We systematically investigated the arsenic (As) 3d core-level x-ray photoelectron spectroscopy (XPS) binding energy and formation energy for As defects in silicon by first-principles calculation with a high accuracy of 0.1 eV by careful evaluation of the supercell size. For As, we adopt a pseudopotential with 3d states as the valence and the spherical hole approximation to ensure the convergence of self-consistent calculation for the XPS binding energy with large size systems. Some of the examined model defects have threefold coordinated As atoms. The XPS binding energies of these As atoms are distributed in the narrow region from −0.66 eV to −0.73 eV in neutral charge states. Such defects in negative charge states have a lower XPS binding energy by about 0.1 eV. From the XPS binding energy and electrical activity, negatively charged defects of a vacancy and two adjacent substitutional As atoms (As2V) are the most probable candidates for the experimentally observed peak at −0.8 eV called BEM from the reference substitutional As peak. Under the experimental condition, we find that As2V−,2− do not deeply trap electrons and are electrically inactive. We also demonstrate the surface effect that surface states near the bandgap decrease the XPS binding energy, which may generate defects with low binding energies similarly to the experimental peak at −1.2 eV called BEL.

Arsenic (As) is the most important n-type dopant element in silicon (Si)-based devices. With the scaling down of device size, shallow junctions with high carrier concentrations are required. Various studies have been carried out on the behavior of As atoms in high-concentration regions.1–11 

Generally, it is very difficult to obtain atomic-level information on dopant behavior. One of the reasons for the difficulty is the low intensity of measurement signals. This is because the dopant concentration is much lower than the number of host atoms, and the proportion of defects at issue is lower than those of all dopants. To compensate for the weak signals, Tsutsui et al. utilized high-intensity x-ray beams generated by large synchrotron radiation facilities for detailed x-ray photoelectron spectroscopy (XPS) measurements, which reveal the depth profile of boron (B) defects in Si crystals.12 Regarding As defects, in 2010, Tsutsui et al. reported that two XPS peaks of As 3d were detected for As-doped Si samples by ion implantation.13 The peaks were named BE1As and BE2As. From Fig. 3 in Ref. 13, BE1As corresponded to the binding energy at about 41 eV and BE2As had a lower binding energy by about 1.2 eV. In 2011, Kanehara et al. measured As-doped Si samples by plasma doping and found the three XPS peaks named BEL (40.9), BEM (41.5), and BEH (42.1) in the order of XPS binding energy, where the figures in parentheses are binding energies in eV.14 Recently, the Tsutsui group investigated As-doped Si samples by ion implantation using XPS and spectro-photoelectron holography measurements and found the similar XPS peaks to those in the previous study. The binding energy of the BEL and BEM peaks measured from the BEH peak was −1.2 eV and −0.8 eV, respectively. By the spectro-photoelectron holography measurements, symmetric images were obtained for the BEH and BEM peaks. With a first-principles analysis, they suggested that the BEH and BEM peaks were due to the substitutional As atom and the As atom embedded in the AsnV(n = 2–4) type cluster.15–17 

Theoretically, we examined the XPS core-level shift of B defects and found that the XPS binding energy calculated by the ΔSCF method with careful evaluation of the boundary condition shows excellent agreement with the experimental results by Mizushima et al.18–21 For As, our group reported preliminary results of our study using a 512-Si-atom supercell.22 In Refs. 15–17, a first-principles study on defects in the neutral electric state was carried out using a 64-Si-atom supercell. However, it is difficult to discuss the XPS core-level shift determined by calculation using a 64-Si-atom supercell because the supercell is too small, as described in Sec. III.

In this paper, we report our comprehensive study on As defect models in Si, which have been suggested theoretically and/or experimentally, with careful evaluation of the boundary condition. We adopted a 1000-Si-atom supercell to obtain more reliable results than those in our preliminary work. The aim of this work is to reexamine the XPS peak assignment using the XPS binding energy shift calculated with high accuracy and determine the n of AsnV clusters, which are the probable candidates for the BEM peak.

