T (2D) S E A Kasi... · Sri Kasi Venkata Nageswara Rao Matta B.Sc. (Physics), B.Tech (Chemical...
Transcript of T (2D) S E A Kasi... · Sri Kasi Venkata Nageswara Rao Matta B.Sc. (Physics), B.Tech (Chemical...
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D
COMPUTATIONAL EXPLORATION OF
TWO-DIMENSIONAL (2D) MATERIALS
FOR SOLAR ENERGY APPLICATIONS
Sri Kasi Venkata Nageswara Rao MattaB.Sc. (Physics), B.Tech (Chemical Eng.), M.Tech. (Chemical Eng.)
Submitted in fulfilment of the requirement for the degree of Doctor of Philosophy
School of Chemistry, Physics and Mechanical Engineering
Science and Engineering Faculty
Queensland University of Technology
2019
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Keywords
Density Functional Theory, Two-dimensional materials, Semiconducting
materials, Mechanical exfoliation, Electronic band structure, Light harvesting,
Band-gap, Electron Transport layer, hole transporting layer, Perovskite Solar Cell,
Photocatalytic water splitting, Exciton binding energy, Bandgap tuning.
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Abstract
Exploration of new materials for optimising solar energy and photovoltaic
applications is crucial for the commercial uptake of renewable energy technology.
Nanomaterials are in vogue owing to their special properties like very high
electrical and thermal conductivity, high specific surface per unit volume good
potential for light-harvesting as well as possessing more active sites for inter
material bonding. The characterisation of new or innovative materials for solar
energy applications viz. photocatalytic water splitting, photovoltaics and as
material components for charge transfer in perovskite solar cells is included in this
current research study.
The development of 2D materials with good light absorption and having
appropriate band-gap energy could boost solar energy conversion. This research
study is based on theoretical physics principles and uses first-principles theory and
calculations, in the methodical exploration of various two-dimensional (2D)
nanomaterials either to envisage new material utilisation or to improve the existing
optoelectronic performance of solar energy conversion applications.
Photocatalytic water splitting is a process of generating hydrogen and oxygen
through the use of light energy. Hydrogen is known as a clean fuel because
combustion of hydrogen doesn’t emit any harmful gases. If such fuel is produced
without the use of any fossil fuels in the process or it doesn’t lead to the release of
harmful substances then we can term it as ‘clean energy’ production. Mimicking
photosynthesis from nature, if we produce Oxygen and Hydrogen from water, using
solar energy, we call it photocatalytic water splitting. This process requires
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semiconductors which can absorb sunlight and use the energy for water splitting.
This is not a new technique, but the exploration of new2D semiconducting material
for this process is undertaken.
The specific properties of semiconductors for use in photovoltaic
applications, water-splitting etc. are excellent visible light absorption, efficient
exciton generation, and effective charge separation for extraction into the external
circuit. The same principles are required when using two-dimensional (2D)
semiconductor materials. In this work, density functional theory (DFT) principles
are applied to studying 2D materials for their visible range wavelength light
absorption and appropriate band edge position for potential use as a photo-electrode
for efficient water-splitting. A systematic study on the physical, electronic and
optical characteristics of three compounds viz. SiP2, SiAs2 and GeAs2 from group
IV-V combination at the 2D scale are conducted. This study depicts the potential
applications for these materials in photocatalytic water splitting and photovoltaic
applications.
The threshold band gap for a semiconductor to be used as photocatalyst for
overall water-splitting is 1.23 eV whereas the maximum should be around 3.00 eV.
In addition, the CBM and VBM positions of the semiconductor material should be
straddling below and above the redox potentials of water, so that a single
semiconductor can produce both Hydrogen and Oxygen evolution in a single
process. The calculated band gap for SiP2 is 2.25 eV and satisfies this requirement
while in addition, this study revealed that the single/monolayer extraction of SiP2
from its bulk counterpart, is in principle experimentally possible by mechanical
cleavage process. The findings revealed that a SiP2 monolayer could be used as
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photocatalyst for overall water splitting into both hydrogen and oxygen because of
its band edge positions.
This study also includes bandgap tuning possibility while applying strain
engineering techniques. It was observed that there is a directional dependence of
expansion or compressive strain in changing the bandgap. In the case of SiP2, in the
direction of lattice ‘a’, the bandgap is slightly increased during compressive strain
by up to 3%. Further compression makes the band gap decrease and that it
transforms into metallic behaviour at a compression of greater than 7%. However,
the same variation of strain results in a gradual increase in the band-gap in the lattice
‘b’ direction i.e. from compressive to expansion strain. The results reveal the
possibility of bandgap tuning so that we can adopt a suitable mechanism to change
its band gap for a specific application.
The single-layered SiAs2 and GeAs2 materials have a predicted band-gap of
1.91 and 1.64 eV respectively, implying that they exhibit good sunlight harvesting
properties. The calculation of exciton binding energy gave values of 0.25 and 0.14
eV respectively, for SiAs2 & GeAs2. The theoretical results also show that layered
extraction may be feasible for SiAs2 and GeAs2 through mechanical cleavage. It is
also found that the 2D SiAs2 and GeAs2 normally possess good light-harvesting
property implying their potential as good light absorbers. The stress and strain
engineering assessment showed similar behaviour to that exhibited by SiP2 and
therefore bandgap tuning is also possible. This tuning of the semiconductor-metal
transformation, suggests many implications for nanoelectronics devices with strain
engineering methods and that these new series of 2D materials have immense
potential for solar energy applications. However, even though the 2D SiAs2 and
GeAs2 materials have shown a bandgap nearing the threshold level required for
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water splitting, due to the exciton binding energy and band edge position location
compared to the water redox potentials, these materials will not be effective for
photo-catalyst water splitting but could be good for other photovoltaic applications.
In the latest experimental studies, the exfoliation technique was successful for
GeAs2, making our prediction a success.
Perovskite solar cells (PSCs) are one of the new generation solar cell
categories. The PSCs based on methylammonium lead triiodide (MAPbI3)
perovskites show very high performance but are commercially not successful due
to instability in the long-term and charge transfer dynamics issues. The Electron
Transport Layer (ETL) and the Hole Transport Layer (HTL) are highly important
components, for effective charge transfer in solar cells to ensure maximum
efficiency. The second aspect of this study investigates inorganic and organic 2D
materials for use as HTL and determines their suitability as effective charge transfer
layers.
A new type of organic 2D material, namely Carbon Quantum dots (C-dots) is
considered for computational analysis as HTLs. A wide range of structural
alternatives of C-Dots (including the functionalized C-dots with –OH and –COOH
groups) are investigated. Results show that smaller hexagonal C-dots, and those
with –OH and –COOH groups, have a suitable valance band maximum (VBM)
position at higher energy levels than the VBM of the perovskite layer, which makes
it suitable for hole transport. Further study on the impact of the functional group’s
position on the C-dot structure indicated that tuning of the band position is possible
and opens up the potential for use in different solar applications, which may require
different band positions for optimal performance. Two possible perovskite surface
/C-Dot interfaces were studied (i.e. MAI and PbI2 as top surfaced perovskites) with
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the C-Dot as the top layer component of the hybrid structure, where it was found
that there is a good probability of charge transport between the perovskite layer and
the C-dots.
Layered crystal structures of inorganic, post-transition metal halides and
oxides (lead iodide (PbI2), lead monoxide (PbO), tin-oxide (SnO)) were also
considered as Hole Transport Layer (HTL) in perovskite solar cells (PSCs). We
found that single-layered PbO and bi-layered SnO materials are potential
candidates for hole transport layers in PSCs.
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Table of Contents
Keywords ............................................................................................................................ 2
Abstract ............................................................................................................................... 3
Table of Contents ................................................................................................................ 9
List of Figures ................................................................................................................... 11
List of Tables .................................................................................................................... 14
List of Research Publications ........................................................................................... 15
Published journal articles .................................................................................................. 16
Conference Poster Presentations ....................................................................................... 17
Abbreviations .................................................................................................................... 18
Statement of Original Authorship ..................................................................................... 20
Acknowledgements ........................................................................................................... 21
Chapter 1: Introduction ...................................................................................... 23
1.1 Background ............................................................................................................. 23
1.2 Research Context .................................................................................................... 28
1.3 Research Problem ................................................................................................... 32
1.4 Research Purpose .................................................................................................... 33
1.5 Significance, Scope and limitations ........................................................................ 35
1.6 Thesis structure ....................................................................................................... 36
Chapter 2: Literature Review ............................................................................ 39
2.1 Historical Background ............................................................................................ 39
2.2 Study of 2D materialS for Photocatalytic water splitting or photovoltaic applications ....................................................................................................................... 42
2.3 Study of 2D material for electron and Hole Transport in Perovskite Solar Cells... 49
2.4 Summary and Impl ica t ions .......................................................................... 53
Chapter 3: Research Design ............................................................................... 55
3.1 Methodology and design ........................................................................................ 55
3.1.1 Methodology ........................................................................................................... 55
3.1.2 Research Design ..................................................................................................... 56
3.1.2.1 The first principles theory ............................................................................ 56
3.1.2.2 Hohenberg-Kohn theorem ............................................................................ 58
3.1.2.3 Kohn-Sham equation .................................................................................... 58
3.1.2.4 Wannier Functions ....................................................................................... 60
3.1.2.5 GW and BSE calculations ............................................................................ 61
3.2 Software used ......................................................................................................... 62
3.2.1 VASP ...................................................................................................................... 62
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3.2.1.1 Analysis ........................................................................................................ 63
3.2.1.2 Completed Computations ............................................................................. 67
3.3 Ethics and Limitations ............................................................................................ 68
Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst .... 70
4.1 Abstract ................................................................................................................... 71
4.2 Introduction ............................................................................................................. 72
4.3 Computational Details ............................................................................................ 74
4.4 Results and discussions ........................................................................................... 76
4.5 Conclusions ............................................................................................................. 84
4.6 Supporting Information ........................................................................................... 85
Chapter-5: Two-dimensional SiAs2 and GeAs2 as photovoltaics .................... 89
5.1. Abstract ................................................................................................................... 91
5.2. Introduction ............................................................................................................. 91
5.3. Computational Details ............................................................................................ 93
5.4. Results and Discussion ........................................................................................... 95
5.5. Conclusion ............................................................................................................ 101
5.6. Supporting Information ......................................................................................... 103
Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells ...... 104
6.1. Abstract ................................................................................................................. 105
6.2. Introduction ........................................................................................................... 106
6.3. Computational Methods ........................................................................................ 110
6.4. Results and Discussion ......................................................................................... 112
6.5. Conclusions ........................................................................................................... 118
6.6. Supporting Information ......................................................................................... 120
Chapter-7: Inorganic 2D materials for charge transport in Perovskite Solar Cells .................................................................................................................... 125
7.1. Abstract ................................................................................................................. 126
7.2. Introduction ........................................................................................................... 126
7.3. Computational Methods ........................................................................................ 130
7.4. Results and discussion .......................................................................................... 132
7.5. Conclusions ........................................................................................................... 136
7.6. Supporting Information ......................................................................................... 138
Chapter 8: Conclusions .................................................................................... 141
Chapter 9: Future work ................................................................................... 145
9.1 Theoretical ............................................................................................................ 145
9.2 Experimental work ................................................................................................ 145
References .......................................................................................................... 148
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List of Figures
Figure 1.1: Global CO2 emissions ............................................................. 25
Figure 1.2: Typical solid-state solar cell configuration ........................... 29
Figure 1.3: Perovskite Solar Cell structure .............................................. 30
Figure 1.4: Artificial photosynthesis-Photocatalysis schematic ............. 31
Figure 1.5: Thesis outline ........................................................................... 37
Figure 2.1 : Water-splitting exciton generation concept ......................... 44
Figure 3.1: Energy optimisation algorithm in VASP software for DFT analysis solving the Kohn-Sham equations ............................... 63
Figure 4.1 (a) Side view of the SiP2 bulk (2 × 2 supercells). (b) top view of the SiP2 monolayer. The pink and green balls represent Si and P atoms, respectively. ........................................................... 76
Figure 4.2: Phonon band structure of SiP2 monolayer along the high-symmetric points in the Brillouin zone. ...................................... 77
Figure 4.3: Band structure for SiP2 calculated by HSE-Wannier function method (a) Bulk, and (b) a monolayer. The Fermi level is set as zero ................................................................................... 78
Figure 4.4: Band positions of monolayer SiP2 compared to redox potentials of water. The green dashed line indicates the CBM after band alignment considering optical level with GW/BSE after exciton separation overcoming the e-h binding energy ... 80
Figure 4.5: Calculated light absorption spectrum of SiP2 monolayer (blue line) using HSE06 functional superimposed to the incident AM1.5G solar flux ......................................................... 81
Figure 4.6: (a) GW band structure with indirect band gap of 2.63 eV, and (b) BSE-Optical Absorption spectrum with optical band-gap of 2.02 eV ................................................................................ 83
Figure 4.S1: Electrostatic Vacuum potential for SiP2 monolayer .......... 86
Figure 4.S2: Band gap as a function of biaxial strain calculated with the PBE functional for SiP2 monolayer ............................................ 86
Figure 4.S3: GW+RPA optical absorbance spectrum for 2D SiP2. ...... 87
Figure 5.1: Crystal structure side view of the (a) SiAs2 bulk (3x2 super cells) (b) GeAs2 Bulk. Silicon (Red), Germanium (Blue) and Arsenic (Green) ............................................................................ 96
Figure 5.2: Phonon band structure of a monolayer of (a) SiAs2, and (b) GeAs2 along the high-symmetric points in the 1st Brillouin zone. (c) Energy of formation of the 2D material from its bulk counterparts. The green bar indicates experimentally synthesised, Red bar indicates experimentally not synthesised and the Blue bar indicates theoretically proven for the possibility of synthesis. ................................................................. 97
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Figure 5.3: Band structure for SiAs2 and GeAs2 calculated by the HSE-Wannier function method. The Fermi level is set as zero. (a), (b) and (c) Bulk, Bilayer and Monolayer of SiAs2 respectively; (d), (e) and (f) Bulk, Bilayer and Monolayer of GeAs2 respectively ................................................................................... 98
Figure 5.4: Calculated light absorption spectrum of monolayers of SiAs2 (green) and GeAs2 (blue) using HSE functional superimposed to the incident AM1.5G solar flux. .................... 99
Figure 5.5: (a) and (c) GW-Band structures, (b) and (d) BSE-Optical Absorption spectra of SiAs2 and GeAs2 respectively ............. 100
Figure 5.S1: Band gap as a function of biaxial strain calculated with the PBE functional for monolayers of (a) SiAs2 and (b) GeAs2 ... 103
Figure 6.1: The structures of Hexagonal C‐dots (Hex‐1 [a] & Hex‐2[b]) and the functionalised Hexagonal C‐dots (Hex‐1 [c] & [d])) with −OH and −COOH groups. Color Code of atoms: Brown (Carbon), Blue (Hydrogen), Red (Oxygen).............................. 113
Figure 6.2: (a) The top view and the side views of (b) C‐Dot/MAI, and (c) C‐Dot / PbI2interfaces. Color Code of atoms: Brown (Carbon), Blue (Hydrogen), Green (Nitrogen), Black (Lead) and Pink (Iodine)........................................................................ 114
Figure 6.3: The calculated band edge positions (i. e. VBM and CBM) of the C‐dots compared with those of MAPbI3 (literature values of VBM and CBM). Hex1=Hexagonal C‐Dot (type‐1, smaller or base size); Hex2=Hexagonal C‐Dot (type‐2, bigger in size) ... 115
Figure 6.4: The side view of the charge density difference between the two interface systems (a) C‐Dot/PbI2, and (b) C‐Dot/MAI. The Yellow and Cyan iso‐surface profiles represent electron accumulation and depletion in 3D space with an isovalue of 0.001 e/Å−3. Colour Code of atoms: Brown (Carbon), Blue (Hydrogen), Green (Nitrogen), Black (Lead) and Pink (Iodine)....................................................................................................... 118
Figure 6.S1: The structures of various Carbon Quantum dots (C-Dots). Trigonal C-Dots (a –c), Hexagonal C-Dots with two –OH functional groups substituted (d) side by side, and (e) opposite to each other. Color Code of atoms: Brown (Carbon), Blue (Hydrogen), Red (Oxygen). ....................................................... 120
Figure 6.S2: The calculated band edge positions (i.e. VBM and CBM) of further C-Dots considered in this study and compared with those of MAPbI3 (literature values of VBM and CBM) [Tri-1 – Tri-3 correspond to three different Trigonal C-Dots (S1(a-c)); Hex-1-OH-SbS (side by side) and Hex-1-OH-oppo (opposite) correspond to S1(d) and S1(e) of Figure-S1 ............................ 121
Figure 6.S3: The structures of Hexagonal (Type-1) Carbon Quantum dots (C-Dots) with different bonding locations of two Carboxyl and two hydroxyl groups. The represented Code-named C-Dots are: (a) H1-2C2O-1, (b) H1-2C2O-2, (c) H1-2C2O-3 and (d) H1-2C2O-4. .......................................................... 121
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Figure 6.S4: The structures of Hexagonal (Type-1:H1) Carbon Quantum dots (C-Dots) with different bonding locations of two Carboxyl and One Hydroxyl groups. The represented Code-named C-Dots are: (a) H1-2C, (b) H1-2C1O-1, (c) H1-2C1O-2. ...................................................................................................... 122
Figure 6.S5: The structures of Rectangular (Type-1 (R1) and Type-2(R2)) Carbon Quantum dots (C-Dots) with different bonding locations of One or two Carboxyl (1C or 2C), One Hydroxyl (1O) and/or One Hydroxyl & One carboxyl (1O-1C) groups. The represented Code-named C-Dots are: (a) R1-1C, (b) R1-1O, (c) R1-2C, (d) R1- 2O, (e) R2-1C, (f) R2-1O, (g) R2-2C and (h) R2-1C1O. ............................................................................... 122
Figure 7.1: The structures of (a –b) PbI2 monolayer, (c-d) PbO, and (e-f) SnO monolayers top-view and perspective side-views respectively. ................................................................................. 131
Figure 7.2: HSE Band structures of (a) PbI2, (b) PbO, and (c) SnO monolayers .................................................................................. 133
Figure 7.3: HSE06 Band edge positions (calculated CBM and VBM) of PbI2, PbO and SnO compared with that of MAPbI3 Legend: 1L=monolayer, 2L=bi-layer ..................................................... 134
Figure 7.4 : The top and side view hybrid structures of PbO/PbI2 and PbO/MAI terminated hybrid structures respectively. ............ 135
Figure 7.5: The side view of the charge density difference at an iso-value of 0.003 e Å-3, between the two interface systems (a) PbO/PbI2, and (b) PbO/MAI. The Yellow and Cyan iso-surface profiles represent electron accumulation and depletion in 3D space. The atom positions in dotted region i.e. bottom two layers was fixed during geometry optimisation (Inset: Color Code of atoms) ............................................................................. 136
Figure 7.S1. Vacuum potential obtained from HSE06 method for PbO (a) mono, and (b) bi-layers ........................................................ 138
Figure 7.S2. Vacuum potential obtained from HSE06 method for PbI2 (a) mono, (b) bi-, and (c) tri-layers ........................................... 138
Figure 7.S3. Vacuum potential obtained from HSE06 method for SnO (a) mono layer, (b) bi-layer, and (c) Tri layers ........................ 139
Figure 7.S4. Band Structures calculated from HSE06 method for PbO (a) Mono, and (b) Bi layers ........................................................ 139
Figure 7.S5. Band Structures calculated from HSE06 method for PbI2 (a) Mono, (b) Bi-, and (c) Tri layers ......................................... 139
Figure 7.S6. Band Structures calculated from HSE06 method for SnO (a) Mono, (b) Bi-, and (c) Tri-layers ......................................... 140
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List of Tables
Table 1.1: Finite and renewable energy reserves (TW-years) ............... 28
Table 4.1: Calculated structural parameters of SiP2 bulk and monolayer along with the corresponding experimental values 77
Table 5.1: Calculated structural parameters of SiAs2 and GeAs2 compared with the experimental values ........................ 98
Table 5.2: Calculated band gaps of SiAs2 and GeAs2 – for bulk, bilayers, and monolayers. ............................................................ 99
Table 6.1. Calculated CBM and VBM band edge positions few two‐dimensional Carbon‐Dots. ......................................................... 116
Table 6.S1: Calculated CBM and VBM band edge positions few two-dimensional Carbon-Dots .......................................................... 123
Table 7.1: Bandgaps of the materials calculated with HSE06 functional...................................................................................................... 135
Table 7.S1. Bandgaps, CBM and VBM obtained from HSE06 method...................................................................................................... 140
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List of Research Publications
This PhD thesis is written in “Thesis by Publication” model. The main
research results are published as three journal articles and the fourth article is
submitted for publication review. All these scientific articles are presented
here in the form of Chapters and have almost the same content as the
published paper except a little more information may have been added on a
few occasions, whereas the section headings, serial numbers are altered to
maintain the sequence of the thesis. Hence, the chapter retains its own
introduction, results, discussion and conclusions. Therefore, each Chapter 4,
5, 6 and 7 is self-explanatory and encompass the focussed research topic in
its completeness within the scope of the overall thesis.
