# Rich Essential Properties of Si-Doped Graphene

Duy Khanh Nguyen<EMAIL_ADDRESS>Laboratory of Applied Physics,
Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh
City, Vietnam, and Faculty of Applied Science, Ton Duc Thang University, Ho
Chi Minh City, Vietnam  Ngoc Thanh Thuy Tran  Hierarchical Green-Energy
Materials (Hi-GEM) Research Center, National Cheng Kung University, Tainan
701, Taiwan  Godfrey Gumbs  Department of Physics and Astronomy, Hunter
College of the City University of New York, 695 Park Avenue, New York, New
York 10065, USA  Ming-Fa Lin<EMAIL_ADDRESS>Department of Physics/Hi-
GEM/QTC, National Cheng Kung University, Tainan, Taiwan

###### Abstract

A theoretical framework, under the first-principles calculations, is developed
to fully explore the dramatic changes of essential properties due to silicon-
atom chemical modifications on monolayer graphenes. For the Si-chemisorption
and Si-substituted graphenes, the guest-atom-diversified geometric structures,
the Si- and C-dominated energy bands, the charge transfers, the spatial charge
densities, and the van Hove singularities in the atom- and orbital-projected
density of states are investigated thoroughly by delicate evaluations and
analyses. Such fundamental properties are sufficient to determine the critical
physical and chemical pictures, in which the accurate multi-orbital
hybridizations are very useful in comprehending the diverse phenomena, e.g.,
the C- and Si-co-dominated energy bands, the semiconducting, semimetallic, and
metallic behavior, and the existence/absence of Dirac-cone structures. This
developing model could be generalized to other emergent layered materials.

###### keywords:

graphene, halogen, first-principles, chemical bonding, energy gap.

DOS, XPS, STM, ARPES, STS

##  1 1\. Introduction

Carbon atoms can form three-dimensional (3D) diamond1, 3D graphites2, two-
dimensional (2D) layered graphenes3, 4, one-dimensional (1D) graphene
nanoribbons5, 6, 7, 1D carbon nanotubes8, 9, 10, zero-dimensional (0D) carbon
toroids11, 12, 0D C60-related fullerenes13, and 0D carbon onions14. The
versatile morphologies directly indicate the peculiar chemical bondings, in
which all carbon-created systems possess ${sp^{2}}$-bonding surfaces except
for the ${sp^{3}}$ bondings in diamond. Specifically, the few- and multi-layer
graphene systems have been manufactured using the various methods15, 16 since
the first experimental observation in 2004 by mechanical exfoliation. Up to
now, they clearly exhibit plenty of remarkable fundamental properties due to
the hexagonal symmetry, the nanoscaled thickness, and the distinct stacking
configurations, such as semiconducting and semi-metallic behaviors17, 18,
anomalous quantum Hall effects19, diverse magnetic quantizations20, 21, 22,
23, rich Coulomb excitations and decays24, 25, 26, 27, 28, different magneto-
optical selection rules29, 30, 31, the exceedingly high mobility of charge
carriers32, 33, and the largest Young’s modulus of materials ever tested34. To
induce the novel phenomena and extend the potential applications, the
electronic properties can be easily modulated by the layer number35, 36,
stacking configuration37, 38, 39, mechanical strain40, 41, sliding42, electric
and magnetic field43, 44, chemisorption45, 46, 47, and direct doping49, 50, 51
. This paper mainly focuses on the latter two factors.

How to modulate the fundamental properties becomes one of the main-stream
topics in materials science, chemistry, physics and engineering. The chemical
modification is the most effective method. Pristine graphene has a rather
strong $\sigma$ bonding of 2s, 2px, and 2py orbitals in a honeycomb lattice.
This system creates a quite active chemical environment since each carbon
contributes one perpendicular 2pz orbital as a dangling bond. That is to say,
the host carbon atoms can bond with the various guest atoms (adatoms)52, 53,
molecules54 and even functional groups55. To date, many theoretical56 and
experimental research papers on surface chemisorptions have been published57.
The previous results show adsorption-diversified physical and chemical
phenomena, such as an opening of the energy gap58, semiconductor-metal
transitions59, the absence/recovery of a Dirac-cone structure60, spin-
splitting energy bands due to specific adatoms61, diverse van Hove
singularities in the density of states (DOS), single- or multi-orbital
hybridizations in C-adatom bonds shown in the spatial charge density and atom-
and orbital-decomposed DOSs62, and the magnetic moments $\&$ spin
configurations63. It is well known that graphitic systems are the most
efficient anode material in Li+-ion-based batteries. Possibly, the battery
efficiency can be enhanced by adding some silicon materials, as observed in
the experimental measurements64. The Si-atom chemisorption might play an
important role in these potential applications. Another chemical modification
is direct doping, the substitution of host carbons by guest adatoms in the
honeycomb lattice. For example, the BxCyNz compounds have been successfully
synthesized in the stable structures of 1D nanotubes65 and 2D layers66.
Apparently, the essential properties are predicted to present drastic changes,
e.g., in the electronic structures67, optical absorption spectra68 and
transport properties69. The above-mentioned chemical modifications on graphene
systems are worthy of a systematic study on the significant fundamental
properties, especially for the critical differences in the orbital
hybridizations between the weak and strong Si-C bonds.

In this paper, a theoretical framework, which is developed within first-
principles calculations, is utilized to fully explore the essential properties
of the Si-adsorbed and Si-substituted graphene systems. The concise chemical
and physical pictures, the multi-orbital hybridizations without the spin
configurations, will be proposed to explain the unusual geometric structures,
electronic energy spectra, spatial charge densities, and atom- and orbital-
decomposed density of states. That is, all the calculated results are
consistent with one another under such mechanisms. Furthermore, they are
responsible for the semiconductor-metal transitions after the guest-atom
chemisorptions and the creation of energy gaps in the substitution cases. The
various experimental characterizations are discussed in detail, and their
measurements are required to examine the theoretical predictions, e.g.,
scanning tunneling microscopy (STM)/transmission electron microscopy (TEM),
angle-resolved photoemission spectroscopy (ARPES), and scanning tunneling
spectroscopy (STS) experiments, respectively, for C-C $\&$ Si-C bond lengths,
low-lying valence bands $\&$ Fermi level, and van Hove singularities in DOSs.