The calculations are based on density functional theory with the generalized gradient approximation (GGA) PBE96 functional.23–25 The atomic configurations are fully optimized for the total energy with a force criterion less than 1 × 10−3 hartree/bohr. The interactions between ions and electrons are described by a norm-conserving pseudopotential for Si26 and ultrasoft pseudopotentials for As, hydrogen (H), and fluorine (F).27 In the As pseudopotential, the 3d orbitals are explicitly dealt with as valence electrons. Unless otherwise mentioned, the calculation model is a cubic supercell with a side of ∼2.5 nm, corresponding to a crystal containing 1000 Si atoms. The sampled k-point is a single Γ point, and the cutoff energy is 30.25 Ry. The calculation code is xTAPP,28 which is a highly parallelized version of the plane-wave-based code TAPP (Tokyo ab initio program package).29 

The formation energy Eform of nAs As atoms, nSi Si atoms, and ne extra electrons is defined as

Eform=E[nAs,nSi,ne]nAsμAsnSiμSineμe,

where E is the total energy calculated in the 1000-atom supercell and μAs, μSi, and μe are the chemical potentials for As, Si, and electrons, respectively. The extra electrons are required to obtain charged states from a neutral state. μSi and μAs are set to the energy per atom of a Si crystal and a substitutional As atom (Ass), that is, μSi = E[Si]/1000 and μAs = E[Ass] − 999μSi, where E[Si] and E[Ass] are the total energies calculated in the 1000-atom supercell for a pure Si crystal and Ass, respectively. Since the Si wafers doped near the surface by methods such as ion implantation and plasma doping are considered, where the region deep from the surface is bulk Si with few As atoms, it is reasonable to take the energy of Ass as μAs, which corresponds to the As-dilute and the Si-rich limit. In this study, μe is the Fermi energy and is set to the calculated energy of the conduction band bottom of the pure Si crystal. It is well known that the bandgaps calculated using the GGA as well as the local density approximation are underestimated. The calculated and experimental bandgaps are 0.64 eV and 1.17 eV,30 respectively. Thus, there is a possibility that the formation energies of negatively (positively) charged defects might be slightly overestimated (underestimated). For the charge state calculation, we consider energy correction. The Makov–Payne correction is well known in this field.31 Although this correction gives very accurate results for atoms and molecules, defect formation energy is fairly overestimated.32,33 In this study, the results for the charged states do not include any correction because supercells are sufficiently large for obtaining accuracy, as described in Sec. III.

For the XPS binding energy calculation of the As 3d states, we adopt the ΔSCF method.34 Using this method, we obtain the XPS binding energy as the difference between the total energy in the ground state and that in the state where one electron in the relevant state is removed. However, removing an electron from one orbital among the nearly degenerate core states such as the five 3d orbitals causes the serious problem that self-consistent calculations do not converge for large systems. Thus, we adopt spherical hole approximation (SHA), by which the remaining hole is distributed in equal parts and assigned to all the nearly degenerate orbitals. This treatment is essentially used for the screened core hole pseudopotentials,35 which are commonly used for the XPS binding energy calculation, because their generation is usually under a spherically symmetrized charge distribution. As a test calculation, we obtained the XPS binding energy shift between the molecules AsF3 and AsF5 to be 2.36 eV and 2.35 eV by the ΔSCF method without and with the SHA, respectively, whereas the experimental value was 2.4 eV.36 For the XPS binding energy calculation of the systems including more than one As atom, owing to the code restriction, we replaced the As pseudopotential for irrelevant As atoms by the pseudopotential in which the 3d orbitals were treated as core states, not as valence states.

In this section, we describe the defect and supercell models, for which the formation energy and the XPS binding energy of As 3d are calculated. The optimized atomic configurations for principal defects in the neutral and spinless states are shown in Fig. 1.

FIG. 1.

Optimized atomic structures of defects in the neutral and spinless states. Yellow and red balls refer to Si and As atoms, respectively. The x, y, and z axes in each figure correspond to [100], [010], and [001] directions, respectively. For the abbreviations for the defect structures, see Sec. III.

FIG. 1.

