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Atomic and electronic structure of doped Si(111)(2root3x2root3)R30(degrees)-Sn interfaces

The hole doped Si(111)(2root3x2root3)R30(degrees)-Sn interface exhibits a symmetry-breaking insulator-insulator transition below 100 K that appears to be triggered by electron tunneling into the empty surface-state bands. No such transition is seen in electron-doped systems. To elucidate the nature and driving force of this phenomenon, the structure of the interface must be resolved. Here we report on an extensive experimental and theoretical study, including scanning tunneling microscopy and spectroscopy (STM/STS), dynamical low-energy electron diffraction (LEED) analysis, and density functional theory (DFT) calculations, to elucidate the structure of this interface. We consider six different structure models, three of which have been proposed before, and conclude that only two of them can account for the majority of experimental data. One of them is the model according to Tornevik et al. [C. Tornevik et al., Phys. Rev. B 44, 13144 (1991)] with a total Sn coverage of 14/12 monolayers (ML). The other is the 'revised trimer model' with a total Sn coverage of 13/12 ML, introduced in this work. These two models are very difficult to discriminate on the basis of DFT or LEED alone, but STS data clearly point toward the T\"ornevik model as the most viable candidate among the models considered here. The STS data also provide additional insights regarding the electron-injection-driven phase transformation as well as the critical role of valence band holes in this process. Similar processes may occur at other metal/semiconductor interfaces, provided they are non-metallic and can be doped. This could open up a new pathway toward the creation of novel surface phases with potentially very interesting and desirable electronic properties.

and theoretical study, including scanning tunneling microscopy and spectroscopy (STM/STS), dynamical low-energy electron diffraction (LEED) analysis, and density functional theory (DFT) calculations, to elucidate the structure of this interface. We consider six different structure models, three of which have been proposed before, and conclude that only two of them can account for the majority of experimental data. One of them is the model according to Törnevik  To understand the driving force of this symmetry-breaking transition in the hole-doped system and particularly the role of dopants, valence band holes, and current injection in the transition, the structure of this interface must first be resolved. This has proven to be a daunting task because the coverage is not DFT and the overall Pendry R-factor [26] from LEED, the likely structure can be narrowed down to two candidate models, the one introduced by Törnevik et al. [18] with 14/12 ML coverage, and the 'revised trimer model' with 13/12 ML, introduced in this work.
Following a brief discussion of the low-temperature 43 phase in Section VI, we present new STS spectra of the 23Sn and 43Sn surface in Section VII. The experimental LDOS will be compared with the computed DOS for the revised trimer and Törnevik models, and it is concluded that the Törnevik model [18] best accounts for the experimental data. In the last section of this paper, Section VIII, we offer a speculative scenario regarding the role of the tunneling electrons and valence band holes in the structural transition from the high-temperature 23Sn to the low-temperature 43Sn configuration, and vice-versa.
Our study indicates that the transition is precipitated by tunneling into 'anti-bonding' dangling bond surface states that are localized on the 'down atoms' of the Sn tetramer. At 4.4 K, the process must involve quantum tunneling of the Sn adatoms between different up-down configurations. The tunneling barrier for this transition is strongly reduced by hole doping, which explains why the 43Sn structure is only observed on the p-type substrates. This concept might be applicable to other doped surface systems, provided they are gapped, and possibly provides a pathway toward the realization of other novel surface phases.

II EXPERIMENTAL AND THEORETICAL PROCEDURES
The sample preparation procedures in this paper are similar to those reported in Ref. Here, we use in-situ probes to provide another coverage estimate for the 23 phase on both n-type and p-type substrates. First, we optimized the sample preparation procedure to cover the surface uniformly with the low-density Si(111)(3×3)R30°-Sn (or 3) phase, whose coverage is known to be exactly 1/3 ML [39].
The uniformity of the surface was checked with STM. Apart from the presence of the usual surface defects, we were able to achieve almost uniform 3 coverage on n-type and lightly-doped p-type substrates, and hence this surface provides a suitable calibration for XPS coverage determination. The Sn coverage on more heavily doped p-type substrates becomes increasingly non-uniform and hence coverage estimates for those samples are less reliable.
