Physica B 406 (2011) 84–87
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Physica B
journal homepage: www.elsevier.com/locate/physb
A computational study of silicon-doped aluminum phosphide nanotubes
Maryam Mirzaei a, Azadeh Aezami b, Mahmoud Mirzaei c,n
a
b
c
Department of Electrical Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran
Department of Physics, Islamic Azad University, Khuzestan Science and Research Branch, Ahvaz, Iran
Young Researchers Club, Islamic Azad University, Shahr-e-Rey Branch, Shahr-e-Rey, Iran
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 14 July 2010
Received in revised form
1 October 2010
Accepted 13 October 2010
We performed density functional theory (DFT) calculations to investigate the properties of silicon-doped
(Si-doped) models of representative (4,4) armchair and (6,0) zigzag aluminum phosphide nanotubes
(AlPNTs). The structures were allowed to relax and the chemical shielding (CS) parameters were
calculated for the atoms of optimized structures. The results indicated that the band gap energies and
dipole moments detect the effects of dopant. The CS parameters also indicated that the Al and P atoms
close to the Si-doped region are such reactive atoms, which make the Si-doped AlPNTs more reactive than
the pristine AlPNTs. Moreover, replacement of P atom by the Si atom makes AlPNT more reactive than the
replacement of Al atom by the Si atom.
& 2010 Elsevier B.V. All rights reserved.
Keywords:
Silicon doping
Aluminum phosphide nanotube
Electronic structure
Density functional theory
1. Introduction
Soon after the discovery of carbon nanotubes (CNTs) [1],
considerable efforts have been dedicated on the investigations of
non-carbon nanotubes among which the counterparts of third and
fifth groups of elements are proposed as proper alternative
materials [2,3]. In contrast to the CNTs, which are metallic or
semiconductor depending on the tubular diameter and chirality,
the counterparts of third and fifth groups of elements are always
viewed as semiconductors independent of any restricting factors
[4,5]. To this time, numerous experimental and computational
studies have been devoted to characterize the properties of boron
nitride nanotubes (BNNTs) and aluminum nitride nanotubes
(AlNNTs) [6–10]. However, the properties of the tubular
structures of other III–V counterparts such as boron phosphide
(BP) and aluminum phosphide (AlP) have not been investigated
much [11,12]. In a recent study, we have investigated the
properties of representative models of armchair and zigzag
AlPNTs by computations of chemical shielding (CS) parameters
[12]. In another study, we have also indicated that the CS
parameters of BPNTs could detect well the effects of impurities
such as carbon atom [11].
Nuclear magnetic resonance (NMR) spectroscopy is a versatile
technique to investigate the electronic and structural properties of
matters [13]. The CS parameters are very sensitive to the electronic
sites of atoms and could detect any effects on these sites. Earlier
n
Corresponding author. Fax: + 98 919 4709484.
E-mail address: mdmirzaei@yahoo.com (M. Mirzaei).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2010.10.026
studies indicated that the properties of nanotubes could be
investigated well by computations of the CS parameters [14,15].
Based on this efficiency, we have investigated the properties of
silicon-doped (Si-doped) models of representative armchair and
zigzag AlPNTs by quantum calculations of the CS parameters for the
optimized structures. Previous studies indicated that the Si-doped
CNTs and BNNTs contribute to physical and chemical interactions
with other atoms or molecules better than the pristine nanotubes
[16,17]. Moreover, the Si-doped nanotubes are viewed as reactive
materials at the Si-doped region [16]. Our results of the optimized
properties and the calculated CS parameters for the considered
Si-doped models of the representative (4,4) armchair and (6,0)
zigzag AlPNTs (Figs. 1 and 2) are listed in Tables 1–3.
