanneal ) 316 ( 38 °C, ΘMn ) 0.12 ML; (4) Tanneal ) 342 ( 38 °C, ΘMn ) 0.22 ML; (5) Tanneal ) 415 ( 44 °C, ΘMn ) 0.04 ML; and (6) Tanneal ) 600 ( 44 °C, ΘMn ) 0.4 ML. The samples are labeled by their respective annealing temperature S(Tanneal). One additional sample, named SH600, was prepared by Mn deposition on the hot sample with ΘMn ) 0.2 ML. The relatively low coverages were chosen to allow for simultaneous analysis of the changes in Mn surface structure and the Si surface. The quality of the Si surface was characterized by the density of defects per unit area (nm2), the area of the surface occupied by defects in percent of the total surface area, and the quality of both types of step edges SA and SB. Step edge quality was evaluated by measuring the number of dimers between kinks along each step edge. The first-nearest (εSa(b)) and second-nearest (δ) neighbor dimer interaction energies for SA and SB type steps were determined from STM images following the procedure described by Zandvliet et al.:17,18
εSa(b) /kbTf ) -ln δ/kbTf ) -ln
(
( ) n+1n-1 n20
)
n(rn0 , n((r-1)n(1
rg2
(1)
(2)
The number of kinks, n(r, of length 2ar (2a is the centerto-center distance between dimers along the direction perpendicular to the dimer axis, r is the number of dimers in a kink) and the number of sites with no kinks, n0, were measured along SA and SB step edges. Two different kink directions are defined as the following: facing the lower terrace as a positive kink (n+r) and facing the upper terrace as a negative kink (n-r). Results and Discussion The room temperature deposition of Mn on the Si(100)(2 × 1) reconstructed surface and subsequent annealing steps lead
to dramatic changes in the Mn nanostructures and bonding at the surface. A considerable modification of the Si surface itself occurs and includes changes in the defect concentrations, dimer vacancy density, condensation of dimer vacancy lines, and step edge roughness. The changes in the Si surface are indicative of the specific interaction of Mn with a Si surface and reminiscent of the interaction of Si(100) surfaces with Ni.19-21 We begin with a discussion of the Si substrate and its modification during the annealing experiment and then focus on the observations of the Mn nanostructure evolution. A. Silicon Surface. The surface defect structures on Si(100)(2 × 1) are quantified by their density, the percentage of surface area covered by defects, and the average defect size. These data are summarized in Figure 1 for samples S115, S268, S316, and S415 before and after the deposition of Mn and after the annealing step. Each annealing step represents a separate sample, which begins with the room temperature deposition of Mn followed by the respective annealing step. Prior to the Mn deposition, the area defect densities lie between 1.5 and 4.5%, and the defect number densities were limited to 0.04-0.06 per nm2. Representative images of defect structures are shown in Figure 1c-e. The quality of the surface is sufficient to form Mn wire structures,14 which can be seen in Figure 2a. For Mn coverages below about 0.1 ML, ultrasmall islands with 1 to a maximum of 4 Mn adatoms form on the surface,14 which grow into longer wires at higher coverage. A defect density below 5% on the Si(100)(2 × 1) surface is required for wire formation; for higher initial defect densities the formation of Mn surface clusters prevails. A slight increase in the Si defect density is often observed after the deposition of Mn at room temperature. The defects are mainly single and double dimer vacancy defects, which have been described in detail in numerous publications.22-24 The defect density and area measured on the Si(100)(2 × 1) surface before and after the room temperature deposition are marked by a box in Figure 1a. The annealing of Mn wires triggers a pronounced change in the Si surface, which is summarized in Figures 1 and 2. For the first two annealing steps, S115 and S268, we observe a considerable increase in the number density of defects with annealing, but the area occupied by those defects increases only slighty. The typical defect structures are still isolated single and double DVs (dimer vacancies); for S268 