Download DOS Calculation Analysis of New Transparent Conductor Mg(OH)2-C

Materials Transactions, Vol. 52, No. 8 (2011) pp. 1689 to 1692
#2011 The Japan Institute of Metals
RAPID PUBLICATION
DOS Calculation Analysis of New Transparent Conductor Mg(OH)2-C
Takahiro Murakami, Takamitsu Honjo and Toshiro Kuji*
Department of Applied Chemistry, School of Engineering, Tokai University, Hiratsuka 259-1292, Japan
In this paper, the new transparent conductive material, Mg(OH)2 -C is analyzed by an ab initio quantum chemical calculation based on the
density of states (DOS) with DV-X calculation. In this study the calculation of DOS for Mg(OH)2 by DV-X calculation with Mg(OH)2 cluster
model was carried out first to assure the validity of our calculation. Next, it was hypothesized that Mg(OH)2 -C is modeled with MgOHOC cluster
as well as the Mg(OH)2 cluster. The expected behavior of the MgOHOC DOS well agrees with the experimental results for Mg(OH)2 -C, and the
hypothesized MgOHOC model well explained the characteristics of the Mg(OH)2 -C. Moreover, replacing a part of the H atoms with C atoms in
some of nonconductive hydroxide materials yields conductivity as well as our MgOHOC, because the reason of the MgOHOC conductivity
appearance is the one by the replacements from the OH bond to the OC bond and the characteristics of Mg atom doesn’t especially take the part
of the conductivity appearance. [doi:10.2320/matertrans.M2011046]
(Received February 2, 2011; Accepted May 16, 2011; Published July 6, 2011)
Keywords: hydroxide materials, magnesium (Mg), brucite (Mg(OH)2 ), carbon (C), transparent conductive films, ab initio quantum chemical
calculations (DV-X)
1.
Introduction
Transparent conductors are essential materials for flat
display and solar cell technology. Tin doped Indium oxide,
ITO has been widely used as a key material for liquid crystal
display technologies because of its high transparency and
electric conductivity. Recently, however, high cost of indium
due to the scarcity (Clarke number is 105 ) and the toxicities
of indium oxides have been strongly pointed out so that
alternative transparent conductive materials have been
actively studied over the last two decades.1–4)
The conventional transparent conductive materials are
based upon metal oxides without exception. It is well known
that the metal oxides are more and less semiconductor due to
the deviation from the stoichiometry.
Recently, Kondoh’s group reported very interesting results
on the colored transparent for Mg-C compounds.5) The
structure of compounds was identified to be amorphous. On
the other hand, the new transparent conductive material
developed in our group, Mg(OH)2 -C, was prepared by the
sputtering Mg and C, and post-reaction of the Mg-C film with
moisture in the air.6–9) The transmittance of the visible ray
was 90% in the average. The electric resistivity of the film
was on the order of 103 cm.9) Experimental details have
been shown in previously reports.6–8) The lattice symmetry of
Mg(OH)2 -C was identified to be Mg(OH)2 structure (P-3m1)
with slightly elongated c-axis compared with hexagonal
Mg(OH)2 .7) The mineral name is brucite. It is believed that
the new material is the first non-oxide type transparent
conductor. Therefore, in this paper, understanding the density
of states (DOS) of the unit-cell of Mg(OH)2 -C by using DVX molecular orbital calculations (electronic state calculations) must be very much important.10) The DV-X method is
an ab initio quantum chemical calculation and the cluster
discrete-variational X method based on the Hatree-FockSlater self-consistent approximation,11) and suitable for the
examination of the electronic state of a random impurity
*Corresponding
author, E-mail: [email protected]
atom in small crystallites or thin films because the method
does not use the plane wave approximation which specializes
in uniformity.
2.
