Half-metallic silicon nanowires
Half-metallic silicon nanowires
E. Durgun,1, 2 D. Çakır,1, 2 N. Akman,2, 3 and S. Ciraci1, 2, ∗
Department of Physics, Bilkent University, Ankara 06800, Turkey
National Nanotechnology Research Center, Bilkent University, Ankara 06800, Turkey
Department of Physics, Mersin University, Mersin, Turkey
(Dated: November 19, 2021)
From first-principles calculations, we predict that transition metal (TM) atom doped silicon
nanowires have a half-metallic ground state. They are insulators for one spin-direction, but show
metallic properties for the opposite spin direction. At high coverage of TM atoms, ferromagnetic sil-
icon nanowires become metallic for both spin-directions with high magnetic moment and may have
also significant spin-polarization at the Fermi level. The spin-dependent electronic properties can
be engineered by changing the type of dopant TM atoms, as well as the diameter of the nanowire.
Present results are not only of scientific interest, but can also initiate new research on spintronic
applications of silicon nanowires.
PACS numbers: 73.22.-f, 68.43.Bc, 73.20.Hb, 68.43.Fg
Rod-like, oxidation resistant Si nanowires (SiNW) can
now be fabricated at small diameters[1] (1-7 nm) and dis-
play diversity of interesting electronic properties. In par-
ticular, the band gap of semiconductor SiNWs varies with
their diameters. They can serve as a building material in
many of electronic and optical applications like field effect
transistors [2] (FETs), light emitting diodes [3], lasers [4]
and interconnects. Unlike carbon nanotubes, the con-
ductance of semiconductor nanowire can be tuned easily
by doping during the fabrication process or by applying
a gate voltage in a SiNW FET.
In this letter, we report a novel spin-dependent elec-
tronic property of hydrogen terminated silicon nanowires
(H-SiNW): When doped by specific transition metal
(TM) atoms they show half-metallic[5, 6] (HM) ground
state. Namely, due to broken spin-degeneracy, energy
bands En(k, ↑) and En(k, ↓) split and the nanowire re-
mains to be insulator for one spin-direction of electrons,
but becomes a conductor for the opposite spin-direction
achieving 100% spin polarization at the Fermi level. Un-
der certain circumstances, depending on the dopant and
diameter, semiconductor H-SiNWs can be also either a
ferromagnetic semiconductor or metal for both spin di-
rections. High-spin polarization at the Fermi level can
be achieved also for high TM coverage of specific SiNWs.
Present results on the asymmetry of electronic states of
TM doped SiNWs are remarkable and of technological in-
terest since room temperature ferromagnetism is already
discovered in Mn-doped SiNW[8]. Once combined with
advanced silicon technology, these properties can be re-
alizable and hence can make ”known silicon” again a po-
tential material with promising nanoscale technological
applications in spintronics, magnetism.
Even though 3D ferromagnetic Heusler alloys and
transition-metal oxides exhibit half-metallic properties
[7], they are not yet appropriate for spintronics because
of difficulties in controlling stoichiometry and the defect
levels destroying the coherent spin-transport. Qian et
al. have proposed HM heterostructures composed of δ-
doped Mn layers in bulk Si [9]. Recently, Son et al.
[10] predicted HM properties of graphene nanoribbons.
Stable 1D half-metals have been also predicted for TM
atom doped arm-chair single-wall carbon nanotubes [11]
and linear carbon chains [12, 13]; but synthesis of these
nanostructures appears to be difficult.
Our results are obtained from first-principles plane
wave calculations [14] (using a plane-wave basis set up to
kinetic energy of 350 eV) within generalized gradient ap-
proximation expressed by PW91 functional[15]. All cal-
culations for paramagnetic, ferromagnetic and antiferro-
magnetic states are carried out using ultra-soft pseudopo-
tentials [16] and confirmed by using PAW potential[17].
All atomic positions and lattice constants are optimized
by using the conjugate gradient method where total en-
ergy and atomic forces are minimized. The convergence
for energy is chosen as 10−5 eV between two steps,
and the maximum force allowed on each atom is 0.05
eV/Å[18].