Optimized atomic structures of defects in the neutral and spinless states. Yellow and red balls refer to Si and As atoms, respectively. The x, y, and z axes in each figure correspond to [100], [010], and [001] directions, respectively. For the abbreviations for the defect structures, see Sec. III.

Close modal

The defect models are constructed based on theoretical and/or experimental proposals. They are classified into three groups: defects including one As atom, combinations of two substitutional As atoms, and vacancy-related defects.

Substitutional As (Ass) is the most important and common defect in Si, which generates electrons and is used as the n-type dopant for Si-based devices. The interstitial As at the hexagonal site (Asi@H) is in a metastable configuration. The hexagonal (H)-site is the center position of the Si six-membered ring. On the other hand, the tetrahedral (T)-site, which is tetrahedrally surrounded by four Si atoms, is unstable for the interstitial As atom. ⟨001⟩ and ⟨110⟩ As–Si are the configurations where the As–Si pair occupies one Si site and is aligned along the ⟨001⟩ and ⟨110⟩ directions, respectively.

The two substitutional As atoms in the first, second, and third nearest neighbor sites: Ass2 (first), Ass2 (second), and Ass2 (third), respectively, are considered, where all the As atoms are fourfold coordinated. DP(2) suggested in Ref. 5 is the configuration where two originally substitutional As atoms in the second nearest neighbors for each other take a threefold coordination and the two remaining dangling bonds of Si are connected.

Vacancies are very important when discussing As defect behaviors such as stability, electric activities, and diffusion.3,4

A pair of As and the nearest neighbor vacancy (AsV) is known as the E center and one of the most studied defects. The spinless high-symmetry structure of neutral AsV has C3v symmetry and twofold degenerate states occupied by one electron. Thus, the lattice Jahn–Teller effect lowers the symmetry into C1h, where two different configurations in pairing and resonant-bond distortions are reported.8 These three types of defects are separately dealt with as AsV(C3v), AsV(P), and AsV(R), which refer to the arsenic and vacancy pairs with C3v symmetry, pairing distortion, and resonant-bond distortion, respectively. In AsV(C3v), three nearest neighbor Si atoms of a vacancy form a regular triangle. The Jahn–Teller effect distorts this regular triangle into an isosceles triangle, where the length of the two equivalent edges is longer (shorter) than that of the rest edge in AsV(P) [AsV(R)]. A pair of an As atom and the second nearest neighbor vacancy (Ass–Si–V) was examined in Ref. 15.

We also adopted clusters of vacancies surrounded by two, three, and four substitutional As atoms, which are abbreviated as As2V, As3V, and As4V, respectively. As4V is the most stable and electrically inactive cluster.2 It has been suggested that As2V plays an important role in diffusion under a heavily doped condition.4 

For the calculation of defects, physical quantities such as formation and XPS binding energies are dependent on the supercell form and size. Expecting the rapid convergence of charged defects, we adopt cubic supercells.31 To discuss isolated defect properties, we should obtain convergent values with respect to the supercell size.

To evaluate the convergence of formation and XPS binding energies, we calculate their values for some defects using supercell sizes of 64, 216, 512, 1000, and 1728 Si atoms. For the 64-Si-atom supercell, the sampled k-point mesh is 3 × 3 × 3. For the other cells, we adopt the single Γ-point. The results are shown in Figs. 2 and 3. The horizontal axis refers to the number of atoms per supercell for a pure Si crystal. The circles, squares, and triangles indicate Ass, Asi@H, and AssV, respectively. The charged defects considered are Ass+, Asi@H+, and AssV. Closed and open symbols refer to the neutral and charged states, respectively. It is found that the convergence of charged defects is slower than that of neutral defects for both the formation and XPS binding energies. From these figures, the supercell with 1000 Si atoms achieves convergence of the formation and XPS binding energies within 0.04 eV, which is better than our criterion of accuracy of 0.1 eV. Thus, we adopt the cubic supercell of 1000 Si atoms in this work.

FIG. 2.