As a next step, we recorded the Si 2p and the Sn 3p, 3d, and 4d core level spectra for three different escape angles in-situ with XPS and subsequently normalized the Sn core level intensities to that of the Si 2p spectrum (see Appendix). Next, we repeated this procedure for the Si(111)(23×23)R30°-Sn surface with the unknown coverage and compared the normalized core level intensities of the 23 and 3 phases, as given in Table I. For further details, we refer to the Appendix. We conclude, ignoring possible photoelectron diffraction effects, that the coverage of the 2√3 phase is 1.05 ± 0.13 ML where the error margin is the standard deviation for the measurements recorded from the different escape angles and core levels. (Excluding the two outliers in Table 1, the total coverage would average to 1.11 ML). Intensity variations due to possible photoelectron diffraction depend on the precise placement of the Sn atoms, which we consider to be unknown at this point, as well as the electron kinetic energy and detector angle. A detailed photoelectron diffraction study is beyond the scope of this work, although it should be noted that our margin of error incorporates measurements with different photoelectron kinetic energies and different escape angles, using low angular resolution. In a second experiment, we exposed the first Sn layer of the 23Sn reconstruction by applying a voltage pulse to the STM tip. Fig. 2(a) shows the exposed surface area surrounded by domains of the √3 and 2√3 phases. The Sn tetramers on top of the first layer have disappeared. The bright feature in the middle of the image likely represents the pile-up of the original tetramer atoms. The exposed area is labeled as a Sn 2√3* phase as it also features a (23×23)R30° unit cell, although with a different structure than the 2√3 cell observed in the top layer. Panels 2(b) and 2(c) are close-up views of the 2√3* structure at different scanning biases. The +0.1 V image shows two trimer units and a central bright feature within the 2√3* unit cell.
These bright features are clearly resolved in the +1.3 V image, and consist of a trimer unit that is rotated 180⁰ relative to the trimers in the +0.1 V image. This structure is clearly metastable as it can only be accessed by pulsing the voltage on the STM tip. This lower level structure was observed on all substrates with pulsing, but on the n-type substrate it requires a much higher voltage pulse of over 5 V, indicating that the n-2√3 structure is relatively more stable than the p-2√3 and B-2√3 interfaces. Although one cannot be sure how many tin atoms were stripped from the original 2√3 structure, these results suggest that the underlayer contains nine tin atoms per 23×23 unit cell, forming two 'up' and one 'down' pointing trimer once the tetramer of the top Sn layer is removed, implying a total coverage of 13 atoms per 2√3 unit cell (1.08 ML).

IV STRUCTURE MODELS FROM DENSITY FUNCTIONAL THEORY
Inspired by the coverage estimates from the previous section, and particularly the atomic resolution images of the exposed underlayer, which revealed the existence of three trimer units, we focus our attention to structure models containing 13 or 14 atoms per unit cell. The Eriksson model with 12 atoms per unit cell was found to be highly unstable. Figure  , which is confirmed in this work (Fig 4). Eight Sn atoms are four-fold coordinated in a distorted tetrahedral bonding configuration. The tetramer atoms as well as the two atoms that are located on the short diagonal of the rhombic unit cell have one dangling bond each. These six dangling bonds are nominally half-filled but the surface structure relaxes so as to create a semiconducting ground state with a 0.55 eV band gap. For a detailed discussion of the electronic structure, we refer to Section VII.
Revised Törnevik model. This model in Fig. 3(b) is essentially the same as the Törnevik model, except for the large lateral displacement of the two Sn atoms on the short diagonal. This structure is very stable.
Both dimers are in the 'up' position, which seems inconsistent with the STM experiment.
Trimer model. The trimer model was inspired by the adatom stripping experiment in Section III ( Fig.   2). Here, we placed three trimer units in the 23 unit cell as suggested by the trimer registry of the exposed underlayer ( Fig. 2(d)), and place four additional Sn atoms on top. The fully relaxed structure is shown in Fig. 3(c). Only the central trimer unit remains recognizable as such. The other two trimers are heavily distorted as the Sn atoms tend to form chain-like structures. This chain-like backbone structure looks very similar to that of the Törnevik model. In fact, the only major difference between these two models is the missing Sn atom that was located on the short diagonal near the up atoms of the Törnevik structure. Other noticeable differences with the Törnevik model are that the structure is almost flat, i.e., it has lost the characteristic bilayer structure suggested by STM, and that the bond lengths of the two dimers within the Sn tetramer have become very different. The dangling bond count is still the same, with one dangling bond now located on the Si atom below the short dimer. The absence of a bilayer configuration suggests that this model should be ruled out.