The computation Model and Calculation Methods
The basic crystal structure of Mg(OH)2 is hexagonal closepacked (hcp), and the lattice geometry data has been reported
by F. Pascale et al.12) or Joint Committee of Powder
Diffraction Standards (JCPDS) data.13) The crystal is composed of Mg layers, and the hydroxyl ligand (OH) bonds are
parallel to the c-axis of the hexagon Mg(OH)2 structure and
the OH ligands which bond with the upper and lower Mg
layer respectively are opposite and alternately arranged. The
unit-cell of Mg(OH)2 is shown in Fig. 1(a) and the lattice
geometry distances are defined as follows.
8
a ¼ 0:31500 nm;
>
>
>
<
c ¼ 0:47700 nm;
ð1Þ
>
R
OH ¼ 0:09583 nm;
>
>
:
ROMg
{{{ ¼ 0:10499 nm;
where a and c are the a- and c-axis in the Mg(OH)2 unit-cell,
respectively. And ROH and ROMg
{{{ describe the distances from
the O atom to the H atom and to the Mg layer, respectively.
Here it should be noted that the film thickness and the
crystallite diameter of the transparent conductive film are
about 1000 nm and 5 nm, respectively.8) Thus, the thickness
and the diameter should influence the electronic state. It is
concluded that the calculation results of cluster models must
be expected to be very much strongly influenced by surface
effects, such as surface dangling bond. Therefore, Fig. 2
shows the defined cluster model of Mg(OH)2 under consideration of the basic crystal model used for the DOS analysis
of Mg(OH)2 -C. As shown in Fig. 2, in our calculation the one
unit-cell shown in Fig. 1(a) is located in the center of the
Mg(OH)2 cluster model in order to prevent the strong surface
effects from the calculation results. The surface region on the
horizontal side to the Mg layer is larger than that on the
vertical side. Because the electron states of Mg in Mg(OH)2
1690
T. Murakami, T. Honjo and T. Kuji
(a)
(b)
Fig. 1 Unit-cells of (a) Mg(OH)2 and (b) MgOHOC crystal structures.
The lattice geometry data; a ¼ 0:31500 nm, c ¼ 0:47700 nm, ROH ¼
0:09583 nm, ROC ¼ 0:11500 nm, and ROMg ¼ 0:10499 nm.
respectively. The distance between the O and the C is
described ROC . We hypothesize ROC ¼ 0:11500 nm, which is
the same degree of Ni(CO)4 , because Ni(CO)4 is an example
of a carbon monoxide ligand in a metal.14) It was reported that
the lattice symmetry of Mg(OH)2 -C was identified to be
Mg(OH)2 structure (P-3m1),7) and the example model of
Mg(OH)2 -C lattice was like Fig. 1(b).8,9,15) Thus the hypothesized unit-cell model is made from exchanging one H in
the unit-cell of Mg(OH)2 with C. And then, the MgOHOC
cluster model was constructed as follows. The hypothesized
MgOHOC cluster model is made by replacing the center unitcell (Fig. 1(a)) of Mg(OH)2 cluster model (Fig. 2) with the
MgOHOC unit-cell model (Fig. 1(b)). The new transparent
conductive material, Mg(OH)2 -C film, was prepared with a
less amount of C than that of Mg,6–9) and then it is thought
that the crystal structure of Mg(OH)2 -C film is composed
dominantly of the Mg(OH)2 unit-cell (Fig. 1(a)) and partially
of the assumed MgOHOC unit-cell (Fig. 1(b)).
We use the Madelung potential of the point charge model
in the DV-X electronic state calculations16) because of
suppressing the surface effect in the calculation results. The
Madelung potential is the electro-static potential of ions
outside the cluster. And the used number of the charge points
is 260 positions of Mg and 492 positions of OH, although the
charge points on the boundary side are made a half to keep
the symmetry. We applied the ionic charge values for each
element under agreement as self-consistency.17) The each
charge value in the position of Mg, O and H is +1.40, 1:12
and +0.42, respectively. These given values are certainly
good agreements with the charge quantities of the calculation
results shown in Table 1.
3.
Fig. 2 Mg(OH)2 cluster model used in DV-X calculations. The big gray
balls, the small black balls and the small gray balls represent Mg atom, O
atom and H atom, respectively. The number of Mg and OH is 28 and 84.