Note:
1. The author naming convention in each journal would vary. However, a
uniform representation is followed below for my name, to list the
publications, for this Thesis.
2. My ORCID ID: https://orcid.org/0000-0003-4465-640X
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PUBLISHED JOURNAL ARTICLES
First-authored papers
1. Sri Kasi Matta; Zhang, C.; Jiao, Y.; O'Mullane, A.; Du, A., Versatile two-
dimensional silicon diphosphide (SiP2) for photocatalytic water splitting.
Nanoscale 2018, 10 (14), 6369-6374. (Q1; IF= 7.36)1
2. Sri Kasi Matta; Zhang, C.; Jiao, Y.; O'Mullane, A.; Du, A., Computational
exploration of two-dimensional silicon diarsenide and germanium arsenide
for photovoltaic applications. Beilstein Journal of Nanotechnology 2018,
9, 1247-1253. (Q1; IF=3.13)2
3. Sri Kasi Matta; Zhang, C.; O'Mullane, A.; Du, A., Density Functional
Theory Investigation of Carbon dots as hole transport material in
Perovskite solar cells. ChemPhysChem. 2018, 19, 3018-3023. (Q1; IF=
3.07)3
4. Sri Kasi Matta; Zhang, C.; O'Mullane, A.; Du, A., DFT exploration of
inorganic 2D materials for charge transport in Perovskite Solar Cells:
Transition and post-transition metal chalcogenides, halides and oxides -
manuscript submitted for review.
Co-authored Papers
5. Zhang, C.; Jiao, Y.; Ma, F.; Sri Kasi Matta; Bottle, S.; Du, A. Free-radical
gases on two-dimensional transition metal disulphides (XS2, X = Mo/W):
robust half-metallicity for efficient nitrogen oxide sensors. Beilstein J.
Nanotechnol. 2018, 9, 1641–1646. (Q1; IF 3.13)4
6. Tang, Cheng; Zhang, Chunmei; Sri Kasi Matta; Jiao, Yalong; Ostrikov,
Kostya (Ken); Liao, Ting; Kou, Liangzhi; Du, Aijun., Predicting New Two-
Dimensional Pd3(PS4)2 as an Efficient Photo-Catalyst for Water Splitting.
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The Journal of Physical Chemistry C. (Q1; IF= 4.484)5
7. T. He, Sri Kasi Matta, A. Du, Single tungsten atom supported on N-doped
graphyne as a high-performance electrocatalyst for nitrogen fixation under
ambient conditions, PCCP. 2019, 21, 1546-1551. (Q1; IF= 3.906) 6-
8. C. Tang, F. Ma, C. Zhang, Y. Jiao, Sri Kasi Matta, K. Ostrikov, A. Du,
2D boron dichalcogenides from the substitution of Mo with ionic B2 pair
in MoX2 (X = S, Se and Te): high stability, large excitonic effect and high
charge carrier mobility, J. Mater. Chem. C. 2019. (Q1; IF= 5.976) 7-
9. Zhang, Chunmei, He. Tianwei; Sri Kasi Matta, Liao. Ting, Kou. Liangzhi,
Chen. Zhongfang, Du. Aijun, Predicting Novel 2D MB2 (M=Ti, Hf, V, Nb,
Ta) Monolayers with Ultrafast Dirac Transport Channel and Electron-
Orbital Controlled Negative Poisson’s Ratio, J. Phys. Chem. Lett. 2019,
10, 10, 2567-2573. (Q1; IF= 7.329).
10. Lei Zhang, Xin Mao, Sri Kasi Matta, Yuantong Gu and Aijun Du, Two-
dimensional CuTe2X (X=Cl, Br and I): Potential Photocatalysts for Water
Splitting under the Visible/Infrared Light
- manuscript submitted for review.
CONFERENCE POSTER PRESENTATIONS
11. Poster presentation in NanoS-E3 2017 Conference, Brisbane held at QUT,
Gardens Point Campus, during 26-29 September 2017.
12. Poster presentation on Carbon Dots as Hole Transporting Material for
perovskite solar cells at AM & ST 2018, held at Brisbane during 22-25 July
2018.
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Abbreviations
2D Two-dimensional
3D Three-dimensional
AIMD Ab-initio molecular dynamics
BSE Bethe-Salpeter equation
BP British Petroleum
CBM conduction band minimum
-COOH Carboxylic group
DFPT density-functional perturbation theory
DFT density functional theory
ETM electron Transport Material
eV electron Volt
FTO Fluorine Doped Tin Oxide
GGA-PBE The generalized gradient approximation in the Perdew-Burke-Ernzerhof form
GW Single-particle Green's function (G) & screened Coulomb interaction (W)
GW Giga Watts
HER hydrogen evolution reaction
HOMO highest occupied molecular orbital
HSE Heyd-Scuseria-Ernzerhof exchange-correlation functional
HTL Hole Transport Layer
IPCC Intergovernmental Panel on Climate Change
LUMO lowest unoccupied molecular orbital
MAI Methyl Ammonium Iodide
MAPbI3 Methyl Ammonium Lead Iodide
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Mtoe Million Tonne of oil equivalent
-OH Hydroxyl group
PAW Projector-augmented-wave
PbI2 Lead iodide
ppm parts per million
PSCs Perovskite Solar Cells
PV Photovoltaic
QUT Queensland University of Technology
SOC spin-orbital coupling
TJ Tera Joules
TMDC transition metal dichalcogenides
TW Tera Watt
UNFCCC United Nations Framework Convention on Climate Change
VASP Vienna ab-initio simulation package
VBM valence band maximum
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Statement of Original Authorship
The work contained in this thesis has not been previously submitted to meet
requirements for an award at this or any other higher education institution. To the
best of my knowledge and belief, the thesis contains no material previously
published or written by another person except where due reference is made.
Signature: _________________________
Date: 12.09.2019
QUT Verfied Signature
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Acknowledgements
Most importantly, I must express sincere gratefulness to my mother and father
for bringing me to this wonderful world, and all my teachers (direct and indirect
teachings from nature as well) since my childhood for bringing me up to this stage.
I need to find special adjectives to praise my Principal supervisor, Professor
Aijun Du, for his simple and focussed approach of guiding and constant support
throughout my PhD tenure and made it possible for me to finish my research in a
record duration of 1.5 years. I wonder how he could have such high patience and at
the same time quick in deciding a solution to computational problems. His
motivation and vast knowledge of VASP Software/UNIX/LINUX has helped me
to quickly resolve the issues faced during computations. It has been an honour to
work with him and I enjoyed working under his guidance.
I must put on record that I have been awarded a Supervisor Scholarship
(Bridging) for the duration of my PhD study, and I am very much thankful to Prof.
Aijun Du for providing this award.
Scanning into the past a bit, when I was looking for a project guide, my luck
favoured to contact Professor Anthony O’Mullane at QUT for discussion on the
PhD topic and as per my research interests, he suggested and took me to Dr Aijun
Du and got his instantaneous acceptance to take me in his group as a PhD student.
Dr Anthony is my Associate Supervisor, and I am really indebted to him, for his
support and patient reading of my manuscripts, and suggestions, of all my journal
articles. He has also helped me in reviewing the Thesis.
My sincere appreciation goes to my teammates Chunmei Zhang and Dr
Yalong Jiao for their support during learning and implementation of new software
when I was using DFT. Without their valuable help, it could have been difficult to
conduct my study efficiently. I also wish to express my regards to other team
members: Tianwei He, Cheng Tang, Xin Mao, Lei Zhang and Gurpreet Kour. They
are of wonderful support from time to time during my research, and I am happy to
be part of this team.
Though not directly related to this specific PhD research, I convey my kind
regards to Associate Professor Dr Yasuhiro Tachibana, RMIT University,
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Melbourne for introducing me to experimental research in Dye Sensitised Solar
cells and Quantum Dot synthesis, and various characterisation techniques during
my tenure at RMIT.
I also wish to express my sincere gratitude to Professor Kay Latham, RMIT
University, for giving valuable suggestions while discussing the experiments
during my tenure at RMIT University. Sincere thanks to Satoshi Makuta, Manning
Liu, and Samuel Chan for their support in laboratory safety coordination work and
participate in prolonged and fruitful discussions on experimental techniques.
Sincere regards to all the QUT-staff in various departments including
Research Administration, SEF-Scholarships, SEF-HDR, CPME and many others
whom I might not have met in person. They have a fundamental and primary
contribution for sure, at key stages of my candidature, during my journey of
research and helping me to reach this stage of Ph.D degree.
I must put on record about the endurance of my family: my wife for her
patience and support during all hard times, daughter and son for their love and
motivation during my journey of research. I thank my sister and brother-in-law and
nieces for their moral support through taking care of mother and household chores
at my native place back in India.
Last but not the least I thank the seemingly unknown almighty or supreme
power for continuing the spiritual help at all stages of my life.
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Page 23 of 163 Chapter 1: Introduction
Chapter 1: Introduction
In this chapter, the main intent of the research is delineated. The background
of the research is described in Section 1.1 by exploring the basis of the central
problem and the motivation behind the selected research topic. The focus point
selected out of many possibilities of the proposed subject is spelt out in Section 1.2
as ‘Research Context’. The main research problem is deciphered in Section 1.3 as
‘Research Problem’, while the specific aims and objectives of the emphasised topic
are delineated along with selected questions, that would be answered subsequently
by the completion of the project are described in Section 1.4 as ‘Research Purpose’.
Section 1.5 describes briefly why the research is significant and then sets the extent
of the scope of this research. The chapters in this thesis and their outlines are
described in Section 1.6.
1.1 BACKGROUND
1.1.1 Global Energy scenario, Global warming and renewable energy mix
One of the most important global developmental aspects is that ‘the energy
supply should be sustainable and should be sourced from environmentally clean
production processes’. Fulfilling this standpoint requires us to reduce or eliminate
fossil fuel consumption for energy generation.
While looking at the global primary energy demand, it is projected to be 718
Million TJ by the year 20508, which is an increase from 567 Million TJ in the year
2015, which is a growth of 26% 8. At the moment, the current total global energy
production in 2017 is 14080 Mtoe9.
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There is however good news in that there is a significant decline in the cost
of renewable energy which is accelerating and therefore is more competitive than
newly built energy generation plants based on fossil fuels (reference period: the
Year 2005 to 2016)8. The combined solar and wind annual capacity rose from a
mere 13 GW (in 2005) to 119 GW (in 2016)8, of which the solar energy component
outgrew the wind energy component in 2016.
The fuel mix for energy production in future, as projected by ‘BP Outlook
2018’ is fairly positive with renewable sources’ contribution increasing to about
25% by 204010. This is a significant rate of increase from the current share of 7%.
A positive trend with respect to reducing the fossil fuel mix, (coal share reduces
from the current contribution of about 40% to 30% by 2040) is observed in the
projections. Nevertheless, it still means that coal-burning contributes to global
greenhouse gases emissions even in 2040. Hence, the concern on climate change
impacts continues.
1.1.2 Fossil fuels for future energy needs – Carbon emissions
Global CO2 emissions as reported by the U.S. Department of Energy 11 is
shown in Figure 1.1. (Redrawn with the data supplied by the reference). The
emissions from fossil fuel burning have considerably increased since 1900 and
much more from 1970 onwards. The large increase is primarily due to burning fossil
fuels and industrial production processes12. Furthermore, the global yearly
consumption of energy is projected to be at 27 TW in the year 2050 and might reach
50 TW by the end of the century13. As delineated above, even in the year 2040 the
coal, gas and oil combined share will contribute to about 50% of power generation.
The remainder is shared by nuclear, hydro and other renewables, of which the other
renewables are about 20%10. About 85% of the present energy demand is produced
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by fossil fuel burning. The fact is that the existing fossil fuel sources are enough to
meet the existing demand, for the next several centuries, at the same rate of
consumption14. However, the continuous consumption of such fossil fuels at that
pace will result in huge amounts of GHG emissions, with an irreversible impact on
the climate. If this is allowed, GHGs would continue to be released to the
atmosphere and is projected to reach about 36 billion tonnes of CO2 from the current
level of about 33 billion tonnes of CO210.
Figure 1.1: Global CO2 emissions
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1.1.3 Climate changes – observed
Over a period of time, it is evidenced by numerous research and database
analysis that the climate system is getting increasingly warmer15. The influences of
these global warming result in the following changes in the climate system12.
1. Earth’s surface warming12 the global surface temperature average is
increased by 0.85 ± 0.08°C, over the period 1880 to 201212.
2. Ocean warming16 leads to an increase in climate system energy that is
accounting for higher than 90% of accumulated energy from 1971 to
2010.
3. Cryosphere16 The frozen water part (Cryosphere), where glaciers have lost
mass resulting in a huge loss over the period from 2002 to 2011, more so than
over the period from 1992 to 2011 and have contributed to rising sea levels
during the 20th century.
4. Sea level change 16 The mean global rise in sea level during 1901–2010
was by 0.19 [0.17 to 0.21] m. This rise is higher from the middle of the
19th century compared with previous millennia.
These changes are only a few that have impacted natural and human
systems across the globe. The change in global climate is perennial and
will continue if unaddressed. However, the rate of change depends mainly
on the quantity of GHGs 1 emitted annually and the sensitivity of the
influence on Earth’s climate.
1 GHGs = Generally known as heat trapping gases - carbon dioxide (CO2), nitrous oxide(N2O), methane(CH4), and the chlorofluorocarbons (CFCs)
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1.1.4 Global problem-Preventing dangerous climate change
Policymakers and scientists have been facing the question for quite a long
time on ‘how to prevent climate change?’ While finding the answer to this
question, the United Nations Framework Convention on Climate Change
(UNFCCC) has considered the ‘Second Assessment-Climate Change 1995’
report by the Intergovernmental Panel on Climate Change (IPCC), for formal
Framework Convention policy. The focus point is to know a numerical set-point
or a threshold value of a ‘change indicator’ at which the climate change starts
aggravating – i.e. would lead to "dangerous" change. In other words, ‘to what
extent the GHGs (CO2 equivalent) are allowed in the atmosphere to bring about
all the negative consequences’ that we deliberated so far.
The debate on finding such a set-point, at various forums concluded that the
grave implications of global warming might be evaded if the average global
temperature rise is restricted to no more than 2°C above pre-industrial levels17,
based on GHG emissions. However, further deliberations lead to a target level
of GHG emissions have given a more stringent value of 350ppm18.
If we aim to counter these global concerns, we face a scientific and technical
challenge to improve the efficiency of current renewable energy technologies
and/or find new technological options. To realize such scenarios, renewable
energy technologies need to develop at a much faster pace than at present. This
calls for improving the current state of fundamental and applied research in these
renewable energy technologies and improve their efficiency and make them
more cost-effective than current conventional technologies. Only then would the
renewable energy share be increased by new additional capacities and
appropriate infrastructure facilities.
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1.2 RESEARCH CONTEXT
1.2.1 Renewable energy resources
The world’s rate of energy consumption is predicted to increase from 13.5
TW to 27 TW from 2001 to 2050. This is predicted to triple in the year 2100, to 43
TW 13, 19. In view of the stringent target of 350 ppm of GHG emissions, considered
in the IPCC report 18, we need to actively aim at Zero-carbon emission-based
technologies for most or all future power generation. The overall energy options
available including renewable energy sources and their potential output are given in
Table 1.1.
Table 1.1: Finite and renewable energy reserves (TW-years)
Global energy reserves, 2009 estimate20
Source
Finite sources TW
Coal 830
Petroleum 335
Natural Gas 220
Uranium 185
Renewables TWy/yr
Solar 23000
Wind 75-130
Waves 0.2-2
Ocean Thermal Energy Conversion (OTEC) 3-11
Biomass 2-6
Hydro 3-4
Geothermal 0.2-3
Tidal 0.3
From Table 1.1, it is obvious that solar energy has a huge potential to provide a
significant amount of energy. However, in parallel, all other possible renewable
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sources should be utilised to the greatest extent possible to attain an
environmentally sustainable energy mix for future energy demand.
Figure 1.2: Typical solid-state solar cell configuration
Over the past few decades, a large amount of research has focussed on renewable
energy sources, in particular, solar energy.
1.2.1.1 Solar cells
A solar cell is a combination of material interfaces that harvest light and convert the
energy into electricity and is based on the photovoltaic effect. In essence, some
materials have the capability to absorb incident light and generate electricity by
promoting or releasing ‘electrons’ that move in the material. Having said this, the
basic requirement for a material to harvest light is the electronic ‘band-gap’ that
determines the light harvesting capacity of the material. A semiconductor that
possesses an electronic band-gap can be used as the main component of solar cells.
When light shines on them, the energy is absorbed and ‘electron-hole’ pairs are
generated. These ‘electrons’ are then separated through electrodes at both ends, thus
completing an electric circuit in which the ‘ejected electrons’ flow causing
‘electricity’ production. A schematic showing this principle is given in Figure 1.2.
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There are many components in a solar cell configuration that play an important
process function and impact its overall efficiency. Each component should be given
a special focus in order to identify a suitable material to fulfil its function. Compared
to the first-generation Silicon-based solid-state solar cell technology, there are now
third-generation solar cells that include Perovskite Solar Cells (PSCs)21 (See
Figure: 1.3). The HTM and ETM play a crucial role in the charge transport
dynamics. At present, the most efficient HTM is an organic material viz. Spiro-
OMeTAD (2,2',7,7'-tetrakis(N,N-di-p-methoxyphenylamino)-9,9'-spirobifluorene)
(Empirical formula C81H68N4O8). However, the production process is cost-
prohibitive and it is not particularly stable. Similarly, there are some effective
inorganic ETLs that were reported22 such as TiO223, SnO2
24, ZnO25 etc. Part of my
research is focused on finding simple materials that have the potential to be easily
produced yet having a suitable bandgap and band edge positions aligned to
perovskite layers to achieve hole transport. The research gaps associated with the
selection of such a study are mentioned in the literature review section.
Figure 1.3: Perovskite Solar Cell structure
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1.2.1.2 Photocatalysis
Clean fuel production via artificial photosynthesis (generating H2 and O2 through
water splitting) using a photoelectrochemical (PEC) system is also an effective way
for sustainable energy storage where electricity is stored as a clean fuel, namely
hydrogen. This PEC system requires a suitable semiconductor having high light
harvesting properties that can be used as a photocatalyst to split water.