Revised trimer model. This model differs from the trimer model in that instead of removing the Sn atom located on the short diagonal and bonded to the up dimer of the Törnevik model, we now remove the other atom on the short diagonal, i.e., the one bonded to the down dimer ( Fig. 3(d)). Unlike the trimer model, this structure retains its bilayer character and maintains the height difference between the two dimers, as in the Törnevik model. The dangling bond and electron count is the same as the trimer model. This structure is quite different from the previous ones, which all contained a similar back bone structure of the underlayer. This structure also seems inconsistent with the bilayer geometry seen in STM.
Formation Energy: To compare the total energies of the above structure models, one needs to take into account the fact that the 13/12 ML and 14/12 ML models differ in coverage. Here, we compare the formation energies Ef as follows: (1) where the formation energy is considered relative to that of the Törnevik model. Emodel is the total energy of a given structure model calculated from DFT using the PBE functional. The total energy scales with the number of Sn atoms in the slab, which can be corrected for by taking into account the chemical potential of the Sn atoms, Sn [40]. The upper limit of Sn corresponds to the chemical potential of bulk -Sn. The lower limit depends on the experimental conditions, as will be discussed in a moment, and is taken as a free distribution that preserved the cm space group symmetry of the 23 structure with four boron atoms per 23 unit cell. The fully relaxed structures appear almost perfectly identical to those without boron underneath, which is fully consistent with our previous report stating that the 23 structures on the n-type and heavily doped p-type systems are identical.

V STRUCTURE DETERMINATION FROM LEED I(V)
LEED patterns of the B-23Sn and n-23Sn surfaces are shown in Fig. 6. The I(V) data of the n-23Sn surface are shown in Fig. 7. The latter are fitted against the calculated LEED intensities for the structure models considered in Fig. 3. We used the optimized DFT coordinates of the (revised) Törnevik and (revised) trimer models as starting point of the structure optimization for the n-23Sn and B-23Sn systems.
The overall Pendry R-factors for both systems are tabulated in Table 2. Evidently, the trimer model agrees best with the LEED data for the n-23Sn system, even though it is one of the least favorable models according to the total energy calculation in DFT. (The trimer model also seems inconsistent with the observed double-layer structure in STM). The R-factors of the Törnevik and revised trimer models for the n-23Sn system are very close, essentially indistinguishable, and the revised Törnevik model is clearly the least favorable. Attempts to find a new stable structures in the DFT, starting from the LEED optimized coordinates, were unsuccessful as the atoms relaxed back to the original positions found with DFT.
Note that the Pendry R-factors of the B-23Sn structure are substantially higher, though it should be kept in mind that the data sets are also larger. Here, the trimer and Törnevik models are in closest agreement with the experimental data. To put the higher R-factors for the B-23Sn models into perspective, we directly compared the experimental I(V) data of the n-23Sn and B-23Sn surfaces and find that the mutual Rp factor is 0.27. Hence, experimentally the structures of these two systems seem reasonably close. This observation is strongly corroborated by the STS tunneling spectra in Section VII.
It is clear that the LEED I-V data have difficulty discriminating between the various structure models, although arguably one could eliminate the revised Törnevik model as the least likely candidate. In restrospect, this difficulty may not be very surprising as the number of atoms per unit cell is large and the differences between the structure models are quite subtle. The relatively large R-factors nonetheless suggest that we may not have found the right structure. However, as we will show in Section VII, among the models considered here, the Törnevik model is in best agreement with our STM and STS data.
For completeness, we tested the validity of the 0.5 ML structure proposed by Srour et al. [25], and found an overall R-factor of 0.64, using their DFT coordinates and 0.58 after further optimization with the SATLEED code. This model can thus be ruled out as a viable candidate.

VI THE LOW TEMPERATURE PHASE
In order to find the structure of the low temperature 4√3Sn phase, we employed a (4√3×2√3)R30° supercell. Calculations starting with the Törnevik coordinates produced a meta-stable 4√3Sn phase with a total energy of +540 meV and +400 meV per unit cell relative to that of the 2√3Sn and B-2√3Sn phase, respectively (Fig. 8). A similar metastable structure was found for the revised trimer model. Its total energy is 300 meV higher than that of the corresponding 23 phase. Simulated STM images for these distorted 43 structures are also shown in Fig. 8. It is clear that the Törnevik model provides a better match in that the intensity of the two dim atoms within each tetramer seems equivalent, consistent with experiment, while in the revised trimer model one of the two dim features appears to be missing in the simulation.