MgOHOC cluster model is almost same. If one H atom in the central unitcell of Mg(OH)2 cluster model is exchanged for C atom, Mg(OH)2 cluster
model becomes MgOHOC cluster model.
extend to the horizontal Mg layer and the surface effect is
strongly reflected on the calculation results, which should be
not neglected for calculation. We basically consider the
center unit-cell for our calculation.
In this study, we hypothesize the unit-cell model of
Mg(OH)2 -C as shown in Fig. 1(b) and the crystal model is
called MgOHOC. In Fig. 1(b), the O atoms bonding with C
and H are described O and O , respectively and the Mg
atoms bonding with O and O are described Mg and Mg ,
Results and Discussions
Figures 3(a) and (b)–(d) show the partially DOS (PDOS)
of the Mg(OH)2 unit-cell (Fig. 1(a)) and the MgOHOC unitcell (Fig. 1(b)) in the cluster model (Fig. 2), respectively.
The calculated band gap (Eg ) shown in Fig. 3(a) is about
1.1 aJ (7 eV) (1 eV ¼ 1:60218 1019 J ¼ 0:160218 aJ), and
well agrees with the experimental value of Eg shown in
Fig. 4. This Eg indicates the characteristic of transparent
insulator as Mg(OH)2 , because the Eg is much more than the
wide-gap semiconductor Eg , i.e. 0.4 aJ (2.2 eV) and the
highest visible photon energy, i.e. 0.5 aJ (3.2 eV). This
implies that the PDOS in Fig. 3(a) represents the typical
enough as the DOS of Mg(OH)2 . The calculated results of the
MgOHOC cluster model could be good enough to analysis
MgOHOC material as well as the calculated results of the
Mg(OH)2 cluster model is good enough to analysis Mg(OH)2
crystal. Figures 3(b), (c), and (d) are almost equivalent
although c changes. Thus, slightly elongating the c-axis
like the experimental fact7) hardly influences the MgOHOC
DOS. The calculated band gaps of MgOHOC with c ¼
0:000 nm (Fig. 3(b)), 0.005 nm (Fig. 3(c)) and 0.010 nm
(Fig. 3(d)) are especially same as 1.0 aJ (6 eV), because the
states in the band gaps are thought to be the impurity energy
levels derived from the C atom. The MgOHOC Eg indicates
the transparent characteristic as well as Mg(OH)2 -C. Then,
in the comparison between the Mg(OH)2 and MgOHOC, the
MgOHOC Eg becomes small and about 0.2 aJ (1 eV) from the
DOS Calculation Analysis of New Transparent Conductor Mg(OH)2-C
1691
Table 1 Effective ionic charge. In ‘Mg(OH)2 formal char.’ column, the values at the left of the arrow are general formal charges of Mg, O,
H, and C, and the values at the right are the values used for the Madelung potential of the point charge model. The columns at the right of
the double line represent the calculated ionic charges in the central unit-cell of the Mg(OH)2 or MgOHOC cluster model.
Mg
Mg(OH)2
formal char.
Mg(OH)2
MgOHOC
c ¼ 0:000 nm
MgOHOC
c ¼ 0:005 nm
MgOHOC
c ¼ 0:010 nm
þ2 ! þ1:40
+1.432
+1.448
+1.447
+1.448
Mg
þ2 ! þ1:40
+1.432
+1.391
+1.388
+1.391
O
2 ! 1:12
1:144
1:129
1:151
1:132
O
2 ! 1:12
1:144
0:652
0:656
0:639
H
þ1 ! þ0:42
+0.434
C
OH
1 ! 0:70
0:710
OC
unit-cell
0 ! 0:00
+0.011
+0.437
+0.437
+0.437
0:017
0:026
0:023
0:692
0:714
0:695
0:669
0:682
0:662
+0.063
+0.026
+0.067
The O (Mg ) atom is on the near side and the O (Mg ) atom is on the far side.