Bare SiNW(N)s (which are oriented along [001] direc-
tion and have N Si atoms in their primitive unit cell)
are initially cut from the ideal bulk Si crystal in rod-like
forms and subsequently their atomic structures and lat-
tice parameter are relaxed [19]. The optimized atomic
structures are shown for N=21, 25, and 57 in Fig. 2.
While bare SiNW(21) is a semiconductor, bare SiNW(25)
and SiNW(57) are metallic. The average cohesive energy
relative to a free Si atom (Ec) is comparable with the
calculated cohesive energy of bulk crystal (4.64 eV per Si
atom) and it increases with increasing N. The average co-
hesive energy relative to the bulk Si crystal, E
c, is small
but negative as expected. Upon passivation of dangling
bonds with hydrogen atoms all of these SiNWs (specified
as H-SiNW) become semiconductor with a band gap EG.
The binding energy of adsorbed hydrogen relative to the
free H atom (Eb), as well as relative to the free H2 (E
are both positive and increases with increasing N. Exten-
http://arxiv.org/abs/0704.0109v1
FIG. 1: (Color online) Upper curve in each panel with
numerals indicate the distribution of first, second, third,
fourth etc nearest neighbor distances of SiNW(N) as cut
from the ideal Si crystal, same for structure-optimized bare
SiNW(N)(middle curve) and structure optimized H-SiNW(N)
(bottom curve) for N=21, 57 and 81. Vertical dashed line cor-
responds to the distance of Si-H bond.
sive ab initio molecular dynamics calculations have been
carried out at 500 K using supercells, which comprise ei-
ther two or four primitive unit cells of nanowires to lift
artificial limitations imposed by periodic boundary con-
dition. After several iterations lasting 1 ps, the structure
of all SiNW(N) and H-SiNW(N) remained stable. Even
though SiNWs are cut from ideal crystal, their optimized
structures deviate substantially from crystalline coordi-
nation, especially for small diameters as seen in Fig.1.
Upon hydrogen termination the structure is healed sub-
stantially, and approaches the ideal case with increas-
ing N (or increasing diameter), as expected. The cal-
culated response of the wire to a uniaxial tensile force,
κ = ∂ET /∂c, ranging from 172 to 394 eV/cell indicates
that the strength of H-SiNW(N)s (N=21-57) is rather
high.
The adsorption of a single TM (TM=Fe, Ti, Co, Cr,
and Mn) atom per primitive cell, denoted by n = 1, have
been examined for different sites (hollow, top, bridge etc)
on the surface of H-SiNW(N) for N=21, 25 and 57. In
Fig. 2(c) we present only the most energetic adsorption
geometry for a specific TM atom for each N, which re-
sults in a HM state. These are Co-doped H-SiNW(21),
Cr-doped SiNW(25) and Cr-doped SiNW(57). These
nanowires have ferromagnetic ground state, since their
energy difference between calculated spin-unpolarized
and spin-polarized total energy, i.e. ∆Em = EsuT −
is positive. We calculated ∆Em =0.04, 0.92 and
0.94 eV for H-SiNW(21)+Co, H-SiNW(25)+Cr and H-
SiNW(57)+Cr, respectively [20]. Moreover, these wires
have the integer number of unpaired spin in their prim-
itive unit cell. In contrast to usually weak binding of
TM atoms on single-wall carbon nanotubes which can
lead to clustering [21], the binding energy of TM atoms
(EB) on H-SiNWs is high and involve significant charge
transfer from TM atom to the wire [22]. Mulliken anal-
ysis indicates that the charge transfer from Co to H-
FIG. 2: (Color online) Top and side views of optimized atomic
structures of various SiNW(N)’s. (a) Bare SiNWs; (b) H-
SiNWs; (c) single TM atom doped per primitive cell of H-
SiNW (n = 1); (d) H-SiNWs covered by n TM atom corre-
sponding to n > 1. Ec, E
c, Eb, E
b, EG, and µ, respectively
denote the average cohesive energy relative to free Si atom,
same relative to the bulk Si, binding energy of hydrogen atom
relative to free H atom, same relative to H2 molecule, energy
band gap and the net magnetic moment per primitive unit
cell. Binding energies in regard to the adsorption of TM
atoms, i.e. EB, E
B for n = 1 and average values EB , E
for n > 1 are defined in the text and in Ref[22]. The [001]
direction is along the axis of SiNWs. Small, large-light and
large-dark balls represent H, Si and TM atoms, respectively.