It is still too early to proclaim the Törnevik model as the model that appears most consistent with experiment. First of all, one cannot be sure that the 4√3 structure found by DFT is the one observed in experiment, especially since its total energy is so much higher than that of the 2√3Sn phase. On the other hand, one recalls that the 4√3 does not form spontaneously and that it can only be formed during empty state imaging, meaning that current is injected into the sample. Hence, it could be a meta-stable state. We also investigated the role of a possible electric field effect on the relative stability of the 2√3 and 4√3 phase, but found this effect to be rather small. Technical details of this procedure can be found in Ref. [41]. The most troubling aspect is that theoretically, the band gap of the metastable 4√3 structure is smaller than that of the 2√3 phase, while experimentally the 4√3 phase has the larger band gap. Hence, it is likely that the 4√3 phase would be the most stable state, contrary to the DFT prediction. This calls the validity of the found 4√3Sn structure into question. To further discriminate these two models, we consider their electronic structures, and particularly compare the local density of states obtained from the tunneling dI/dV spectra, measured at 4.4 K, and the DFT results. To this end, we implemented a separate set of DFT calculations using the HSE functional [35].

VII ELECTRONIC STRUCTURES
The hybrid exchange functional produces band gaps that are more accurate than those obtained with the (cheaper) PBE calculations, which tend to underestimate the band gaps. However, before comparing the theoretical and experimental results, key aspects of the experimental dI/dV data will be discussed first.
In Ref. 17, it was shown that the dI/dV spectra of the n-type and p-type 23Sn surfaces, including the B-23Sn surface, were very similar, except for the rigid 0.36 eV shift of the chemical potential from 0.03 eV above the conduction band minimum for n-23Sn to 0.12 eV above the valence band maximum for the p-23Sn and B-23Sn systems. These spectra were acquired at 77 K and the band gap was 0.45 eV. As pointed out in Ref. 17, the presence of a boron (33)R30° underlayer prior to the deposition of Sn does not leave any boron-induced signature in the dI/dV data or LDOS (77 K). This will be an important point in our effort to reconcile the results from STS, LEED, and DFT, to be discussed below.
Here we present new STS data, this time the data are acquired at 4.4 K. Due to the high resistivity of the n-type material at 4.4 K, we could only measure dI/dV spectra reliably for the hole-doped systems [42,17]. However, in light of the 77 K data mentioned above, we conjecture that the dI/dV spectra of the B- In Fig. 11(a) and 11(b), we compare the normalized dI/dV spectra of the B-23Sn and B-43Sn phases.
These are single-point spectra recorded on a down-atom. The band gaps are 0.45 and 0.70 eV, respectively, which strongly indicates that the B-43Sn structure is lowest in energy. Fig 11(c) demonstrates an almost perfect line up of the spectral features of the 2√3Sn and 4√3Sn phases, after accounting for the difference in band gap, except for the missing peak at 1.7 V in the B-43Sn spectrum. As we will show in Fig. 12, the B-43Sn spectrum does in fact contain a peak at 1.7 V when recorded on the up-atom location. While there is no 'a priori' reason why the spectra of the 2√3Sn and 4√3Sn structures should be lined-up this way, such precise matching of the peak positions is probably not coincidental. Such a line-up should be reproduced in the theoretical DOS of the 2√3Sn and 4√3Sn structures. Fig. 12 shows single-point spectra recorded at different locations within neighboring B-23Sn (left) and B-43Sn (right) domains. In particular, the B-23Sn structure shows a strong site-dependent variation of the empty-state LDOS. The peaks at + 0.45 V, + 1.05 V and + 1.45 V appear to be most prominent when measured on the 'down atoms' of the Sn tetramer (atom 2 of the 23 domain), while the small peak at +1.35 V appears to be most pronounced when measured on the 'up atom' (atom 1). The peak at +0.7 V is mostly associated with atoms in the first layer of Sn (atom 3), away from the tetramer atoms. The LDOS amplitudes of the 43Sn structure are much less site specific with the exception of the peak at +1.2 V: it appears to be associated with tunneling into the down atoms (atom 5). This is more clearly seen in the dI/dV spectra, i.e., prior to normalization (see Appendix). Note that the peak at +1.7 V is absent for location 5 in Fig. 12 (b), i.e., the down atom location. This position is registry aligned with the up-atom location of the 23 structure, meaning it is located above the 2nd layer Si atom.