an increase in defect area and size (Figure 1b) indicates the onset of defect agglomeration. The growth of defects and condensation of DVLs continues for S316 (Figure 1d and Figure 2d), but this sample also exhibits a unique bonding situation for the Mn-Si surface, which might change defect formation and stability (see section B). For higher annealing temperatures, S342 and S415, the DVLs continue to grow, and the area occupied by the defects and defect size (Figure 1b) increases considerably, albeit the DVLs are still relatively short with many kinks and crooked sections (Figure 2e). The average size of the defects as a function of annealing temperature reflects the condensation of multiple DV structures into extended DVLs. This is most dramatically seen in S600, which is shown in Figure 4a, where the DVLs extend almost across the entire width of the individual terraces. In contrast, the deposition of Mn on a hot substrate, which is sample SH600 shown in Figure 4b, yielded significantly smaller defect concentrations in both defect density and area, and no extended DVLs are visible. Figure 3a shows the average number of dimers between kinks for step edges SA and SB and gives therefore a measure of the roughness of the step edges. On the rougher SB step, the number
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Figure 1. (a) Change in defect morphology characterized by defect number density and percent area covered by defects. The area enclosed by the box contains the measurements for the Si(100)(2 × 1) surface before and after room temperature Mn deposition. (b) Average defect size as a function of annealing temperature. A single dimer vacancy occupies an area of 0.309 ( 0.028 nm2. STM images of representative defect structures observed after annealing: (c) S268, (d) S316, and (e) S415. These defect images show the filled states (-1.5 V bias voltage).
of dimers between kinks is small and decreases from only 2.7 to 1.7 dimers between kinks with increasing sample temperature, while on the SA step, the length of smooth step edge sections decreases by an order of magnitude over the same temperature range. This development is also seen in the STM images shown in Figure 2. The step edge formation energy was then calculated to obtain a quantitative measure of the influence of Mn on the evolution of SA and SB step edges as a function of annealing temperature. The nearest-neighbor interaction energies of a clean Si(100)(2 × 1) surface are (7.0 ( 0.2)kbTf and (3.9 ( 0.2)kbTf for the SA and SB step edge, respectively, where Tf is the freezeout temperature of step edge adatom mobility. The values for dimer interaction energies (eq 1) on the Si(100)(2 × 1) surface prior to Mn deposition can be directly compared to the literature: the value obtained for the SB step edge is in good agreement with the one reported by Zandvliet, (3.6 ( 0.2)kbTf. However, our value for the SA step edge exceeds the value given by Zandvliet [(5.7 ( 0.3)kbTf], which corresponds to a smaller number of single kinks on our sample.
The freeze-out temperature for a pristine Si surface is given as 350-450 °C in the literature; below this temperature the step edge is stable.25-27 However, the substantial changes in edge roughness with annealing temperature, which are observed for the Mn-covered surfaces, might be indicative of a lowering of the freeze-out temperature, and we therefore cannot use the value of Tf of the pristine Si surface. All energies are therefore given as multiples of kbTf (see eq 1). The following values were determined for the samples after annealing with Mn: S115 (5.5 ( 0.3)kbTf [(4.0 ( 0.3)kbTf]; S268 (4.2 ( 0.3)kbTf [(3.4 ( 0.3)kbTf]; S316 (3.6 ( 0.4)kbTf [(2.4 ( 0.4)kbTf]; S342 (2.6 ( 0.4)kbTf [(3.3 ( 0.4)kbTf]; and S415 (2.8 ( 0.3)kbTf [(1.8 ( 0.3)kbTf] for SA[SB] step edges. Using these values, the step edge formation energy was calculated according to the following:
ESa /kbTf )
εSb /kbTf + δ/kbTf 2
(3)
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Figure 2. STM images of Si(100)(2 × 1) Mn samples (a) before annealing of sample S316 and after annealing: (b) S115 (-1.5 V), (c) S268 (-1.5 V), (d) S316 (+1.5 V), and (e) S415 (-1.5 V bias).