Side views of atomic structure comprise two primitive unit
cells of the SiNWs. Binding and cohesive energies are given
in eV/atom.
SiNW(21) is 0.5 electrons. The charge transfer from
Cr to H-SiNW(25) and H-SiNW(57) is even higher (0.8
and 0.9 electrons, respectively). Binding energies of ad-
sorbed TM atoms relative to their bulk crystals (E′B) are
negative and hence indicate endothermic reaction. Due
to very low vapor pressure of many metals, it is proba-
bly better to use some metal-precursor to synthesize the
structures predicted here.
The band structures of HM nanowires are presented
in Fig.3. Once a Co atom is adsorbed above the center
of a hexagon of Si atoms on the surface of H-SiNW(21)
the spin degeneracy is split and whole system becomes
magnetic with a magnetic moment of µ=1 µB (Bohr mag-
neton per primitive unit cell). Electronic energy bands
become asymmetric for different spins: Bands of major-
ity spins continue to be semiconducting with relatively
smaller direct gap of EG=0.4 eV. In contrast, two bands
of minority spins, which cross the Fermi level, become
metallic. These metallic bands are composed of Co-3d
and Si-3p hybridized states with higher Co contribution.
The density of majority and minority spin states, namely
D(E, ↑) and D(E, ↓), display a 100% spin-polarization
P = [D(EF , ↑)−D(EF , ↓)]/[D(EF , ↑)+D(EF , ↓)] at EF .
Cr-doped H-SiNW(25) is also HM. Indirect gap of major-
ity spin bands has reduced to 0.5 eV. On the other hand,
two bands constructed from Cr-3d and Si-3p hybridized
states cross the Fermi level and hence attribute metal-
licity to the minority spin bands. Similarly, Cr-doped
H-SiNW(57) is also HM. The large direct band gap of
undoped H-SiNW(57) is modified to be indirect and is
reduced to 0.9 eV for majority spin bands. The mini-
mum of the unoccupied conduction band occurs above
but close to the Fermi level. Two bands formed by Cr-3d
and Si-3p hybridized states cross the Fermi level. The
net magnetic moment is 4 µB . Using PAW potential
results, we estimated Curie temperature of half-metallic
H-SiNW+TMs as 8, 287, and 709 K for N=21, 25, and
57, respectively.
The well-known fact that density functional theory un-
derestimates the band gap, EG does not concern the
present HM states, since H-SiNWs are already verified
to be semiconductor experimentally[1] and upon TM-
doping they are predicted to remain semiconductor for
one spin direction. In fact, band gaps predicted here are
in fair agreement with experiment and theory. As for par-
tially filled metallic bands of the opposite spin, they are
properly represented. Under uniaxial compressive strain
the minimum of the conduction band of majority spin
states rises above the Fermi level. Conversely, it becomes
semi-metallic under uniaxial tensile strain. Since conduc-
tion and valence bands of both H-SiNW(21)+Co and H-
SiNW(25)+Cr are away from EF , their HM behavior is
robust under uniaxial strain. Also the effect of spin-orbit
coupling is very small and cannot destroy HM properties
[12]. The form of two metallic bands crossing the Fermi
level eliminates the possibility of Peierls distortion. On
FIG. 3: (Color online) Band structure and spin-dependent to-
tal density of states (TDOS) for N=21, 25 and 57. Left panels:
Semiconducting H-SiNW(N). Middle panels: Half-metallic H-
SiNW(N)+TM. Right panels: Density of majority and mi-
nority spin states of H-SiNW(N)+TM. Bands described by
continuous and dotted lines are majority and minority bands.
Zero of energy is set to EF .
FIG. 4: (Color online) D(E, ↓), density of minority (light) and
D(E, ↑), majority (dark) spin states. (a) H-SiNW(25)+Cr,
n = 8; (b) H-SiNW(25)+Cr, n = 16. P and µ indicate spin-
polarization and net magnetic moment (in Bohr magnetons
per primitive unit cell), respectively.
the other hand, HM ground state of SiNWs is not com-
mon to all TM doping. For example H-SiNW(N)+Fe is
consistently ferromagnetic semiconductor with different
EG,↑ and EG,↓. H-SiNW(N)+Mn(Cr) can be either fer-
romagnetic metal or HM depending on N.