2. Computational details
In this computational work, we have performed density functional theory (DFT) calculations to investigate the Si-doped models
of representative (4,4) armchair and (6,0) zigzag single-walled
AlPNTs (Figs. 1 and 2). The formula of pristine armchair model is
Al36P36H16 and the formula of pristine zigzag model is Al36P36H12 in
which the roles of hydrogen atoms are to saturate the tips of
nanotubes [12]. To create the Si-doped models, one Al atom or one P
atom is substituted by one Si atom to make the SiAl or SiP model
(Figs. 1 and 2). To avoid the effects of the tips of nanotubes on the
Si-doped regions and also the effects of the Si-doped regions on the
tips of nanotubes, the doping regions are placed as much far from
the tips as possible whereas the effects are not negligible in other
cases [14,18]. Initially, the geometries of models have been allowed
M. Mirzaei et al. / Physica B 406 (2011) 84–87
85
Table 1
Optimized structural propertiesa.
Property
Armchair models
EG (eV)
DM (Debye)
dAl P (Å)
Zigzag models
SiAl
SiP
Pristine
SiAl
SiP
Pristine
2.05
0.34
2.31
1.87
1.11
2.31
3.87
0.00
2.31
1.60
7.00
2.31
1.87
6.70
2.31
3.03
6.93
2.31
dAl Si (Å)
–
2.40
–
–
2.40
–
dSi P (Å)
2.27
–
–
2.27
–
–
dAl H (Å)
1.59
1.59
1.58
1.58
1.58
1.58
dP H (Å)
1.42
1.42
1.42
1.42
1.42
1.42
dTip (Å)
8.52
8.52
8.52
–
–
–
dAl-tip (Å)
–
–
–
7.00
7.00
7.00
dP-tip (Å)
–
–
–
8.10
8.10
8.10
a
See Figs. 1 and 2. For distances (d), the averaged values are reported. For
pristine model, the values are from Ref. [12].
Table 2
CS parameters for the
Fig. 1. 2D views of the Si-doped structures of the (4,4) AlPNT: SiAl (a) and SiP (b).
27
Al atom
27
Armchair models
SiP
SiAl
Al1
Al2
Al21
Al3
Al31
Al32
Al4
Al41
Al5
Al51
Al52
Al6
Al atomsa.
332;
337;
–
354;
350;
–
354;
360;
354;
276;
–
–
134
88
74
86
77
104
75
122
332;
337;
–
357;
360;
–
352;
346;
353;
336;
–
–
135
86
69
63
78
111
75
92
Zigzag models
Pristine
SiAl
332;
337;
–
356;
–
–
353;
–
356;
–
–
–
345;
342;
340;
345;
344;
344;
352;
286;
350;
356;
356;
315;
134
88
70
67
69
SiP
120
77
80
86
96
96
71
123
70
64
64
132
345;
342;
345;
341;
329;
329;
349;
347;
346;
346;
346;
314;
Pristine
121
75
75
96
124
124
83
117
74
71
71
132
345;
342;
–
347;
–
–
346;
—
346;
—
—
314;
120
78
82
79
74
133
a
See Figs. 1 and 2. The properties are in ppm. The first value of each row is for
isotropic chemical shielding and the second value is for anisotropic chemical
shielding. The underlined values are for 29Si atoms. For pristine model, the values are
from Ref. [12].
Table 3
CS parameters for the
31
P atom
Fig. 2. 2D views of the Si-doped structures of the (6,0) AlPNT: SiAl (a) and SiP (b).
to relax by all atomic optimizations using B3LYP exchangefunctional and 6-31G* standard basis set. Subsequently, at the
same DFT level, the CS parameters for the 27Al, 31P and 29Si atoms of
the optimized structures have been calculated based on the gaugeincluded atomic orbital (GIAO) approach [19]. The quantum
calculations yield the CS tensors (sii) in the principal axes
system (PAS) in which the orders of their eigenvalues are
s33 4 s22 4 s11 [13]. Therefore, directly relating to the
experimentally NMR measurements, the calculated CS tensors
are converted to the absolute values of isotropic CS (CSI) and
anisotropic CS (CSA) parameters using Eqs. (1) and (2) [13]. The
optimized properties and the calculated CS parameters for the
Si-doped models of (4,4) and (6,0) AlPNTs (Figs. 1 and 2) are shown
P atomsa.
