Change of Electronic Structures by Dopant-Induced Local Strain

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Abstract Ag-induced Si(111)-"Equation missing" surfaces ("Equation missing"-Ag) exhibit unusual electronic structures that cannot be explained by the conventional rigid band model and charge transfer model. The ("Equation missing"-Ag surfaces feature a free-electron-like parabolic band, the S 1 band, that selectively shifts downward upon the adsorption of noble metal or alkali metal adatoms. Furthermore, the downward shift of S 1 is independent of the type of dopants, Au, Ag and Na. According to charge transfer analysis, Au adatoms accumulate electrons from the substrate and become negatively charged, whereas Na adatoms become positively charged, which indicates that S 1 should shift in the opposite direction for both the adatoms. Investigation of calculated structures, calculation of model structures and tight-binding analysis disclose that the changes in the electronic structure are closely related to the average Ag-Ag distance in the substrate and have their origin in the local strain induced by dopants (adatoms). This explanation implies that the electronic structure is irrespective of the dopant characters itself and paves a new way for understanding the electronic structures associated with the presence of dopants.

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received: 20 January 2015

accepted: 12 May 2015

Published: 10 June 2015

# Change of Electronic Structures by Dopant-Induced Local Strain

Gyu Hyeong Kim & Sukmin Jeong

Ag-induced Si(111)- 3 × 3 surfaces ( 3 -Ag) exhibit unusual electronic structures that cannot be
explained by the conventional rigid band model and charge transfer model. The ( 3 -Ag surfaces
feature a free-electron-like parabolic band, the _S_ 1 band, that _selectively_ shifts downward upon the
adsorption of noble metal or alkali metal adatoms. Furthermore, the downward shift of _S_ 1 is
_independent_ of the type of dopants, Au, Ag, and Na. According to charge transfer analysis, Au
adatoms accumulate electrons from the substrate and become negatively charged, whereas Na
adatoms become positively charged, which indicates that _S_ 1 should shift in the opposite direction for
both the adatoms. Investigation of calculated structures, calculation of model structures, and tightbinding analysis disclose that the changes in the electronic structure are closely related to the
average Ag-Ag distance in the substrate and have their origin in the local strain induced by dopants
(adatoms). This explanation implies that the electronic structure is irrespective of the dopant
characters itself and paves a new way for understanding the electronic structures associated with the
presence of dopants.

The electronic structure of a material can undergo changes in the presence of foreign atoms (dopants).
These changes form the basis of a fundamental research topic in the field of condensed matter physics.
Electronic structures that may be tuned through control over the type or quantity of dopant present
in the material feature in a wide range of practical applications. Current semiconductor device designs
exploit these effects by introducing heterogeneous impurities that act as electron donors or acceptors
with respect to the semiconductor. The electronic structure of graphene, including the band gap and the
polarity change, may be modified using electron or hole doping. These methods are currently the subject
of intensive investigations that seek to improve the utility of graphene in a variety of practical applications. The rigid band model, in which the electronic structure is understood in terms of the host material’s electronic structure 1, offers a broadly useful model of doping. The dopant donates or accepts charge
to or from the host material. The electronic structures of doped topological insulators 2,3 or graphene 4
may be understood in terms of this framework.

The electronic structure of Ag-induced Si(111)- 3 × 3 (hereafter, 3 -Ag) surfaces is strange in
this sense. The 3 -Ag surfaces act as a two-dimensional electron gas (2DEG) system in which the surface
bands ( _S_ 1) are characterized by a parabolic dispersion that creates the free electron gas conditions 5–13 .
The introduction of a dopant (adatom, in this case), such as an alkali or noble metal, shifts only the _S_ 1
band downward in proportion to the dopant coverage. These selective shifts of _S_ 1 are inconsistent with
the standard rigid band model. Furthermore, an interesting feature of this system is that the electronic
structures observed using angle-resolved photoemission spectroscopy (ARPES) are nearly equivalent in
the context of doping with a variety of adatoms: Na, Ag, or Au 10 . These band shifts have been ascribed
to charge transfer from the dopant to the surface band 6–12 ; however, the electron affinities of the elements,
1.39 eV for Si, 1.30 eV for Ag, 2.31 eV for Au, and 0.55 eV for Na 14–17, indicate that Au functions as an
acceptor whereas Na functions as a donor. That is, the _S_ 1 band should shift in the opposite direction upon
Au or Na adatom doping. Clearly, a traditional charge transfer model fails in the present system; thus a
new mechanism must be proposed to explain the changes in the electronic structures of the 3 -Ag
surfaces in the presence of adatoms.