To see whether spin-dependent GGA properly repre-
sents localized d-electrons and hence possible on-site re-
pulsive Coulomb interaction destroys the HM, we also
carried out LDA+U calculations[23]. We found that in-
sulating and metallic bands of opposite spins coexist up
to high values of repulsive energy (U = 4) for N=25. For
N=57, HM persists until U∼1. Clearly, HM character
of TM doped H-SiNW revealed in Fig.3 is robust and
unique behavior.
Finally, we note that HM state predicted in TM-doped
H-SiNWs occurs in perfect structures; complete spin-
polarization may deviate slightly from P=100% due to
the finite extent of devices. Even if the exact HM charac-
ter corresponding to n = 1 is disturbed for n > 1, the pos-
sibility that some H-SiNWs having high spin-polarization
at EF at high TM coverage can be relevant for spintronic
applications. We therefore investigated electronic and
magnetic structure of the above TM-doped H-SiNWs at
n > 1 as described in Fig. 2(d). Figure 4 presents the
calculated density of minority and majority spin states
of Cr covered H-SiNWs.
It is found that H-SiNW(21) covered by Co is non-
magnetic for both coverage of n = 4 and 12. H-SiNW(25)
is, however, ferromagnetic for different level of Cr cover-
age and has high net magnetic moment. For example,
n = 8 can be achieved by two different geometries; both
geometries are ferromagnetic with µ=19.6 and 32.3 µB
and are metallic for both spin directions. Interestingly,
while P is negligible for the former geometry, the lat-
ter one has P = 0.84 and hence is suitable for spin-
tronic applications (See Fig. 4). Similarly, Cr covered
H-SiNW(57) with n = 8 and 16 are both ferromagnetic
with µ= 34.3 (P =56) and µ=54.5 µB (P =0.33), respec-
tively. The latter nanostructure having magnetic mo-
ment as high as 54.5 µB can be a potential nanomagnet.
Clearly, not only total magnetic moment, but also the
spin polarization at EF of TM covered H-SiNMs exhibits
interesting variations depending on n, N and the type of
In conclusion, hydrogen passivated SiNWs can exhibit
half-metallic state when doped with certain TM atoms.
Resulting electronic and magnetic properties depend on
the type of dopant TM atom, as well as on the diam-
eter of the nanowire. As a result of TM-3d and Si-3p
hybridization two new bands of one type of spin direc-
tion are located in the band gap, while the bands of
other spin-direction remain to be semiconducting. Elec-
tronic properties of these nanowires depend on the type
of dopant TM atoms, as well as on diameter of the
H-SiNW. When covered with more TM atoms, perfect
half-metallic state of H-SiNW is disturbed, but for cer-
tain cases, the spin polarization at EF continues to be
high. High magnetic moment obtained at high TM
coverage is another remarkable result which may lead
to the fabrication of nanomagnets for various applica-
tions. Briefly, functionalizing silicon nanowires with TM
atoms presents us a wide range of interesting properties,
such as half-metals, 1D ferromagnetic semiconductors or
metals and nanomagnets. We believe that our findings
hold promise for the use of silicon -a unique material
of microelectronics- in nanospintronics including magne-
toresistance, spin-valve and non-volatile memories.
∗ Electronic address: ciraci@fen.bilkent.edu.tr
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mailto:ciraci@fen.bilkent.edu.tr
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the following expression, EB = ET [H − SiNW (N)] +
ET [TM ] − ET [H − SiNW (N) + TM ] in terms of the
total energy of optimized H-SiNW(N) and TM-doped H-
SiNW(N) (i.e. H-SiNW(N)+TM) and the total energy of
the string of TM atoms having the same lattice parameter
co of H-SiNW(N)+TM, all calculated in the same super-
lattice. Hence EB can be taken as the binding energy of
single isoalted TM atom, since the coupling amaong ad-
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energy, and hence EB includes the coupling between TM
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B > 0 for H-SiNW(21)+Co at
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