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Materials Today: Proceedings 5 (2018) 10570–10576 www.materialstoday.com/proceedings

AEMC_2017

First-Principles Calculations of the Electronic and Optical

Properties of CH3NH3PbI3 for Photovoltaic Applications
Ibrahim O. A. Alia,b,*, Daniel P. Jouberta, Mohamed S. H. Suleimana,c
a
The National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics,University of the
Witwatersrand, Johannesburg, Wits 2050, South Africa
b
College of Science, Department of Science Laboratory, Sudan University of Science and Technology, Khartoum, Sudan.
c
Department of Basic Sciences, Imam Abdulrahman Bin Faisal University, Dammam, KSA.

Abstract

Since the first efficient solid-state perovskite solar cells were reported in 2012, rapid development of the organic-inorganic hybrid
halide perovskites has been made, and a new era in optoelectronic and solar cells technologies has emerged. The unique attributes
of these hybrid halide perovskites make them highly promising materials for various practical applications including high
performance in converting solar energy into electrical power, with very recent results demonstrating a 20.1% efficiency.
However, the electronic and optical properties of these materials at low temperature have not been investigated extensively.
Herein we analyse the electronic and optical properties of methyl-ammonium lead iodide perovskite, CH3NH3PbI3, using density
functional theory (DFT) and many-body perturbation theory (MBPT). The electronic band gap and energy bands of CH3NH3PbI3
have been investigated using different density functional approximations with and without the effect of the spin orbit-coupling
(SOC). Depending on the calculation method, we predicted the band gap to be in the range from 0.46 eV to 2.66 eV. In order to
obtain optical spectra, we carried out Bethe-Salpeter equation (BSE) calculations on top of non-self-consistent G0W0
calculations. We have presented the absorption coefficient, refractive index and reflectivity to describe optical properties of the
investigated material. The phase is found to be semi-conducting with a direct band gap in the visible range of the spectrum and
strong optical absorption in the visible range.

© 2017 Elsevier Ltd. All rights reserved.

Selection and/or Peer-review under responsibility of 1st Africa Energy Materials Conference.

Keywords: DFT; CH3NH3PbI3; optical properties; solar cell

1. Introduction

* Corresponding author. Tel.: +27719226718.

E-mail address:ibraphysics@gmail.com

2214-7853© 2017 Elsevier Ltd. All rights reserved.

Selection and/or Peer-review under responsibility of 1st Africa Energy Materials Conference.
 Ali et al / Materials Today: Proceedings 5 (2018) 10570–10576 10571

Perovskites are materials described by the chemical formula ABX3 such as CH3NH3PbI3 (MAPbI3) which were
synthesized and characterized by Weber in 1978 [1]. Depending on temperature, perovskites can possess cubic,
tetragonal or orthorhombic structural phases [2], where at low temperature, an orthorhombic phase with space group
Pnma (62) is found [3].This family of perovskite materials possesses interesting properties such as high carrier
mobility, an adjustable spectral absorption range, strong solar absorption, long diffusion lengths, and ease of
fabrication [1,2]. The unique attributes of these perovskites make the hybrid halide perovskites highly promising
materials for various practical applications including - but not limited to - high performance in converting solar light
into electrical power [1,4], light emitting diodes (LED), photo-detectors and lasers [1]. Therefore, theoretical studies
on electronic, structural and optical properties of perovskite materials are very important to gain insight into this
kind of material. The goal of this work is therefore, to analyse the structural, electronic and optical properties of
CH3NH3PbI3 using density functional theory (DFT) from first principles.

2. Computational Method

The investigation of the electronic structure properties was performed using the Vienna Ab-initio Simulation
Package (VASP) [5−8] based on density functional theory (DFT). The projected augmented wave (PAW) [9,10]
method was employed to treat electron-ion interactions. To describe the electron exchange and correlation effects,
we used the Generalized Gradient Approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof
(PBEsol and PBE) [11,12]. 4×4×2 Monkhorst-Pack meshes were used in sampling the Brillouin zones with an
energy cut-off of 520 eV. The ionic positions were fully optimized until all components of the forces were less than
1 mev/Å. Our computed energy versus volume data were fitted to the 3rd-order isothermal Birch-Murnaghan
equation of state (EOS) [13]. Equilibrium cohesive energy E0, equilibrium volume V0, and equilibrium bulk
modulus B0 were then obtained. In order to obtain optical spectra, we carried out Bethe-Salpeter equation (BSE)
calculations on top of non-self-consistent G0W0 calculations [14−16]. The unit cell of the orthorhombic
CH3NH3PbI3, space group 62 (Pnma), with the unit cell containing 48 atoms, and its corresponding Brillouin zone
are shown in Figure 1 below.

3. Results and discussion

3.1. Structural properties

We first present the calculated total binding energy against cell volume for the studied structure under two
generalized gradient parameterizations PBEsol and PBE to find the most suitable method for this material. In Fig.2
we obtained a solid line by means of the Birch-Murnaghan equation of state (EOS) [13]. The corresponding
calculated lattice parameters, cohesive energy (E0), bulk modulus (B0), and cell volume (V0) compared with
experiment and with previous calculations are summarized in Table 1. From Table 1, it can be seen that the
calculated equilibrium cell volume using the PBE functional is overestimated compared to the experimental values.
In the meantime, the optimized cell volume from PBEsol is close to the experimental results. For the orthorhombic
phase the previous theoretical studies computed lattice constants including van der Waals (vdW) interactions [17]
and DFT + D2 implementation [18,20] are presented in Table 1.

