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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. 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