##  2 2\. Computational methods

The rich geometric structures and electronic properties of Si-adsorbed and Si-
doped graphene systems are thoroughly explored using the density functional
theory (DFT) implemented by Vienna ab initio simulation package (VASP). The
many-body exchange and correlation energies, which come from the electron-
electron Coulomb interactions, are calculated from the Perdew-Burke-Ernzerhof
(PBE) functional under the generalized gradient approximation. Furthermore,
the projector-augmented wave (PAW) pseudopotentials can characterize the
intrinsic electron-ion interactions. As to the complete set of plane waves,
the kinetic energy cutoff is set to be
$\hbar^{2}\left|{k+G}\right|^{2}/2m=500$ eV, being suitable for evaluating
Bloch wave functions and electronic energy spectra. A vacuum space of $10$ Å
is inserted between periodic images to avoid any significant interaction. The
first Brillouin zone is sampled by $9\times 9\times 1$ and $100\times
100\times 1$ k-point meshes within the Monkhorst-Pack scheme for geometric
optimizations and electronic structures, respectively. Such points are
sufficient in obtaining the reliable orbital-projected DOSs and spatial charge
distributions. The convergence for the ground-state energy is $10^{-5}$ eV
between two consecutive steps, and the maximum Hellman-Feynman force acting on
each atom is less than $0.01$ eV/Å during the ionic relaxations.

Via delicate VASP calculations on certain physical quantities, the critical
physical and chemical pictures, i.e., the multi- or single-orbital
hybridizations in chemical bonds due to host and guest atoms, can be achieved
under a concise scheme. They will be useful in fully comprehending the
fundamental physical properties. These important concepts are obtained from
the adsorption- and doping-diversified geometric structures, carbon- and
silicon-dominated valence and conduction bands, the total charge distributions
and their drastic changes after adatom chemisorption or guest-atom doping, and
the atom- and orbital-decomposed density of states through detailed analyses.
Also, such physical quantities could shed light on the significant differences
between the chemical adsorptions and dopings, such as the metallic or
semiconducting behaviors, the normal and irregular electronic energy spectra,
and the complicated van Hove singularities, being attributed to the diverse
chemical bondings. The developed theoretical framework could be conceivably
generalized to emergent 2D materials, e.g., the chemical absorption and
dopings in layered silicene70, germanene71, and tinene systems72.

##  3 3\. Results and discussions

###  3.1 3.1. Geometric structures of Si-adsorbed and Si-substituted graphene

Monolayer graphene has a planar geometry with a honeycomb lattice, being
different from the buckled structures in layered silicene73, germanene74, and
tinene75. Apparently, this crystal is formed by the very strong $\sigma$
bonding of 2s, 2px, and 2py orbitals, and the weak $\pi$ bonding of 2pz
orbitals perpendicular to the graphitic plane. However, the other group-IV
systems, with the buckled structures, are stabilized by the optimal
competition between the ${sp^{2}}$ and ${sp^{3}}$ chemical bondings. The bond
length among all the group-IV systems remains shortest for the C-C (1.42 Å in
Table 1). After the Si-chemisorption on the graphene surface, the bridge site
is the most optimal adsorption position among the top and hollow sites, as
shown in Fig. 2. The hexagonal honeycomb lattice of carbon atoms remains a
planar structure, while C-C bond lengths are lengthened ${\sim\,1.45}$ Å -
${1.49}$ Å under various adatom concentrations, as shown in Table 1 and Fig.
1(a). Part of the carbon electrons participate in the multi-orbital
hybridizations of C-Si bonds, leading to the weakened C-C bondings. As for the
Si-substituted cases, the silicon-carbon honeycomb lattices remain planar
structures, indicating sufficiently strong quasi-$\sigma$ bondings due to the
${sp^{2}}$-${sp^{2}}$ multi-orbital hybridizations in the Si-C bonds. The Si-C
and C-C bond lengths are, respectively, ${\sim\,1.62}$ Å - ${1.83}$ Å and
${\sim\,1.35}$ Å - ${1.47}$ Å under various substitution cases [Table 1]. The
1:1 substituted system [Fig. 1(b)], the pure silicon-carbon compound, has an
optimal Si-C bond length of 1.78 Å , much longer than that C-C of 1.42 Å in
pristine graphene. This will lead to a great decrease of the strength in
quasi-$\sigma$ bonding, being further identified by the largely reduced charge
density in the Si-C bonds. In addition, the guest-atom distribution
configurations could be classified into three kinds under specific
concentrations lower than 50$\%$ [Figs. 3(a)-(c)], namely, the ortho-, para-
and meta-substitution cases. However, the former two are degenerate just at
50$\%$ [Fig. 3(b)].

Table 1: Energy gap $E_{g}$ (eV)/metal(M)/semimetal(SM); C-C bond length (Å), Si-C bond length (Å), and Si height (Å) for Si-substituted/adsorbed graphene. Configuration |  Ratio of Si and C | Percentage |  $E_{g}^{d(i)}$ (eV) semimetal(SM) metal(M) |  C-C (Å) |  Si-C (Å) |  Si height (Å)
---|---|---|---|---|---|---
Pristine | X | X | $E_{g}^{d}=0$ | 1.420 | X | X
Adsorption | Si:C=6:6 | $100\%$ | SM | 1.492 | 2.535 | 2.422
Si:C=3:6 | $50\%$ | SM | 1.490 | 2.514 | 2.400
Si:C=1:6 | $16.6\%$ | M | 1.456 | 2.138 | 2.000
Si:C=1:8 | $12.5\%$ | M | 1.450 | 2.118 | 1.989
| Si:C=1:24 | $4\%$ | M | 1.454 | 2.125 | 1.996
Substitution | Si:C=3:3 | $100\%$ | $E_{g}^{i}=2.56$ | X | 1.780 | X
Si:C=2:4 |  $50\%$ ortho | $E_{g}^{d}=0.04$ | 1.478 | 1.833 | X
Si:C=2:4 |  $50\%$ meta | $E_{g}^{d}=0.56$ | 1.465 | 1.829 | X
Si:C=1:5 | $20\%$ | $E_{g}^{d}=0$ | 1.351 | 1.621 | X
| Si:C=1:17 | $5.8\%$ | $E_{g}^{d}=0$ | 1.372 | 1.631 | X
| Si:C=1:23 | $4.3\%$ | $E_{g}^{d}=0$ | 1.379 | 1.649 | X
Figure 1: Dependence of total ground state energy on C-C and Si-C bond lengths
for (a) 100$\%$ double-side adsorption and (b) 100$\%$ substitution,
respectively. Figure 2: Geometric structure of the 100$\%$ Si-adsorbed
graphene: (a) top view and (b) side view. Figure 3: Geometric structures of
Si-substituted graphene systems: (a) 100$\%$ substitution, (b) 50$\%$
ortho-/para-substitution, and (c) 50$\%$ meta-substitution.