We have calculated the LDOS of the 23Sn and 43Sn structure for both the Törnevik and Revised Trimer model, both with and without boron at the S5 lattice location. The results for the 23Sn structures are shown in Fig. 13. One of the most pertinent observations is that the theoretical DOS of the undoped systems and boron-doped systems are very different while no such difference is seen in experiment. A reasonable interpretation of this discrepancy is that the boron atoms of the B-√3 template surface move away from the S5 lattice location during the deposition and annealing of the Sn layer. Since the experimental LDOS of the n-2√3Sn and B-2√3Sn surfaces seem to be identical, at least at 77 K, the boron atoms probably diffused into the bulk. This would be consistent with the fact that the Rp factor in the LEED I-V fitting increased significantly when placing boron at the S5 lattice location. Hence, the present results suggests that the atomic arrangement of the subsurface layers differs from that of the pristine B√3 substrate. For this reason, we will focus on the line-up between the theoretical LDOS of the undoped 2√3Sn and 4√3Sn structures and the normalized dI/dV spectra of the B-2√3Sn and B-4√3Sn surfaces, measured at 4.4 K (ntype data are not accessible at 4.4 K).
Attempts to line up the theoretical DOS of the revised trimer model in Fig. 13(c) with the experimental LDOS presented in Fig. 11 were unsuccessful. In particular, the empty state spectra align rather poorly and one would have to assume that HSE underestimates the gap here. On the other hand, the LDOS of the 2√3Sn Törnevik model in Fig. 13(a) lines up reasonably well, after correcting for the difference in band gap. This is shown in Fig. 14(a). Here HSE seems to overestimate the gap. The agreement is almost perfect when comparing the 2√3Sn Törnevik DOS with the 4√3Sn spectra, as shown in Fig. 14(b). While this comparison may appear odd, keep in mind that experimentally, the peak positions of the 2√3Sn and 4√3Sn spectra in Fig.   11 also line up nicely after correcting for the band gap difference. We finally notice that the HSE LDOS calculation of the Törnevik 4√3Sn structure (not shown) does not align well with the experimental result for either the B-2√3Sn or B-4√3Sn surface. Hence, the 4√3Sn structure from DFT can most likely be disqualified, as we already suspected in Section VI.

VIII DISCUSSION AND SUMMARY
On the basis of DFT total energy calculations, the Törnevik model, revised Törnevik model, and the revised trimer model are viable candidates for the 2√3Sn structure. Their relative stability depends on the precise value of the Sn chemical potential, which in turn depends on the experimental growth conditions. Because STM images indicate the presence of a double layer structure, we rule out the revised Törnevik model, the trimer model, and Ichikawa's model. Their simulated STM images also do not reproduce the observed contrast between the up atoms and down atoms within each tetramer. The revised Törnevik model also has a relatively poor Pendry Rp factors in LEED I(V). While the Törnevik and revised trimer models are about equally favored according to our LEED I(V) studies for the n-type samples, the agreement between the theoretical DOS from the DFT-HSE calculations and experimental LDOS from the normalized dI/dV spectra favor the Törnevik model. We therefore conclude that among the five different models considered in this paper, the Törnevik model best agrees with the experimental results.
A number of problems remain. The relatively high Rp factors in LEED I(V) suggest that there is room for further structure optimization. The fact that the revised trimer model appears favored under the experimentally realized chemical potential is somewhat troubling, as is the fact that the DFT calculations have not been able to identify a 4√3Sn structure as the lowest energy configuration. These uncertainties make it difficult to identify the nature of the 2√3Sn to 4√3Sn transition. However, on the basis of the experimental data presented in Fig. 12, we make the following conjecture.
Up-down buckling on semiconductor surfaces is generally accompanied by charge transfer. Here, the dangling bond orbital on the 'up atom' usually acquires additional charge while the one on the 'down atom' gives up some of its charge [45]. Now, the lowest unoccupied state of the 2√3Sn structure has the greatest amplitude on the down atom, see Fig. 12(a), and the 2√3 to 4√3 conversion only happens as electrons start tunneling into this 'anti-bonding' orbital. If the tunneled electrons cannot be drained fast enough, the transient filling of this orbital will 'pull' the down atom upward. This will destabilize the 2√3 buckling geometry of the 2√3 structure, which then would rationalize a displacive transition to a 43 structure with the buckling geometry. According to the 43 spectra in Fig. 12(b), the peak at +1.2 eV now has the largest amplitude on the down atoms of the 4√3Sn structure and one would expect this geometry to become unstable when tunneling into the +1.2 eV state of the 4√3Sn structure. Indeed, this is what happens. Fig. 15 shows a series of images showing the appearance of the 4√3Sn structure when tunneling into the lowest unoccupied state of the 2√3Sn structure and the reversal of this process for tunneling bias greater than 1.25 eV.