Department of Physics and Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 561[756, Korea. Correspondence and requests for materials should be addressed to S.J. (email: jsm@chonbuk.ac.kr)](mailto:jsm@chonbuk.ac.kr)

Figure 1. Calculated atomic structures of ( a ) the 3-Ag substrate and substrates prepared with ( b ) one Au
(0.021 ML), ( c ) two Au (0.042 ML), or ( d ) three Au adatoms (0.063 ML), respectively. White spheres
represent the substrate Si atoms that formed Si triangles (SiTs), and the yellow and red spheres represent
substrate Ag atoms and Au adatoms, respectively. The green and blue solid lines in ( a ) indicate the large
triangle (LT) and the small triangle (ST) in the IET model, respectively. The dashed triangles in ( b )–( d )
represent the STs expanded by the exchanged Ag atoms.

In this report we investigate the anomalous band shift observed in systems comprising 3 -Ag surfaces doped with Au, Na, or Ag adatoms using first-principles calculations for the atomic and electronic
structures obtained under a variety of coverage levels. The charge analysis described here reveals that
charge transfer occurs from the substrate to the adatom in the context of Au doping, and the direction
of charge transfer is reversed in the context of Na doping, as expected based on the electron affinities.
Despite the differences in the charge polarities of the adatoms relative to the substrate, the electronic
structures calculated for a given adatom coverage are similar for Au, Na, and Ag adatom doping, in
agreement with the ARPES data. Furthermore, the downward shift in _S_ 1 increases in magnitude with the
adatom coverage. We find that the magnitude of the band shift is correlated with the average distance
between the surface Ag atoms. A plot of the calculated band shift as a function of the adatom height and
a simple tight-binding argument support this model.

Results
The atomic structure of the 3 -Ag surface is appropriately modeled using the inequivalent triangle (IET)
model 18, in which the surface Ag atoms form two types of inequivalent triangles: small triangles (ST) and
large triangles (LT), and the Si atoms formed Si trimer (SiT) surrounded by six Ag triangles, as shown
in Fig. 1(a). An Ag adatom occupies on a ST site which is the most stable, and its incorporation into the
substrate is accompanied by considerable changes in the bond network around the adatom 19 . On the
other hand, according to our recent paper 20, the Au adatom that has deposited at the LT site easily
exchanges the position with the neighboring Ag atom occupying nearby ST site, as indicated by the
dashed triangle in Fig. 1(b). The structure shown in Fig. 1(b) is nearly equivalent to the structure obtained
upon occupation of an ST site with a single Ag adatom. We find that a greater number of Au adatoms
occupy stable positions upon the formation of an Au cluster, as shown in Fig. 1(c,d). The structures of
the Ag 11 and Na 21 adatom clusters differ slightly from those shown in Fig. 1.

Substrate Si

Atoms

Structure Adatom Si trimers

Ag
atoms

1Au 0.45 - 0.29 - 0.03 - 0.13

1Ag 0.01 - 0.01 0.09 - 0.09

1Na - 0.80 0.42 0.44 - 0.06

Table 1. Calculated Bader charges of the most stable Au, Ag, and Na adatom structures on the 3 -Ag
surface. The Bader charges of the 3-Ag substrate were set to zero. The minus sign indicates electron loss
from the neutral atom.

