2012 International Conference on Solid-State and Integrated Circuit (ICSIC 2012)
IPCSIT vol. 32 (2012) © (2012) IACSIT Press, Singapore
Theoretical investigation of electronic and optical properties of
C32H18 N8
J. Baedi1, M. R. Benam3 M. E. Moazemi1
Department of physics, Sabzevar Tarbiat Moallem university, Sabzevar, Iran
2
Department of Physics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran
1
Abstract. In this paper we have calculated some electronic properties such as band structure, density of
states and energy gap for C32H18N8 compound by first principle. We have also presented some optical
properties such as dielectric function, Electrical loss function, optical conduction and refractive index.
Calculations were performed in the framework of density functional theory (DFT), using the full-potential
linearized augmented plane wave (FP-LAPW) method. This studies presented the electrical gap energy of
phthalocyanine, Eg = 2.4 eV which is in good agreement with experimental value. A trap energy level is
also observed. The Calculated optical band gap is about 2.48 eV with an optical trap level at 1.48 eV. In
addition , we obtained the static refractive index in the x-,y- and z- directions as n0xx=2.43, n0yy=2.06 and
n0zz=2.32. lastly, Absorption spectra display the existence of strong absorption bands in the range of 400
and 800 nm which compares favorably with experiment.
Keywords: phthalocyanine, band structure, density functional theory.
1. Introduction
Metal-free phthalocyanine (H2Pc) was first discovered in 1907 by Braun and Tcherniac. One of the most
interesting derivatives is a dianion that may be complexed with up to 70 different metal cations [1].
This organic semiconductor has excellent stability against heat, light, moisture and oxygen. Because of
these distinct characteristics, Pcs have been widely used as pigments for coloring plastics and metal
surfaces, and as catalysts in the oil industry [3, 4]. In recent years, new applications have emerged for Pcs
due to their semiconducting properties. They have been used in photovoltaic devices [3,5] photodetectors
[6],organic transistors [7] and sensors [8]. Pcs are also commonly used as a hole injection layer in organic
light emitting diodes (OLEDs) [9].
2. Method of calculations
Contributions The calculations were performed in the framework of density functional theory (DFT)
[10], using the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in
Wien2k codes [11,12]. We selected the generalized gradient approximation (GGA) of Perdew et al [13,
14] for the exchange-correlation energy in our calculations. The chosen radii of MT spheres for atoms are
RMT (C) = 1.16 Å , RMT (N) = 1.13 Å and RMT (H) = 0.61 Å . The cut-off energy, which defines the
separation of the valence and core states, was chosen to be about −6.0 Ryd. Figure 1 pictures the crystal
unit cell of H2Pc; it has monoclinic structure with P21/a space group. Its lattice parameters are a = 19.4
Å , b = 4.8 Å , and c = 14.6 Å ; β = 120° [15].
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Figure 1. Structure and atomic positions of C32H18N8.
Dielectric tensor is used for analyzing the behavior of crystal before the electromagnetic field.
We applied Kramers–Kronig transformation to analyze the data. This transformation allows us to
calculate the real part of the dielectric function when having its imaginary part. The imaginary and real
parts of the dielectric constant at the frequency of the incident photon can be written as [14,16]:
(1)
(2)
and
are conduction and valence states of the electron in a given wave vector k, and the
Where
delta function implies the conserving of the energy in transitions, where ckand vkare energies of the
scattered electron in the initial valence and final conduction states, respectively. Two factors are effective
for determining optical properties, density of states (DOS) above the Fermi level and the number of
crystal symmetries which are discussed in the following sections.
3. Results and discussion
3.1. Electronic properties
The total density of states (DOS) is exhibited in figure 3. Zero energy marks the Fermi level and is shown
by the dashed line. The major contribution at the top of the valence band belongs to nitrogen atoms,
159
which is due to their stronger electronegativity than carbon atoms in carbon-nitrogen bond (peaks of 11,
12, and 13). In addition, the peaks of 3, 5, 6, and 9 denote overlapping of N-2P and C-2S orbitals. It
should be noticed that there are two types of hybride orbital for carbon-carbon bond (peaks of 8, 14). SP2
orbitals are related to benzene rings; the other hybrid orbitals which are due to electron cloud overlapping
of carbons are out of the benzene rings. The conduction band mostly contains hybrid orbitals of carbonnitrogen bonds. There also exists a trap band at the position of 15th peak [17]. It is remarkable that the
contribution of H-1S orbitals is the least because of its low electronegativity.