At 4.4 K, the 2√3 to 4√3 conversion likely involves quantum tunneling of the Sn adatoms through a tunneling barrier [46,47]. The barrier is likely asymmetric as the 4√3 structure appears lowest in energy, at least for the p-type system (Fig. 16). While we do not know the geometry of the transition state in between The experimental observations suggest that the transient filling of the 2√3 down-atom dangling-bond orbital destabilizes the 2√3 structure relative to the transition state, i.e., it reduces the activation barrier, resulting in a local 2√3 to 4√3 conversion. Likewise, transient filling of the 4√3 down-atom dangling-bond orbitals destabilizes the 4√3 structure relative to the transition state, resulting in a 4√3 to 2√3 conversion.
These conversions happen at different bias, as shown in Fig. 15.
From the fact that the transition is only seen on the p-type substrates, we infer that the total energy of the 2√3 and 4√3 structures (and the energy barrier between the two) also depends on the fixed doping level and dopant type (Fig. 16). Indeed, our DFT calculations for the 43 structures identified in Section VI indicate that hole doping reduces the total-energy of the 43 phase relative to the 23 phase by as much as 150 meV per 23 unit cell [48]. Note, however, that the 23 structure is still the most stable structure in these calculations, so the precise role of the dopant atoms remains unclear at this point.
Summarizing, the experiments indicate that both fixed and transient doping destabilizes the 23Sn and 43Sn states relative to the transition state, and facilitates the transition between the two states. Clearly, better understanding of the thermodynamic and kinetic aspects of the transition requires a firm resolution of the 4√3Sn ground state structure and identification of a transition pathway. It also requires a better understanding of the excited state decay and carrier dynamics under the tunneling conditions. Nonetheless, the arguments presented here are rather generic and hence, they should be more broadly applicable. As such, hole doping appears a viable strategy toward the creation of novel surface phases with potentially interesting and desirable electronic properties.   Table I. Ratio of normalized core level peaks for different Sn core levels and escape angles, along with the calculated coverage (in monolayers) from a layer-by-layer attenuation model (see Appendix).   created 3-Sn structure and an unknown 23* phase. The latter is the exposed underlayer of the 23-Sn surface. It also has a (2√3×2√3)R30° periodicity but the structure is different from the 23 reconstruction.
The 23* layer is higher than the neighboring 3 structure but lower than the neighboring 23 structure, indicating that the 23* structure is a single layer structure but with a higher Sn atom density as compared to the 3 phase. The line scan illustrates the bilayer nature of the original 23 reconstruction. Outside the circular 23* region, the native 23 phase is coexisting with 43 phase. The latter must be induced by the positively biased pulse or during the scanning process. Panels       Table 2.    Note the absence of a peak at +1.7 V in the B-43Sn spectrum. Such a peak does exist, however, when the spectrum is recorded on the up-atom (Fig. 12).     can be seen that the 43 fraction reaches at maximum at a scanning bias between 1.00 and 1.25 V. Figure 16. A possible transition state diagram for the quantum tunneling transition between the 23 and 43 structures, where the 43 structure is assumed to be the most stable configuration for both the n-and ptype samples. The energy diagrams of the electron-doped and hole-doped systems are indicated by the dashed and solid lines, respectively. In this particular case, the barrier for the 23 to 43 conversion is lowest for the p-type system, while the reverse transition remains highly unlikely for both the n-type and the p-type systems. The total-energy minimized structures of the 23Sn (left) and 43Sn (right) phases are shown for easy comparison.  where P1 = 0.894 and P2 = 0.926.
The spectra were taken at three different escape angles  of 52°, 27°, and 12°. The Sn 3p, 3d, 4d, and Si 2p core level peak intensities were obtained by integrating the core level spectra using either a Shirley or linear background, depending on the background conditions. Plasmon-loss satellites were included in the fit. Using Eq. A6 with d = 2.4 Å (Fig. 1) and λ= 26 Å [49], we obtain the absolute coverage of the 23Sn surface, as shown in Table 1 of the main text. The above value of  was calculated for -Sn. Since the atomic density in the 23 surface is higher than that of an -Sn(111) layer,  is likely overestimated. While can be corrected for the difference in atomic densities [49], it would hardly affect the outcome of the coverage calculation.