Figure 1.4: Artificial photosynthesis-Photocatalysis schematic
This study of exploring the band edge positions of new materials is part of my
core study on 2D materials. Finding a material with suitable band edge positions
that are aligned with the redox potential of water while possessing a bandgap
suitable for effective water splitting through the photoelectrochemical process (see
Figure 1.4) is also part of my research. Such a semiconductor should have a
bandgap of around 1.5 to 1.8 eV26 for practical purposes. and therefore this study is
to assess innovative 2D materials for overall water splitting and photovoltaic
applications.
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1.3 RESEARCH PROBLEM
The special and remarkable electronic and physical properties27-33 of 2D materials
such as high carrier mobility, good light absorption, mechanical flexibility,
thermal conductivity have given rise to promising research in both fundamental
and applied areas. Although there has been immense research progress in the last
decade on these materials, many challenges remain regarding the number of
materials that are yet to be studied and characterised and compared to their bulk
counterparts in order to identify possible applications in solar cells, water-splitting
and nanoelectronics.
1. It is determined from a literature review that the 2D layered GeAs2, SiAs2 and
SiP2 materials significantly less studied than other 2D materials and there is a
shortfall of theoretical data on their properties. There a few available
experimental results but they have not yet been compared with theoretical
studies. This computational investigation based on DFT is undertaken for
checking their applicability in water splitting and photovoltaic applications.
2. Further study on suitable materials for use as HTMs in Perovskite solar cells is
highly desired for this fast-growing perovskite field. A new class of organic 2D
materials and other inorganic materials are considered using DFT analysis to
delineate their suitability in PSCs and thus in solar energy applications.
The research gap is very clear, and my research contributes to filling this gap
to some extent and will pave the way for selecting new materials for solar cells
or in water splitting studies. The bulk and 2D structures of the materials
considered in this research are given in their corresponding chapters and thus
not given here to avoid repetition.
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1.4 RESEARCH PURPOSE
My research focusses on finding a suitable semiconductor, with a specific
emphasis on two-dimensional materials (2D materials) - also known as ‘single-layer
materials’- that are crystalline in nature and composed of a single layer of
atoms/unit cell layer. 2D materials have been put to use in a wide range of
applications, including high-performance gas sensors34, electronics, photovoltaics,
spintronics, catalysis, and Li ion-batteries35, 36. These materials are said to have
special properties such as absorbing much higher incident light compared to the
bulk materials, easy to integrate into waveguides which would help in high
performance light modulation for optoelectronics, easily suited for heterostructures
etc. Thus, my core research area has the benefit of potentially applying the same
material for solar cell/photovoltaic applications and water splitting applications that
can produce green energy fuels such as Hydrogen.
1.4.1 Research Aim
The fundamental aim of the study is to identify and suggest new 2D layered
materials for improving the efficiency of solar-based technologies.
Under the above aim, the specific technologies selected are: -
(1) Photo-catalysis applications for clean solar fuel production –for solar water
splitting to generate hydrogen and oxygen
(2) Perovskite solar cell applications – to find innovative 2D materials for
aiding charge transfer focusing on electron and hole transport layers that are
compatible with the perovskite active layer.
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1.4.2 Research Objectives
With the declared aims, few objectives are derived to give further emphasis
on the selected research problem. Each objective is based on a set of basic
and specific parameters that need to be assessed in order to investigate the
central point of the research gap with respect to two-dimensional (2D)
materials.
The basic characterisation parameters such as optical, electronic, phonon
spectra and bandgap etc. and prediction of their suitability for solar cell
applications. Specific parameters such as 2D material formation energy, the
binding energy of the hybrid structures/systems designed for a specific study,
charge density difference in hybrid systems to assess the effectiveness of
charge transfer mechanisms etc. are a few factors that need to be considered.
This is applied to new generation solar cell technology (Perovskite solar
cells), and solar applications like water splitting to generate Hydrogen and
Oxygen.
Objectives:
1. To model and analyze the 2D structures of three very less studied Group
IV-V compounds viz. GeAs2, SiAs2 and SiP2 for their suitability in
photoelectrochemical water splitting to generate clean fuels (Hydrogen) or
for general photovoltaic applications. This work aims to develop an in-depth
understanding of their special properties with respect to their bulk structure
counterparts.
2. To design new 2D organic Carbon-Quantum dots (C-Dots) and analyze
their suitability and select the most appropriate structures for use as ‘hole-
transporting’ material for perovskite solar cells (PSCs).
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3. To design 2D inorganic materials (transition and post-transition metal
chalcogenides (InS, InSe, TcS2, TcSe2), post-transition metal halides and
oxides (PbI2, PbO, SnO) and analyze their suitability and select the most
appropriate structures for use as an electron or hole-transporting materials
for perovskite solar cells (PSCs).
1.5 SIGNIFICANCE, SCOPE AND LIMITATIONS
The importance of the current research study is highlighted here in terms of
the selected topic, the gravity of the problem to be solved, and other factors.
1.5.1 Significance of the research
The significance of the research study is described below: -
1. This is fundamental research to theoretically predict the characteristics of
either new materials or those materials that are studied in depth so far.
2. This research is primarily focused to contribute to solving the global
problem of climate change.
3. This theoretical exploration helps in pre-empting the results before
proceeding with any experimental studies, helping in saving time and
money, whereby this research could avoid futile efforts of potentially non-
productive experiments.
4. This study emphasises the theoretical characterisation of less known or
less studied 2D materials (oxides or chalcogenides of elements from
Group IV-V) for finding alternatives for existing materials for perovskite
solar cells and provide scope for further studies.
5. This research aims at identifying simply structured materials for possible
low-cost processing and production.
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6. New and simple organic structures for Carbon Quantum dots are designed
and explored for aiding charge transport in solar cells.
7. The study is also engaged in the production of solar fuels (Hydrogen and
Oxygen) from solar water-splitting.
8. This investigation contributes to providing scope for further study on the
emerging photovoltaic technology i.e. Perovskite solar cells.
1.6 THESIS STRUCTURE
The organization of this thesis is described here. In Chapter 2, the literature
review and the research problem are given. The research design, theoretical physics
models or computational methods considered, resources used etc. are given in
Chapter 3. The completed work and the results in the form of published / ‘submitted
manuscript for publication’ of articles are given in Chapter 4 through Chapter 7.
Chapter 8 gives the conclusion. The future scope of the research is briefed in
Chapter 9, and then the final section ‘References’ provides the Bibliography. The
basic thesis snapshot is depicted in the Figure-1.5.
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Figure 1.5: Thesis outline
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Chapter 2: Literature Review
2.1 HISTORICAL BACKGROUND
As proclaimed in the previous section ‘research context’, my research focusses
on Two-dimensional (2D) materials that could possess appropriate characteristics
as that of semiconductors for use in solar energy applications. Identifying new
semiconductor materials involve either of the two ways-
1. Make a guess of a probable material, with some experience on known
materials, and then experimentally synthesise, then characterise to find
its suitability for the intended use
2. Make a material guess, again with some previous experience with similar
materials, and then theoretically predict its properties through first
principles of physics, and if found suitable for the desired use, then
proceed with synthesis and characterisation to compare with the
predicted results, and then use in applications, if the experimental results
match considerably with the predicted theoretical values.
The second method is very useful, in such cases, where we do not know
anything or have very little information about a material. This would save time and
money, as some materials after synthesis and characterisation may not be useful.
The current research uses the second method for predicting the probable
semiconductor compound characteristics using fundamental principles of quantum
physics and chemistry. The computational study is based on quantum mechanical
modelling that uses Density Functional Theory (DFT) with ab initio calculations to
predict the properties such as the light absorption spectrum, electronic bandgap,
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conduction band minimum (CBM), valance band maximum (VBM) and other
properties such as electronic band structure, phonon spectrum etc. Using these
analytical data, the use of the material can be extrapolated or perceived.
Once suitable characteristics for the material is found it can be explored
further through future research via synthesis by experimental researchers at lab-
scale and the predicted properties can be experimentally determined and compared.
In general, the elements from group IV of the periodic table or a compound
formed with a group III element and a Group V element, or from group II and group
IV mostly have semiconducting properties. In this study, the compounds formed
from the combination of group IV-V are considered and Two-dimensional (2D)
layered materials. Also, a few other materials viz. Lead and Tin are considered. An
innovative and new class of organic carbon-quantum dots are also explored for
usage in solar energy material applications.
Then ‘Why 2D materials?’ The simple answer is – ‘make use of their
remarkable properties’ identified through the introduction of graphene in 200437
(though the layered materials were predicted theoretically much earlier). This has
since become an interesting and intensely studied research field. The reason being
its special properties of having very high thermal38 and electrical conductivity39,
transparency to visible light40, and greater strength than steel41 by weight.
Nanostructured crystalline materials such as nanowires, nanotubes are a new
class of contenders to replace conventional silicon solar cells due to photo-
conversion improvements42. However, size-dependent synthesis of nanomaterials
and their characterisation is time-consuming with many futile trials before one
achieves the right-sized Nano-structure. Therefore, fundamental principle
calculation methods can help to predict material properties before synthesis. Many
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researchers have emphasised the importance of computational studies and reviewed
its progress. Martin O. Steinhauser and Stefan Heirmaier [2009]43 have reviewed
on molecular dynamics (MD) in material science, Anubhav Jain et al. [2016]44 have
reviewed the DFT predictions of materials for energy. Further studies of theoretical
predictions include Shengli Zhang et al. 45 revealed that antimonide oxide has direct
band-gap which ranges from 0.0 to 2.28 eV that is suitable for solar cell materials,
with high carrier mobility. Whereas the non-oxide form of antimonide is an indirect
bandgap semiconductor which is not suitable for light absorption and thus for solar
cells.
Furthermore, the prediction of the bandgap as accurate as possible is crucial
for selecting solar materials. Using DFT and post-DFT approximation methods
which include hybrid functionals to get more accurate results for the bandgap that
is comparable to experimental values were obtained by Kittiphong Amnuyswat et
al. 46 for methylammonium lead iodide (CH3NH3PbI3) which is a material for
perovskite solar cells (PSCs). In 2008, Macho Anani et al.47 have considered
Nitrides of group-IIIA elements for a computational study and found a theoretical
efficiency of about 35% making them worth an experimental study for use as solar
cell materials. They proposed these Nitrides in out-door applications because of
their large energies of formation and comparatively better resistance than III-IV
semiconductors to various temperatures.
Though most of the characteristics of 2D materials are similar exceptions still
exist, and each material calls for a thorough study in order to find a suitable material
with desirable properties. The reduced size of nanomaterials helps exciton charge
separation 48-52, while few two-dimensional materials are relatively insensitive to
thickness 53, 54, however Boron Phosphorous has a thickness-dependent direct
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bandgap 55-59. Thus, though my research would focus on similar or some of the
characterisations as discussed above it considers new or existing materials that are
currently not well explored.
The latest developments in computational studies, thus emphasise its
importance especially when there is limited scope for synthesis and characterisation
studies on nanomaterials. These DFT studies include investigation of band-gap type
i.e. direct or indirect, difference in value of bandgap with respect to stress or strain,
electronic band structure, hybrid structure binding energies and charge density
differences in hybrid structures, VBM and CBM etc. and many more characteristics
that are useful for predicting the suitable applications in any industry. In my
research, DFT is used to predict characteristics of materials which can be utilised
in solar energy utilisation.
2.2 STUDY OF 2D MATERIALS FOR PHOTOCATALYTIC WATER
SPLITTING OR PHOTOVOLTAIC APPLICATIONS
The concept of photocatalytic water splitting was introduced by Fujishima
and Honda in 1972. They used TiO2 as the photo-catalyst60 in a photo-
electrochemical (PEC) cell. This cell makes use of light energy (in this case solar
light) and splits water into its chemical constituents i.e. hydrogen (H2) and oxygen
(O2) in gaseous form, where the former is considered a clean fuel, as there is no
carbon source used in this process. To make use of the light, either the anode or
cathode (dipped in an electrolyte connected through the exterior circuit) should be
a light-absorbing semiconductor. Depending on which component is the light-
absorbing semiconductor (anode or cathode), the relevant electrode reaction takes
place and the constituent gas is evolved from the cell at the semiconductor-
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electrolyte (in this case, water), the second electrode is typically a metal. However,
if both the anode and cathode can be of light-absorbing type semiconductors, then
it is known as a tandem photoelectrochemical cell. Having mentioned this, if a
single semiconductor has the appropriate CBM and VBM positions in its band
structure, then a single semiconductor is enough to achieve HER and OER in the
same cell. This is also one of the main objectives of my research to identify such
material.
The principle of this cell can be described as follows. When solar light shines
on the photosensitive semiconductor electrode, the part of the sunlight, which has
a higher level of energy than the band-gap energy of the semiconductor, is absorbed
by some electrons in the valence band (VB). Attaining more energy, these electrons
jump to the conduction band (CB). This creates a ‘hole, h+’, i.e. positive charge in
the VB. These electron-hole pairs are called excitons. (See Figure 1.6) If we
achieve separation of these excitons into an electron and a hole, within the field
formed in the space-charge region, then these will cross the electrode-electrolyte
interfaces in the system. This electron flow creates electricity. The pH of the cell
system determine the reactions associated with water splitting. In an acidic
environment (at low pH) this charge transfer process occurs through the ‘holes (h+)’
and generates H+ ions at anode’s surface and generates the ‘oxygen evolution
reaction (OER).
2H2 O( l ) + 4h+ → O2 ( g ) + 4H+ (at low pH) – a t anode
Hydrogen ions diffuse through the electrolyte (water) while electrons in the
anode travel through an external circuit and reach the cathode. When these electrons
combine with the Hydrogen ions at the cathode, it produces Hydrogen (gas), known
as the Hydrogen evolution reaction (HER), also, at low pH.
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4H+ + 4e− → 2H2 ( g ) (a t low pH) – a t cathode
In the case of an alkaline electrolyte system (i.e. at high pH), instead of Hydrogen
ions, Hydroxyl ions (OH-) take part in the reaction.
4OH− + 4h+ → 2H2O + O2(g) (at high pH) – at anode
4H2O + 4e− → 2H2(g) + 4OH− (at high pH) – at cathode
The water oxidation and reduction potentials are pH-dependent, but the standard
potential of the PEC doesn’t depend on pH. So, the overall water splitting reaction
is given below (Bozoglan, Midilli, & Hepbasli, 2012)61
2hν + H2O(l) → H2(g) + O2(g) …………………………… (2.1)
The process described in equation (1) takes place at the photo-anode when the
absorbed solar photon energy is equal to or larger than the threshold energy. Using
the formula given below62 we can calculate this minimum energy requirement;
Em i n = ∆G 0( H 2 O ) / 2N
Where ∆G0(H2O) is the standard free enthalpy per mole of H2O in eq (1). i.e.
237.14 kJ/mol; N is Avogadro’s number 6.022 × 1023 mol−1. Thus Emin = 1.23 eV.
So, the bandgap of the semiconductor electrode to be used in the PEC must be at
least 1.23 eV.
Figure 2.1 : Water-splitting exciton generation concept
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In a PEC, hydrogen and oxygen evolution reactions are separated in different
regions as they evolve at different electrodes. Where photons have an energy
higher than the bandgap energy of the material the surplus energy, ( photon – band-
gap) is lost as heat during the relaxation of energy to Eband-gap. It is thus clear that the
Bandgap energy should be such that it should be high enough to be able to harvest
a major portion of the solar spectrum. To assess the optimum bandgap value, the
internal energy losses (Eloss) linked to the solar energy conversion should be taken
into consideration. James R. Bolton [1996]63 reported that these losses are in the
range of 0.6 to 1.0 eV. A reasonable practical photocatalyst, therefore, should have
a bandgap in the range of 2.0 to 2.25 eV64.
Although having the desired bandgap value, the band edges positions of material
are also an important prerequisite for attaining oxidation and reduction reactions.
The CBM energy of the material should be higher than the water reduction
potential i.e. H+/H2 (−4.44 eV) and the VBM energy should be lower than the water
oxidation potential i.e. O2/H2O(−5.67 eV)65. The difference between the CBM and
the water reduction potential and the VBM to the water oxidation potentials are
called over-potentials, which drive the water-splitting reaction.
For the aim of reducing the overall cost of PECs, it is better to have a single
semiconductor material that satisfies all the salient characteristics; these being light
harvesting properties, exciton separation, charge transfer and transport and having
CBM and VBM at appropriate positions, thus achieving Hydrogen and Oxygen
evolution.
Semiconducting materials that have been studied include Titanium dioxide
(TiO2), Tungsten trioxide (WO3) and alpha Iron oxide (α-Fe2O3)66, bismuth
vanadate (BiVO4) and tantalum nitrate (Ta2N5)67 are a few. TiO2 nanotube arrays
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(TNTs) were studied by Tan et al. (2016)68 to improve hydrogen production rate
under UV light.
Studies have also been undertaken with 2D materials as photocatalysts. In 2008,
Fujishima et al. suggested a 2D model with TiO2 to obtain both gases with a single
electrode69. A review article reported by Lin et al. [2011]70 referred to studies done
with nanocrystalline films of Fe2O3, WO3, BiVO4, and InP for water splitting.
Graphitic-carbon Nitride (g-C3N4) nanosheets were also explored for improved
photocatalytic activities (Ping Niu et al.[2012]53. In 2013, Marco Bernadi et al.
studied three transition metal dichalcogenide monolayers viz. MoS2, MoSe2, and
WS2 and predicted that they could be used for water splitting applications. Also,
group-III single-layered monochalcogenides i.e. (MX, where M = Ga and In, and
X = S, Se, and Te) are predicted to have small formation energies and thus are
suitable for photocatalytic water-splitting71. Finding a single photocatalyst for
overall water-splitting seems difficult and recently, studies are being conducted on
2D heterostructure z-schemes to achieve water-splitting72.
In this context, my research is focused on finding a 2D material that can have
such band edge positions, with the desired bandgap, and having enough driving
force to achieve the HER and OER.
Here I focus on a computational study on three compounds which are much less
studied for their feasibility as either appropriate for solar cell materials
(photovoltaics) or for photoelectrochemical water splitting (artificial
photosynthesis).
Recently, research efforts are geared towards utilising advanced materials at the
micro and nanoscale level by controlling the overall size and cost of the materials73.
This supports the use of the special properties of two-dimensional (2D) materials
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for photovoltaic applications and as a catalyst for water splitting techniques which
could add new materials to the existing list of materials to produce the clean and
sustainable energy. Regarding 2D materials, I consider either a single layer or
multi-layered structures that have distinct mechanical and optical properties
compared to that of their bulk counterparts.
Layered materials possess weak van der Waals forces between the neighbouring
layers, which in principle makes it feasible to isolate one or more layers from their
bulk crystal forms by means of exfoliation techniques40. Experimental exfoliation
was successful in single-layer extraction of graphene, Boron Nitride, MoS2, and
black phosphorus. This paves an operative means to derive more 2D layered
materials from their bulk counterparts.
Since the introduction of 2D graphene in 200437, many other single-layered
materials have been predicted and also experimentally realized. However,
considering the desirable characteristics required for solar energy applications,
some 2D materials did not meet the specific application-based requirements. For
instance, a Boron Nitride (BN) layer has a very large bandgap (5.97 eV)74 which
hampers the desired capacity of light harvesting. Phosphorene is also known to be
unstable upon exposure to air75. Though single-layered MoS2 has a relatively
suitable bandgap (1-2 eV)76, it is strongly affected by structural defects77, charged
impurities78, dielectric environment79 etc. The HER efficiency must be improved
as most of the known catalysts have non-favourable Gibbs free energies for
hydrogen adsorption. These examples indicate that such materials may not be
useful for exploiting their properties at large commercial scales. This objective
motivates one to find alternatives, and therefore the search for 2D catalysts for
water splitting has received great attention in recent years71. In this regard, 2D
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materials are required which are more stable, have a suitable bandgap and band
edge levels compared with water redox potentials, as well as dynamic stability
which is highly important for highly efficient HER activity.