Armchair models
SiP
SiAl
P2
P21
P3
P31
P32
P4
P41
P5
P51
P52
P6
31
503;
–
521;
525;
–
500;
452;
490;
415;
–
–
176
127
156
100
79
125
145
502;
–
522;
518;
–
502;
493;
509;
161;
–
–
175
124
146
120
130
105
484
Zigzag models
Pristine
SiAl
504;
–
524;
–
–
512;
–
513;
–
–
–
500;
498;
470;
433;
433;
473;
388;
487;
491;
491;
488;
179
116
110
106
SiP
168
169
135
163
163
133
149
124
130
130
194
501;
497;
479;
474;
474;
482;
139;
485;
487;
487;
487;
Pristine
165
158
129
148
148
135
495
130
151
151
190
501;
–
486;
–
–
489;
–
485;
–
–
488;
167
124
125
120
193
a
See Figs. 1 and 2. The properties are in ppm. The first value of each row is for
isotropic chemical shielding and the second value is for anisotropic chemical
shielding. The underlined values are for 29Si atoms. For pristine model, the values are
from Ref. [12].
in Tables 1–3. All calculations are performed by the Gaussian 98
package [20].
1
CSI ðppmÞ ¼ ðs33 þ s22 þ s11 Þ
3
ð1Þ
86
M. Mirzaei et al. / Physica B 406 (2011) 84–87
1
CSA ðppmÞ ¼ s33 - ðs22 þ s11 Þ; ðs33 4 s22 4 s11 Þ
2
ð2Þ
3. Results and discussion
3.1. Investigated structures
Our investigated structures consist of the Si-doped models of
representative (4,4) armchair and (6,0) zigzag AlPNTs in which one Al
atom is replaced by one Si atom in the SiAl models (Figs. 1a and 2a)
whereas one P atom is replaced by one Si atom in the SiP models
(Figs. 1b and 2b). Table 1 shows the optimized structural properties of
the Si-doped models of this study and the pristine models
from an earlier study [12]. In comparison to the pristine 3model,
the values of band gap energies (EG) are decreased in the Si-doped
models. The SiAl models could be considered as n-type semiconductors and the SiP models could be considered as p-type
semiconductors because the number of electrons in valence shell
of the Si atom is more than that of the Al atom but it is fewer
compared to the P atom. Therefore, the changes in the values of EG are
reasonable for the Si-doped models of AlPNTs. The armchair AlPNT
has two similar tubular tips but the zigzag AlPNT has two different
tips of Al- and P-tip. Therefore, the value of dipole moment (DM) for
the pristine armchair model is zero but the value of DM for the pristine
zigzag AlPNT is not zero due to the situations of tubular tips.
Interestingly, the values of DM for the Si-doped models of armchair
AlPNTs are not zero and the values of DM for the Si-doped models of
zigzag AlPNTs are changed. There are Si P bonds in addition to the
initial AlP, Al H and PH bonds in the SiAl model and there are
Al Si bonds in addition to the initial Al P, Al H and P H bonds in
the SiP model. Although different types of bonds exist in the Si-doped
models, but the averaged values of the bond distances and also the tip
diameters do not detect any changes in comparison to the pristine
models. This trend could approve the traceless concentration of the Si
atom in the Si-doped models in which the bond distances and the tip
diameters do not detect the effects of dopant.