ESb /kbTf )
εSa /kbTf + δ/kbTf 2
(4)
In Figure 3b the step edge formation energies are illustrated as a function of sample annealing temperature. The SA step edge formation energy remains as 0.9 eV/kbTf per kink atom constant within the margin of error and is positioned at the higher end of literature values, which range from 0.74 to 0.9 eV/kbTf per kink atom.18 For the SB step, the formation energy decreases with increasing annealing temperature up to sample S342 where it reaches a steady state value of 1.29 eV/kbTf per kink atom. The step edge is a source and a sink for defects and adatoms and is in thermodynamic equilibrium with adatoms and defects on the terrace itself. The step edge therefore adopts an equilibrium shape, which is controlled by the interaction with the terrace until the diffusion of Si atoms along the step edge begins and the step edge thaws. The presence of Mn adatoms decisively influences the step edge formation energies and thus the roughness of the step edges, which was expressed as the number of dimers between kinks. It can be seen in Figure 3 that the SB step becomes more kinked with increasing temperature, which corresponds to a smaller step edge formation energy in the SA step. The step edge formation energy of SA decreases due to the fact that the kinked portions of an SB step are actually an SA step edge, which has a lower formation energy than an SB-type step edge.28 For samples S342 and S415, the step edge formation energy for the SB step reaches a minimum. It is around this temperature that a step edge for pristine Si(100)(2 × 1) is expected to thaw, and the number of kink sites will begin to fluctuate as dimer vacancies are generated and terminated at the step edge at an appreciable rate. The overall change in the step edge roughness is driven by an increase in the defect concentration on the surface, a change in the step edge formation energy, and most likely also a modification of the freeze-out temperature of the step edge. However, all these parameters are connected and most likely driven by the interaction between Mn and the surface defects. The behavior of the Si surface during the annealing process can be understood by the interplay of defect formation, their
Figure 3. (a, top) Average number of dimers between kinks along an SA and SB type step edge. (b, bottom) Step edge formation energy of SA and SB steps as a function of the sample annealing temperature. The data point at 25 °C corresponds to a representative clean Si(100)(2 × 1) surface after in situ cleaning.
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Figure 4. Representative STM images of the two high-temperature samples: (a) S600 and (b) SH600.
stabilization by Mn, the condensation of defects to DVLs, and the interaction of the step edges with adatoms and defects. Annealing even at relatively low temperatures has a significant impact on the Si surface, and the presence of Mn in submonolayer concentrations decisively impacts the defect formation and condensation into DVLs. The vacancy concentration surpasses by far that of a clean Si(100)(2 × 1) surface especially at relatively low substrate temperatures, and DVL condensation begins far below the threshold temperature reported for a clean surface.29-31 These observations are reminiscent of the effect of Ni, which is known to stabilize DVs and drive the condensation of DVLs.19-21 We suggest that a similar mechanism is at work for Mn on Si(100)(2 × 1) surfaces. B. Mn Surface Structures. The evolution of the Mn surface structures with annealing (Figure 2) begins with a transition from the Mn wire structures to clusters, which is followed by the movement of Mn into subsurface sites. Finally, Mn transitions to form larger crystallites. The Mn wires and adatoms for all samples are distributed randomly on the Si terraces prior to annealing. The ultrasmall Mn structures observed on S115 prior to annealing contain only 1-4 atoms (average size 0.22 nm2) and can be considered the critical nuclei for wire formation if the Mn deposition is continued. The subsequent annealing leads to the formation of larger islands with a broad size distribution, which extends from 0.22 nm2 to clusters as large as 3.16 nm2. The clusters are distributed randomly across terraces and did not display a preference for nucleation on the step edges. However, measurement of exact cluster sizes in STM is rather unreliable for cluster diameters below 10 nm due to the convolution of the image with the tip shape. Fortunately, for S115 the smallest islands/clusters are only a single atom high, and the measurement of the diameter of these structures is still fairly accurate. Clusters imaged on S268 are often much higher, and the numbers given here present only a rough estimate of the cluster size. For S268 the cluster size is considerably larger, the ultrasmall clusters are missing, and the clusters range in size from 2.56 nm2 to a maximum size of 36.25 nm2 (23 clusters measured in total). The clusters are positioned primarily at the step edges, which is generally a preferred nucleation site. The diffusion length of Mn adatoms therefore exceeds the terrace width, which is 15 (5 nm for S268 and 13 (5 nm for S115. The different location of the Mn clusters on S115 and S268 can therefore be attributed to the increase in Mn adatom diffusion length with temperature. S316 displays an entirely different surface morphology, which is shown in Figure 5a. This image is representative of the surface structure of S316 and taken at a bias voltage of +1.5 V, which probes the empty states. The filled state image taken at -1.5 V
Figure 5. (a) STM image of S316 after annealing. The large image shows the empty states (+1.5 V), and the inset depicts the filled state (-1.5 V) image for the same area. (b) Representative line scan across a high-contrast region, where the reconstruction is preserved and the apparent height is modified. The change in apparent height is indicative of subsurface Mn, which acts as an electronically active dopant. (c) Line scans across a region without enhanced contrast: the broken line is perpendicular to the dimer rows, and the solid line crosses two dimer vacancy defects. The arrow marks a C-type defect.