Supercell size dependence of formation energy for defects. The horizontal axis refers to the number of atoms per supercell of a pure Si crystal. The circles, squares, and triangles indicate substitutional As (Ass), interstitial As at the H-site (Asi@H), and the pair of the substitutional As atom and a vacancy (AssV), respectively. Closed and open symbols refer to the neutral and charged states, respectively. The charged defects are Ass+, Asi@H+, and AssV. The origin of the formation energy for each supercell is set to that for neutral Ass, whose symbols are not shown.

FIG. 2.

Supercell size dependence of formation energy for defects. The horizontal axis refers to the number of atoms per supercell of a pure Si crystal. The circles, squares, and triangles indicate substitutional As (Ass), interstitial As at the H-site (Asi@H), and the pair of the substitutional As atom and a vacancy (AssV), respectively. Closed and open symbols refer to the neutral and charged states, respectively. The charged defects are Ass+, Asi@H+, and AssV. The origin of the formation energy for each supercell is set to that for neutral Ass, whose symbols are not shown.

Close modal
FIG. 3.

Supercell size dependence of the As 3d core-level shift of XPS binding energy for defects. The horizontal axis refers to the number of atoms per supercell of a pure Si crystal. Closed and open symbols refer to the neutral and charged states, respectively. The origin of the core-level shift for each supercell size is the XPS binding energy of the neutral substitutional As, whose symbols are not shown. The symbols are the same as those in Fig. 2.

FIG. 3.

Supercell size dependence of the As 3d core-level shift of XPS binding energy for defects. The horizontal axis refers to the number of atoms per supercell of a pure Si crystal. Closed and open symbols refer to the neutral and charged states, respectively. The origin of the core-level shift for each supercell size is the XPS binding energy of the neutral substitutional As, whose symbols are not shown. The symbols are the same as those in Fig. 2.

Close modal

For the calculation of defects, we must compare the XPS binding energies for each defect in different supercells. The origins of the energy should coincide among the supercells, that is, the local potential in the most remote atom from a defect is the same among the supercells. To evaluate the local potential at the supercell boundary, we calculate the average local potential within a sphere of a radius of 1.6 bohrs centered on a Si atom near the vertex of the cubic supercell. These values for the 1000-Si-atom supercell are described in Sec. IV.

We consider spin polarization for the configurations with odd numbers of electrons in the gap states, and the difference between the numbers of up-spin and down-spin electrons is denoted Δspin. In the non-spin-polarized calculation, there are no defects with doubly or triply degenerate highest occupied orbitals with more than one electron in the bandgap. Thus, we only consider the case of Δspin = 1. The Fermi level is assumed to be at the bottom of the conduction band because we are considering donor-doped systems. We examined the possibilities of charged states for the defect models whose highest occupied orbitals or lowest unoccupied orbitals of the neutral states are close to the Fermi level. Such configurations have empty states below the conduction band bottom and/or occupied states near the conduction band bottom. The exception is AsV+, whose donor state in the lower half of the bandgap was evaluated experimentally and theoretically,10 although it usually behaves as an acceptor.

In Table I, we summarize the calculated formation energies and XPS binding energies for the As defects in Si. Δspin is the difference between the electron numbers with major and minor spins. For the spin-polarized defects with Δspin = 1, there are two rows of XPS binding energies, where the upper and lower binding energies correspond to the photoelectrons with major and minor spin components, respectively. ΔLPT is the difference between the local potential average of the most distant atom from the defect and that of an atom in the pure Si crystal. From Table I, the values of ΔLPT are within 0.1 eV, which means that the calculated XPS binding energies are expected to be compared for each other with this accuracy.

TABLE I.

Formation energy (energy) and As 3d core-level shift of x-ray photoelectron spectroscopy binding energy (XPS BE) of arsenic defects. The origin of the energies is non-spin-polarized substitutional arsenic (Ass). Δspin refers to the difference between the numbers of electrons with major and minor spins. The Fermi energy is set to the conduction band bottom. ΔLPT is the difference between the local potential average of the most distant atom from the defect and that of an atom in the pure Si crystal. Defects with Δspin = 1 have two XPS binding energies, where the upper and lower binding energies correspond to the photoelectrons with major and minor spin components, respectively.