Scanning tunneling microscopy (STM) is very powerful in identifying the nano-
scaled surface morphology76, 77. This tool can characterize the real-space
surface structures under the lateral and vertical atomic resolution, such as
the very short bond length, planar or buckled geometries, crystal
arrangements, achiral or chiral edges, bridge-, hollow- $\&$ top-site
adsorptions, local substitutions, and few-atom clusters. Up to now, a lot of
high-resolution STM measurements have confirmed the diverse geometric
symmetries on the graphene-related systems with the significant ${sp^{2}}$
chemical bondings, covering the chiral or achiral hexagons on the hollow and
cylindrical carbon nanotubes78, the various edge structures in nanoscaled-
width graphene nanoribbons79, the folded, curved, scrolled $\&$ stacked
hexagonal lattices80, and the AAB, ABC $\&$ ABA stackings in few-layer
graphene systems81 . The theoretical predictions on planar graphene after
chemisorptions and substitutions, the positions of Si-guest atoms, and Si-C
$\&$ C-C bond lengths could all be verified by STM experiments, being useful
in examining the specific multi-orbital hybridizations in chemical bonds.

Transmission electron microscopy (TEM) is one of most powerful tools for
characterizing nano-scaled geometric structures, especially with respect to
the side-view properties82. A high-energy electron beam, with a very narrow
distribution width, can penetrate through an ultra thin sample to generate a
diffraction spectrum by the interactions of charge carriers and condensed-
matter systems. To date, high-resolution TEM measurements can directly
identify the side-view crystal structures better than other experimental
methods. Plenty of previous experimental studies show that they have
accurately identified the rich and unique geometric properties arising from
the carbon-${sp^{2}}$ bondings in various layered structures, such as 1D
single- $\&$ multi-walled carbon nanotubes83, 2D curved84, folded85,
scrolled86, and stacked graphene nanoribbons87, and the 2D AA-, AB-, ABC- and
AAB-stacked few-layer graphene systems88, 89. The theoretical predictions that
cover graphene plane, adatom height and bridge side under the Si-
chemisorptions, could be examined by the TEM measurements, indirectly
supporting the sp3-p multi-orbital hybridizations in Si-C bonds.

###  3.2 3.2. Electronic structures

A pristine monolayer graphene exhibits an unusual band structure, as clearly
indicated in Figs. 4(a) and 4(b). The occupied valence bands are asymmetric
about the unoccupied ones, mainly owing to the multi-orbital $\sigma$
bondings. The low-lying valence and conduction bands, which are initiated from
the K and K′ valleys (the corners of the first Brillouin zone), are linearly
intersecting there. There exist the isotropic Dirac-cone structures at low
energy, in which the Fermi level (${E_{F}=0}$) just crosses at the Dirac
point. Apparently, this system belongs to a zero-gap semiconductor because of
the vanishing density of state at ${E_{F}}$. The low-energy bands mainly come
from the $\pi$ bondings of the perpendicular C-${2p_{z}}$ orbitals. The Dirac-
cone structure, being due to the hexagonal symmetry, is predicted to display a
lot of unusual phenomena, e.g., diverse magnetic quantizations90, Hall
effects91 and optical properties92, being consistent with the experimental
measurements93. The linear energy dispersions will gradually become parabolic
ones as the state energy of ${|E^{c,v}|}$ grows, or the wave vector deviates
from the K/K′ point. Specifically, the middle-energy parabolic valence and
conduction bands present the saddle points at M point, respectively,
corresponding to ${\sim-2.4}$ eV and 1.8 eV. Such critical points in the
energy-wave-vector space could be regarded as the significant band-edge states
in creating the important van Hove singularities. That is to say, they are
thus expected to induce special structures in the essential physical
properties. The $\sigma$ valence bands at the deeper energy come into
existence at ${E^{v}\sim\,-3}$ eV from the $\Gamma$ point, being regarded as
the extreme point of parabolic energy dispersion. Their electronic states are
formed by the 2s, 2px, and 2py orbitals of carbon atoms, or the very strong
$\sigma$ bondings on the graphene plane.

The band structure is dramatically changed by the Si-chemisorptions. The band
asymmetry about the Fermi level becomes more obvious. For the $100\%$ double-
side adsorption, as shown in Fig. 4(c), there exist some valence and
conduction bands simultaneously intersecting with the Fermi level
(${E_{F}=0}$), so this system exhibits semi-metallic behavior. Apparently, the
distorted Dirac-cone structure appears near the $\Gamma$ point. The separation
of valence and conduction Dirac points could reach ${\sim\,0.5}$ eV. The
electronic energy spectrum is highly anisotropic energy one along $\Gamma$M
and $\Gamma$K. The occupied electronic states come to exit between the Fermi
level and the bottom of the conduction-band states. This clearly indicates the
creation of free conduction electrons by the effective adatom dopings. On the
other hand, free holes are generated in the unoccupied valence states along
M$\Gamma$ and K$\Gamma$ lines. As a result, it is difficult to identify Si-
adsorbed graphene as a n-type or p-type system. However, this system belongs
to a 2D semimetal, since it has a finite density of states at the Fermi level
(Fig. 8(b)) arising from the crossing valence and conduction subbands. The
above-mentioned unusual band structures are closely related to the very strong
competition/cooperation of orbital hybridizations in Si-C and C-C bonds. Also,
some drastic changes in electronic structures are revealed in the $100\%$
single-side adsorption case, as clearly indicated by a comparison of Fig. 4(d)
and Fig. 4(c). The chemisorption of silicon adatoms induces the free electrons
and holes simultaneously, similar to the double-side case (Fig. 4(c)). The
low-lying conduction bands near the $\Gamma$ point and the vacant valence
bands along M$\Gamma$ and K$\Gamma$ lines reduced in number. That is to say,
the number of energy bands intersecting with the Fermi level declines for a
further decrease of the Si-concentration, and the 2D free carrier density
behaves so. As to both adsorption cases, carbon host atoms and silicon guest
ones make significant contributions to the electronic structures of the whole
energy range, in which their dominances are obviously displayed by the red
triangles and blue circles. These important results mean that there exist non-
negligible multi-orbital hybridizations in Si-C, C-C and Si-Si bonds.
Furthermore, there is an obvious difference from the aforementioned $100\%$
adsorption cases when the concentration decreases [Figs. 4(e) and 4(f)]. That
is, only the valence energy bands intersect with the Fermi level. This
indicates that unoccupied electronic states between the Fermi level and the
top of the valence-band states all belong to free holes. As a result, these
systems can be regarded as the p-type metal. Especially, the anisotropic Dirac
cone structure without/with separation [Fig. 4(e)/(f)] between the $\Gamma$
and K points appears below the Fermi level. Such unusual valence Dirac cone
structure is responsible for the deformed V-shape structure in Fig. 8(d)
[discussed in the density of states section].