Figure3. Total DOS of C32H18N8.
Table 2.The highest density of state related to different orbitals.
Peak
number
Related to
Atom-Orbitals
Peak
Number
1
C10,C12,C13,N3-2S
8
2
C9-2S
9
3
C-2P,N2,N4-2P
4
5
6
7
N3-2P
C3,…,C9,C12,C13,C16-2P
N2,N3,N4-2P
Peak
Number
Related to
Atom-Orbitals
15
C1,C8,C9,C16-2P
N1,N2,N3-2P
C2,…,C7,C12,C13,N2-2P
16
C11,C13,C14,N1-2P
10
C2,…,C7-2P
H1,H5-1S
17
C4,C5,C6,C9,C10-2P,
C12,C13,C14-2P
11
N1,N2,N4-2p
18
12
Related to
Atom-Orbitals
C4,C5,C10,C12,C13,C16-2P
N1-2P
C1,C3,…,C8,C10,C12,…,C16-2P
N-2P
19
C1,C2,C8,C9,C16-2P
C1,C8,C9,C13,N2-2P
13
N2,N4-2P
20
C1,C2,C3,C5,…,C11,C13-2P
N1,N4-2P
C1,C3,C6,C8,N2,N3-2P
H1,H5,H7,H8-1S
14
C1,C8,C9,C12,C13,C16-2P
21
C1,…,C12,C16,N-2P
160
Figure 4. Side view of (110) plate.
Figure 5. Contours of electron charge density in the (110) plate.
Figure 4 represents the (110) plate and contours of the electric charge density are shown in figure 5. It is
evident that apart from N-H bond which is a hydrogen bond, all other bonds are covalent
Figure6. First brillouin Zone. K .1, K .2, K .3 are the chosen points (right) . Band structure of Pc compound along
the lines with high symmetry (left). The Fermi energy has been set to zero.
The band structure is displayed in figure 6 . It should be noted that the energies have been shifted so that
the Fermi energy is located at the top of the valence band as zero energy. It is observed that this
compound has an indirect band gap with an energy gap of about Eg = 2.4 eV which is in good agreement
with experimental value [18].
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3.2. Optical properties
The real part of the dielectric functions for the x- , y- and z- directions is illustrated in ̒figure7 ̓. As shown
in the diagrams any of the directions has different value for dielectric function. The values related to
E=1.32 eV in x-, y- and z- direction are 14.29, 14.52, and 21.77, respectively. Indeed, there is anisotropy
with the energies less than 5 eV because of no accordance between diagrams in all three directions.
Roots of the real part of the dielectric function are a necessary condition for plasmon oscillations, but are
not enough. We must also study the energy loss function for exact determination.
Figure 7. Real part of the dielectric function of
Phthalocyanine.
Figure 8. Energy loss function of Pc.
Figure 8 shows the energy loss function in all three directions. The maximum values of energy loss
function in x- direction are at energies of 5.32, 3.36 and 1.89 eV which are in good agreement with roots
of figure 7 at energies of 5.21, 3.36 and 1.89 eV. Therefore, this compound has three Plasmon
oscillations.
In figures 9and10 , energies related to maximums in the imaginary part of dielectric function and optical
conduction, are the same. So we just analyze optical conduction since analyzing the imaginary part of
dielectric function results is nothing new.
Figure 9. imaginary part of the dielectric function of
Phthalocyanine
Figure 10. Optical conduction of Pc
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The electrons of occupied states are excited to unoccupied states above the Fermi level by absorption of
photon energy. This is called optical conduction which happens to be the same in all three directions.
Threshold optical conduction occurs at about 2.48 eV; there is also an optical trap level at 1.48 eV.