Neutral stateCharged state
ΔspinEnergy (eV)XPS BE (eV)ΔLPT (eV)ΔspinEnergy (eV)XPS BE (eV)ΔLPT (eV)
Ass 0.00 0.00 0.03 Ass+ 0.01 0.40 0.04 
 0.00 0.02 0.03      
   −0.07       
Asi@H 3.39 −0.48 0.04 Asi@H+ 3.39 −0.34 0.05 
 3.39 −0.48       
   −0.50       
⟨001⟩ As–Si 3.23 −0.80 0.02 ⟨001⟩ As–Si 2.74 −1.15 −0.01 
 2.96 −0.99 0.02      
   −1.00       
⟨110⟩ As–Si 3.01 −0.82 0.02 ⟨110⟩ As–Si 2.70 −1.39 −0.01 
 2.96 −0.77 0.02      
   −0.78       
Ass2(first) 0.08 −0.64 0.02 Ass2(1st)+ 0.23 −0.13 0.05 
      0.20 −0.08 0.05 
        −0.12  
     Ass2(1st)2+ 0.48 0.37 0.07 
Ass2(second) 0.09 −0.17 0.05 Ass2(2nd)+ 0.12 0.09 0.06 
      0.12 0.10 0.06 
        0.00  
     Ass2(2nd)2+ 0.18 0.54 0.07 
Ass2(third) 0.05 −0.21 0.05 Ass2(3rd)+ 0.08 0.06 0.06 
      0.08 0.07 0.06 
        −0.02  
     Ass2(3rd)2+ 0.13 0.51 0.07 
DP(2) 0.99 −0.73a 0.01      
   −0.68a       
AsV(C3v2.46 −0.71 −0.01 AsV(C3v)+ 2.77 −0.62 0.01 
 2.41 −0.71 −0.01 AsV(C3v) 2.28 −0.81 −0.04 
   −0.71       
AsV(P) 2.41 −0.68 −0.01 AsV(P)+ 2.78 −0.61 0.01 
 2.29 −0.66 −0.01 AsV(P) 2.10 −0.77 −0.03 
   −0.66       
AsV(R) 2.41 −0.68 −0.01 AsV(R)+ 2.77 −0.62 0.01 
 2.33 −0.68 −0.01 AsV(R) 2.03 −0.72 −0.04 
   −0.68       
As–Si–V 3.31 −0.09 −0.01      
 3.25 −0.08 −0.01      
   −0.08       
As20.78 −0.67 0.00 As2V 0.76 −0.73 −0.01 
      0.73 −0.77 −0.02 
        −0.77  
     As2V2− 0.75 −0.74 −0.01 
As3−0.36 −0.69 0.00 As3V −0.60 −0.82 −0.02 
 −0.48 −0.66 0.00      
   −0.67       
As4−1.99 −0.69 0.01      
Neutral stateCharged state
ΔspinEnergy (eV)XPS BE (eV)ΔLPT (eV)ΔspinEnergy (eV)XPS BE (eV)ΔLPT (eV)
Ass 0.00 0.00 0.03 Ass+ 0.01 0.40 0.04 
 0.00 0.02 0.03      
   −0.07       
Asi@H 3.39 −0.48 0.04 Asi@H+ 3.39 −0.34 0.05 
 3.39 −0.48       
   −0.50       
⟨001⟩ As–Si 3.23 −0.80 0.02 ⟨001⟩ As–Si 2.74 −1.15 −0.01 
 2.96 −0.99 0.02      
   −1.00       
⟨110⟩ As–Si 3.01 −0.82 0.02 ⟨110⟩ As–Si 2.70 −1.39 −0.01 
 2.96 −0.77 0.02      
   −0.78       
Ass2(first) 0.08 −0.64 0.02 Ass2(1st)+ 0.23 −0.13 0.05 
      0.20 −0.08 0.05 
        −0.12  
     Ass2(1st)2+ 0.48 0.37 0.07 
Ass2(second) 0.09 −0.17 0.05 Ass2(2nd)+ 0.12 0.09 0.06 
      0.12 0.10 0.06 
        0.00  
     Ass2(2nd)2+ 0.18 0.54 0.07 
Ass2(third) 0.05 −0.21 0.05 Ass2(3rd)+ 0.08 0.06 0.06 
      0.08 0.07 0.06 
        −0.02  
     Ass2(3rd)2+ 0.13 0.51 0.07 
DP(2) 0.99 −0.73a 0.01      
   −0.68a       
AsV(C3v2.46 −0.71 −0.01 AsV(C3v)+ 2.77 −0.62 0.01 
 2.41 −0.71 −0.01 AsV(C3v) 2.28 −0.81 −0.04 
   −0.71       
AsV(P) 2.41 −0.68 −0.01 AsV(P)+ 2.78 −0.61 0.01 
 2.29 −0.66 −0.01 AsV(P) 2.10 −0.77 −0.03 
   −0.66       
AsV(R) 2.41 −0.68 −0.01 AsV(R)+ 2.77 −0.62 0.01 
 2.33 −0.68 −0.01 AsV(R) 2.03 −0.72 −0.04 
   −0.68       
As–Si–V 3.31 −0.09 −0.01      
 3.25 −0.08 −0.01      
   −0.08       
As20.78 −0.67 0.00 As2V 0.76 −0.73 −0.01 
      0.73 −0.77 −0.02 
        −0.77  
     As2V2− 0.75 −0.74 −0.01 
As3−0.36 −0.69 0.00 As3V −0.60 −0.82 −0.02 
 −0.48 −0.66 0.00      
   −0.67       
As4−1.99 −0.69 0.01      
a