of the same area is shown in the inset, and S316 is the only annealing stage where the filled and empty states exhibit marked differences. The majority of surface defects and extended defect structures are surrounded by regions of enhanced brightness in the empty state images (larger apparent height), which is also reflected in the line scans included in Figure 5b, c. The extension of these areas is about 3-4 equivalent dimer widths, and the line scans clearly show that the Si reconstruction is preserved. The appearance of the contrast pattern is markedly different from the representation of dangling bonds,20 which are commonly observed at DV defects. Some of these spatially confined defects (C-type defects) can be seen in Figure 5a, and one of them is marked by an arrow. The preservation of the dimer reconstruction and the pronounced differences between the filled and empty state images are commensurate with an electronic rather than a topographic modification of the surface.
19732 J. Phys. Chem. C, Vol. 114, No. 46, 2010 A strong modulation of surface features while retaining the surface structure is characteristic for the presence of subsurface dopant atoms, which introduces additional states in the band gap and shifts the position of the Fermi energy within the gap.32-40 For Si(100)(2 × 1) the observation of dopants is usually hindered by the pinning of the Fermi level through surface states, and thus the occupancy of the dopant-related state cannot be observed by changing the tip bias. The electronic signature of subsurface dopants is therefore only seen on Si(100)(2 × 1) if the modulation of the tip work function and local band bending are such that the dopant state can be filled and emptied through the tip-surface interaction as shown in refs 34-36. The observation of dopants and their impact on the electronic structure is frequently reported for passivated Si(100),32,39 which does not possess an extended surface state. Mn has been studied extensively in conjunction with the magnetic doping of GaAs,37,38,41 and in Ga(Mn)As, substitutional Mn can be imaged at the surface due to charge-induced band bending which extends over large volumes relative to atomic length scales. The images then contain locally confined regions with strongly modified apparent heights, whose characteristic shape reflects the interaction of Mn dopants with the electronic system of the host matrix. The geometric structure of the surface is preserved in these regions.34,35 Subsurface Mn-related structures on Si(100) have also been reported by Krause et al.,11 who described the formation of a specific local surface reconstruction, which coexists with large silicide crystallites in a high-temperature annealing experiment (T ) 650 °C). However, the subsurface states observed by Krause et al. are accompanied by a local modification of the surface reconstruction and are therefore most likely representative of the early stages of silicide formation rather than local doping. Through a comparison with this work32-40 on the detection and signatures of subsurface dopants in STM images of semiconductors, we conclude that the extended regions with a larger apparent height in S316 are related to the presence of electronically active subsurface states caused by the presence of Mn dopant atoms. The extension of the areas of larger apparent height is comparable to the observation of P and B acceptors on Si(100)(2 × 1) described in the literature.32-36,40 The subsurface Mn therefore acts as an acceptor, which is of considerable interest for the formation of dilute magnetic semiconductors, where the magnetic interaction is mitigated by holes injected from the magnetic dopant Mn. The true position of the Mn subsurface atoms cannot be readily identified, but we can suggest two different scenarios which agree well with our observations: (1) the Mn subsurface atoms are tied to the defects structures and positioned within the extended network of short DVLs, or (2) only those dopant atoms located in the vicinity of defects can be observed, due to a local perturbation of the surface state in the vicinity of defects and possibly local unpinning of the Fermi level, which enables imaging of the electronic signature of the electronically active Mn.22 The subsurface Mn structure is particularly important for magnetic doping of Si,42 and the mechanism of its formation and stability will be the subject of future studies. A rough estimate of the Mn concentration in the three topmost Si layers yields concentration on the order of 1018 cm-3 (0.1 ML deposited), which exceeds by far the solubility limit of Mn in bulk Si.43 The supersaturation of the topmost layers of Si and Ge with Mn has been described previously,44-47 but the mechanisms leading to the supersaturation are not well understood. The interplay between supersaturation and thin film