The calculated adsorption energies, defined as the energy gain of the cluster structures with respect
to the energies of the substrate and free atoms, are 3.25, 3.34, and 3.58 eV/Au for one, two, and three
Au adatoms, respectively. These values exceed the values obtained from Ag adatoms (~2.50 eV/Ag) or
Na adatoms (~1.81 eV/Na). The higher adsorption energies of the Au adatoms are a consequence of the
larger Au-Au, Au-Ag, and Au-Si bond energies compared with the Ag-Ag and Ag-Si bond energies. The
bond energies of Au-Au, Au-Ag, Ag-Ag, Au-Si, and Ag-Si are calculated as 2.29, 2.20, 1.79, 3.70 and
2.80 eV, respectively, for the Au-Au, Au-Ag, Ag-Ag dimer, and (Ag, Au)-SiH3 complex structures. The
Au-Au, Ag-Au, and Au-Si bond lengths of the most stable structures prepared using three Au adatoms
are 2.95, 2.80, and 2.44–2.65 Å, respectively, that is, comparable to the bond lengths of the three Ag
adatoms 11 .

The Bader analysis is used to calculate the magnitude of charge transferred from the Au, Ag, and Na
adatoms to the substrate (see Methods). The calculation results are summarized in Table 1. The Au adatom extracts a 0.45 _e_ electronic charge from the surface (Ag layer + Si trimer) and bulk Si atoms, mainly
from the Si trimers, whereas the Na adatom donates a charge of 0.80 _e_ to the surface Ag atoms and Si
trimers. On the other hand, the Ag adatom remains almost neutral. These results indicate that the Au
(Na) adatom functions as an electron acceptor (donor) on the 3 -Ag surface, and the Ag adatom does
not affect the charge state of the substrate. The adatom charge accumulation trend is consistent with the
trend in the electron affinities. The magnitude of charge transfer increases with the adatom coverage, i.e.,
the magnitude of the charge transferred per adatom remains nearly constant.

We next simulate the ARPES spectra of the pristine 3 -Ag surface and the surface in the presence of
Au adatoms, as represented in the surface Brillouin zone (SBZ) of the 3 × 3 unit cell. During the
ARPES spectra simulations, as shown in Fig. 2, the electronic bands in the SBZ of the super cell are
unfolded into the SBZ of the 3 -Ag using the method described in Methods. The calculated results can
be compared directly with the experimental results 9 by plotting the electronic bands around Γ2, the
center of the second SBZ. In the pristine 3 -Ag case shown in Fig. 2(a), the simulated spectrum displays
a characteristic free electron-like band near the Fermi level and a rather flat band near a binding energy
of 0.7 eV. Both bands correspond to the experimentally observed _S_ 1 and _S_ 2 bands. In the present calculations, the _S_ 1 band is separated from the _S_ 2 band by 0.51 eV, which is smaller than the experimental
value of ~0.75 eV. The _S_ 1 band mainly originates from the _px_ and _py_ orbitals of Ag and the _S_ 2 band corresponding to the Ag 5 _s_ orbital. The simulated spectrum obtained for the 3 -Ag substrate is consistent
with the spectra calculated previously 11 or derived from experiment 10 .

Figure 2(b–d) show the simulated ARPES spectra obtained from a surface in the presence of a single
Au adatom, two Au adatoms, or three Au adatoms in the super cell, corresponding to 0.02, 0.04, or
0.06 ML, respectively. The parabolic _S_ 1 band shifts downward as the Au adatom coverage increases, in
accordance with the experimental results 9 . The magnitudes of the band shift at Γ2 were 0.11, 0.19, and
0.31 eV for 0.02, 0.04, and 0.06 ML, respectively. Experimentally, the observed band shifts are ~0.16 and
~0.28 eV for 0.02 and 0.03 ML, respectively. Although the calculated values are smaller than the experimental values, the overall features agree well with experiments, considering the small band separation
between _S_ 1 and _S_ 2 in the calculation.