DP(2) defect has two inequivalent As atoms. The As atoms reveal slightly different core-level shifts.

Hereafter, we adopt the As 3d core-level XPS binding energy of non-spin-polarized substitutional As (Ass) as the origin for the binding energy and discuss the relative shift, where a positive (negative) value refers to a larger (smaller) binding energy than that of Ass. For the formation energy, we also adopt that of non-spin-polarized Ass as the origin and discuss the relative values.

Overall, the spin polarization slightly decreases the formation energy. Since, for the spin-polarized region, the local potential with the major spin is lower than that with a minor spin owing to the exchange energy, the XPS binding energy of the photoelectron with a major spin (upper row) tends to be larger than that with the minor spin (lower row).

Among AsV defects, AsV(C3v), whose configurations are optimized under C3v symmetry, is a saddle point of total energy in the negative and neutral charge states and a minimum in the positive charge state. In the neutral state, AsV(P) has 0.04 eV lower energy than AsV(R). In contrast, in the negative charge state, AsV(R) has a lower energy by 0.07 eV. These most stable types are in agreement with the result in Ref. 8. As pointed out in Ref. 10, the potential surface of the AsV defects is very flat. In Table II, the edge lengths of the isosceles triangle, which define the AsV type of C3v, pairing, and resonant bond, are shown. In the positive charge states, owing to the flat energy surface, the optimizations of AsV(P) and AsV(R) were stopped by the force criterion, before they reached the C3v structures. The length of two equivalent edges (L1) and that of the other edge (L2) in AsV(P)0 are 3.57 (3.37) and 3.07 (2.85), respectively. The values in parentheses are taken from Ref. 8, which are slightly smaller than the present ones. Since their calculations are based on the cluster models up to AsSi206H158, it may be difficult for Si atoms to expand outward.

TABLE II.

Edge length (Å) of the isosceles triangle formed by the Si atoms adjacent to the vacancy in defects of the pair of As and vacancy (AsV). L1 and L2 correspond to the length of two equivalent edges and that of the other edge, respectively.