In 2005, Novoselov et al. reported a stable single or multi-layered atomically
thin sheets of two-dimensional crystals boron nitride, graphite, several
dichalcogenides, and complex oxides, using a micromechanical cleavage
method40. This opens the opportunity to develop other 2D materials in a similar
manner. Therefore, the three compounds that are the focus for this section of
research are Silicon Diphosphide (SiP2), Silicon Arsenide (SiAs2) and Germanium
Arsenide (GeAs2) which have not been studied or explored as much to date.
In 1963, F. Hulliger et al80. predicted that SiAs, GeAs and GeAs2 should show
semiconductor behaviour. Referring to this study, Tommy Wadsten in1967
synthesised and analysed the crystals of group IV-V2-type compounds viz.: SiP2,
SiAs2 and GeAs2 having the space group of Pbam for all the three compounds
which are orthorhombic with eight formula units per cell81. He also studied other
derivatives of Si and Ge with As and Phosphorous in the same work, but no in-
depth research was done w.r.t band structure, bandgap etc.
Later, in 2011, F.Bachhuber et al.82 conducted a theoretical study on SiP2, using
a Gaussian type function scheme and predicted that the pyrite type SiP2 to be a
semiconductor with Hartree-Fock (HF) and Becke-Lee-Yang-Parr (B3LYP)
methods, but local density approximation (LDA) and generalised gradient
approximation (GGA) predicted it to be semimetal that is more towards the
semiconductor like behaviour.
In 2015, Ping Wu et al. conducted more theoretical explorations on Si and Ge
arsenides 83, where they confirmed that m-GeAs /SiAs, o-GeAs2/SiAs2 are
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semiconductors due to the band structure estimates and was in agreement with
experimental results.
However, most of the above studies are focussed on bulk materials and very few
or no studies have yet been reported for two-dimensional counterparts of these
three compounds as per my knowledge. Therefore, in keeping the view of the
special properties that 2D materials possess, there is a wide gap of knowledge
regarding these compounds at the two-dimensional level.
2.3 STUDY OF 2D MATERIAL FOR ELECTRON AND HOLE
TRANSPORT IN PEROVSKITE SOLAR CELLS
The new class of solar cell being developed based on the crystal structure of
perovskites has attracted considerable interest because of its relatively low cost and
high efficiency 84-86.
Miyasaka and co-workers87 reported the first perovskites-based photovoltaic
application. The efficiency for CH3NH3PbBr3 (MAPbBr3) cells was reported
around 2.2% which was later increased to 3.8% by changing the halide from
bromine to iodine in 2009. At the end of 2013, Seok’s group achieved energy
conversion efficiencies of 16.2% by using a mixed-halide CH3NH3PbI3-xBrx(10–
15% Br) and a poly-triarylamine HTM. By 2016, the efficiency of these solar cells
was reported at 22.1% which is considered as record growth in solar cell
technology. 88.
Electrical and structural properties are reliably predicted by the DFT method.
Umebayashi et al.89 and Mosconi et al.90 evaluated the band structure of
CH3NH3PbI3 with and without intervening methylammonium ions, and indicated
that the conduction and valence bands were comprised of the lead iodide
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framework, but that there was a limited effect due to the organic molecule. Giorgi
et al. 91 estimated the effective masses of photo-carriers of CH3NH3PbI3 and found
that the value is comparable to silicon in commercial solar cells, which suggests
their great potential for use in PV cells. The development of perovskite solar cell
technology is moving quickly but still needs improvement in efficiency and
stability. Theoretically, management of the constituting elements could improve
charge transportation and stability and thereby increase efficiency in CH3NH3PbI3
solar cells.
Among other components and parameters, the subject of interest for my research
is about finding suitable new and simple Electron Transport Materials (ETM) and
hole-transport material (HTM) with suitable band alignment. An effective ETM
material should promote electron mobility and have band edge energy positions
aligned with respect to the perovskite layer. This material should allow electron
transport but block hole transport, be optically transparent and exhibit low photo-
degradation 92. Some of the effective inorganic ETLs that have been reported22 are
TiO223, SnO2
24, ZnO25 etc., and NiO93, CuOx94, CuI95, CrOx
96 etc. as HTLs. An
interesting study done by Robert J.E. Westbrook et al.97 on interfacial charge
transfer energetics between perovskite and organic HTMs using time-resolved
transient absorption and photo-luminescence indicated that only a small driving
force energy of ~ 0.07 eV would be enough to promote efficient hole transport
between the perovskite-HTM interfaces. They further emphasised that the open-
circuit voltage can be further improved if this interfacial energy offset is within the
range of 0 < ∆E < 0.18 eV.
Qiang Teng et al.98 demonstrated that there is a difference in the hole transport
behaviour when perovskite surfaces are terminated with either Methyl Ammonium
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Iodide (MAI) or Lead Iodide (PbI2) and suggested that the PbI2 surface terminated
perovskite has the advantage of better hole transport to contacting HTMs.
Therefore, I have considered the two-possible surface terminated perovskites for
my research on HTM materials. Moreover, it is reported99 that currently, the HTMs
are very costly which prohibit large-scale applications, in spite of the fact that
many organic and inorganic HTMs were studied at the lab scale and found to
perform at reasonable efficiencies ~20% but long-term thermal and operational
stability is still a major concern, for operation at higher temperatures around 60oC.
Thus, there is an inevitable need to find new materials that could be suitable as an
HTM in PSCs. Therefore, this research considered an innovative organic material
for use as an HTL in PSCs. Carbon quantum dots (CQDs) are a new type of 2D
material. In 2009, Xu et al. discovered CQDs100 and further research on their
synthesis and characterization indicated the potential for many applications.
CQDs101 are relatively simple to synthesise and are also fluorescent nanomaterials.
They have shown stability, conductivity, low toxicity and are considered
environmentally friendly. These CDQs have optical properties similar to that of
conventional semiconductor quantum dots102. Graphene quantum dots (GDQs) are
single-layered nanoscale-sized graphene sheets having only carbon atoms.
Functionalized GQDs were studied earlier for tuning the bandgap for suitable
applications103. If the terminal carbon atoms of the GQDs are functionalised with
hydrogen, then these are known as Carbon quantum dots (simply noted C‐dots)
where they were studied earlier by a few researchers103, 104. Photocatalysts, derived
through C‐dots, have very good catalytic activity as reported104 while a few other
studies revealed that the C‐dot edges have an influence on their light harvesting
properties105, 106. Metal-free g‐C3N4 combined with C‐dots have shown excellent
photocatalytic water splitting activity107.
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The inorganic materials Lead Iodide (PbI2), Lead Monoxide (PbO) and Tin
Oxide (SnO) also considered for this study. Lead Iodide (PbI2), as reported, is a
layered material with semiconducting properties which has many applications in
the optics field108-110. The theoretical investigation has proven that the bandgap
changes from direct to indirect when the bulk form is modified to a single-layered
two-dimensional material.
Two-dimensional Lead Monoxide (PbO) is another inorganic semiconducting
material who’s mechanical, and exfoliation feasibility and optical properties were
investigated and reported35, 111-113. Favourable attributes for charge transfer or
charge accumulation, high resistivity and low-cost could make PbO a potential
candidate for an HTM, in addition, PbO is hydrophobic which could further help
in the long-term stability of the HTM and thereby perovskite as well113.
Pure Tin Oxide (SnO), having a tetragonal unit cell with P4/nmm space group
with lattice parameters a=b=3.802 Å and c=4.836 Å is also considered for this
study. It’s reported that the pure phase of SnO might not have high hole mobility,
but would show high mobility when it is doped with controlled residual amounts
of metallic tin114. However, our current study is intended to analyse the band
alignment w.r.t the perovskite’s band positions to elucidate the feasibility of hole
transport for PSC, therefore we restricted the focus on pure SnO monolayers. The
experimental realization of few-layered SnO was reported with p-type property
making it a favourable component for 2D logical devices 115, 116.
Thus, my research through prediction of new materials from first principles is
highly advantageous for the research community to save money and time in
synthesis, by exploring through computational studies and thus attains significance
in materials research.
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2.4 SUMMARY AND IMPLICAT IONS
Summarising the literature review above there is a shortfall of information and
characterisation of the proposed subject materials. The theoretical framework for
my study includes systematic analysis for finding the essential properties to check
their suitability for solar energy applications.
Deriving from the history of the research work on the selected compounds, there
is a large gap of knowledge and potential scope for exploring the characteristics
and check the possibility for the desired applications. So the research problems can
be expressed as below: -
1. What are the essential properties such as electronic band structure,
phonon spectrum, optical absorption spectrum, tuning of bandgap
through the tensile strain etc. for the selected compounds viz.: SiP2, SiAs2
and GeAs2.
2. Whether these materials SiP2, SiAs2 and GeAs2 at the 2D level, are
suitable for the desired application or not and declare their potential uses.
3. It is also postulated here that C-dots and PbI2, PbO and SnO are quite
suitable for use as HTLs in PSCs.
The actual outcomes of the study are described in subsequent chapters in the
form of published journal articles or submitted for publication.
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Chapter 3: Research Design
3.1 METHODOLOGY AND DESIGN
3.1.1 METHODOLOGY
The methodology is the implementation of theoretical quantum physics
principles to identify and predict the characteristics of nanoscale materials. In this
process, a computer software-based computational study is performed for all the
topics in the presented research.
A stage-wise or step-wise process is adopted to calculate the final desired
representative parameters for the research problem at hand. The steps include
creating or designing the molecular/compound structure, geometry optimisation
via. minimising the energy of the structure to find the ground state energy, then the
optimised configuration is subjected to the next stages of calculations. Further
stages include electronic band structure, optical absorption spectra, phonon
spectrum and Bader analysis for charge density differences in hybrid structures.
This computational method uses Density Functional Theory (DFT) for such
predictions based on quantum mechanical considerations
In this computational physics investigation, I am using elemental electronic
structural relaxations or ground state energy, and calculating properties such as
magnetic, electronic properties of molecules, materials and hybrid solar cell
configurations. This gives rise to finding other associated properties of the unit
cells of the compounds using DFT parametrizing with “Perdew-Burke-Ernzerhof
(PBE)” for “generalized gradient approximation (GGA)117”, which is implemented
in “Vienna ab initio simulation package (VASP)” code118, 119. Improved band
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structure assessments are based on hybrid functional calculations as per the “Heyd-
Scuseria-Ernzerhof (HSE06)” method. These functionals will also be used to
explore the dynamic stability of these systems, phonon spectrum analysis will be
executed using the finite displacement method120 and implemented in phonopy
code121. The phonon spectrum or band structure will be computed using “density
functional perturbation theory (DFPT)”122, 123 as executed in the “Quantum-
ESPRESSO” package124.
3.1.2 RESEARCH DESIGN
This research is a qualitative approach to the defined problem. The problem is to
know how the material would behave or react under the designed configuration of
selected solar energy applications. The qualitative methodology mentioned in the
previous section would result in the behavioural prediction of subject materials
based on quantitative or analytical output from the calculations. The computational
principles and the linked concepts of research design outcomes are briefly
explained in this chapter.
3.1.2.1 THE FIRST PRINCIPLES THEORY
Density functional theory (DFT) is developed from first principles which support
to convert many electron-electron interactions effectively into a “one-electron
potential” which is a “functional” of the electron density125. Note that a
“functional” is ‘a function of a function’. Herein, the “electron density” is
functional, which in turn is a function of ‘space and time’. This ‘electron density’
functional is the fundamental property in a DFT study. However, there is another
theory i.e. Hartree-Fock (HF) theory which considers the many-body wavefunction
directly126.
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The VASP code that uses the DFT functionals include “local density
approximations (LDA)”, GGA, hybrid functional mixing with DFT and HF
exchange, ‘many-body perturbation theory’ (GW) for quasiparticle spectra Bethe-
Salpeter equations (BSE) etc. VASP uses iterative methods to DFT Hamiltonian
and then allows one to optimise the energy and structure of ‘systems with
thousands of atoms’ and for molecular dynamics of ‘systems with few hundreds of
atoms’. The Hamiltonian of any system is the sum of the kinetic and the potential
energies of the particles or constituents associated with that system. For different
situations or a number of particles, the Hamiltonian is different127.
The Hamilton for an N-electron system can be represented with a total energy
i.e. potential and kinetic energy component, as:
H r, R = ----------- (3.1)
Where is the mass of the electron, the position coordinates of the
electron, the mass of the Ith nucleus, the position coordinates of the
electron. The other terms refer to as, Te-electron kinetic energy, Vee-Coulomb
interaction between electrons, TN-nucleus kinetic energy, VNN-the interaction
between two nuclei and VNe-interaction between nucleus and electrons
respectively. The complications for the many-particle systems is that the energies
depend on the spatial arrangement of the particles.
And the solution to the following Schrodinger’s equation from first principles,
reveals the physical and chemical properties of the systems:-
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) = E ------------------------ (3.2)
3.1.2.2 HOHENBERG-KOHN THEOREM
Hohenberg-Kohn theorem128 proposes a solution to the multi-electron system, in
1964, which is the foundation of ‘Density functional theory (DFT)’ and it comes in
a two-part theorem.
Theorem 1.
“The ground state energy of a system of electrons is a unique function of the
ground state density”
n(r)= (3.3)
Theorem 2.
“The ground state energy can be obtained variationally: the density that
minimises the total energy is the exact ground state density”. In Hohenberg-Kohn
theory, the Hamilton of the system can present as
H= (3.4)
The total energy is:
(3.5)
Where, T(n) and Eint(n) are the Kinetic and the potential energies respectively
of the system, and is the external potential, and is the interaction
between nuclei.
3.1.2.3 KOHN-SHAM EQUATION
The density functional and effective potential can be represented as in equations
(3.6) and (3.7):
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n(r)= (3.6)
(3.7)
Where, is the exchange-correlation potential written as,
(3.8)
The Kohn-Sham equation can be written as:
(r)= (r) (3.9)
While the kinetic and electron-electron interactions are exact, the correlation
and exchange functional to the system are not exact. So, two types of
approximations are introduced to interpret certain physical quantities/parameters
quite accurately.
Type-1: ‘Local Density Approximation (LDA)’
This LDA is a very widely used method of approximation, where the functional
is assumed to depend only on the electron density at the coordinate r, at which the
functional is assessed. However, the spin-density is not considered.
(3.10)
The assumption of having the same density everywhere, tend to over-estimate the
exchange-correlation energy in case of LDA.
Type-2: ‘Generalised Gradient Approximation (GGA)’
To correct the overestimation tendency by LDA, the density gradients are used to
expand the terms. This facilitates the error correction due to density variations from
the centre point of the coordinate. These expansion terms are referred to as
GGA129 and have the following form:
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(3.11)
Among them, is Infinite-dimensional function and is the exchange
energy of the electron gas. GGA approximations for molecular geometry
optimisation and ground-state energies have yielded good results. The main
common functional of GGA includes PBE130, which is most widely used functional.
3.1.2.4 WANNIER FUNCTIONS
The electronic structure in periodic materials is solved generally in terms of Bloch
states, Ψnk. in the first-principles methods. These states are portrayed by n and k
where n is band index and k is crystal momentum, respectively.
Alternatively, these states can be represented by ‘spatially localised functions’
known as ‘Wannier functions (WF)’. The WF is briefly given here, but full details
are found in reported literature 131-133.
The WFs can be written through Bloch states centred on a lattice site R, ѡnR(r),
as;
(3.12)
where V – the volume of the unit cell, integrated over the 1st Brillouin zone (BZ),
and U(k) - unitary matrix mixes with Bloch states at each ‘k’. The unitary matrix,
U(k) has various choices that would lead to various spatial localised WF.
Wannier90 is a code implemented in VASP compute “maximally-localised
Wannier functions (MLWF)” as per Marzari and Vanderbilt (MV)131 and entangled
energy bands, as per Souza, Marzari and Vanderbilt (SMV) 132, 133. This Wannier90
method calculates the band structure of the compounds selected along with HSE06.
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3.1.2.5 GW AND BSE CALCULATIONS
In this quantum mechanical context, the electronic excitations are studied in
different ways in the system of interacting electrons and nuclei in the presence of
time-dependent external fields. The Wave function methods (Hartree-Fock, Mote
Carlo etc.), Greens’s function method, and Time-dependent Density Function
Theory (TDDFT) methods. The GW method is an approximation procedure in
which the self-energy of a many-body system is approximated with a simple term.
In fact, the actual many-body system equation for self-energy contains the sum of
all terms of Green’s function G and the screened Coulomb interaction term W of
the bodies in the system. However, in this approximation, only the first term of the
Tylor series expansion of the series i.e. iGW is considered.
Self-Energy (3.13)
Where, exact Hartree-Fock exchange potential = -iGv,
and iG(W-v) = correlation, screening due to other electrons.
Thus, this GW approximation gives the self-energy of the system after performing
standard DFT calculations. However, the GW approximation doesn’t include
excitonic effects. Then Bethe-Salpeter equations (BSE) are used to predict the
optical response functions including the excitonic effects134. That is the inclusion
of electron-hole interactions. The optical response calculation is synonymous to
frequency-dependent dielectric functions. In other words, it aims at finding the
macroscopic dielectric function135, ɛM(ω). The imaginary part of this function gives
the absorption spectrum. A detailed explanation of the terms of summation in GW
approximation and the Bethe-Salpeter Equations is beyond the scope of this thesis.
The process of BSE calculation is a three-step method involving, (i) standard DFT
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calculation, using for example LDA, (ii) GW approximation i.e. self-energy with
screened coloumb interactions, (can plot GW band structures and find a bandgap of
the materials, and finally doing (iii) BSE calculations to estimate e-h+ interactions
and plot absorption spectra using the imaginary part of the dielectric function. The
exciton binding energies were estimated for electron-hole pairs in some of the
materials under this study and are discussed in relevant chapters.
3.2 SOFTWARE USED
3.2.1 VASP
The “Vienna ab initio simulation package (VASP)”136 is a software package
program for materials modelling at the atomic scale e.g. quantum-mechanical
molecular dynamics, electronic structure estimation from first principles and DFT.
The principal algorithm flow chart is given in Figure 3.1 to resolve the Kohn-Sham
equation (K-S Equation). At the start of the iteration, the electron density ρ(r) is
assigned with an initial guess value, to calculate the effective potential Veff(r), then
the diagonalization of the K-S equations, and subsequently ρ(r) is evaluated
including total energy (E(tot)). Before the start of the calculation, a convergence
criterion will be given and will be tested after each iteration. If the criterion (given
as a tag in the input file), is not fulfilled, these iterations will be continued with the
ρ(r) just calculated in the last step. This process continues until the criterion is
satisfied, the output quantities are written to the output file.
In addition, the plane-wave base set is used in the code and periodic boundary
conditions (PBC). Therefore, for lower dimensional molecules and solids there
should be enough separation (i.e. vacuum) between the periodically repeated
crystals/cells. Generally, a space vacuum distance of about 10Å to 15Å or even
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more will be added depends the crystal being tested. This will eliminate the
interaction between the periodic crystals to get the features of layered materials.
A brief of input file data to be fed to the software is discussed in the next
section (‘Analysis’)
Figure 3.1: Energy optimisation algorithm in VASP software for DFT analysis solving the Kohn-Sham equations
3.2.1.1 ANALYSIS
All the material models and compounds related data are given as input to the
software. No statistical analysis etc. are required to be done externally. The
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software would be given five input files viz. INCAR, POSCAR, POTCAR,
KPOINTS and Linux OS dependent job-script file.