The atom- and orbital-dominated energy bands are worthy of a closer
examination. For 100$\%$ double-side and single-side adsorption cases, most of
energy bands are co-contributed by C-host and Si-guest atoms, with part of
them mainly coming from either the former or the latter. In general, the low-
lying and middle-energy valence and conduction bands are dominated by the Si-
guest atoms. The percentage of atom contribution is about $4:1$ ($2:1$) in the
Si-100$\%$ (Si-50$\%$) adsorption case, as shown in Fig. 4(c) (Fig. 4(d)),
being estimated from the $sp^{3}-p$ bonding in the Si-C bond [the conclusion
from the atom- and orbital-projected density of states; discussed later in
Figs. 8(b) and 8(c)]. The four (3s, 3px, 3py, 3pz) orbitals of silicon and the
single 2pz orbital of carbon make important contributions to such energy
bands. Apparently, there are few $\sigma$ valence bands of (2px, 2py) orbitals
near the $\Gamma$ point; they belong to the concave-downward energy
dispersions at ${E^{v}\sim\,-4.1}$ eV $\&$ $-4.2$ eV for the 100$\%$
adsorption cases [Figs. 4(d) and 4(c)], as identified from Figs. 8(c) and
8(b). It should be noted that the pristine $\sigma$ valence bands come into
existence at ${E^{v}\sim\,-3.0}$ eV [Figs. 4(a,b) and 8(a)]. As the
concentration declines, Si adatom- and C atom-co-dominated energy bands only
appear at specific energies, while other bands are mainly dominated by C
atoms, as indicated in Figs. 4(e) and 4(f) for $16.6\%$ and $12.5\%$
adsorption cases, respectively. Also, the $\sigma$ valence bands of (2px, 2py)
orbitals situate at ${E^{v}\sim\,-3.5}$ eV and ${E^{v}\sim\,-3.2}$ eV [Figs.
4(e) and 4(f)]. This clearly illustrates that the shorter C-C bond lengths
under low-concentration adsorptions, as compared with the 100$\%$ cases [Figs.
4(c,d)].

Both silicon and alkali adatoms can create free carriers, while their band
properties are quite different from each other. The alkali-adsorbed graphene
systems present approximately rigid energy bands and a few Li-dominated
conduction bands, clearly indicating the blue shift of the Fermi level62.
Their free carriers purely originate from the electron charge transfer from
the outermost s orbital of each alkali adatom to the carbon host atom.
Furthermore, the atom- and orbital-projected densities of states clearly show
the weak, but significant s-pz orbital hybridization in every alkali-carbon
bond. On the other hand, the free electrons and holes in the Si-adsorbed cases
are associated with a strong overlap of valence and conduction bands, so the
shift of $E_{F}$ is very difficult to characterize in value, except for the
low-concentration adsorptions, in which the Fermi level exhibits a red shift.
There are a lot of extra Si-dominated and (Si, C)-co-dominated energy bands in
the whole energy spectrum, especially for those crossing at the Fermi level.
The complicated chemical bondings are deduced to survive in Si-adsorbed
graphene systems, in which they cover the 2pz-(3s, 3px, 3py, 3pz), (3s, 3px,
3py, 3pz)-(3s, 3px, 3py, 3pz) and (2s, 2px, 2py)-(2s, 2px, 2py) multi-orbital
hybridizations in the C-Si, Si-Si and C-C bonds. Most importantly, the above-
mentioned differences obviously illustrate the adatom-adsorption-induced
diverse phenomena and the critical mechanisms/pictures in determining the
fundamental properties.

Electronic structures obviously show drastic changes in the presence of Si-
substitutions, as clearly indicated in Figs. 5(a-f). The asymmetry of valence
and conduction bands about $E_{F}=0$ is greatly enhanced after various
substitutions, e.g., 100$\%$ case in Fig. 2-5(a), 50$\%$ case in Figs. 5(b)
and 5(c), 20$\%$ case in Fig. 5(d), 5.8$\%$ case in Fig. 5(e), and 4.3$\%$
case in Fig. 5(f). The substitution and adsorption cases sharply contrast with
each other in Figs. 5 and 4. First, all the substitution configurations and
concentrations show the semiconducting behavior with a finite or vanishing
band gap. For example, the 100$\%$ Si-substituted graphene is a wide-gap
semiconductor with an energy gap of $E_{g}^{i}=2.56$ eV. Energy gaps are
direct or indirect being determined by the highest valence and the lowest
conduction state near the $\Gamma$ point. Their values decline with decreasing
of the Si-concentrations and are strongly depended on the guest-atom
distribution configurations, e.g., $E_{g}^{d}=0.56$ eV for the meta-
configuration [Fig. 5(c)] under the 50$\%$ substitution. Also, the zero-gap
semiconducting behavior is revealed in the 50$\%$ ortho-case [Fig. 5(b)],
where an anisotropic Dirac-cone structure appears at a certain ${\bf k}$-point
between $\Gamma$ and K. Only one Dirac point intersects with the Fermi level,
so its density of states vanishes there [Fig. 9(b)]. This is responsible for
the zero-gap semiconductor. When the substitution concentration declines, the
unusual zero-gap semiconducting behavior appears, in which only one conduction
Dirac point intersects with the Fermi level near the $\Gamma$ point, as shown
in Figs. 5(d-f). Second, the linear Dirac cone at $\Gamma$ point in Fig.
4(a,b) is seriously separated and distorted in Fig. 5(b), or even thoroughly
destroyed in Figs. 5(a) and 5(c). Also, this Dirac cone structure is
significant deformed without separation and slightly shifted to the valence
band at $\Gamma$ point, as shown in Figs. 5(d-f). Third, the valence and
conduction bands near the Fermi level are initiated from the $\Gamma$ point,
but almost independent of the M and K points. Finally, all the energy bands
are mainly co-dominated by the Si-guest and carbon-host atoms under the high
substitutions [Figs. 5(a-c)]. However, these Si-guest and C-host atoms-co-
dominated energy bands only exist at certain energies under the lower
substitutions [Figs. 5(d-f)]. Furthermore, the separated $\sigma$ bands at
deep energies purely due to C-(2px, 2py) orbitals are absent. These results
suggest the existence of quasi-$\sigma$ and quasi-$\pi$ bondings,
respectively, originating from the (3s, 3px, 3py)-(2s, 2px, 2py) $\&$ 3pz-2pz
orbital hybridizations [supported by the spatial charge distributions in Fig.
7 and the atom- and orbital-projected density of states in Fig. 9].