Table 1. Calculated and experimental equilibrium parameters: lattice constants (a (Å), b (Å), c (Å)), cell volume V0 (Å3) and
cohesive energy E0 (eV) .
Functional A (Å) b (Å) c (Å) V0 (Å3) E0 (eV/atom) B0 (GPa)
PBE 9.346 12.908 8.581 1034.8 -3.07 14.91
PBEsol 9.062 12.632 8.364 957.44 -3.06 17.16
Experiment3 8.836 12.580 8.555 951.01 ------ ------
OptB86b+vdwF17 8.831 12.648 8.570 957.18 ------ ------
DFT+D218 8.871 13.123 8.638 1005.5 ------ 18.1
19
Experiment 8.861 12.659 8.581 962.54 ------ ------
10572 Ali et al / Materials Today: Proceedings 5 (2018) 10570–10576

Fig. 1. The crystal structure of CH3NH3PbI3 orthorhombic (left) and its corresponding Brillouin zone of the orthorhombic lattice (right). Filled
red circles are the high symmetry point, while the red bold lines indicate segments of the high symmetry path (Γ-X-S-Y-Γ) used in the band
calculations.

3.2. Electronic properties

Fig. 2. Equation of states using PBEsol (left) and PBE (right)

The Kohn-Sham band structure of the studied material was calculated using the PBE and PBEsol, both the
valence band maximum (VBM) and conduction band minimum (CBM) were found to be located at the gamma Г
point of the Brillouin zone (BZ), as shown in Fig. 3 and Fig. 4. Our results agree with previous studies in showing
that the orthorhombic phase has a direct band gap at the gamma point [3]. Our calculated, theoretical and
experimental electronic band gaps of the CH3NH3PbI3 orthorhombic phase are listed in Table 2. From this table we
note that our calculated PBEsol electronic gap is in good agreement with that reported in experiment [3]. Fig. 5
shows the total density of states (TDOS) and the projected density of states (PDOS) using the PBEsol functional.

Table 2.Calculated and experimental electronic band gap in eV

Method Band gap Reference
PBE 1.80 Present work
PBEsol 1.57 Present work
G0W0 2.66 Present work
PBEsol + SOC 0.46 Present work
optB86b+ vdwF 1.74 [17]
Experiment 1.61 [3]
 Ali et al / Materials Today: Proceedings 5 (2018) 10570–10576 10573

Fig. 3. DFT calculated electronic structure for CH3NH3PbI3 : (a) band structure; (b) partial density of states (PDOS); (c) total density of states
using PBE.

Fig. 4. DFT calculated electronic structure for CH3NH3PbI3: (a) band structure ; (b) partial density of states (PDOS); (c) total density of states
using PBEsol.

Fig. 5. Band structure calculated using PBEsol with spin orbit-coupling (SOC).
10574 Ali et al / Materials Today: Proceedings 5 (2018) 10570–10576

3.3. Optical properties

The investigation of the optical properties of CH3NH3PbI3 perovskite is very important, because it is potentially
good candidate for photo and optoelectronic applications. Our GW calculations were performed without including
the effect of the spin orbit coupling. Using the real part εre(ω) and the imaginary part εim(ω) of the dielectric tensor
ε(ω), we computed the absorption spectra α(ω), refractive index n(ω), and reflectivity R(ω) [25]. From the
absorption coefficient (α(ω)) spectrum, the highest absorption peaks occur in the optical region (1.65−3.26) eV. The
results in Figure.6, show that the highest absorption peak of εzz(ω) component is higher than that of εxx(ω) and
εyy(ω). Moreover, the anisotropicity of the phase is evident from the clear differences between the three spectra.

Fig. 6. Absorption coefficient α(ω)

The other corresponding derived optical constants such as refractive index n(ω), energy loss and reflectivity are
presented in Fig. 7−9, respectively.

Fig. 7. Refractive index n(ω).

The maximum value of refractive index n(ω) for CH3NH3PbI3 structure is obtained to be 4.3 in z-direction at
optical frequency of 2.64 eV, while the maximum value of the refractive index for x and y directions are observed at
2.08 eV and 2.25 eV optical frequency with magnitude of 3.29 and 3.4 respectively as presented in Fig.7. We have
computed also the reflectivity of CH3NH3PbI3 structure using the equation in ref. 16 for x, y, z directions. From Fig.
 Ali et al / Materials Today: Proceedings 5 (2018) 10570–10576 10575

8 it is noted that the maximum value of reflectivity for the studied structure is observed in the ultraviolet (UV)
region at 4.05 eV in the z-direction and the corresponding value is 0.7.

Fig. 8. Reflectivity R(ω)

Fig. 9. Energy loss spectrum L(ω)

10576 Ali et al / Materials Today: Proceedings 5 (2018) 10570–10576

4. Conclusions

In summary, we have investigated the structural, electronic and optical properties of the organic-inorganic halide
perovskite. We found that the PBEsol predicted structural lattice parameters and volume are in good agreement with
experimental values. Electronic properties were investigated by calculating the band structure, partial density of
states (PDOS), and the total density of states (TDOS). Optical absorption spectra, refractive index, and reflectivity
were calculated at BSE level of approximation showing that the material is a good absorber of electromagnetic
radiation in most of the visible and ultraviolet regions.

Acknowledgements

We thank the CHPC for providing the supercomputer facilities. IOAA would like to acknowledge the support he
received from WITS, NRF-TWAS for funding, and Sudan University of Science and Technology (SUST).

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