A detailed explanation of the contents of each input file is not a prudent option
here in this report. This is because, despite any written explanation, unless a proper
discussion-based basic training is imparted, it is extremely difficult to use the
software without face-to-face discussion, explanation and work with some
examples. Therefore, a brief conceptual clarification of each input file is discussed
below.
The INCAR file is a set of ‘key-tags’ that are specific to the software and a
numerical value assigned to them based on the desired characteristic related
calculation.
POSCAR file contains the sequence of elements and their atomic Cartesian
coordinate positions of each atom of the subject material within the defined crystal
structure.
POTCAR file consists of ‘pseudopotential’ of each atomic species of the
material used in the calculations. The VASP software supplier would provide the
POTCAR files of all elements in a periodic table so that the users can use them in
simulations/calculations. If there are more than one atom species in the subject
material, one needs to ‘add’ or ‘concatenate’ POTCAR files of each element in the
same sequence as they appear in POSCAR file.
KPOINTS file contains the coordinates of the symmetry points in the first
Brillion zone of the material as per its crystal lattice. A Brillouin zone is a specific
choice of the unit cell of the reciprocal lattice of the crystal of the material.
Job-script file contains a set of commends to invoke VASP software to do the
quantum computing from first principles under the Linux or UNIX Operating
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System (OS). As this is OS-dependent shell script file, it should have an associated
file extension such as filename.sh etc.
The names of the first four input files (INCAR, POSCAR, POTCAR,
KPOINTS) should not be changed for any system of material/s, whereas the job-
script file can be named as per conventional computer file names.
Each job-run after successful completion gives an output data file (known as
OUTCAR) in a text file format. All the data which is relevant to the task on hand
for the problem will be gathered through a specific shell script or programming
code written in other programming languages such as Perl, Python etc. These
programmes would either be edited time to time or customised for the said problem
in hand, or a ‘pre-compiled’ version will be used to generate the desired data
analysis.
The convergence test in the VASP means, say for geometry optimisation,
whether the selected parameters of Energy cut-off and k-points mesh is enough to
give the consistent value of lowest possible energy of the system. So, basically,
these two parameters are set in INCAR or (default values in POTCAR) and in
KPOINTS files, respectively. The ENCUT is the tag that sets this cut-off energy in
INCAR file in terms of eV. This value is used in the VASP algorithm to check the
difference between the energy of the current geometry of the system and the
previous iteration. Once the value of this difference is within the set point of
ENCUT value, its iterations stop the final energy of the system is written in the
standard output. Similarly, the other parameters for convergence, i.e. number of k-
points specified in KPOINTS file. To check the convergence, a different number of
k-points shall be specified and run the energy convergence and plot a graph or
collate the results of k-points Vs final energy. This gives an indication for which
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and how many numbers of k-points would be enough for conducting the
optimisation for the specific system under study. Care should be taken, only one
parameter i.e. either ENCUT or KPOINTS shall be changed at a time and checked
for convergence. If the ENCUT is not explicitly specified in the INCAR file, the
maximum ENMAX value specified in the POTCAR file of the system is considered
or used as ENCUT value as a default by the VASP. In general, in this research, the
PREC (i.e. precision) tag is set as ‘HIGH’. If this is set, the VASP would consider
1.3 times of the maximum of all ENMAX values of elements in the POTCAR file,
as the ENCUT value for convergence test. This yields good results, but of course
with some additional computational cost.
Here I am briefing an example of one such analysis, considering the VASP
software used. Once the geometry optimisation is done for any material structure
or combinations of structures the optimised structure would be written a file called
CONTCAR. This file contains the coordinates of the various elemental positions of
the subject material. This file then, along with other essential input data files, would
be given as input for the next step for calculations to find say, electronic band
structure. Once this job is submitted under the Linux environment of HPC
computing system of QUT, an OUTCAR file is created as an output, that contains
all necessary results written in it for generating the model for the band structure and
then to find the bandgap of the material. This specific data is picked-up and collated
in text file through an executable file created from a Linux system compiled Perl
programme. This text file could then be opened as an MS-Excel file or any other
application which can be used to draw graphs. The result then graphically shows
the band structure. From that structural figure, we can approximately measure the
electronic bandgap (i.e. difference of energy between the lowest of the conduction
band energies (known as CBM) and the highest of valance band energies (known
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as the VBM) for the material. However, the accurate numerical value of the
bandgap can also be obtained from the same Perl programme command as a screen
output. The graph will help in assessing whether it is a direct or indirect bandgap
depend on the CBM and VBM position on k-point symmetry represented by a point
on the x-axis.
This procedure of analysis is similar for finding different desired
characteristics for the material or system of materials. However, the command line
executable files would be different. We can thus, obtain light absorption spectrum,
excitation binding energy of electron-hole pair released in a material upon light
incidence etc. Some other parameters such as binding energy between two interface
materials, the energy of formation of 2D material from its bulk counterpart, band-
gap variation with respect to stress and strain applications on materials etc. can also
be obtained from these methods.
To give another example of analysis the energy of formation can be obtained
from the difference in free energy between 2D material and the lowest energy value
of its bulk counterpart. To obtain this value two different sets of programmes for
2D and 3D are ‘run’ on Linux. Then the output from both jobs is used to calculate
the formation of energy from pre-defined equations.
3.2.1.2 COMPLETED COMPUTATIONS
All the calculations required for the research topics are completed through
supercomputing facilities from National Computational Infrastructure (NCI)
supported by the Australian Government through QUT and using High-
Performance Computing (HPC) at QUT.
The results were published through three peer-reviewed journal articles, and a
fourth article has been submitted for review and publication.
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The materials for the study are bulk and two-dimensional (2D) structures of the
selected compounds GeAs2, SiAs2, SiP2, Carbon Quantum Dots with and without
additional functional moieties (i.e. –OH and –COOH), Perovskite surfaces
terminating with MAI and PbI2, Lead Iodide (PbI2), Lead monoxide (PbO) and Tin-
Oxide (SnO). The methods for this study are:-
a) Geometrical optimisation through ground state energy relaxation
b) Phonon structure
c) PBE, HSE06 /Wannier90 band structures and the bandgap estimation
d) Optical properties for estimating the light harvesting properties
e) Band-gap variation with respect to tensile strain and compressive stress
f) Schematic representation of the calculated properties to assess the potential
applications in the field of solar cell and photocatalytic applications.
g) Band edge calculations and alignment correcting with vacuum potential,
after HSE06 band structure predictions
h) Interface charge density difference calculations for perovskite surfaces and
the potential HTM materials – Organic and inorganic
3.3 ETHICS AND LIMITATIONS
All the computational works are done using reliable software. The material
structures and analysis are performed within the scope of the software limitations
if any. However, all the methods and options of the software are well within the
scope and the desired output. All the software used are under proper license by the
University.
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Chapter 3: Research Design
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QUT Verfied Signature
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
Chapter-4: Two-dimensional silicon
diphosphide (SiP2) as photocatalyst
DOI: 10.1039/C7NR07994J (Paper) Nanoscale, 2018, 10, 6369-6374
4.0 Versatile two-dimensional silicon diphosphide (SiP2) for
photocatalytic water splitting†
Sri Kasi Matta , Chunmei Zhang, Yalong Jiao, Anthony
O'Mullane and Aijun Du *
School of Chemistry, Physics and Mechanical Engineering, Queensland University of
Technology, Gardens Point Campus, QLD 4001, Brisbane, Australia. E-
mail: [email protected]
Received 27th October 2017, Accepted 27th February 2018
First published on 28th February 2018
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
4.1 ABSTRACT
The development of two-dimensional (2D) photocatalysts with excellent visible
light absorption and favourable band alignment is critical for high-efficient water
splitting. Here we systematically study the structural, electronic and optical
properties for an experimentally unexplored 2D Silicon Diphosphide (SiP2) based
on density functional theory (DFT). We find that the single-layer SiP2 is highly
feasible to be obtained experimentally by mechanical cleavage and it is dynamically
stable by analyzing its vibrational normal mode. Two dimensional SiP2 possesses
a direct bandgap of 2.25 eV, which is much smaller than more widely studied
photocatalysts including titania (3.2 eV) and graphitic carbon nitride (2.7eV), thus
displaying excellent ability for sunlight harvesting. Most interestingly, the position
of the conduction band minimum (CBM) and valence band maximum (VBM) in
2D SiP2 fits perfectly water oxidation and reduction potentials, making it a potential
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
new 2D material that is suitable as a nanoscale photocatalyst for photo-
electrochemical water splitting.
4.2 INTRODUCTION
Solar energy derived fuels are sustainable and regarded as being clean fuels.
Hydrogen production through photocatalytic water splitting that uses solar
radiation60 - also known as artificial photosynthesis - is an attractive option
as an addendum to renewable energy production which facilitates a cleaner
and greener production environment by contributing to the global energy
mix137-139. In this process140, a semiconductor having specific electronic
properties is used as a photocatalyst to absorb sunlight. This light energy
produces excitons in the catalyst, whereby after charge separation can split
water into its constituent elements viz. hydrogen and oxygen. Ideally, the
specific properties of the plausible photocatalyst semiconductor should
simultaneously have band edge positions above and below the redox
potentials of the water. Therefore, the bandgap is higher than the threshold
value of 1.23 eV but should be less than 3.00 eV. A gap larger than 3.00 eV
will induce poor light harvesting141. Moreover, if the recombination of
electron-hole pairs is also suppressed then this is a favourable situation for
photoelectrochemical (PEC) water splitting137. Due to these stringent
requirements, the number of qualified photocatalysts which can undertake the
production of both hydrogen and oxygen is limited.
Two-dimensional (2D) catalysts138, 142-146 for water splitting have drawn great
attention in recent years due to their extraordinary properties such as very
high surface to volume ratios and a small charge transport distance. This
reduces the probability of exciton recombination thereby enhancing catalytic
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
performance71. Some promising 2D materials for H2 production through
water splitting have been revealed including transition-metal dichalcogenides
such as MoS2 and WS2, phosphorene, nanocarbon and g-C3N4 41, 140, 147-154.
However, there still exists a few drawbacks such as non-stability at ambient
conditions that prevent large scale production155. Significantly, for
nanostructured materials, the reduced size promotes charge separation i.e.
exciton separation156. However, thickness-dependent bandgap variation55, 56,
59 is not a common feature for all 2D materials53, 54 and thus each material
must be thoroughly studied for its stability as well as identifying other
properties which are suitable for water splitting.
Based on the predicted semiconductor behaviour of the group IV-V
compounds80, in 1967, Tommy Wadsten synthesised and studied the crystal
structures of group IV-V2-type compounds including SiP2 with the space
group of Pbam which is orthorhombic with eight formula units per cell 81 but
did not determine its electronic and optical properties. In 1969, SiP2 was
synthesised from a molten tin solution to produce a layer-like structured
single crystal of orthorhombic SiP2 by Sprinthrope et al. which is a p-type
semiconductor with an optical energy gap of 1.89 eV157. It has also been
reported that SiP2 has both cubic (space group Pa-3 (No.205)) and
orthorhombic (Pbam) structures81, 158. In 2014, another orthorhombic type
but with space group Pnma (No. 62) was synthesised and a theoretical study
indicated that the bulk phase has an optical band gap of 1.45 eV and an
indirect bandgap of 1.24 eV158. To the best of our knowledge, very limited
theoretical studies are reported but mostly on pyrite type SiP282, 159 and no
clear experimental or theoretical study has yet been reported on 2D SiP2.
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
Our computational study is focussed on the rarely studied 2D SiP2, for
calculating the electronic band structure, phonon vibration frequencies,
optical properties, bandgap modulation behaviour with respect to the tensile
strain, exciton binding energy etc. and predicts the potential application for
photocatalytic water splitting. We found that it is feasible to extract a
monolayer of SiP2 from the bulk and the obtained single layer has a
favourable bandgap and the band positions which are perfectly suited to water
redox potentials. Thus, 2D SiP2 is identified as a competitor for acting as a
single photocatalyst for further experimental studies, to perform both
oxidation and reduction reactions for overall water splitting to produce
optimum yields of hydrogen and oxygen.
4.3 COMPUTATIONAL DETAILS
Density Functional Theory (DFT) using plane-wave Vienna Ab initio
simulation package (VASP) code is used for first-principle calculations for
this study119. The geometry optimisation is done with a generalized gradient
approximation in Perdew-Burke-Ernzerhof form (GGA-PBE) exchange-
correlation functional160. A Monkhorst−Pack k-points grid161 of 10 x 3 x 2
and 8 x 3 x 1 was used for sampling in the first Brillouin zone for bulk and
monolayer, respectively for geometry optimization. Both bulk and monolayer
systems are set for relaxing until residual force and energy were converged
to 0.005eV/ Å and 10-6eV, respectively. The electronic band structure is
predicted through hybrid density functional theory based on the Heyd-
Scuseria-Ernzerhof (HSE) exchange-correlation functional162 and Wannier90
package163 on VASP code. The stability of the photocatalytic material in the
aqueous phase is an important factor and for a 2D material, it is indicated by
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
the formation energy as ‘the difference in free energy of 2D and the lowest
value of the bulk equivalent of the same material’, Ef. The equation is given
below;
Ef= E2dn2d
- E3dn3d
----------------------- (4.1)
Where, , are the energies of monolayer and the bulk materials
respectively and are the number of atoms present in the unit cells
considered for the calculation65, 71, 164. The positive sign of formation energy
indicates energy is required for the formation, and the negative sign indicates
energy is given out during the formation of the material165. The more negative
the value of formation the more relatively stable it is166. The optical properties
are evaluated by determining the frequency-dependent dielectric tensor
matrix using density functional perturbation theory. The corrected average
electrostatic potential in the unit cell to the vacuum potential is obtained from
HSE Band calculations and then by using it as a generic reference for aligning
band positions that were obtained from HSE06-Wannier90 calculations. A
zero-damped van der Waals correction was incorporated using Grimme’s
scheme 167, 168 to better describe non-covalent bonding interactions. The
projector augmented wave (PAW) method169 was used to describe the
electron-ion interaction and the plane-wave energy cut-off was set to ~ 255
eV. To study 2D monolayer systems under the periodic boundary condition,
a vacuum layer of at least 15 Å was introduced to minimize the spurious
interaction between neighbouring layers. The phonon spectrum was
computed using the density functional perturbation theory122 as implemented
in the Quantum-ESPRESSO package170. The more often used standard
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
oxidation and reduction potentials of water splitting were employed65,
namely = −5.67 eV and = −4.44 eV, as reference for
comparing the predicted band edge positions of the 2D-SiP2. The excitonic
properties are studied using Green’s function, G0W0-Bethe-Salpeter
equation (BSE) approach171-174. The exciton binding energy is calculated as
the difference between quasi particle (QP) band gap (from GW band
structure) and the optical band gap (from BSE light absorbance spectrum) 175,
176. A Monkhorst−Pack k-points grid161 of 13 x 5 x 1 was used for sampling
in the first Brillouin zone.
Figure 4.1 (a) Side view of the SiP2 bulk (2 × 2 supercells). (b) top view of the SiP2 monolayer. The pink and green balls represent Si and P atoms, respectively.
4.4 RESULTS AND DISCUSSIONS
Silicon diphosphide has been fabricated and its crystal structure is assigned
to be an orthorhombic structure with the space group Pbam (no.55) with eight
symmetry operators81. Fig. 4.1(a) shows that the bulk configuration consists
of two layers and that the monolayer interacts with neighbouring layers
through weak van der Waals forces. The SiP2 monolayer (Fig. 4.1(b)) is
composed of “atomic layers” which are connected by P-P covalent bonds.
Detailed structural parameters for bulk and monolayer SiP2 are listed in
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
Table 4.1. The calculated lattice constants for the bulk SiP2 are a=3.443 Å,
b=9.890 Å, c= 14.419 Å, which are in good agreement with previous
experimental values81. The lattice constants of monolayer SiP2 are a=3.440
Å, b=10.000 Å.
Figure 4.2: Phonon band structure of SiP2 monolayer along the high-symmetric points in the Brillouin zone.
Table 4.1: Calculated structural parameters of SiP2 bulk and monolayer along with the
corresponding experimental values
Bulk (Cal.) Bulk (Exp.) Monolayer (Cal.)
a(Å) 3.443 3.51# (3.436)* 3.440
b(Å) 9.890 10.08# (10.08)* 10.000
c(Å) 14.419 13.97# (13.97)* -
* 81 # 177
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
Figure 4.3: Band structure for SiP2 calculated by HSE-Wannier function method (a) Bulk, and (b) a monolayer. The Fermi level is set as zero
The thermodynamic stability identified through the energy of formation
(equation (1)) determines the strength of van der Waals interactions in the
bulk SiP2. The lower the formation energy the easier it can be extracted from
the bulk material. It is reported that less than 200 meV/atom of formation
energies are considered to be a low enough formation energy that the free-
standing 2D layer can be extracted from the bulk counterpart164. In our
calculations the Ef for SiP2 monolayers is found to be 54 meV/atom thus in
principle it is easy to extract single layers from the bulk form. The dynamic
stability of SiP2 monolayer is evaluated by calculating the phonon band
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
spectrum. As shown in Figure 4.2, negligible or no imaginary frequency can
be found at any wave vector, confirming that the single-layer SiP2 is
dynamically stable.
Now, we turn to investigate the electronic properties of SiP2. The band
structures by HSE-Wannier90 calculations demonstrate that SiP2 bulk
(Figure 4.3(a)) is a semiconductor with a direct bandgap of 1.89 eV. The
VBM and CBM are located along the Γ-Z line. The result is consistent with
previous experimental work which reported a similar bandgap determined by
optical transmission measurements157.
When the thickness of SiP2 is decreased, the quantum confinement effect
becomes increasingly significant and the bandgap of the system should rise59.
Thus, when the thickness decreases to one layer, we find that the 2D SiP2
shows an increase in bandgap to 2.25 eV, in which both the VBM and CBM
locate along the Y-Γ line (Figure 4.3(b)). The bandgap and electronic band
structure strongly affect a photocatalyst’s activity and water splitting
performance. As mentioned previously, to realise an efficient light harvesting
photocatalyst for water splitting, the bandgap should be between 1.23 eV and
3.00 eV. Therefore, with a bandgap value of 2.25 eV, single-layer SiP2
perfectly meets this criterion.
The electrostatic vacuum potential of 3.49 eV (Supporting information
Figure 4.S1) obtained from the Distance from Z-direction Vs Energy plot
derived from HSE06 calculations is used to align the band edge positions of
HSE-Wannier calculations. The CBM and VBM thus obtained are located
at -3.76 eV and -6.01 eV respectively.
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
Figure 4.4: Band positions of monolayer SiP2 compared to redox potentials of water. The green dashed line indicates the CBM after band alignment considering optical level with GW/BSE after exciton separation overcoming the e-h binding energy
To further identify the suitability of SiP2 monolayer for efficient
photocatalytic activity, we align the band edge positions of the VBM and
CBM with respect to the already mentioned redox potentials of water w.r.t
absolute vacuum. We can see from Figure 4.4 that the band edge positions
of SiP2 perfectly encompass the redox potentials of water, suggesting great
applicability for photocatalytic water splitting. The energy difference
between the hydrogen reduction potential and the CBM is known as the
reducing power which is found to be 0.68 eV for a SiP2 monolayer. The
oxidizing power is the energy difference between the VBM and water
oxidation potential and is found to be 0.34 eV. The values of reducing and
oxidizing power are therefore large enough to trigger high performance for
photocatalytic water splitting178.