The ARPES spectra of the Na and Ag adatoms (not shown) are nearly identical to those obtained in
the presence of the Au adatoms, consistent with the experimental results. Despite the different charge
polarities of the adatoms (positive Na, neutral Ag, and negative Au), the observation of similar _S_ 1 band
shifts require a completely different interpretation. We note three effects that result from the presence of
all kinds of the adatoms: (i) a downward band shift signifies a higher binding energy, (ii) the _S_ 1 band
mainly originates from the Ag _px_ and _py_ orbitals, and (iii) the immersed adatom induces significant
distortions in the local structure of the 3 -Ag surface. These three effects suggest that the band shift is
strongly related to the local structure induced by the immersed adatoms, i.e., the Ag-Ag bonds in the
substrate are strengthened.

Because the bond strength is inversely proportional to the corresponding bond lengths, we investigate
the shift in the _S_ 1 band as a function of the Ag-Ag bond length, as shown in Fig. 3. The average Ag-Ag
distance ( _davg_ ) is calculated using the equation _davg_ = ∑ _i_ R _i_ - R _i_ + _δ_ / _N_ bond, where the index _i_ indicates
the _i_ -th Ag atoms other than the adatoms, _i_ + _δ_ represents the nearest neighboring Ag atom of the atom

Figure 2. Simulated ARPES spectra for the ( a ) 3-Ag substrate, ( b ) one, ( c ) two, or ( d ) three Au adatoms
on the 3-Ag substrate with 4 3 × 4 3 periodicity, corresponding to adatom coverages of 0.02, 0.04, and
0.06 ML, respectively. The inset in ( d ) displays the first and second surface Brillouin zone (SBZ) of the 3
-Ag substrate. The black, red, green, and blue lines in ( e ) indicate the intensity profiles of _S_ 1 at the Γ2
position for ( a ) 3-Ag, ( b ) one, ( c ) two, and ( d ) three Au adatoms, respectively.

Figure 3. Binding energies of the _S_ 1 band minima at the Γ2 point as a function of the average Ag-Ag
distance. The red circles, green triangles, and blue rectangles indicate the results obtained from the Ag, Au,
and Na adatoms, respectively.

_i_, and _N_ bond indicates the total number of Ag-Ag bonds present in the calculated super cell. As shown in
the figure, the magnitude of the band shift is approximately proportional to the decrease in the Ag-Ag
distance, which is related to the adatom coverage. Thus, the adatom coverage and the band shift appear
to be linearly related, as measured in the ARPES experiments.

Discussion
The relationship between the adatom coverage and the magnitude of the band shift is further explored
by performing calculations using a model system in which an adatom is present at a fixed height on the

3 -Ag surface. The adatoms are positioned at the ST site, and all coordinates except for the height are
relaxed along the direction of force. The electronic structure of the model system is calculated for various
heights and displays a shift in the _S_ 1 band for the Au, Ag, and Na adatoms, as shown in Fig. 4. The average Ag-Ag distance decreases as the adatom is incorporated into the surface level. Consequently, the _S_ 1
bands shifts downward in the presence of all types of adatom. The results obtained here reveal a very
important property of the origin of the band shift. _Without_ a change in the adatom coverage, the band
could be shifted only through structural changes.

The physical origin of the selective band shift is investigated using a simple tight-binding model. The
Ag overlayer is described using the Hamiltonian, _H_ 0 = ∑ _i_, _δ_ _Wci_ - _ci_ + _δ_, where the index _i_ indicates the _i_ -th

Figure 4. Binding energies of the _S_ 1 band minima at the Γ2 point as a function of the average Ag-Ag
distance, which was controlled by the adatom height. The insets in ( b - d ) show the side views of the model
structures in the presence of the Au adatoms at heights of 0.00, 0.75, and 1.50 Å from the surface,
respectively.