Figure 4: Electronic structures with the dominances of host and guest atoms
for Si-adsorbed graphene systems: (a) pristine case, (b) pristine graphene
under the enlarged unit cell identical to the 100$\%$ case, (c) $100\%$
double-side adsorption, and (d) $100\%$ single-side adsorption, (e) $16.6\%$
adsorption, and (f) $12.5\%$ adsorption. Figure 5: C- and Si-dominated valence
and conduction bands of Si-substituted graphene systems: (a) 100$\%$
substitution, (b) 50$\%$ ortho-substitution, (c) 50$\%$ meta-substitution, (d)
20$\%$ substitution, (e) 5.8$\%$ substitution, (f) 4.3$\%$ substitution.

Angle-resolved photoemission spectroscopy (ARPES) is the only tool for
measuring the wave-vector-dependent occupied electronic states, especially for
valence and conduction bands crossing at the Fermi level. Details of the
experimental equipments can be found in the books written by Tran., et al93
and Lin., et al94. To date, high-resolution ARPES measurements have identified
the rich band structures in graphene-related systems, being greatly
diversified by the distinct geometric symmetries, dimensions, stacking
configurations, numbers of layers, and adsorptions, substitutions $\&$
intercalations. For example, the verified electronic structures, which are
consistent with the theoretical predictions95 and the experimental
measurements96, include parabolic valence bands with an energy gap in the 1D
graphene nanoribbons97, the linear Dirac-cone structure in monolayer
graphene98, the blue shift of the Fermi level in alkali-adsorbed graphene
systems99, two parabolic valence bands near $E_{F}$ without an energy gap in
bilayer AB-stacked graphene100, the monolayer- and bilayer-like valence bands
in trilayer ABA stacking, the partially flat, sombrero-shaped, and linear
bands in trilayer ABC stacking101, and the parabolic $\&$ linear energy
dispersions near the K and H points (${k_{z}=0}$ and $\pi$) in a natural
graphite102. Similar ARPES measurements are available for thoroughly examining
the significant effects on band structures after the chemisorption and
substitution of Si adatoms. They are conducted on the finite or vanishing band
gap, the numbers of the valence and conduction bands intersecting with the
Fermi level near the $\Gamma$, K and M points, or only the valence energy
bands intersecting with the Fermi level, and the existence/destruction of the
carbon-dominated $\sigma$ bands at the $\Gamma$ point initiated from ${-4.1}$
eV, ${-4.2}$ eV, and ${-3.5}$ eV. Such detailed information is sufficient to
determine the critical multi-orbital hybridizations of C-Si bonds, the p-sp3
or sp2-sp2 bondings.

##  4 3.3. Spatial charge densities

The multi-orbital hybridizations in chemical bonds, which are responsible for
the rich geometric structures, energy bands and density of states, could be
delicately identified from the spatial charge densities (${\rho}$’s) and their
variations (${\Delta\rho}$’s) after various modifications. The latter is
obtained from the difference between the Si-chemisorption/Si-substitution and
pristine cases. A pristine graphene, as clearly shown in Fig. 6(a), presents a
very high carrier density between two carbon atoms [red region enclosed by a
black rectangle], indicating a rather strong $\sigma$ bonding due to three
C-(2s, 2px, 2py) orbitals on the honeycomb lattice. Such bonding is hardly
affected by the Si-adatom adsorptions [Figs. 6(b), 6(d), and 6(f)]. Also,
there exists the $\pi$ bonding near the plane boundary along the $z$-direction
[area covered by a red rectangle]. The 2pz-2pz orbital hybridizations in C-C
bonds might be drastically changed under the Si-chemisorptions. The charge
distributions related to silicon adatoms and carbon atoms along the $x$-,
$y$-, and $z$-directions present obvious variations. The strong evidences are
illustrated by ${\Delta\rho}$’s in Figs. 6(c), 6(e), and 6(g). The charge
density is enhanced near the carbon atoms on the ${(z,x)}$\- and
${(z,y)}$-planes [red regions]. This result means that some electronic charges
transferred from Si adatoms to C atoms. In addition to the $z$-direction, the
important charge variations along the $x$\- and $y-$directions survive between
silicon adatoms and carbon atoms/silicon ones, indicating the multi-orbital
hybridizations in Si-C and Si-Si bonds. According to the direction- and
position-dependent variations of charge densities, there exist (3s, 3px, 3py,
3pz)-2pz and (3s, 3px, 3py, 3pz)-(3s, 3px, 3py, 3pz) complicated interactions
in Si-C and Si-Si bonds, respectively.

Figure 6: Spatial charge density/its variation after chemisorption for (a)
pristine system, (b)/(c) 100$\%$ double-side adsorption, (d)/(e) 100$\%$
single-side adsorption, and (f)/(g) $16.6\%$ adsorption.