(a) Mg(OH)2
(b) MgOHOC with Δc = 0.000nm
(c) MgOHOC with Δc = 0.005nm
(d) MgOHOC with Δc = 0.010nm
Fig. 3 The PDOS in the Mg(OH)2 model and the MgOHOC model. D and En indicate the density of states and the energy level,
respectively. 1 eV is 0.160218 aJ. When the density of states was calculated, we used the Gaussian function whose full width at half
maximum (FWHM) is 0.1 aJ (0.5 eV). En ¼ 0:0 aJ is defined the HOMO. The each Eg represents the band gap. In (b), (c), and (d), the
states in the band gaps are thought to be the impurity energy levels. The green lines, the red lines, the gray lines and the black lines derive
from Mg, O, H, and C in the center unit-cell, respectively. The blue dashed lines are the total density of Mg, O, H, and C. And the dot lines
and the solid lines derive from the atom on the far and near side from the C atom, respectively. In Fig. 2(b), the O (Mg ) atom is on the
near side and the O (Mg ) atom is on the far side.
Mg(OH)2 Eg . This value well agrees with the experimental
value of the Eg changing.9,15) Next, the impurity energy level
was paid to attention. The impurity DOS peak at 0.0 aJ
(0.0 eV) in Figs. 3(b)–(d) has the two electronic orbital states
where one electron enters, and the energy level difference
between the two electronic orbital states is under 0.1 aJ
(0.5 eV). Thus the impurity DOS peak can generate the both
of electron and hole carrier so that it is difficult to distinguish
whether the majority carrier is electron or hole. Moreover,
the impurity DOS peak corresponding to the insertion of
carbon atoms in Mg(OH)2 lattice is almost in the middle of
the band gap. Therefore it could be estimated that the carriers
can move around the impurity-energy-level network generated by many C atoms. In this case, the material is very
unique and to be applied to even quantum devices, for
instance, quantum computer or communication. However we
1692
T. Murakami, T. Honjo and T. Kuji
Fig. 4 The experimental photo transmittances for Mg(OH)2 . T and "
indicate the photo transmittances and the photon energy level, respectively. 1 eV is 0.160218 aJ, and " eV ¼ 1239:84=ð nmÞ, where is light
wavelength. The Mg(OH)2 thin film was prepared on a glass substrate, and
the solid line and the dot line are the Mg(OH)2 and the glass, respectively.
The dash line is the extrapolation line for the solid line, and the band gap of
Mg(OH)2 is estimated to be about 1.1 aJ (7 eV).
avoid quantitative discussion about the Eg and the impurity
energy level because of the following problems. The strict
accurate exchange-correlation potential is unknown, and also
we do not know the precise distances between atoms in the
MgOHOC enough to calculate the precise electronic states.
Thus it is necessary to note that the error margin of a few
electron volts is contained in the total energy or Eg . In fact,
the calculation results in this paper leave the possibility that
the impurity energy level is not in the middle of the band gap
but in the near of the conduction band or the valence band
enough to yield electronic conductivity. Here, for simplicity,
we approximately neglect the charge-carrier pathway or Mott
insulator. The detail role of such charge carriers will be
discussed elsewhere. Anyway the both of highest occupied
molecular orbital (HOMO) of Mg(OH)2 and MgOHOC are
mainly composed of O and Mg orbitals as shown in Fig. 3.
The hybridizing O-C orbitals may also be generated above
the HOMO. It is thought that similar phenomenon should
happen for other hydroxide materials. Therefore, replacing a
part of the H with C generates the O C hybrid orbtals in the
band gap, and there is the possible that some of the impurity
energy levels yield electronic conductivity as well as
Mg(OH)2 -C.
The bonding calculation analysis of the MgOHOC
including the valence electron distribution in the C will be
reported in near future. The analysis indicates the possible
existence of the MgOHOC and slightly elongating the c-axis
like the experimental fact.7)
4.