The ability to harvest solar light is also required for photocatalytic water
splitting. Therefore, the light absorption spectrum is derived by using the
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
frequency-dependent dielectric matrix obtained from density functional
perturbation (DFPT). The spectrum in the visible light region (approx.350 -
800 nm) is plotted and compared to the incident AM1.5G solar spectrum as
illustrated in Figure 4.5. It can be found that the absorption onset of single
layer SiP2 is at about 570 nm and that the layer has excellent light absorption
performance in the short wavelength region (350 - 550 nm).
Figure 4.5: Calculated light absorption spectrum of SiP2 monolayer (blue line) using HSE06 functional superimposed to the incident AM1.5G solar flux
The external strain on semiconductor nanostructures impact electronic
properties and thereby optical properties 179, 180. This external strain can be
imparted in many ways at a laboratory scale such as adlayer-substrate lattice
mismatch, external load, bending or by applying stress on the material 181-184.
We studied the PBE functional band gap variation w.r.t tensile strain
(Supporting information Figure 4.S2) where the bandgap variation is
dependent on the direction of the lattice. The expansion or compressive strain
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
in the direction a can transform the semiconductor to metal. However, at
higher percentages of strain (extrapolation not has shown), the same variation
in strain causes a continuous increase in bandgap in the direction b, from
compressive strain to expansion strain. This indicates that bandgap variation
is possible and allows the semiconductor to be tuned to the desired electronic
application. However, this bandgap variation is only indicative as it is studied
using a PBE functional which is known to underestimate the results of the
predicted bandgap, but for the purposes of testing dependence of strain on
bandgap variation, these calculations can give indicative results.
The excitons (the electron-hole pairs, also treated as quasiparticles, QP) that
generate during photoexcitation have binding energy due to mutual
electrostatic force which is one of the key factors to be considered for
designing a catalytic activity system which can be found as the difference
between QP direct bandgap and the optical band gaps. We thus found QP
bandgap from BSE Band structure for SiP2 monolayer as 2.63 eV (Figure 4.6
(a)) and the optical band gap as 2.02 eV, from the first absorption peak of
absorption spectra (Figure 4.6 (b)) calculated from Greens function (GW
method)185, 186. Thus, the exciton binding energy is 0.61 eV185, 187, 188. (The
absorbance spectrum with GW+RPA method is given in Supporting
Information at Figure 4.S3). In water-splitting, the exciton first diffuses to
the photocatalyst /water interface and then dissociates into an unbound
electron and hole 164. It is important to have an exciton binding energy that
keeps the e-h pair intact without dissociation during the drift from its
originating point till it reaches the catalyst/water interface. This would avoid
recombination of the exciton e-h, else the electrons tend to recombine with
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
the holes in the conduction bands. The CBM band edge position would,
therefore, be shifted when the electron-hole binding energy is introduced and
the revised CBM is marked in Figure 4.4. It is evident from the figure that
even after considering the effect of e-h binding energy on the shifting of
CBM, the new CBM position still facilitates the desired Hydrogen evaluation.
Figure 4.6: (a) GW band structure with indirect band gap of 2.63 eV, and (b) BSE-Optical Absorption spectrum with optical band-gap of 2.02 eV
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
4.5 CONCLUSIONS
In conclusion, we have presented 2D SiP2 as a promising nano-photocatalyst
for water splitting. By using a mechanical cleavage strategy, we find that this
sheet is highly feasible for experimental realisation. Moreover, the calculated
phonon spectrum reveals its high dynamical stability. Additionally, the band
alignment of SiP2 can perfectly encompass the redox potentials of water,
indicating its great potential for photocatalytic water splitting. Most
importantly, our results highlight a new two-dimensional (2D) photocatalyst
for water splitting and it is expected to guide future experiments to produce
H2 with high efficiency based on this material.
Conflicts of interest. There are no conflicts to declare.
Acknowledgements
A.D acknowledges the financial support by Australian Research Council under
Discovery Project (DP170103598) and computer resources provided by high-
performance computer time from computing facility at the Queensland University
of Technology, NCI National Facility, and The Pawsey Supercomputing Centre
through the National Computational Merit Allocation Scheme supported by the
Australian Government and the Government of Western Australia.
Footnote † Electronic supplementary information (ESI) available: Electrostatic potential of SiP2 monolayer and band gap variation with respect to tensile strain figures. See DOI: 10.1039/c7nr07994j
This journal is © The Royal Society of Chemistry 2018
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
Electronic Supplementary Material (ESI) for Nanoscale.
This journal is © The Royal Society of Chemistry 2018
4.6 SUPPORTING INFORMATION
Versatile Two-dimensional Silicon Diphosphide (SiP2) for
Photocatalytic Water Splitting
Sri Kasi Mattaa, Chunmei Zhanga, Yalong Jiaoa, Anthony O'Mullanea and Aijun Dua,*
a School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Gardens Point Campus, QLD 4001, Brisbane, Australia.
Corresponding Author
Computational details for BSE calculation
For the optical property calculations, NBANDS=160 is used, and the plane-
wave energy cut-off was set to 100eV. And the numbers of occupied and
virtual bands for electron-hole treatment were set to 8 each. The electrostatic
vacuum potential obtained from HSE06 functional is given below. The value
of 3.49 eV is used to shift the CBM and VBM values w.r.t vacuum and to
compare with water redox potentials.
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
Figure 4.S1: Electrostatic Vacuum potential for SiP2 monolayer
We studied the PBE functional band gap variation w.r.t tensile strain, the
bandgap variation is dependent on the direction of the lattice. The external
strain on semiconductor nanostructures would impact electronic properties
and thereby optical properties 179, 180.
Figure 4.S2: Band gap as a function of biaxial strain calculated with the PBE functional for SiP2 monolayer
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
For the calculated absorbance spectrum, it can be seen clearly that the SiP2 starts
absorbing light at about 2.5 eV using GW+RPA method.
Figure 4.S3: GW+RPA optical absorbance spectrum for 2D SiP2.
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Chapter-4: Two-dimensional silicon diphosphide (SiP2) as photocatalyst
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Chapter-5: Two-dimensional SiAs2 and GeAs2 as photovoltaics
Chapter-5: Two-dimensional SiAs2 and
GeAs2 as photovoltaics
Beilstein J Nanotechnol. 2018; 9: 1247–1253.
Published online 2018 Apr 19. DOI: 10.3762/bjnano.9.116 PMCID: PMC5942365 PMID: 29765802
5.0 Computational exploration of two-dimensional silicon
diarsenide and germanium arsenide for photovoltaic
applications
Sri Kasi Matta,1 Chunmei Zhang,1 Yalong Jiao,1 Anthony O'Mullane,1 and Aijun Du*,1
1School of Chemistry, Physics and Mechanical Engineering, Queensland University of
Technology, Gardens Point Campus, QLD 4001, Brisbane, Australia.
* E-mail: [email protected]
Nunzio Motta, Associate Editor
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Chapter-5: Two-dimensional SiAs2 and GeAs2 as photovoltaics
SiAs2 and GeAs2 for Photovoltaic solar cell Applications
Computational exploration of two-dimensional
silicon diarsenide and germanium arsenide for
photovoltaic applications
Sri Kasi Matta, Chunmei Zhang, Yalong Jiao, Anthony O'Mullane and Aijun Du*
Full Research Paper Address: School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology,
Open
Beilstein J. Nanotechnol. 2018, 9, 1247–1253.
Email: Aijun Du* -
Received: 27 November 2017 Accepted: 29 March 2018 Published: 19 April 2018
* Corresponding author © 2018 Matta et al.; licensee Beilstein-Institut.
Keywords: License and terms: see end of document
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Chapter-5: Two-dimensional SiAs2 and GeAs2 as photovoltaics
5.1. ABSTRACT
The properties of bulk compounds required to be suitable for photovoltaic
applications, such as excellent visible light absorption, favourable
exciton formation, and charge separation are equally essential for two-
dimensional (2D) materials. Here, we systematically study 2D group IV–
V compounds such as SiAs2 and GeAs2 for their structural, electronic and
optical properties using density functional theory (DFT), hybrid
functional and Bethe–Salpeter equation (BSE) approaches. We find that
the exfoliation of single-layer SiAs2 and GeAs2 is highly feasible and in
principle could be carried out experimentally by mechanical cleavage due
to the dynamic stability of the compounds, which is inferred by analyzing
their vibrational normal mode. SiAs2 and GeAs2 monolayers possess a
bandgap of 1.91 and 1.64 eV, respectively, which is excellent for
sunlight harvesting, while the exciton binding energy is found to be 0.25
and 0.14 eV, respectively. Furthermore, band-gap tuning is also possible
by application of tensile strain. Our results highlight a new family of 2D
materials with great potential for solar cell applications.
5.2.INTRODUCTION
The potential applications of two-dimensional (2D) materials are one of
the key research areas for many researchers since graphene was isolated
and characterized in 200427. The number of applications is vast including
photovoltaics, nanoelectronics, Dirac materials and solar fuels through
water splitting, to name but a few. Although single elemental 2D
materials from groups IV and V, such as like phosphorene and stanine,
have been studied in detail 189, 190 we focus our study on the less well-
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known combination of IV–V compound semiconductor materials at the
two-dimensional scale for their possible electronic applications. The less
extensively studied compounds SiAs2 and GeAs2 are considered here for
a computational study. The synthesis of these compounds 191, 192 was
reported a few decades ago as well as their basic crystal structures and
corresponding phase diagrams193, 194.
In 1963, Hulliger et al.195 predicted that the group IV–V compounds
SiAs, GeAs and GeAs2 would show semiconductor behaviour. The
synthesis and crystal structures of the group IV–V2- type compounds
SiP2, SiAs2 and GeAs2 were reported later. All three compounds exhibit
the orthorhombic space group Pbam with eight formula units per
cell191. However, they did not report the band structure or the bandgap
values of these materials. Later, Wu et al. performed theoretical studies
on silicon and germanium arsenides196 to predict and reaffirm that m-
SiAs/ GeAs and o-SiAs2/GeAs2 are indeed semiconductors. The
studies were based on band-structure calculations and agree with
experimental observations.
A recently reported computational study on 2D GeAs2 was performed to
investigate its thermal conductivity and its suitability for thermoelectric
applications 197. In order to further study GeAs2 and to compare it with a
similar material from the same IV–V group combination, we focus our
study on two-dimensional SiAs2 and GeAs2 and compare them with
their bulk counterparts with regard to electronic band structure, phonon-
vibration frequencies, optical properties, bandgap modulation behaviour
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Chapter-5: Two-dimensional SiAs2 and GeAs2 as photovoltaics
and predict their potential applications.
5.3.COMPUTATIONAL DETAILS
Density functional theory (DFT) using plane-wave Vienna ab initio
simulation package (VASP) code is used for first-principle calculations
for this study 136, 198. The geometry optimisation is done with generalized
gradient approximation in the Perdew–Burke–Ernzerhof form (GGA-
PBE) exchange-correlation functional 160. A Monkhorst–Pack k-points
grid 161 of 9 × 3 × 2 and 9 × 3 × 1 was used for sampling the first Brillouin
zone for bulk and monolayer for geometry optimizations. Both bulk and
monolayer systems are set for relaxing until residual force and energy
converged to 0.005 eV/Å and 10−7eV, respectively. To study 2D
monolayer systems under periodic boundary conditions, a vacuum layer
of about 15 Å was introduced to minimize the spurious interaction
between neigh- boring layers. The electronic band structure is
predicted through hybrid density functional theory based on the
Heyd–Scuseria–Ernzerhof (HSE) exchange–correlation functional 162, 199
and Wannier90 package200 implemented in the VASP code. The
thermodynamic stability of the material is assessed by the formation
energy for the 2D material and is indicated as “the difference in free energy
of the 2D material and the lowest value of the bulk equivalent of the same
material”, Ef:
(5.1)
where, E2D and E3D are the energies of the monolayer and the bulk
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material, respectively. n2D and n3D are the numbers of atoms present
in the unit cells considered for the calculations 71, 201, 202. The optical
properties are evaluated by determining the frequency-dependent
dielectric tensor matrix through hybrid DFT based on the Heyd–
Scuseria–Ernzerhof (HSE) exchange-correlation functional162, 199,
implemented in VASP 171, 203, 204. The corrected average electrostatic
potential in the unit cell with the vacuum potential is obtained from HSE
band calculations. It was subsequently used as a generic reference for
aligning the band positions that were obtained from HSE06-Wannier
calculations. A zero-damped van der Waals correction was
incorporated using the DFT-D3 method of Grimme’s scheme 167, 168 to
better describe non-covalent bonding interactions. The projector-
augmented-wave (PAW) method169 was used to describe the electron-ion
interaction. Also, the plane-wave energy cut-off was set to ca. 255 eV
and, in addition, a high precision option (PREC = high) is used in the input
file, which would further set cut-off energy and other defaults such as
grid spacing representing the augmentation charges, charge densities
and potentials (NGFX, NGFY, NGFZ) so as to get accurate results. The
phonon spectrum was computed using the density functional
perturbation theory (DFPT) 205 as implemented in the Quantum-
ESPRESSO package 170. The excitonic properties are studied using
Green’s function, GW-Bethe–Salpeter equation (BSE) approach
implemented in VASP code 171-174. The GW calculations were
performed with a 13 × 5 × 1 k-grid, the energy cut-off for response
function is set at 100 both in GW and BSE approach for exact
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Chapter-5: Two-dimensional SiAs2 and GeAs2 as photovoltaics
compatibility. Over and above the GW results, the BSE method was
adopted to obtain the light absorption spectrum 203, 204 and the optical
bandgap. BSE was solved by using the ten highest valance bands and
ten lowest conduction bands and with a 13 × 5 × 1 k-grid. Using the
band gaps obtained from GW and BSE functional methods the exciton
binding energy was obtained 206.
5.4.RESULTS AND DISCUSSION
The crystal structures of SiAs2 and GeAs2 are orthorhombic with the
space group Pbam (no. 55) having eight symmetry operators or atoms
in the unit cell 191. Figure 5.1 shows the side views of the bulk
configurations of SiAs2 and GeAs2 with atomic layers interacting with
neighbouring layers through weak van der Waals forces. Detailed
structural parameters for bulk and monolayers of SiAs2 and GeAs2 are
listed in Table 5.1. The calculated lattice constants for the bulk
materials are in good agreement with previous experimental values 191.
The calculated lattice constants for single-layered SiAs2 and GeAs2 are
slightly smaller than those calculated for the bulk phases. The lattice
constant c is kept constant and greater than 15 Å by adding a vacuum
layer.
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Figure 5.1: Crystal structure side view of the (a) SiAs2 bulk (3x2 super cells) (b) GeAs2 Bulk. Silicon (Red), Germanium (Blue) and Arsenic (Green)
The dynamical stability of SiAs2 and GeAs2 monolayers is evaluated by
analysing the phonon band spectrum. As shown in Figure 5.2a and Figure 5.2b,
no imaginary frequency can be found at any wave vector, confirming that the
single-layer SiAs2 and GeAs2 are dynamically stable. The thermodynamic
stability identified through the energy of formation, Ef, calculated from Equation
1 determines the strength of van der Waals interactions in the bulk materials of
SiAs2 and GeAs2. Thus, the lower the formation energy the easier it can be extracted
from the bulk material. It has been reported that less than 200 meV/atom is
considered to be sufficiently low formation energy that the free-standing 2D
layer can be extracted from the bulk material202. In our calculations, Ef for SiAs2
and GeAs2 is found to be 66.8 and 76.0 meV/atom, respectively. These values are
smaller than the Ef values of already exfoliated 2D materials. The values are
compared with the Ef values reported for chalcogenides of Sn and Pb 202, 207 and
are depicted in Figure 5.2c. According to this evaluation, the exfoliation of
monolayer for these materials from their bulk forms is highly feasible.
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The band structures determined by HSE-Wannier calculations demonstrate that
bulk, bilayer and monolayer structures of SiAs2 and GeAs2 (Figure 5.3a–d) are
semiconductors with indirect band gaps (the VBM and CBM locations are
marked). The bandgaps are given in Table 5.2. These results are consistent with
previously reported calculated values for both bulk and mono-layers of GeAs2 with
values of 0.99 and 1.64 eV, respectively 197. The decrease in the thickness of both
SiAs2 and GeAs2 leads to a quantum confinement effect 208 and thus the band
gap is increased significantly from the bulk to the monolayer structures in both
materials. In addition, the experimentally reported indirect bandgap of 1.06 eV
by Rau et al. for single crystal orthorhombic GeAs2 is in agreement with our
calculated result for the bulk material 192.
Figure 5.2: Phonon band structure of a monolayer of (a) SiAs2, and (b) GeAs2 along the high-symmetric points in the 1st Brillouin zone. (c) Energy of formation of the 2D material from its bulk counterparts. The green bar indicates experimentally synthesised, Red bar indicates experimentally not synthesised and the Blue bar indicates theoretically proven for the possibility of synthesis.
The ability of a GeAs2 monolayer to harvest solar light in the visible region is
higher, both in absorption intensity and in the range of wavelengths covered than
that of SiAs2. This is shown in Figure 5.4, which shows the light absorption
spectrum calculated from HSE functional in the visible light region (approx.
350–800 nm) compared with the AM1.5G solar spectrum. However, both
materials exhibit an almost equal absorption in the wavelength region of 350–
600 nm. Above this, GeAs2 still has good absorption up to around 700 nm.
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Table 5.1: Calculated structural parameters of SiAs2 and GeAs2 compared with the
experimental values
SiAs2 GeAs2
bulk (calc.)
bulk (exp.)
monolayer (calc.)
bulk (calc.)
bulk (exp.)
Monolayer (calc.
a (Å) 3.691 3.636 191 3.676 3.795 3.728 209 (3.721 210)
3.760
b (Å) 10.124 10.37 191 10.258 10.362 10.16 209, 210 (10.12 210 )
10.397
c (Å) 14.857 14.53 191 — 14.666 14.76 209, 210 (14.74 210)
--
Figure 5.3: Band structure for SiAs2 and GeAs2 calculated by the HSE-Wannier function method. The Fermi level is set as zero. (a), (b) and (c) Bulk, Bilayer and Monolayer of SiAs2 respectively; (d), (e) and (f) Bulk, Bilayer and Monolayer of GeAs2 respectively
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Table 5.2: Calculated band gaps of SiAs2 and GeAs2 – for bulk, bilayers, and monolayers.
SiAs2 GeAs2
Bulk Bilayer Monolayer Bulk Bilayer Monolayer
Bandgap
(eV) 1.34 1.86 1.91 0.99 1.34 1.64
Figure 5.4: Calculated light absorption spectrum of monolayers of SiAs2 (green) and GeAs2 (blue) using HSE functional superimposed to the incident AM1.5G solar flux.
It has been reported that exterior strain on semiconductor nanostructures,
especially at the two-dimensional level, influences the electronic properties and
the corresponding optical properties179, 180. We, therefore, studied the PBE
functional band gap variation as a function of tensile strain (Figure 5.S1). The
bandgap variation depends on the viewing direction along the lattice. In the
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laboratory, an external strain can be imparted by different means such as adlayer–
substrate lattice mismatch, external loading, bending or by applying stress on the
material 181, 182, 184, 211. While the expansion or compressive strain in the direction
of a can transform the semiconductor into a metal 201. Higher strains (deduced by
extrapolation, not shown in the figure) and compression can cause a continuous
increase in the bandgap from compressive strain to expansion strain in both SiAs2
and GeAs2. This indicates that there is the possibility of bandgap tuning to make
Figure 5.5: (a) and (c) GW-Band structures, (b) and (d) BSE-Optical Absorption spectra of SiAs2 and GeAs2 respectively
the semiconductor suitable for a desired electronic application. However, this
bandgap variation was calculated using a PBE functional that is known to
underestimate the value of the bandgap. However, for the purpose of illustrating
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the dependence of the bandgap variation on the strain, these calculations can be
helpful.