k ⋅ R

lattice point and _i_ + _δ_ indicates the nearest neighbor of _i_ . With _ci_ = (1/ _N_ ) ∑ k _e_ _i_ k ⋅ R _ic_ k, the eigenvector

and eigenvalue of _H_ 0 are _ψ_ k = ∑ _i_ _e_ _i_ k ⋅ R _i_ _i_ and _E_ k = _W_ ∑ _δ_ _e_ _i_ k ⋅ δ = 2 _W_ ∑ _δ_ cos k ⋅ δ, respectively. The

lattice point and _i_ + _δ_ indicates the nearest neighbor of _i_ . With _ci_ = (1/ _N_ ) ∑ k _e_ _i_ k ⋅ R _ic_

and eigenvalue of _H_ 0 are _ψ_ k = ∑ _i_ _e_ _i_ k ⋅ R _i_ _i_ and _E_ k = _W_ ∑ _δ_ _e_ _i_ k ⋅ δ = 2 _W_ ∑ _δ_ cos k ⋅ δ, respectively. The

adatom effects are observed by replacing a Ag atom at the _i_ ′ site with an adatom. Instead of changing the
atomic structure, for simplicity, the bond strength around the atom _i_ ′ is enhanced, and the corresponding hopping parameter is increased to _W_ ′ . The Hamiltonian could be written as
_H_ = _H_ 0 + _H_ 1 = _W_ ∑ _i_, _δ_ _ci_ - _ci_ + _δ_ + Δ _W_ ∑( _δ_ _ci_ †′ _ci_ ′+ _δ_ + _ci_ †′+ _δ_ _ci_ ′), where Δ _W_ = _W′_ - _W_ . The
time-independent perturbation theory is applied: _∆E_ = _ψ_ k _H_ 1 _ψ_ k, and the eigenvalue changes to
_E_ ′ k = _W_ ∑ _δ_ _e_ _i_ k ⋅ δ + (Δ _W_ / _N_ ) ∑( _δ_ _e_ _i_ k ⋅ δ + _e_ - _i_ k ⋅ δ ). The eigenenergy could be rewritten as

_ψ_ k = ∑ _i_ _e_ _i_ k ⋅ R _i_ _i_ and _E_ k = _W_ ∑ _δ_ _e_ _i_ k ⋅ δ = 2 _W_ ∑ _δ_ cos k

k = ∑ _i_ _e_ _i_

k _e_ _i_

_E_ ′ k = _W_ ∑ _δ_ _e_ _i_ k ⋅ δ + (Δ _W_ / _N_ ) ∑( _δ_ _e_ _i_ k ⋅ δ + _e_ - _i_ k ⋅ δ ). The eigenenergy could be rewritten as

_E_ ′ k = 2 ∑( _δ_ _W_ cos k ⋅ _δ_ + 2Δ _W_ / _N_ cos k ⋅ _δ_ ), given the inversion symmetry. Because the minimum
of _Ek_ is − _W_, the energy minimum of the impurity system shifts downward to − _W_ - 2Δ _W_ / _N_ because
Δ _W_ - 0. The coefficient of the second term, 1/ _N_, is related to the adatom coverage because in the present model, only one atom among the _N_ atoms is designated an adatom. The last expression above indicates that the band shift resulting from the strengthened bond in the presence of the adatoms is
proportional to the number of adatoms present. These features are consistent with the experimental
observations.

The downward shift in the _S_ 1 band indicates an increase in the band occupancy. It could still be
argued that because the main components of the _S_ 1 band are the substrate Ag orbitals, electronic charge
is transferred from the adatoms to the substrate; however, it is nearly impossible to clearly distinguish
between the substrate and the adatoms because the adsorbed adatoms induce structural rearrangements
in the substrate. Thus, the adatoms and the substate are considered to form a single system, and the
electronic charge of the whole system increases as the band shifts downward.

The Bader charge data in Table 1 shows that charge is mainly depleted from the Si trimers in the presence of Au adatoms and that the Si trimers and the Ag atoms obtains charge by almost equal amounts
in the presence of Na adatoms. It is of note that the total charge of the whole surface layer (adatom + Si
trimers + Ag atoms) is slightly negative and shows little variation according to the adatom. Although the
surface bands other than _S_ 1 have their characteristic orbital features, the characteristics are weak since
the surface bands are a mixture of the orbitals of many atoms. Thus the charge redistribution produced
by the adatoms seems to have little effects on the surface bands except for _S_ 1.