3.2. CS parameters for the
27
Al atoms
Table 2 shows the calculated isotropic and anisotropic chemical
shielding (CSI and CSA) parameters for the 27Al atoms of the pristine
and Si-doped models of armchair and zigzag AlPNTs. An earlier
study [12] indicated that the CS parameters for the 27Al atoms of the
pristine model could be divided into layers based on the similarities
of values for atoms of each layer. Al1 stands for the Al atoms at the
tips of nanotubes in which the values of CS parameters for Al1
atoms are similar for the Si-doped and pristine models of the
armchair and zigzag AlPNTs. This trend reveals that the Al atoms at
the tips of nanotube do not detect the effects of traceless
concentration of dopant. In the armchair SiAl AlPNT, where Al51
is replaced by the Si atom, the values of CS parameters for Al31 and
Al41 atoms detect the effects of dopant. According to the Eqs. (1)
and (2), it is important to note that the CSI parameter means the
averaged values of electronic densities at the atomic sites but
the CSA parameter means the difference between the orientation of
the electronic densities perpendicular to the molecular plane
(z axis) and the orientation of the electronic densities in the
molecular plane (x–y axes). Indeed, the s22 and s11 eigenvalues
belong to the orientations of the CS tensors in the molecular plane
but the s33 eigenvalue belongs to the orientations of the CS tensors
perpendicular to the molecular plane. In earlier studies, we have
indicated that the electronic properties of the doped nanotubes
could be detected well by computing the CS properties in the
doped and pristine models [14,21,22]. However, if an interested
researcher would like to exhibit the exact contributions of the
atomic orbitals, performing natural bond orbital (NBO) analysis
could be a proper tool for the purpose [23] but it is not the purpose
of this study. Indeed the CS parameters indicate the overall
electronic contributions of the atoms to the doped regions and
we have employed these parameters to interpret the Si-doped
models of the AlPNTs. In comparison to the pristine model, the
changes in the values of CSA parameters for Al31 and Al41 atoms are
more significant than the changes in the values of their CSI
parameters, which mean that the total electronic density almost
remained unchanged but the orientation in the molecular frame is
changed.
In the zigzag SiAl AlPNT, where A41 is replaced by the Si atom,
similar results are found for the values of CS parameters for Al31 and
Al32 atoms. Moreover, the CS parameters for Al51 and Al52 also
detect the effects of dopant in which the value of CSI parameters are
increased whereas the values of CSA parameters are decreased in
comparison to the pristine model. The changes in the CS parameters for other Al atoms are almost negligible. In the armchair SiP
model, due to the replacement of P51 by the Si atom, three Al Si
bonds are resulted instead of the initial three Al P bonds. The CS
parameters for Al31 detect slight changes but the most significant
changes in the CS parameters are observed for Al41 and Al51 atoms
that are in chemical bonding with the Si atom. The reductions in CSI
values and the increments in the CSA values for these two Al atoms
indicate that the tendency of these atoms for contribution to Al Si
bonds is less than the tendency for contributions to the Al P
bonds. For the zigzag SiP model, similar results are found for Al31,
Al32 and Al41 atoms that are directly bonded to the Si atom. Parallel
to the previous trend about the more reactivity of the Si-doped
nanotubes than the pristine nanotubes [16], our results also
indicate that the Si-doped AlPNTs could be more reactive than
the pristine AlPNTs because of larger values of CSA parameters for
Al atoms at the Si-doped regions.
3.3. CS parameters for the
31
P atoms
The calculated CSI and CSA parameters for 31P atoms of the SiAl
and SiP models of (4,4) armchair and (6,0) zigzag AlPNTs (Figs. 1b
and 2b) are listed in Table 3. According to the earlier study on
pristine AlPNTs [12], the CS parameters for 31P atoms of the pristine
AlPNT are divided into layers based on similarities in the values for
atoms of each layer. The values for P1 atoms of the Si-doped and
pristine models do not show any difference, which implies that the
electronic properties of the P atoms at the tips of Si-doped
nanotubes do not detect the effects of dopant. In the armchair
SiAl AlPNT, Al51 atom is replaced by the P atom; therefore, three
Si P bonds are resulted instead of three Al P bonds. Although
both of P41 and P51 atoms are chemically bonded to the Si atom, but
the electronic properties of these two atoms detect different effects
of the Si-doped region. By the optimization process, the
geometrical position of P51 is relaxed inwardly but the initial
status of geometrical position of P41 remained unchanged. Due to
the different geometrical positions, the calculated CS parameters
are different for P41 and P51 atoms of the SiAl model. The electronic
distribution of P41 atom is remarkably oriented in the molecular
plane whereas the electronic distribution of P51 atom is remarkably
oriented perpendicular to the molecular plane as indicated by the
smaller value of CSA parameter for P41 atom and the larger value of
CSA parameter for P51 atom. The CSA parameter for P31 atom of the
SiAl model also detects the effects of Si doping in which the
electronic distribution for this atom is oriented perpendicular to
the molecular plane.