The quasi-particle band gaps of SiAs2 and GeAs2 monolayer compounds were
found to be 2.26 and 1.86 eV, respectively (Figure 5.5). These values are
comparable with the band gaps obtained by using the HSE-Wannier method (1.91
and 1.64 eV for SiAs2 and GeAs2, respectively) with similar and negligible variation
amongst the two methods. The corresponding first absorption peaks in the
absorption spectra are the optical band gaps at 2.01 and 1.72 eV, respectively.
Thus, the calculated exciton binding energies212-214 are 0.25 and 0.14 eV for
SiAs2 and GeAs2, respectively. Semiconductors with exciton energies in this
range of a few hundred milli-electron volts are supposed to play a key role in
photovoltaic applications 215.
5.5.CONCLUSION
We have presented 2D monolayer compounds of SiAs2 and GeAs2 as promising
light harvesting semiconductor materials for solar cell applications. The
extraction of a monolayer of these materials is likely to be feasible by mechanical
exfoliation. Moreover, the calculated phonon spectrum reveals its high dynamical
stability for both materials. Additionally, the exciton binding energies are quite low
and are comparable to quantum dot semiconductors. It might be possible that these
semiconductors could be synthesized as quantum dots and studied in further detail.
Bandgap tuning appears also possible and could be used to tailor the compounds
for various electronic applications.
Acknowledgements
We acknowledge generous grants of high-performance computer time from
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computing facility at the Queensland University of Technology, The Pawsey
Supercomputing Centre and Australian National Facility. A.D. greatly
appreciates the financial support of the Australian Research Council under
Discovery Project (DP130102420 and DP170103598).
ORCID® iDs
Sri Kasi Matta - https://orcid.org/0000-0003-4465-640X
License and Terms This is an Open Access article under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The license is subject to the Beilstein Journal of Nanotechnology terms and conditions: (https://www.beilstein-journals.org/bjnano)
The definitive version of this article is the electronic one which can be found at: doi:10.3762/bjnano.9.116
Supporting Information Supporting Information shows the band gap variation as a function of tensile strain.
Supporting Information File 1 Additional computational data. [https://www.beilstein-journals.org/bjnano/content/ supplementary/2190-4286-9-116-S1.pdf]
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5.6.SUPPORTING INFORMATION
Computational exploration of two-dimensional silicon
diarsenide and germanium arsenide for photovoltaic
applications
Sri Kasi Matta1, Chunmei Zhang1, Yalong Jiao1, Anthony O'Mullane1 and Aijun Du1,*
Address: School of Chemistry, Physics and Mechanical Engineering, Queensland University of
Technology, Garden Point Campus, QLD 4001, Brisbane, Australia
* Corresponding author Email: Aijun Du - [email protected]
Additional computational data
We studied the variation of the bandgap as a function of the tensile strain by
using the PBE functional (Figure 5 . S1). The bandgap variation depends on
the viewing direction along the lattice. The external strain on semiconductor
nanostructures influences electronic properties and, thereby, optical properties 179,
180.
Figure 5.S1: Band gap as a function of biaxial strain calculated with the PBE functional for monolayers of (a) SiAs2 and (b) GeAs2.
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
Chapter-6: Carbon Dots for Hole‐
Transport in Perovskite Solar Cells
6.0 Density Functional Theory Investigation of Carbon Dots as
Hole‐transport Material in Perovskite Solar Cells
Sri Kasi Mattaa, Chunmei Zhang a, Prof. Anthony P. O'Mullane a, Prof. Aijun Dua,*
a School of Chemistry, Physics and Mechanical Engineering, Queensland University of
Technology, Gardens Point Campus, QLD 4001, Brisbane, Australia. *E-
mail: [email protected]
Version of Record online:08 October 2018
Accepted manuscript online:25 September 2018
Manuscript received:29 August 2018
https://doi.org/10.1002/cphc.201800822
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
6.1.ABSTRACT
Charge transfer in solar cells is crucial, and so is the hole transporting layer (HTL)
component in perovskite solar cells (PSCs). Finding a suitable material for this
purpose that is inexpensive – either organic or inorganic – is currently one of the
prime research objectives to improve the performance, through charge transfer
dynamics, of PSCs. One such recent finding is carbon quantum dots (C‐dots), which
is a simple and low‐cost organic material that could be an alternative option to the
currently employed high ‐cost and complex ‐structured hole-transporting materials
(HTMs) utilized in perovskite solar cells. A series of C‐dots functionalized with
hydrogen, hydroxyl (−OH), and carboxyl (−COOH) groups are considered in this
study for their hole‐transporting properties. The results reveal that simple
hexagonal structured C‐dots including −OH and −COOH group substituted C‐dots
have suitable valance band maximum (VBM) positions, which are suitable for hole
transport. It is discovered that the position of the functional moieties on the C‐dots
would impact the band-edge positions of the C-dots. This implies that tuning the
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band position is possible so that these two‐dimensional C‐dots could, in principle,
be used for other solar-cell applications that may require different band positions
for optimal performance. As a representative example, we studied the perovskite/C‐
Dot interface of two different possible surfaces (i. e. MAI and PbI2 terminated
perovskites) combined with a hexagonal C‐Dot layer and found that there is a good
probability of charge transfer between the perovskite layer and the C‐dots, which
promotes hole transfer between the perovskite and the C‐dots.
6.2. INTRODUCTION
Conventional photovoltaic solid‐state solar cells (e. g. crystalline silicon solar cells)
work on the simple principle of charge generation through the use of light energy,
upon which there is charge transport through the material components of the cell
which are collected at counter electrodes without any chemical reaction occurring
in the process216. The solar cell efficiency for such conventional devices has been
stabilized which are now commercially used. Therefore, efficiency is not being
improved, but research is on for low-cost alternative materials. The emphasis now
is on developing cost‐effective production processes to reduce the net product cost.
In addition, there is also a need for finding alternatives to conventional solar cells
which has resulted in the rapid emergence of perovskite solar cells (PSCs). This
technology is unique due to the sweeping improvement in power conversion
efficiency (PCE), from 3.9 %87 when it was first introduced in 2009, to 22.7 %217
in 2017. This is significant progress when compared to other solar cell technologies.
The perovskite structure was first reported by Weber in 1978, as an organometal
halide CH3NH3MX3 (M=Pb, X=Chlorine (Cl), Bromine (Br) or Iodine(I)) with a
cubic structure. Significantly, these structures are stable at ambient temperature
which may have varying unit cell parameters of 5.68, 5.92 and 6.27 Å for chloride,
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
bromide and iodide anions respectively 218.In this study, a perovskite with iodide,
in the cubic phase considered having a lattice parameter of a=6.29 Å219.In general,
a PSC consists of a transparent conducting glass layer i. e. Fluorine Doped Tin‐
oxide (FTO) coated glass, a TiO2 layer, a perovskite layer, a hole transporting
material (HTM), and a counter electrode220, 221.,The open-circuit voltage (Voc) of
such a cell is governed by the quasi‐Fermi level difference of electrons and holes
at the contact interfaces97. Thus, the introduction of HTM layer in the interface
leads to an increase in holes and thus Voc would decrease. While many
improvements have been achieved by changing the PSC constituents, development
of superior quality HTMs is relatively little. Spiro‐OMeTAD (2,2′,7,7′‐tetrakis‐
(N,N‐di‐p‐methoxy‐phenylamine)‐9,9′‐spiro‐ bi‐fluorene) is one of the most widely
used HTMs in recently developed PSCs 221-223. Based on its special characteristics
of having a stable amorphous structure, excellent ability to form thin films and good
electrical conductivity upon doping led to its use as an HTM224, 225.,However, there
is an ongoing challenge to find alternative materials to spiro‐OMeTAD due to the
expense involved in its synthesis226 and therefore many endeavours have been
successfully made in this direction227. Examples of simple and low‐priced
alternatives for HTMs are phenylamines228,azine229, carbazole230, 231, fluorine232,
furan233, azomethine234, silolothiophene235 which have either linear or star‐shaped
structures236.
As reported previously, there is an indirect impact of structural geometry on the
charge collection efficiency (hcol) and the rate of interfacial charge
recombination223, 237-239. The existence of an alkyl chain in HTMs changes their
physical and chemical properties and therefore influences the performance of
PSCs240, 241. In addition, hole mobility, thermal and photochemical stability are
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
expected characteristics of a good HTM242, 243. The thickness of the HTM layer also
influences the series resistance and therefore needs to be optimal, or else the fill
factor will be affected. An optimum thickness should generally be within the 100–
200 nm range244. The hole transfer layer (HTL) and the electron transport layer
(ETL) play an important role in charge carrying but must be economical, highly
durable and more environmentally friendly to ensure commercial viability. 243 In
addition, the HTM in PSCs must minimize or avoid charge recombination at the
metal‐perovskite interface. An HTM's basic requirement is that its valence band
maximum (VBM) position should be at a higher energy level than the VBM of the
perovskite. If this can be achieved, then it will enhance the Voc of the PSC. Laura
Calio et al. reported that hole capture is influenced by the difference in the HTM's
Fermi level and the holes generated in the perovskite layer after illumination245. It
was recently reported that the Voc is controlled by splitting of the quasi‐Fermi levels
and charge recombination246. As mentioned Spiro‐OMeTAD has drawbacks of
being expensive, negatively impacting on device stability as well as possessing sub‐
optimal charge transport as evidenced by modest hole mobility and conductivity of
1.67×10−5 cm2/V−1 s−1 and 3.54×10−7 S/cm−1 respectively243. Therefore, dopants
are required for better performance, but their presence often reduces device
stability243, 247. It is suggested here that an HTM with a simple structure, to aid
device manufacturing at scale, while also possessing the desired properties for an
HTM is possible. Therefore, the focus was on a theoretical study of carbon quantum
dots (CQDs) and demonstrate their capacity for charge transfer between a
perovskite layer and the carbon dots. This interfacial hole transfer study is crucial
to establishing the viability of CQDs for the desired objective.
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Xu et al. discovered CQDs in 2004100 and subsequently, extensive studies have
been undertaken towards their synthesis, characterization, and applications101.
CQDs are part of a new category of carbon fluorescent nanomaterials having
relatively simple synthesis methods, good stability and conductivity, low toxicity
and thus being environmentally friendly, and having optical properties analogous
to conventional semiconductor quantum dots102.
Graphene quantum dots (GDQs i. e. lateral nanoscale dimensioned graphene
sheets) possess only carbon atoms, and the functionalized GQDs are studied earlier
for bandgap tuning and apply for suitable application103. When the carbon atoms at
the edge of these GQDs, are saturated with hydrogen atoms, are denoted as Carbon‐
quantum dots (or also called as C‐dots) which have been studied earlier103,
104.,Various photocatalysts, based on C‐dots, which have outstanding catalytic
activity have been reported104 while other studies have proved that the edges of C‐
dots have an influence on light harvesting105, 106, 248.-Recently, it has been reported
that metal‐free g‐C3N4 in combination with C‐dots, showed excellent results for
photocatalytic water splitting.249
Here, the study on C‐dots for a new application as a hole transport material in
perovskite solar cells. The exploration study on the interaction between the
perovskite material and C‐dots has divulged a finding that some structures of C‐
dots can be used as an HTM. This study also explored the effect of structural design
changes in C‐dots on the bandgap by functionalizing the surface with electron-
withdrawing oxygenated moieties such as −COOH and −OH groups giving the C‐
dots p‐type conductivity250-252. It is observed that some C‐dots have comparable
band edge positions to Spiro‐OMeTAD and could in principle be a potential
alternative to this material.
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6.3. COMPUTATIONAL METHODS
The concept of Density Functional Theory (DFT) using a plane-wave basis set
based Vienna Ab initio simulation package (VASP) code is used to do first‐
principle calculations for this study119.,Geometry optimization calculations were
done with a generalized gradient approximation in Perdew‐Burke‐Ernzerhof form
(GGA‐PBE) exchange‐correlation functional160. A Monkhorst‐Pack k‐points
grid161 of 5×5×5 was used for sampling in the first Brillouin zone for bulk
perovskite (MAPbI3) for geometry optimization. The system relaxation was done
until the residual force and energy were converged to 0.005 eV/Å and 10−6 eV,
respectively. The individual C‐dots and the C‐dot/MAPbI3 system geometries were
optimized with 1×1×1 k‐point grid, at Gamma point only, for two reasons. Firstly,
because the system considers pure C‐dot clusters, and the hybrid system is very
large having more than 400 atoms, so the computation cost would be very high, and
secondly, the only point of interest in this study is the charge transfer between the
perovskite and carbon‐dot interface, and thus the calculation at Gamma point would
give enough information about the charge transfer. The VBM and Conduction Band
Minimum (CBM) for different C‐dot clusters are estimated with respect to vacuum
potential using hybrid density functional theory based on the Heyd‐Scuseria‐
Ernzerhof (HSE) exchange‐correlation functional162 on VASP code. The
interaction energy between C‐dot and perovskite terminated with either methyl‐
ammonium‐iodide (MAI) (001) or with PbI2 (001) surfaces as top layers (i. e. with
respect to C‐dot position) was calculated by using the following equation;
(6.1)
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Where , and are the total energy of the hybrid structure, and
the individual C‐dot and perovskite (i.e. either MAI or PbI2 terminated MAPbI3
surfaces), respectively253. The characterization of electron coupling at the hybrid
component interface is obtained through charge density difference in a hybrid
system, and is calculated using the following equation;
(6.2)
Where, , and are the total charge density of hybrid structure,
individual C‐dot and perovskite (i.e. either MAI or PbI2 terminated MAPbI3
surfaces), respectively.
The hybrid structure is designed with hexagonal C‐dot and perovskite as follows.
The hexagonal Carbon‐dot structure‐1 (named as CDH‐1) cluster is placed at an
approximate distance of 1.8 Å, on top of a 1×3×3 eight‐layer geometry optimised
cubic perovskite structured MAPbI3 (a=6.29 Å) surface slab (containing Pb=36,
I=108, C=34, N=36, H=216, atoms). The C‐dot cluster is placed in such a way that
there is a considerable distance between any two C‐dot clusters, to avoid any mutual
cluster interactions, had the system been extended in x or y directions. In the x-y
direction, the perovskite super cell’s periodic boundary conditions are used (i.e. 3
x 3 supercell in x-y direction) while a vacuum space of about 20 Å in the c‐direction
is added and is large enough to avoid inter slab interactions between neighbouring
layers. It is expected that the atoms/ions on the surface layer of perovskite, above
which the C-dot is placed would de-orient to some extent and is included within the
optimization of the geometry of the hybrid system so as to minimize the energy
within the cut-off set value. However, as the aim of study is more towards
assessment of charge transfer between perovskite and C-dot, the minor orientation
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effects were not delineated in this study. Two systems were designed to place the
C‐dot on either the top of the PbI2 layer‐side or on the MAI layer‐side. In both
cases, the system is very big, and therefore only the Gamma point was used in
1stBrillouin Zone sampling. The projector augmented wave (PAW) method169 was
used to describe the electron‐ion interaction and the plane‐wave energy cut‐off is
set at 400 eV. It's prudent here to mention that the same cut‐off energy value is
maintained for hybrid C‐dot/MAI or PbI2, and the individual MAI and PbI2
structure optimization, and thus further calculating the interface energies with
equation (6.1). The supercell while subjected to system relaxation and geometry
optimization calculations with the GGA‐PBE method, the atom coordinates of the
two layers at the bottom of the perovskite were marked as fixed at the same position
as that of its bulk state position. That means the bottom two layers of atoms are not
subject to change during ionic relaxation. This is done through a ‘selective
dynamics’ setting during VASP input and a corresponding setting at each layer of
co‐ordinates254. The complete system (C‐dot/MAPbI3 structure) contained a total
of 468 atoms with 1548 valence electrons.
A zero‐damped van der Waals correction was included using Grimme's
scheme167, 168, for effectively expressing non‐covalent bonding interactions. The
spin‐orbital‐coupling (SOC) effect was not considered in our calculations for the
reason that the PBE level calculations could elucidate the electrical properties
comparable to experiments, though it was incidental i. e. the unintended
cancellation of the underestimation by the GGA–PBE method90, 91, 255.
6.4. RESULTS AND DISCUSSION
The C‐dots considered for this study are shown in Figure 6.1. The hybrid system
design used in our calculations is depicted in Figure 6.2. The C‐dots are constructed
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as such that the terminal carbon atoms are saturated with hydrogen atoms. In
addition to these C‐dots functionally modified structures were also considered, i. e.
−OH and −COOH group attached to C‐dots, to study the possibility of band edge
position tuning. The various types and sizes of C‐dots studied here are given with
a code notation outlined in Figure 6.1. Further examples of C‐dots considered in
this study are shown in Figure 6.S1. These C‐dots are considered as individual
entities and therefore are disjoint to each other and thus are regarded as being
clusters. The C‐dot clusters are structured in the unit cell such that the inter-cluster
distance (i. e. between any two C‐dots) is about 5 Å, which is large enough (more
than twice that of the crystallographic Van der Waals Radii of edge hydrogen atoms
(1.2 Å256)), to avoid any interaction between the periodical C‐dots. Geometry
optimisation or relaxation was performed for these C‐dots and the MAPbI3 unit cell
by using the conjugate gradient method (CGA) on VASP.
Figure 6.1: The structures of Hexagonal C‐dots (Hex‐1 [a] & Hex‐2[b]) and the functionalised Hexagonal C‐dots (Hex‐1 [c] & [d])) with −OH and −COOH groups. Color Code of atoms: Brown (Carbon), Blue (Hydrogen), Red (Oxygen).
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Figure 6.2: (a) The top view and the side views of (b) C‐Dot/MAI, and (c) C‐Dot / PbI2interfaces. Color Code of atoms: Brown (Carbon), Blue (Hydrogen), Green (Nitrogen), Black (Lead) and Pink (Iodine).
The study of charge transfer between C‐dots and the perovskite surface atoms
requires determining the band edge positions of each component of the hybrid
system. The band edge positions i. e. VBM and CBM of all C‐dots are calculated
with an HSE06 exchange‐correlation functional162. As the primary focus of the
study is on the assessment of new C‐Dots, the band edge positions of perovskite
(MAPbI3) are taken from literature. The summary of band positions of important
C-dots compared with the literature value257 of the band edge positions of MAPbI3
is depicted in Figure 6.3. The band edge positions for other C‐dots considered in
this study are given in the Supporting Information (Figure 6.S2). The quantum
confinement effect is clear when the bandgap of Hex‐2 (bigger sized C‐dot) is
compared with that of Hex‐1 (smaller sized C‐dot). For the current study, the VBM
positions of Hex‐1, Hex1‐OH, and Hex1‐COOH have reasonable energies for the
purpose of hole transport.