The Si-substitution cases exhibit diversified charge densities, compared with
the pristine and Si-chemisorption ones. For the 100$\%$ substitution, the Si-C
bonds, which form a honeycomb lattice [Fig. 3(a)], present sufficiently high
charge densities between two neighboring atoms [Fig. 7(a)]. They are formed by
the quasi-$\sigma$ bondings, in which the charge-density-dependent strengths
are greatly reduced, compared to the $\sigma$ ones in C-C bonds [Fig. 6(a)].
This is consistent with the longer Si-C bonds and the shorter C-C bonds.
Similar results are revealed in other substitution cases, e.g., ${50}$$\%$
substitution under the ortho-, and meta-configurations [Figs. 7(c) and 7(e)],
and ${20}$$\%$ substitution in Fig. 7(g). There also exist the quasi-$\pi$
bondings near the boundary. These present the non-well-behaved charge
distributions, compared with those of a pristine graphene [Fig. 6(a)]. The
obvious variations of charge densities on the ${(z,y)}$\- and
${(z,x)}$-planes, being clearly show in Figs. 7(b), 7(d), 7(f), and 7(h),
suggest significant (3s, 3px, 3py)-(2s, 2px, 2py) $\&$ 3pz-2pz orbital
hybridizations in Si-C bonds. The coexistence of multi- and single-orbital
interactions are further supported by the atom- and orbital-decomposed
densities of states [discussed later in Figs. 9].

Figure 7: Similar plot as Fig. 6, but shown for Si-substituted graphene
systems for (a)/(b) 100$\%$ substitution, (c)/(d) 50$\%$ ortho-substitution,
(e)/(f) 50$\%$ meta-substitution, and (g)/(h) 20$\%$ substitution.

##  5 3.4 Orbital-projected density of states

The main features of energy dispersions are directly reflected in the
diversified density of states. Special structures, the van Hove singularities,
mainly originate from the critical points in the energy-wave-vector space, in
which the band-edge states might belong to the local minima $\&$ maxima, and
the saddle points. In general, there are three kinds of novel structures, the
V-shaped structure crossing at the Fermi level, logarithmically divergent
peaks [${E\sim\,}$${-2.4}$ eV $\&$ 1.8 eV] and shoulders [${E\sim\,-3}$ eV],
as clearly observed in a pristine graphene [Fig. 8(a)]. They are,
respectively, due to the linear Dirac cone at the K/$\Gamma$ point in Fig.
4(a)/(b), the saddle points at the M points, and the extreme points of
parabolic dispersions at the $\Gamma$ point. Specifically, the former two
structures are generated by the $\pi$ bonding of $2p_{z}$ orbitals (dashed red
curve), whereas the initial $\sigma$ bands are closely related to the (2px,
2py) orbitals [dashed green and blue curves]. The $\pi$-bonding structures are
separated from those of the $\sigma$ bondings.

Apparently, a lot of van Hove singularities in the density of states are
created by the Si-adatom chemisorption in the $100\%$ double- and single-side
cases, being obviously displayed in Figs. 8(b) and 8(c), respectively. The
finite density of states at the Fermi level indicate the semi-metallic
behavior, while the vanishing value in the pristine case [Fig. 8(a)]
corresponds to a zero-gap semiconductor. The chemical bonding between Si and C
atoms is responsible for the significant overlap of the valence and conduction
bands and the creation of new energy bands [Figs. 4(c) and 4(d)]. The
significant contributions of carbon-2pz orbitals appear in the whole energy
range of ${-6}$ eV ${\leq\,E\leq\,3}$ eV. Specifically, for that above ${-4}$
eV, the non-negligible contributions from the four Si-(3s, 3px, 3py, 3pz)
orbitals come into existence, respectively, indicated by the solid pink,
green, orange and purple curves in Figs 8(b) and 8(c). The van Hove
singularities from these orbitals are merged. This clearly indicates the p-sp3
orbital hybridization in C-Si bonds. The multi-orbital hybridizations, which
replace the 2pz-orbital bondings on the graphene plane, are also confirmed by
the previous charge density distributions [Figs. 6(b)-(g)]. However, the
$\sigma$ bonding of carbon atoms are hardly affected by the Si adsorptions, in
which they are represented by the isolated shoulder structure below ${-4.2}$
eV (${-4.1}$ eV) in the Si-100$\%$ (Si-50$\%$) adsorption cases. When the
concentration decreases, as shown in Fig. 8(d), only a few of van Hove
singularities at certain energies are created by Si-guest atoms. The seriously
deformed valence V-shaped structure and two logarithmic divergent peaks at
$-3$ eV and $-0.5$ eV come to exist, respectively, resulting from the
significant distorted valence Dirac cone structure and two saddle points at
the M point in Fig. 4(e). The finite density of states at the Fermi level also
exist; however, it is responsible for the metallic behavior. Furthermore, the
$\sigma$ shoulder structure of C-(2px and 2py) orbitals appears at $-3.5$ eV,
indicating the stronger $\sigma$ C-C bonds (shorter C-C bond lengths) in the
low-concentration system compared with the $100\%$ adsorption cases.

Why are valence and conduction bands in Fig. 4 dramatically altered by the Si-
adsorbed graphene? The diversified band properties are clearly identified from
three critical mechanisms. First, the chemical modification belongs to the
significant surface adsorption, but not the stronger substitution. This means
that $\sigma$ bondings in planar C-C bonds exist even after significant Si-
chemisorptions. As a result, the $\sigma$ bands of the C-(2px, 2py) orbitals
exhibit a significant red shift of ${\sim\,1}$ eV [red triangles at
${E^{v}\sim\,-4.1}$ eV and ${E^{v}\sim\,-4.2}$ eV in Figs. 4(d) and 4(c)]
under $100\%$ adsorption cases, and this red shift is smaller ${\sim\,0.5}$ eV
[Fig. 4(e)] in the low-concentration case. The red shift value is determined
by the ionization-energy difference between carbon and silicon atoms. Second,
the important sp3-p multi-orbital hybridizations are covalently formed by the
four half-occupied orbitals of (3s, 3px, 3py, 3pz) in Si adatoms and one
similar orbital of ${2p_{z}}$ in the C host atoms. For example, plenty of low-
lying valence and conduction bands are dominated by the silicon guest atoms.
Furthermore, their contributions to the total density of states are higher
than those due to the carbon atoms except in the energy range below ${-4}$ eV,
respectively, indicated by the solid and dashed curves Figs. 8(b) and 8(c).
Finally, from the viewpoint of the separated atomic orbital energies, all the
atomic orbitals in the silicon adatoms have larger spatial distributions and
smaller binding energies, compared with those of the carbon atoms. These
orbitals, which take part in the Si-C bonds, create many energy bands in the
available energy range of the electronic energy spectrum, especially for the
valence and conduction bands intersecting with the Fermi level. Apparently,
the Dirac-cone band structure without any valence and conduction overlap, is
thoroughly replaced by the Si-dominated electronic structures under full
chemisorptions. The other essential physical properties are expected to show
diverse phenomena under the Si-chemisorptions, e.g., magnetic quantizations89,
optical absorption spectra91, and transport properties69.