In the armchair SiP AlPNT, P51 is replaced by the Si atom,
resulting three Al Si bonds instead of three Al P bonds. The P
M. Mirzaei et al. / Physica B 406 (2011) 84–87
atoms are not chemically bonded to the Si atom, but the CS
parameters for the P atoms detect the effects of the Si-doped
region. The CS parameters for P31 and P41 atoms, which are close to
the Si-doped region, detect the effects of Si doping as could be seen
by decreasing the value of CSI parameter and increasing the value of
CSA parameter. In the zigzag SiAl AlPNT, replacement of Al41 by the
Si atom results in three Si P bonds where P31, P32 and P41 are
chemically bonded to the Si atom. In comparison to the results of
the pristine zigzag AlPNT, the CS parameters for the mentioned
P atoms are changed due to the Si doping. Moreover, the results
indicate that the tendency of P atom for contribution to the
Si P bond is less than the tendency for contribution to the
Al P bond. In the SiP zigzag AlPNT, where P41 is replaced by Si
atom, the P atoms are not in direct chemical bonding to the Si atom
but their CS parameters detect the effects of the Si-doped region.
The CS parameters for P31, P32, P51 and P52 atoms detect the most
significant changes in comparison to the pristine model. The results
indicate that the averaged electronic densities at these atomic sites
are not changed; however, the electronic distributions are remarkably oriented perpendicular to the molecular plane. Parallel to the
results for Al atoms of the Si-doped AlPNTs, the results for the P
atoms also indicate that the Si-doped AlPNTs are more reactive
than the pristine AlPNTs, which are in agreement with the previous
trend about the Si-doped nanotubes [16].
3.4. CS parameters for the
29
Si atoms
CS parameters for the 29Si atoms, which are underlined in
Tables 2 and 3, indicate that the orientations of the electronic
distributions of Si atoms of the SiAl models are more oriented in the
molecular plane whereas these distributions of the SiP models are
more oriented perpendicular to the molecular plane. There are
three Si P bonds in the SiAl models of AlPNT and there are three
Al Si bonds in the SiP models. It is important to note that the
electronegativity of the Al atom is smaller than the P atom.
Moreover, the electronegativity of the Si atom is larger than that
of the Al atom but smaller than that of the P atom. According to the
order of the values of electronegativities, P4Si 4Al, the Al atom of
the SiAl model is doped by the Si atom with a larger value of
electronegativity but the P atom of SiP model is doped by the Si
atom with a smaller value of electronegativity. Therefore, the initial
ionic properties of Al P bonds are changed in the new Al Si and
Si P bonds. The values of the CS parameters for the 29Si atoms
reveal that the initial properties of the Al P bonds are changed less
in the SiAl model than the SiP model. It could be concluded that the
SiP model is more reactive than the SiAl model because of more
changes in electronic properties of the SiP model than the SiAl
model. In these cases, it seems that Si doping of the Al atom is more
favorable than that of the P atom. In other words, the formations of
the Si P bonds in the SiAl model are preferred than the formations
of the Al Si bonds in the SiP model.
87
4. Concluding remarks
Our DFT calculated parameters indicated that the electronic and
structural properties of the (4,4) and (6,0) AlPNTs detect the effects
of Si-doped region. The optimized properties indicated that the
bond distances and tip diameters do not detect any effects, but
the values of band gap energies and dipole moments exhibit the
changes in the effects of Si-doped region. The CS parameters for the
atoms at the tips of nanotubes do not detect the effects of dopant,
but both Al and P atoms close to the Si-doped region detect
remarkable changes. The values of CS parameters for the Al and P
atoms close to the Si-doped region indicate that the Si-doped
AlPNTs are more reactive than the pristine AlPNTs. Moreover, this
reactivity for the SiP model, where the P atom is replaced by the Si
atom, is more remarkable than the SiAl model, where the Al atom is
replaced by the Si atom.
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