C3vPairingResonant
L1L2L1L2L1L2
AsV0 3.55 3.55 3.57 3.07 3.33 3.60 
AsV 3.44 3.44 3.37 2.86 2.91 3.54 
AsV+ 3.56 3.56 … … … … 
C3vPairingResonant
L1L2L1L2L1L2
AsV0 3.55 3.55 3.57 3.07 3.33 3.60 
AsV 3.44 3.44 3.37 2.86 2.91 3.54 
AsV+ 3.56 3.56 … … … … 

Considering the combination of a vacancy and adjacent As atoms, and DP(2), the distribution of the XPS binding energy is in the very narrow region from −0.82 to −0.66, where the positive charged states are neglected. All such As atoms have locally threefold configuration bonding to three silicon atoms. This means that the XPS binding energy of As 3d is mainly affected by the connecting Si atoms.

The XPS binding energies are −0.66 (−1.05), −0.67 (−0.94), −0.69 (−0.99), and −0.69 (−0.68) for defects AsV, As2V, As3V, and As4V, respectively, where the values in parentheses are taken from Ref. 15. It seems that the defects with states in the gap show large discrepancies. Such discrepancies are probably due to the small 64-Si-atom supercell.

In this section, we discuss the assignment of the experimental peaks.

Tsutsui and co-workers investigated As 3d in Si by XPS and spectro-photoelectron holography measurements and found the three XPS peaks BEL, BEM, and BEH in the order of XPS binding energy. They also reported that the carrier concentration is 7.5 × 1019 cm−3 (0.15 atom %) with an experimental error of ±20%, which corresponds to the activation rate of 50%. The relative peak intensities of BEH, BEM, and BEL were reported as 37%, 39%, and 24%, respectively. Assuming BEH is due to Ass and electrically active, BEM and BEL are expected to be electrically inactive As defects. Thus, Tsutsui et al. suggested that AsnV (n = 2–4) cause BEM and that BEL is due to electrically inactive disorder structures because the holographic image had no clear regular patterns.15 

In Ref. 15, BEM and BEH are reported as 0.4 eV and 1.2 eV measured from BEL, respectively. From electrical activation, BEH is considered to be Ass. In this work, we refer to BEH, BEM, and BEL as 0.0 eV, −0.8 eV, and −1.2 eV, respectively, measured from the value of Ass.

Before the assignment of the peaks, we mention the previous assignment by our group in Ref. 22. Although the calculated XPS binding energies are similar to the present ones, the vacancy-related defects were assigned to BEL whose binding energy was about −1.2 with the reference energy of Ass+, not Ass. This assignment was based only on the previous work by Tsutsui et al.13 and not on the work by Kanehara et al.14 In the former work, only two peaks, BEH and BEL, were reported. At a high carrier concentration, the neutral substitutional arsenic is the most common charge state because conduction electrons screen the Ass+ ion well. Thus, the assignment of BEH to Ass+ was considered incorrect.

Considering the XPS binding energy of BEM (−0.8 eV), from Table I, the probable candidates are ⟨001⟩ As–Si, ⟨110⟩ As–Si, DP(2), and negatively charged AsnV (n = 1–3). The XPS binding energies of these defects range from −0.73 eV to −0.82 eV. ⟨001⟩ As–Si and ⟨110⟩ As–Si are negatively charged under the n-type condition. The XPS binding energies of ⟨001⟩ As–Si and ⟨110⟩ As–Si are −1.15 eV and −1.39 eV, respectively, which are markedly different from −0.8 eV. Thus, these two defects can be excluded. According to Ref. 15, BEM is expected to be electrically inactive. Among the vacancy-related defects AsnV (n = 1–3), As1V and As3V are negatively charged under the n-type condition. Therefore, these defects are not electrically inactive, trap electrons, and compensate carriers. In this sense, DP(2) is favorable. The structure of DP(2) is, however, largely distorted from lattice sites and seems difficult to explain the spectro-photoelectron image for BEM. The last candidate is negatively charged As2V, that is, As2V and As2V2−. From the small formation energy difference between the neutral and charged states, the excess electrons occupy a shallow level and/or the conduction band. That is, As2V and As2V2− do not deeply trap electrons and are electrically inactive. The high carrier concentration of 0.15 at. % obtained in experiments means that there are 1.5 electrons in our model supercell. In the presence of these excess carriers, As2V are effectively in negative charge states. Therefore, we suggest that the most favorable defect candidates for BEM are negatively charged As2V.