In the present mechanism, the electronic structure can be changed through the lattice distortion
induced by foreign atoms. This suggests that the mechanism has no restriction on the atomic species
involved in the system neither the dimension in which the foreign atoms are located. Hence, we expect
that the mechanism could be equally applied to a three-dimensional (3D) bulk crystal with interstitial impurities. What is important is how much the host material reacts with respect to the impurities.
Further experimental and theoretical investigations would be required in search for materials showing
this mechanism.

In conclusion, first-principles calculations are used to study the atomic and electronic structures of a
3 -Ag surface in the presence of Au, Ag, and Na adatoms for different coverage levels. The adatoms tend

to form clusters as the coverage level increases. The simulated ARPES spectra are consistent with the
experimental spectra, and the _S_ 1 band shifts are reproduced well. The charge transfer calculations reveal
that the Au and Na adatoms induce opposing charge transfer effects, and the charge transfer model and
the rigid band model are not valid in this system. Instead, model calculations of the artificial structures
and a simple tight-binding argument are applied to determine that the downward shift in the _S_ 1 band
arise from strengthened substrate Ag-Ag bonds. The present findings describe a new class of mechanisms
by which the electronic structures of a host material change upon introduction of impurity atoms. This
mechanism provides a new framework for interpreting the electronic structures associated with the presence of impurity atoms in all kinds of the one-, two-, and three-dimentional systems.

Methods
All calculations are performed using the Vienna _ab-initio_ simulation package (VASP) 22,23, which incorporates ultrasoft pseudopotentials 24 and the general gradient approximation (GGA) of Perdew and
Wang 25 for the exchange-correlation energy of the electrons. We simulate the surfaces using a repeated
slab model with a 4 3 × 4 3 lateral periodicity to include six Si layers and 10 Å vacuum layers. The
2 × 2 k-point mesh, including the Γ point, is used for surface Brillouin integration. These parameters
produce convergent results 20 . All atoms except for the bottom-most Si and H atoms are relaxed until the
residual force acting on each atom drops below 0.02 eV/Å. The 13 Ry cutoff energy is used to expand the
wave functions in the plane-wave basis in all calculations.

Charge transfer is calculated according to the Bader definition 26, using the code implemented into
VASP by Henkelman _et al._ 27 . In calculating the Bader charges, the projector-augmented waves 28 are used
instead of the ultrasoft pseudopotentials.

ARPES simulation has been performed by using the Fermi’s golden rule. The intensity of the ARPES

~ Φ _f_ _H_ _ph_ - _el_ Φ _i_ 2 _δ_ (  _ω_ + _E_ _i_ - _E_ _f_ ), where the

simulation, _I_, is formulated by the equation 29,30, _I_ ~ Φ _f_ _H_ _ph_ - _el_ Φ _i_ 2 _δ_ (  _ω_ + _E_ _i_ - _E_ _f_

Φ _f_, Φ _i_, _Hph_ - _el_,  _ω_, _Ei_, and _Ef_ are the Kohn-Sham final and initial states, the interaction Hamiltonian
between the photon and the electron, the photon energy, and the initial-state and final-state eigenvalues,
respectively. The unfolded energy band is obtained from the folded 4 3 × 4 3 supercell eigenstates by
investigating coefficients of redefined k-space vectors. We have implemented this formalism into the
VASP code, independently of the recent work by Medeiros _et al._ 31 .

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Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF-2013R1A1A2011271).

Author Contributions
G.H.K. performed all theoretical calculations and S.J. designed the research and wrote the main
manuscript text.

Additional Information
Competing financial interests: The authors declare no competing financial interests.

How to cite this article : Kim, G. H. and Jeong, S. Change of Electronic Structures by Dopant-Induced
Local Strain. _Sci. Rep._ 5, 11227; doi: 10.1038/srep11227 (2015).

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