Conclusions
The hypothesized MgOHOC model is transparent semiconductor, although it is not clear whether the conductivity is
yielded by a n(p) type semi-conductor or an impurity-energylevel network generated by many C atoms. The reason of the
transparency is that the hypothesized MgOHOC model keeps
sufficiently wide band gap for visible light to transmit. And
the reason of the conductor is that the C atom generates the
impurity energy level in the band gap of Mg(OH)2 . The
expected behavior of the hypothesized MgOHOC model well
agree with the experimental results for Mg(OH)2 -C, i.e. the
characteristic of transparent conductor, the band gap reduction of about 0.2 aJ (1 eV) and elongating the c-axis. From
our discussions, it can be well explained that the hypothesized MgOHOC model is approximate for the Mg(OH)2 -C.
Moreover, replacing a part of the H atoms with C atoms in
some of nonconductive hydroxide materials yields conductivity as well as our MgOHOC, because the reason of the
MgOHOC conductivity appearance is the one by the
replacements from the OH bond to the OC bond and the
characteristics of Mg atom doesn’t especially take the part of
the conductivity appearance. And some of hydroxide
materials replacing a part of the H atoms with C atoms
might have so peculiar impurity-energy-level network. This
could imply the potential application to electric devices or
quantum devices, even if Mg(OH)2 -C doesn’t have the
unique impurity-energy-level network.
Acknowledgments
Authors greatly acknowledge for valuable suggestions
from Prof. M. Sato of Tokai University and Dr. J.-C. Crivello
of National Center for Scientific Research (CNRS) in France
as well as Prof. M. Morinaga, Dr. H. Yukawa and Dr. M.
Yoshida of Nagoya University and Prof. T. Ishii of Kagawa
University.
REFERENCES
1) The 166th Committee on Photonic and Electronic Oxide, and JSPS,
Toumei-dou-denmaku no gijyutu (in Japanese), (Ohmsha Ltd., Tokyo,
2007).
2) K. Ellmer, R. Cebulla and R. Wendt: Thin Solid Films 317 (1998) 413–
416.
3) Y. Hayashi, K. Kondo, K. Murai, T. Moriga, I. Nakabayashi, H.
Fukumoto and K. Tominaga: Vacuum 74 (2004) 607–611.
4) T. Minami, H. Nanto and S. Takata: Appl. Phys. Lett. 41 (1982) 958–
960.
5) K. Kondoh, T. Serikawa, K. Kawabata and T. Yamaguchi: Scr. Mater.
57 (2007) 489–491.
6) T. Honjo, M. Chiba, T. Nobuki and T. Kuji: Hyomen Kagaku (J. Surf.
Sci. Jpn.) 29 (2008) 532–536 (in Japanese).
7) T. Kuji, T. Honjo and M. Chiba: e-J. Surf. Sci. Nanotech. 6 (2008)
15–16.
8) T. Honjo, M. Chiba and T. Kuji: e-J. Surf. Sci. Nanotech. 7 (2009) 791–
794.
9) T. Honjo, T. Murakami and T. Kuji: Vaccum Special Issue (2011)
submitted.
10) H. Adachi, M. Tsukada and C. Satoko: J. Phys. Soc. Jpn. 45 (1978)
875–883.
11) D. E. Ellis, H. Adachi and F. W. Averill: Surf. Sci. 58 (1976) 497–510.
12) F. Pascale, S. Tosoni, C. Z.-Wilson, P. Ugliengo, R. Orlando and R.
Dovesi: Chem. Phys. Lett. 396 (2004) 308–315.
13) JCPDS on No. 07-0239, Quality: I.
14) W. Braun, H.-P. Steinruck and G. Held: Surf. Sci. 575 (2005) 343–357.
15) T. Honjo, J.-C. Crivello and T. Kuji: Minerals, Metals & Materials
Society (TMS) 2011 Annual Meeting & Exhibition, (2011) submitted.
16) C. Satoko, M. Tsukada and H. Adachi: J. Phys. Soc. Jpn. 45 (1978)
1333–1340.
17) M. Tsukada: J. Phys. Soc. Jpn. 49 (1980) 1183–1184.