Nolph et al. growth will drive future strategies for the formation of Mndoped Si layers. For the next two annealing steps, S342 and S415, a multitude of different surface structures coexist, which include large crystallites with an extension of several tens to a hundred nanometers and small clusters similar to those observed at lower temperatures. These different surface structures are interspersed by large regions of Si(100)(2 × 1) with extended DVLs. The STM itself is not sensitive to the chemical composition of the clusters, but previous studies, which focused on this hightemperature regime, demonstrated the formation of silicide crystallites, albeit of varying stoichiometry.48,49 The coexistence of different crystallites and surface structures is characteristic of the high-temperature regime and is even more pronounced in S600 as shown in the inset of Figure 4a. Sample S415 links the intermediate-temperature regime, which is the focus of our study, to the high-temperature regime described in several other publications.49-52 As a last step in this investigation about the role of annealing in the control of Mn surface structures on Si(100)(2 × 1), we prepared one sample in which Mn was deposited on a hot substrate, SH600, which is shown in Figure 4b. This surface is dominated by very large (up to 200 nm in length) rodlike crystallites. The crystallites are often embedded in the Si surface, and a groove developed at their base, where apparently a relatively large amount of Si was consumed in the reaction. The intercrystallite distance exceeds several tens of nanometers and is indicative of a large mean free path of Mn diffusion on the surface. In addition, the absence of extended DVLs is surprising and can only be explained by a nearly complete Mn depletion of the Si surface. The Mn diffusion and reaction to Mn silicides therefore has to be considerably faster than the movement of DVs to form DVLs at this temperature. Conclusions In summary, we were able to identify the structural evolution of both the Si(100)(2 × 1) surface and Mn nanostructure within a wide temperature range. The annealing of Mn wires leads to a very rich phase diagram, and small changes in the substrate temperature result in dramatic modifications in the Mn surface structures. The Mn wires, which are produced during the initial room temperature deposition, are rather unstable and degrade rapidly to ultrasmall clusters. However, the most intriguing observation is the movement of Mn adatom into subsurface sites at about 300 °C, where Mn acts as an acceptor. This electronic interaction is expressed as a local modification of the apparent height in the STM images while the characteristic dimer-row reconstruction is conserved. In the high-temperature regime above about 400 °C, the emergence of relatively large silicide crystallites dominates the surface. The concurrent modification of the defect population on the Si surface can be understood by the stabilization of surface defects by Mn adatoms and the interaction of defects with the step edges. This is expressed by the change in (1) step edge formation energy and (2) the number of dimers between kinks along the step edge with annealing temperature. Given the catalog of data we have collected on dimer vacancy concentrations on the terrace, step edge roughening, and step edge formation energy as a function of annealing temperature, it is now possible to begin thermodynamic and kinetic modeling of the Mn-modified Si(100) surface to further our understanding of this system. We gained a comprehensive insight into the formation of Mn surface structures on Si, including the discovery of subsurface doping in a narrow temperature range around 300 °C. Our study
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