The refractive index of Pc for all three diections, x- , y- and z- directions, are illustrated in ̒ figure11 ̓. We see
a small difference in these directions that means that this compound can have birefractive characteristic at
these frequencies. In fact, this characteristic has been observed in XY- direction more than XZ- direction. In
addition, at high frequencies all directions reach an agreement and there is no birefracting behavior. In order
to obtain the static refractive index we employed the following equation that relates the magnitude of
refractive index with dielectric function:
(3)
According to this relation and noting that the imaginary part of the dielectric constant vanishes at zero
frequency, we obtained the static refractive index in the x-,y- and z- directions as
=
,
=
and
=
, which are nearly the same as the values of figure 11 at zero
energy. The maximum values of refraction index for x- , y- and z- directions are 4.75, 3.91 and 4.21,
respectively, which are gained at the energy of 1.32eV .
As shown in ‘figure 12’ absorption spectra display the existence of strong absorption bands in the range of
400 and 800 nm which compares favorably with experiment and it caused by the π-π*transitions of the
conjugated macrocycle of 18π-electrons [2].
Figure 11. Refractive Index of Pc.
Figure 12. Absorption Index of Pc.
4. Conclusions
A detailed investigation of the band structure and DOS by means of the DFT-GGA method was carried out.
Electrical band gap is about 2.4eV with a trap band . The dielectric function, Electric loss function,
absorption index, optical conductivity and refractive index were calculated. As results: This compound has
three Plasmon oscillations at energies of 5.21, 3.36 and 1.89 eV and static refractive index in the x-,y- and zdirections are n0xx=2.43, n0yy=2.06 and n0zz=2.32. absorption spectra display the existence of strong
absorption bands in the range of 400 and 800 nm. On the whole, Calculated values of band gap and
absorption is in good agreement with experiments and there are no reported values for others.
References
[1] McKeown, N. B, 1998, Phthalocyanine Materials: Synthesis, Structure and Function.Cambridge: Cambridge
University Press.
[2] Benny Joseph and C S Menon, 2008, E-Journal of Chemistry,5, 86-92.
[3] Z T Liu , H S Kwok , and A B Djuriˇsi´c, 2004, J. Phys. D: Appl. Phys, 37, 678–688.
[4] Kobayashi N, 2002, Bull. Chem. Soc. Japan, 751.
[5] G McHale, M I Newton, P D Hooper and M R Willis,1996, 6, 89-92.
[6] Kaneko M, Taneda T, Tsukagawa T, Kajii H and Ohmori Y, 2003, Japan. J. Appl. Phys, 42 (part I), 2523.
[7] Chen , Yung-Hsing Chen and Bo-Ruei Lin, 2011, Cambridge Jouurnalonline .
163
[8] Mohammad E. Azim-Araghi, Mohammad J. Jafari, Samira Barhemat, and Ebrahim Karimi, 2011, Kerdabadiu
Sensor Lett, 9, 1349-1355.
[9] D. Hohnholz , S. Steinbrecher and M. Hanack, 2000, Journal of Molecular Structure , 521, 231-237.
[10] Kohn W and Sham L J, 1965, Phys. Rev. 140A , 1133.
[11] Blaha P, Schwarz K, Madsen G K H, Kvasnicka D and Luitz J WIEN2k, An Augmented Plane Wave Plus Local
Orbital, Program for Calculating Crystal Properties (Vienna,Austria: Vienna University of Technology).
[12] Schwarz K, Blaha P and Madsen G K H, 2002, Comput. Phys.Commun. 147, 71–6.
[13] Perdew J P, Burke S and Ernzerhof M, 1996, Phys. Rev. Lett. 7, 3865.
[14] Javad Baedi, M R Benam and Masoud Majidiyan, Phys. Scr, 2010, 81 , 5.
[15] Morgan M Hart, 2004, Cationic exchange reactions involving DilitiomPhthalocyanine- A thesis submitted in
partial fulfillment of the requirements for the degree of Master of Science, University of Dayton .
[16]de L Kronig R, 1926, J. Opt. Soc. Am,12, 547–57.
[17]A COX and P C KNIGHT, 1973, J.phys.solids, l.34 , 1655- 59.
[18]B.R.Hollebone and M.J.Stillman , 1978, J.chem.Soc, 2107.
164