Figure 8: Orbital-projected density of states for Si-adsorbed graphene
systems: (a) pristine case, (b) 100$\%$ double-side adsorption, (c) 100$\%$
single-side adsorption, and (d) 16.6$\%$ adsorption.

The substitution and adsorption cases are thoroughly different from each other
in the main feature of density of states. For the former chemical
modifications, the number of electronic states, which is revealed in Fig. 9,
vanishes within the specific band-gap region centered at the Fermi level. Most
of the substitution configurations and concentrations correspond to the finite
gap semiconductors, e.g., energy gaps due to the highest occupied valence
state and the lowest unoccupied conduction one at the $\Gamma$ point under the
100$\%$ substitution [Fig. 5(a)] and meta-50$\%$ substitution [Fig. 5(c)].
Only the ortho-50$\%$ case in Fig. 5(b) belongs to the zero-gap semiconductors
with a seriously distorted Dirac-cone structure between the $\Gamma$ and K
points. In the case of the lower concentration substitutions, the unusual
zero-gap semiconducting behavior and the distorted valence Dirac cone
structure [Fig. 5(d)], respectively, resulting in the almost negligible
density of states at the Fermi level and the seriously deformed V-shape
structure in Fig. 9(d). The van Hove singularities can create many various
special structures, namely, the obvious V-shape structure across ${E_{F}}$,
strong shoulders/asymmetric peaks, and prominent symmetric peaks, as observed
in the chemisorption cases [Fig. 8]. Apparently, the atom- and orbital-
projected densities of states show that the contributions coming from the
Si-3pz and C-2pz orbitals [solid purple and dashed red curves in Figs. 9(a-d)]
appear simultaneously. Furthermore, the merged special structures are also
revealed in the other orbitals, e.g., the interactions of Si-(3s, 3px, 3py)
and C-(2s, 2px, 2py) orbitals. These results clearly illustrate the multi-
orbital hybridizations of sp2-sp2 $\&$ p-p in Si-C bonds. That is to say, the
Si-C bonds present quasi-$\sigma$ and quasi-$\pi$ chemical bondings. In
addition, it should have the $\sigma$ and $\pi$ bondings in C-C bonds. The
predicted orbital hybridizations are consistent with the spatial charge
distributions in Fig. 7 and can account for the Si-substitution-enriched band
structures in Fig. 5, respectively.

Figure 9: Similar plot as Fig. 8, but displayed for Si-substituted graphene
systems: (a) 100$\%$ substitution, (b) 50$\%$ ortho-substitution, (c) 50$\%$
meta-substitution, and (d) 20$\%$ substitution.

Scanning tunneling spectroscopy (STS) can provide sufficient information on
the density of states at the Fermi level and the various van Hove
singularities due to the valence and conduction bands simultaneously. High-
resolution STS measurements are available for distinguishing the
semiconducting and metallic behavior. Furthermore, they are very useful in
identifying the close relations between the electronic energy spectra and the
orbital hybridizations of the significant chemical bonds. Such experimental
measurements have been successfully utilized to verify the band properties
near the Fermi level and the dimension-diversified van Hove singularities in
the graphene-related systems even in the presence of magnetic field, such as
2D few-layer graphene systems with the AB, ABC, AAB stackings103, 104, 1D
metallic and semiconducting carbon nanotubes105, 106, and 3D Bernal
graphite107. Apparently, the theoretical predictions on the Si-adsorption- and
Si-substitution-diversified density of states in monolayer graphene systems,
which could be examined by the STS experiments, cover the finite or vanishing
density of states at the Fermi level, and the low- and middle-energy van Hove
singularities. That is, such experimental examinations can provide the
critical information on the multi-orbital hybridizations in the p-sp3 or
sp2-sp2 chemical bondings.

The essential properties of Si-adsorbed graphene systems might sharply
contrast with other adatom-decorated ones. For example, graphene oxides have a
bridge-site adsorption position93, as observed in the Si-adsorption case.
However, the former present slight buckling and a shorter adatom-C bond
length. All graphene oxides belong to wide-, narrow- or zero-gap
semiconductors, without any band-overlap-induced free electrons and holes. The
O-${2s}$ orbitals do not take part in the low-lying energy bands, while the
opposite is true for the Si-${3s}$ ones. Under high adatom concentrations
($\geq 50\%$), valence and conduction bands in the range of $-1.5\leq
E^{c,v}\leq 1.5$ eV are absent for graphene oxides, being thoroughly different
from the frequent crossing over the Fermi level in the current case.
Apparently, the $\sigma$ bands purely due to the carbon atoms disappear.
Moreover, the three (2px, 2py, 2pz) orbitals of oxygen and carbon atoms would
dominate the multi-orbital hybridizations in O-C, O-O and C-C bonds. On the
other side, the 2pz and (2px, 2py) orbitals of carbon atoms, respectively,
make important contributions to C-C and Si-C bonds; furthermore, the Si-(3s,
3px, 3py, 3pz) orbitals participate in the Si-C and Si-Si bonds. The above-
mentioned important differences could be verified by high-resolution STM, TEM,
ARPES and STS measurements.

##  6 4\. Conclusion

The essential properties of Si-modified graphene systems have been explored by
the first-principles method in detail. Apparently, the geometric structures,
band structures, spatial charge densities, and atom- and orbital-projected
density of states exhibit rich and unique phenomena, being sensitive to the
chemisorption $\&$ substitution cases, and the concentration $\&$ distribution
configuration of the Si-guest atoms. The complex multi-orbital
hybridizations/significant chemical bondings are proposed to explain the Si-
induced chemical modifications on graphene systems. The calculated results
clearly show that free carriers and an energy gap might be created by the
chemical adsorptions and substitutions, respectively. The distinct
modification ways of silicon guest atoms can modulate the semiconducting,
metallic, and semi-metallic behavior, in a way difficult to observe in other
kinds of atoms108. For example, there are certain important differences
between silicon and alkali atoms109 in terms of chemisorptions, e.g., the
multi-orbital or single-orbital hybridizations, the existence or absence of a
charge transfer, a blue or undefined shift of the Fermi level, only conduction
electrons or free conduction electrons $\&$ holes, and the dramatic or slight
changes for the low-lying energy bands. The Si-adsorbed and Si-substituted
graphenes could serve as potential candidates in nanoscaled-applications110,
111. A similar theoretical framework could be generalized for emergent layered
materials, such as chemical adsorptions and substitutions on silicene112,
germanene113, stanene114, phosphorene115, and bismuthene116.