Next, we discuss the peak of BEL. From the calculated XPS binding energy, ⟨001⟩ As–Si has the value closest to −1.15 eV. The formation energy for this defect (2.74 eV) may be high for the candidates. Tsutsui et al. suggested that the origin of BEL is disordered structures such as As–Si precipitates or the amorphous area in matrix Si from holographic images. In the amorphous area, the structures similar to ⟨001⟩ As–Si might be stabilized. Although the suggestion of disordered structures is convincing, let us consider the surface effect as another possible origin of defects with a low XPS binding energy. It is reported that low XPS binding energies appear owing to the large relaxation energy, when localized electron states are near the atom emitting a photoelectron.37,38 If surface states act as local states, it is expected that As near the surface shows low XPS binding energies similar to BEL.

We examined the depth dependence of the XPS binding energy of Ass from the surface for two kinds of surfaces, a hydrogen (H)-terminated surface [Si(001) (1 × 1)-H structure] and a dimer surface [Si(001) p(2 × 2)-antisymmetric dimer surface]. We use slab models. The back surfaces of the slabs for the above two models are H-terminated. In the unit of a common cubic cell of eight Si atoms, the H-terminated surface model has a 5 × 5 × 4 Si slab in a 5 × 5 × 5 supercell and the dimer surface model has a 42×42×4 Si slab in a 42×42×42 supercell. The results are shown in Fig. 4. The open and closed circles correspond to the XPS binding energy shift for the H-terminated and dimer surfaces, respectively. The range of surface effects is about 7 Å from the surface. We can find the trend that XPS binding energies become large and small for the H-terminated and dimer surfaces, respectively, as the As atom approaches the surface from the slab center. The H-termination forms solid bonds between Si and H with a relatively low energy. The dimer surface has surface states in the bandgap.39 The relaxation energies of As 3d for the H-terminated and dimer surfaces are small and large, which causes large and small XPS binding energies, respectively. Thus, the defects near surface states with high energies are expected to have low XPS binding energies.

FIG. 4.

Depth dependence of As 3d XPS binding energy shift of substitutional As (Ass). The horizontal axis is the distance of an As atom from the slab center. Open and closed symbols correspond to the H-terminated Si(001) (1 × 1) surface and the Si(001)-p(2 × 2) antisymmetric dimer surface, respectively. The rightmost symbols for each data correspond to the first surface layer.

FIG. 4.

Depth dependence of As 3d XPS binding energy shift of substitutional As (Ass). The horizontal axis is the distance of an As atom from the slab center. Open and closed symbols correspond to the H-terminated Si(001) (1 × 1) surface and the Si(001)-p(2 × 2) antisymmetric dimer surface, respectively. The rightmost symbols for each data correspond to the first surface layer.

Close modal

We performed the comprehensive first-principles calculation of the As 3d core-level XPS binding energy and formation energy for As defects in Si with high accuracy by careful evaluation of the supercell size. With large size systems, the convergence of self-consistent calculations is ensured for the XPS binding energy using the spherical hole approximation. Some of the examined defect models have locally threefold coordinated As atoms. The XPS binding energies of such As atoms are distributed in the narrow region from −0.66 eV to −0.73 eV. Such negatively charged defects have lower XPS binding energies by about 0.1 eV than those in the neutral state. From the XPS binding energy and electrical activity, we suggest that negatively charged As2V defects are the most probable candidates for the experimental peak BEM. Under the experimental condition in Refs. 15–17, we find that As2V−,2− do not deeply trap electrons and are electrically inactive. We also demonstrate the surface effect that surface states near the bandgap lower the XPS binding energy, which may cause defects with low binding energies similarly to the experimental peak BEL.

This work was supported by a Grant-in-Aid for Scientific Research (Grant No. 22104006) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT). Part of the computations was performed at the Research Center for Computational Science, Okazaki, and the Supercomputer Center, Institute for Solid State Physics, University of Tokyo, Japan.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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