The chemisorptions and substitutions of Si-guest atoms on monolayer graphene
present unusual geometric properties, being directly revealed in the spatial
charge distributions. Si-adsorbed graphene is a non-buckled plane, in which
the optimal position corresponds to the bridge site. A planar structure
clearly indicates a very small variation in the $\sigma$ bonding of C-(2s,
2px, 2py) orbitals after the Si-chemisorptions; that is, these three orbitals
do not take part in Si-C bonds. This adsorption configuration is similar to
monolayer graphene oxide [93], while there is a slight buckling in the latter.
The Si-C bond length is ${\sim\,2.1}$ Å- ${2.5}$ Å, suitable for the
significant multi-orbital hybridizations of Si-C bonds. Furthermore, the C-C
bond lengths display a minor change. Via detailed analyses on the 3D charge
density, its spatial variation, and the atom- and orbital-projected density of
states, the sp3-p multi-orbital hybridizations are deduced to dominate the
chemical Si-C bonds. Apparently, the three physical quantities are consistent
with one another. The theoretical predictions of the bridge site and C-C bond
length (Si height) could be examined by high-resolution STM (TEM)
measurements. Concerning Si-substituted graphene systems, they remain in the
planar structure, as observed under the chemisorption cases. There exist very
strong multi-orbital chemical bondings between Si and C atoms. The Si-C bond
length is about 1.62 Å - 1.83 Å, being shorter than those in the Si-adsorbed
systems. This means that more C-orbitals are strongly hybridized with the four
Si-orbitals. STM experiments are available for examining the predicted Si-C
and C-C bond lengths.

Any chemisorptions and substitutions of Si-guest stoms thoroughly alter the
unusual band structure of monolayer graphene, especially for the zero-gap
semiconducting behavior and linear Dirac cone due to the $\pi$ bondings of the
2pz orbitals. In the $100\%$ double- and single-side adsorption cases, the Si-
adsorbed graphene systems are semi-metals with free conduction electrons and
valence holes. For the low-concentration systems, they belong to the p-type
metals with only free valence holes. The Dirac-cone structure near the
$\Gamma$ point is seriously distorted after the Si-chemisorptions. There are
more valence and conduction bands, accompanied by various band-edge states, in
the whole electronic energy spectrum, e.g., the emergent low-lying energy
bands along the K$\Gamma$ and M$\Gamma$ directions. However, the $\sigma$
bands, which arises from the (2px, 2py) orbitals of carbon atoms, exhibit a
rigid red shift of ${\sim\,1}$ eV and ${\sim\,0.5}$ eV for $100\%$ cases and
lower-concentration cases, respectively. The above-mentioned important results
directly reflect the critical mechanisms, namely, the multi-orbital
hybridizations of sp3-p in Si-C bonds, sp3-sp3 in Si-Si bonds and sp2-sp2 in
C-C bonds. Such chemical bondings consist of four Si-orbitals and one
C-orbital, being closely related to the bridge-site adsorption positions, and
the binding energies $\&$ charge distributions of the separated orbitals.
High-resolution ARPES measurements are very useful for verifying the low-
energy valence bands crossing the Fermi level along K$\Gamma$ and M$\Gamma$
and the rigid $\sigma$ bands initiated from the $\Gamma$ point. On the other
hand, all substitution cases result in semiconducting behavior with a finite
or vanishing band gap. The Dirac-cone structure presents a deviation from the
$\Gamma$ point, a strong distortion, or even a full destruction. The number of
valence and conduction bands remains the same after the chemical
substitutions; furthermore, they are co-dominated by the Si-guest and C-host
atoms. Apparently, the main features of the band structures in Si-substituted
graphene systems arise from the sp2-sp2 $\&$ p-p orbital hybridizations in
Si-C bonds.

A lot of van Hove singularities in the atom- and orbital-decomposed density of
states, which mainly come from the band-edge states, are created by the Si-
guest-atom chemisorption and substitution. A pristine monolayer graphene only
presents a V-shaped structure with a vanishing value at the Fermi level, the
logarithmically symmetric peaks at ${-2.4}$ eV and 1.8 eV, and a shoulder
structure at ${-3.0}$ eV, in which the former two and the last one,
respectively, correspond to the $\pi$ and $\sigma$ bondings of carbon atoms.
The strong $\pi$-bonding evidences are totally destroyed by any chemisorption
cases except for the very diluted Si-adatoms. They are replaced by a finite
density of states at ${E_{F}=0}$ and many shoulder and peak structures.
Furthermore, they are co-dominated by the four Si-(3s, 3px, 3py, 3pz) orbitals
and the single C-2pz orbital, since their contributions are merged.
Specifically, the $\sigma$-band shoulder appears at ${-4.2}$ eV and ${-4.1}$
eV or ${-3.5}$ eV, and the ${1.0}$ eV or ${0.5}$ eV red shift is mainly
determined by relative ionization energy of Si and C atoms. The above-
mentioned significant features further support and illustrate the sp3-p $\&$
sp2-sp2 multi-orbital hybridizations in Si-C bonds and C-C bonds,
respectively. As for the substitution cases, the density of states is zero
within a finite energy range centered at the Fermi level, except for few
systems with deformed V-shaped structures at $E_{F}$. All the Si-substituted
graphene systems are finite- or zero-gap semiconductors. The special
structures, which originate from Si-3pz and C-2pz orbitals, appear
simultaneously. Also, a similar behavior is revealed in Si-(3px, 3py) and
C-(2px, 2py) orbitals. These clearly indicate the critical single- and multi-
orbital hybridizations in Si-C bonds. The above-mentioned theoretical
predictions could be verified by high-resolution STS measurements.

Conflict of interest

There is no conflicts of interest in this paper.

Acknowledgments

This work was financially supported by the Ministry of Science and Technology
(MOST) under grant number 108-2112-M-006-022-MY3, and the Hierarchical Green-
Energy Materials (Hi-GEM) Research Center, from The Featured Areas Research
Center Program within the framework of the Higher Education Sprout Project by
the Ministry of Education (MOE) and the MOST (108-3017-F-006 -003) in Taiwan.

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