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Figure 6.3: The calculated band edge positions (i. e. VBM and CBM) of the C‐dots compared with those of MAPbI3 (literature values of VBM and CBM). Hex1=Hexagonal C‐Dot (type‐1, smaller or base size); Hex2=Hexagonal C‐Dot (type‐2, bigger in size)
The VBM of Hex 1 of −5.23 eV is comparable to poly [bis (4 phenyl) (2,4,6
trimethylphenyl) amine] (PTAA97),(2,2′,7,7′ tetrakis (N,N di p methoxyphen
ylamine) 9, 9′ spriobifluorene (Spiro OMeTAD)219 and poly[N,N′ bis (4
butylphenyl) N,N′ bisphenyl benzidine] (PTPD97). For Hex 2 the VBM of −4.92
eV is comparable to poly((4,8 bis(octyloxy) benzo(1,2 b:4,5b′) dithiophene 2,6
diyl) (2((dodecyloxy) carbonyl) thieno (3,4b) thiophenediyl) (PTB1)97 and poly(3
hexylthiophene2,5 diyl) (P3HT97).The VBM of Hex1 COOH with a value of
−5.37 eV is comparable to poly 4′,4′′(4 (2 octyldodecyl) N, N diphenylaniline)
alt 2,7 (9,9′ spirobi[fluorene]) (ASFH97). Upon further consideration of more
functionalized C dots through the same analysis, it was found that Hex 1 2COOH
2OH (Code: H1 2 C2O), would give similar band edge positions, for both VBM
and CBM to that of Spiro OMeTAD (Table 6.1). This implies that the
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functionalization of C dots would in principle impact the band positions. Further
investigation done on the effect of changing the bonding position of the functional
groups in the Hex 1 structure. This revealed an interesting feature in that the band
edge positions can be further modified. This indicates that fine tuning of the band
gap and the edge positions is possible. The band edge position diagram for the
additional C dots considered in this study along with their structures is given in the
Supporting information.
Table 6.1. Calculated CBM and VBM band edge positions few two‐dimensional Carbon‐
Dots.
C‐Dot (Code Name) [a] CBM* VBM*
H1‐2C2O −2.16 −5.24
H1‐2C2O‐1 −2.39 −5.39
H1‐2C2O‐2 −2.17 −5.29
H1‐2C2O‐3 −2.49 −5.28
H1‐2C1O −2.20 −5.37
H1‐2C1O‐1 −2.48 −5.44
* CBM and VBM of Spiro‐OMeTAD are −2.2 eV and −5.22 eV respectively
[a] H1 or Hex1=Hexagonal‐1; 2 C=2‐COOH; 2O=2‐OH; The suffix ‘1’,’2’ and ‘3’
represent different positions of functional groups. (Ref: Supporting Information for
figures)
The difference in energy between the VBM of MAPbI3 and the VBM of the above
C‐dots is in the range of 0.06 to 0.51 eV. As per a recent study on the effect of
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interfacial energies between perovskite and organic hole transfer materials, it was
found that a very small driving force, i. e. a driving potential of about 0.07 eV would
be enough to achieve efficient hole transfer, and suggested a range of 0<∆E<0.18
eV as being appropriate97. It's inferred from Transmission Absorption Spectroscopy
(TAS) and Photoluminescence (PL) studies that over and above, ∆E 0.18 eV, the
recombination of holes with electrons in perovskite would be faster than hole
transport from perovskite to HTM97. Considering this range, it is suggested that C‐
dots, Hex‐1 (∆E=0.17 eV) and Hex‐1‐COOH (∆E=0.03 eV) could be used as
potential hole transfer materials for perovskite solar cells.
The interface binding energy is calculated as per equation (1) and is found to be
−2.50 eV for C‐dot/MAI perovskite hybrid, and −3.00 eV for the C‐dot/PbI2
perovskite hybrid, which indicates stronger structural stability with the C‐dot/PbI2
hybrid. However, it was observed that the strong interface between the C‐dots and
MAI and PbI2 led to some structural changes in the different layers. It is apparent
that the interaction is greater at the topmost layers and gradually decreases while
approaching the bottom layers. No such change is observed at the bottom two layers
as the atoms’ position was fixed during optimization. The changes in the C−C and
C−H bond lengths in the optimized hybrid structure compared with that of the
pristine C‐dot reveals a subtle increase but they are insignificant (the maximum
change in bond length observed is 0.001 Å) in C−C bonds whereas no change
observed in C−H bonds.
The charge density difference between hybrid and pristine components of the
system, calculated using equation (2), are shown in the three‐dimensional (3D)
graphic in Figure 6.4. For the C‐dot/PbI2 system charge transfer from the C‐dot to
the PbI2 surface in the ground state is observed. More charge accumulation is
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observed just below the surface of the C‐dot indicating that charge gathering occurs
because of the C‐dots presence on the surface results in strong interface energy.
Moreover, charge accumulation is also observed at each of the MAI layers in C‐
dot/PbI2 system (Figure 6.4(a)) which gradually increases from the bottom to the
top layers. Interestingly, though there is a gradual change in charge accumulation
observed in the MAI layers case of the C‐dot/MAI system, this change in
accumulation is much less when compared with C‐dot/PbI2 system. This could be
attributed to the interface binding energy difference between the two systems.
Figure 6.4: The side view of the charge density difference between the two interface systems (a) C‐Dot/PbI2, and (b) C‐Dot/MAI. The Yellow and Cyan iso‐surface profiles represent electron accumulation and depletion in 3D space with an isovalue of 0.001 e/Å−3. Colour Code of atoms: Brown (Carbon), Blue (Hydrogen), Green (Nitrogen), Black (Lead) and Pink (Iodine).
6.5. CONCLUSIONS
Different structural types of C‐dots including those functionalized with −OH and
−COOH moieties have been identified as potential hole transfer materials for
perovskite solar cells. It is also observed that not only functionalizing the surface
with −OH and −COOH groups but also that their bonding position on the C‐Dot
would impact the bandgap and band edge positions. This reveals an excellent
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
method of tuning the band positions of C‐dots to the desired value. The VBM levels
for these selected C‐dots are suggested to be more favourable for the objective of
good hole transfer after considering the minimum driving force that is required for
an effective hole transferring material. Furthermore, the typical charge transfer
study based on charge density difference estimations prove that there is more
efficient charge transfer between the C‐Dot/PbI2 system interfaces compared to that
of C‐Dot/MAI system interface. C‐dots can be effective hole transfer materials that
can be synthesized easily compared to organic materials while being cost‐effective
as well as processable to fabricate thin layers which are required for solar cell
applications. In addition, this would have a future scope for experimental studies
for testing the predictions made here in this study and for their non‐toxicity, to
justify their environmentally friendly characteristics, compared with other
conventional organic HTMs.
Acknowledgements
Acknowledgements Text A.D acknowledges the financial support by Australian
Research Council under Discovery Project (DP170103598) and
computer resources provided by high‐performance computer time from computing
facility at the Queensland University of Technology, NCI National Facility, and
The Pawsey Supercomputing Centre through the National Computational Merit
Allocation Scheme supported by the Australian Government and the Government
of Western Australia.
Conflict of interest
The authors declare no conflict of interest.
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
6.6. SUPPORTING INFORMATION
© Copyright Wiley-VCH Verlag GmbH & Co. KGaA, 69451
Weinheim, 2018
Density Functional Theory Investigation of Carbon
Dots as Hole-transport Material in Perovskite Solar
Cells
Sri Kasi Matta, Chunmei Zhang, Anthony P. O’Mullane, and Aijun Du*
Figure 6.S1: The structures of various Carbon Quantum dots (C-Dots). Trigonal C-Dots (a –c), Hexagonal C-Dots with two –OH functional groups substituted (d) side by side, and (e) opposite to each other. Color Code of atoms: Brown (Carbon), Blue (Hydrogen), Red (Oxygen).
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
Figure 6.S2: The calculated band edge positions (i.e. VBM and CBM) of further C-Dots considered in this study and compared with those of MAPbI3 (literature values of VBM and CBM) [Tri-1 – Tri-3 correspond to three different Trigonal C-Dots (S1(a-c)); Hex-1-OH-SbS (side by side) and Hex-1-OH-oppo (opposite) correspond to S1(d) and S1(e) of Figure-S1
Figure 6.S3: The structures of Hexagonal (Type-1) Carbon Quantum dots (C-Dots) with different bonding locations of two Carboxyl and two hydroxyl groups. The represented Code-named C-Dots are: (a) H1-2C2O-1, (b) H1-2C2O-2, (c) H1-2C2O-3 and (d) H1-2C2O-4.
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
Figure 6.S4: The structures of Hexagonal (Type-1:H1) Carbon Quantum dots (C-Dots) with different bonding locations of two Carboxyl and One Hydroxyl groups. The represented Code-named C-Dots are: (a) H1-2C, (b) H1-2C1O-1, (c) H1-2C1O-2.
Code name notation: H1 or Hex1= Hexagonal-1; 2C = 2-COOH; 2O = 2-OH; The suffix ‘1’ and ’2’ represent different positions of functional groups
Figure 6.S5: The structures of Rectangular (Type-1 (R1) and Type-2(R2)) Carbon Quantum dots (C-Dots) with different bonding locations of One or two Carboxyl (1C or 2C), One Hydroxyl (1O) and/or One Hydroxyl & One carboxyl (1O-1C) groups. The represented Code-named C-Dots are: (a) R1-1C, (b) R1-1O, (c) R1-2C, (d) R1- 2O, (e) R2-1C, (f) R2-1O, (g) R2-2C and (h) R2-1C1O.
Code Name notation: R1 & R2 = Rectangular (1 (small or base size) & 2 (Bigger size)); 1C = 1-COOH; 1O = 1-OH; 2C = 2-COOH; 2O = 2-OH
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Chapter-6: Carbon Dots for Hole‐Transport in Perovskite Solar Cells
Table 6.S1: Calculated CBM and VBM band edge positions few two-dimensional
Carbon-Dots
C-Dot (Code)
CBM* VBM*
H1-2C2O -2.16 -5.24
H1-2C2O-1 -2.39 -5.39
H1-2C2O-2 -2.17 -5.29
H1-2C2O-3 -2.49 -5.28
H1-2C -2.22 -5.59
H1-2C1O-1 -2.20 -5.37
H1-2C1O-2 -2.48 -5.44
R1-1C -3.05 -4.38
R1-1O -3.23 -3.83
R1-2C -3.18 -4.53
R1-2O -2.88 -4.23
R2-1C -3.33 -3.95
R2-1O -3.22 -3.83
R2-2C -3.44 -4.07
R2-1C1O -3.34 -3.95
* CBM and VBM of Spiro-OMeTAD are -2.2 and -5.22 respectively. Code name notation given in Figure captions, above.
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Chapter-7: Inorganic 2D materials for charge transport in Perovskite Solar Cells
Chapter-7: Inorganic 2D materials for
charge transport in Perovskite Solar Cells
7.0 Band alignment investigation of multi-layered Lead Iodide,
Lead monoxide and Tin monoxide: Inorganic Hole-transporting
materials for Perovskite Solar Cells
Sri Kasi Mattaa, Chunmei Zhang a , Prof. Anthony P. O'Mullane a, Prof. Aijun Du a ,*
a School of Chemistry, Physics and Mechanical Engineering, Queensland University of
Technology, Gardens Point Campus, QLD 4001, Brisbane, Australia. *E-
mail: [email protected]
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Chapter-7: Inorganic 2D materials for charge transport in Perovskite Solar Cells
7.1.ABSTRACT
Exploring innovative two-dimensional (2D) materials for hole transporting layers
(HTL) in Perovskite Solar Cells (PSCs) is emphasized in this study with Density
Functional Theory (DFT) analysis as a study tool. Simple and layered crystal
structures of inorganic, post-transition metal halides and oxides (lead iodide (PbI2),
lead monoxide (PbO), tin-oxide (SnO)) are considered. The band edge alignment
of the materials with respect to the perovskite (MAPbI3) layer, is studied to check
their suitability for HTL. Conventional DFT with more accurate hybrid functionals
(HSE06) is used in this computational study, including variation in band edges and
bandgaps with an increase of 2D layers for PbI2, PbO and SnO. We found that a
single-layered PbO and bi-layered SnO are potential candidates for a hole transport
material. Further representative studies on the charge density difference at
perovskite-HTL material interfaces were conducted for PbO with both Methyl
Ammonium-Iodide (MAI) and Lead Iodide (PbI2) surface terminated perovskite
(MAPbI3), with 3D visualisation techniques to establish hole transport.
7.2.INTRODUCTION
Since being introduced by Akihiro Kojima et al. in2009 with an efficiency
of 3.8%87, 216, perovskite solar cells’ (PSCs) power conversion efficiency
(PCE) had shown an almost six-fold improvement within a span of eight
years, to around 22%87, 258-264. This shows the promise and potential
feasibility of improving the efficiency further by tuning and optimizing the
parameters involved in their operation. Out of the various parameters that
influence efficiency, electron and hole transfer from the perovskite layer to
the ETL and HTL materials plays a key role in PSC architecture. The PSCs
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architecture comprises of FTO glass, TiO2 film, perovskite film with the hole
transporting material (HTM) and electron transporting material (ETM) on
either side of it and a counter electrode after the HTM219-221. For the most
efficient operation, the VBM position of the HTM should be above the
valance band energy of the perovskite. Similarly, the CBM position of the
ETM shall ideally be at lower energy than the conduction band of the
perovskite223. Many organic and inorganic ETMs and HTMs were identified
and tested since its inception. However, there are still issues with cost-
effectiveness and development of simple synthesis methods to produce
effective ETM and HTM at scale. It is well established that the open-circuit
voltage (Voc) is the difference between the quasi-Fermi level of the electrons
in the TiO2 layer and valance band position of the HTM265, 266. Increasing this
difference would thus achieve a higher Voc and is a subject of intense
research226. Recently an inorganic CsMBr3 (M=Sn, Bi, Cu) material used as
an HTL resulted in a Voc value of up to 1.61 V92. The driving energy for hole
capture is the difference between the Fermi level of the hole transporter and
that of the holes in the perovskite under illumination245. It has recently been
reported that the Voc is also controlled by splitting of the quasi-Fermi levels
and recombination246. The organic HTM that currently shows the highest
performance in PSCs is the Spiro-OMeTAD which has drawbacks of being
expensive, process-intensive and with the need for dopants267 to get better
performance, however with the disadvantage that they reduce stability. It is
suggested here that an HTM should have as simple a structure as possible to
manufacture, but at the same time possessing the desired VBM band position
to promote hole transport and have longer stability.
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In this study, we focused our attention on inorganic two-dimensional (2D)
materials viz. Lead iodide (PbI2), Lead Monoxide (PbO) and Tin-monoxide
(SnO), to study their band structure, band edge positions using ab initio
calculations and compared with that of a perovskite MAPbI3 to select their
potential suitability as HTMs.
Lead Iodide (PbI2), as reported, is a layered material with semiconducting
properties that has many applications in the optics field 108-110. Theoretical
investigation proves the bandgap changes from direct to indirect when the
bulk form is modified to a single-layered two-dimensional material. The
single crystalline quasi monolayers and few layers have been synthesized and
utilized in photodetectors110. The most stable form of PbI2 crystals, at room
temperature, is of the 2H form polytype 268-270. Single layered PbI2 nanotube
synthesis 108 and a theoretical study on PbI2 nanosheets have been reported.
The PbI2 structure of the 2H form is considered for this study with the space
group P3m1268 and is optimized. The lattice constants of the optimized
structure are a=b=4.67 Å. The vacuum slab to avoid the interaction between
layers is set to 30 Å. The PBE band gap has already been reported as 2.51
eV271. The HSE06 hybrid functional resulted in predicting an indirect
bandgap at 3.32 eV, confirming the reported feature271 which is very close to
the published results110. The VBM and CBM are estimated with HSE06 band
structure and are corrected with vacuum potential as depicted in Figure 7.S2
and Table 7.S1.
Two-dimensional Lead Monoxide (PbO) is another inorganic
semiconducting material who’s mechanical, and exfoliation feasibility and
optical properties were investigated and reported35, 111-113. Favourable
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attributes for charge transfer or charge accumulation, high resistivity and
low-cost availability could make PbO a potential candidate for an HTM. In
addition, PbO is hydrophobic which could further help in the long-term
stability of the HTM and thereby the overall perovskite solar cell 113. In this
study, the P4/nmm space group structure of PbO is considered with lattice
parameters a≠c, a=4.02 Å and c= 5.02 Å. The PbO monolayer exhibits n-type
conduction, as reported, the reason being the holes are stagnant and the
conduction happens due to electrons113. Successful exfoliation of α-PbO is
feasible as reported113 due to a very low interlayer interaction energy ~0.016
eV113. α-PbO (ICSD2-94333) belongs to the P4/nmm space group and
photoluminescence decay studies on PbO revealed that these atomic sheets
are more robust compared to many quantum dots113. A positive tensile strain
of the monolayer changes it from a direct bandgap material to an indirect
bandgap material272. However, the unstrained monolayer is non-magnetic,
but when it is doped with a hole, it induces ferromagnetism. The VBM and
CBM are estimated with HSE06 hybrid functional and are shown in Figure
7.3.
Pure Tin Oxide (SnO), having a tetragonal unit cell and with a P4/nmm
space group having lattice parameters a=b=3.802 Å and c=4.836 Å is
considered for this study. It is reported that the pure phase of SnO might not
have high hole mobility but would show high mobility when it is doped with
controlled residual amounts of metallic tin114. However, our current study is
intended to analyse the band alignment w.r.t the perovskite’s band positions
to elucidate the feasibility of hole transport for a PSC, therefore we restricted
2 Inorganic Crystal Structure Database
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the focus on pure SnO monolayers. The experimental realization of few-
layered SnO was reported with p-type behaviour making it a favourable
component for 2D logical devices115, 116. The layered SnO structure
comprises, that each Sn atom bonded with four O atoms and vice versa 273, 274
Figure 7.1 (e-f). It is theoretically and experimentally determined that the
direction of high mobility is along the c-axis, that is perpendicular to the SnO
layer/s. The Band structure of SnO monolayer and the band alignment of SnO
bi-layer are shown in Figure 7.2 (c) and Figure 7.3 respectively.
7.3.COMPUTATIONAL METHODS
The Density Functional Theory (DFT) method using a plane-wave basis
set based Vienna Ab initio simulation package (VASP) code is used for first-
principle calculations for this study118. The geometry optimization is done
with a generalized gradient approximation in Perdew-Burke-Ernzerhof form
(GGA-PBE) exchange-correlation functional160. A Monkhorst−Pack k-points
grid of 7 x 7 x 1 was used for sampling in the first Brillouin zone for Lead
Iodide (PbI2) monolayer and 9 x 9 x 1 grid was used for both Lead Monoxide
(PbO) and Tin Oxide (SnO) monolayers for structure optimizations. All these
systems are subjected to geometry relaxation until the convergence criteria
for residual force and energy were achieved at 0.005eV/ Å and 10-6 eV,
respectively. A vacuum space of about 30 Å in the c-direction and is well
enough to avoid inter slab interactions between neighbouring layers. The
projector augmented wave (PAW) method169 was used to articulate the
electron-ion interface and the plane-wave energy cut-off is used at 400 eV.
Grimme’s scheme167, 168 was used to incorporate zero-damped van der Waals
correction for effectively describing non-covalent bond interactions. The
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spin–orbital-coupling (SOC) effect was not taken into consideration in this
study as the electrical properties are satisfactorily described at the PBE level
compared with experiments,91.
The Valence Band Maximum (VBM) and Conduction Band Minimum
(CBM) for these materials are estimated and corrected with their
corresponding vacuum potentials using hybrid density functional theory
based on the Heyd-Scuseria-Ernzerhof (HSE) exchange-correlation
functional162 in VASP code. These band positions are compared with
perovskite band positions to check the feasibility and type of charge transport
mechanism in a perovskite solar cell architecture.
Figure 7.1: The structures of (a –b) PbI2 monolayer, (c-d) PbO, and (e-f) SnO monolayers top-view and perspective side-views respectively.
The two structures were designed such that there is the closest possible
lattice match between the materials and the perovskite. Accordingly, an eight-
layered 1 x 2 x 2 MAPbI3 is used as a base, on top of which PbO monolayer
is placed with 3 x 3 x 1 supercell. Herein, the PbO is placed on top of two
possible surfaces of perovskite i.e. the perovskite (MAPbI3) surfaces
terminated with PbI2 (001) and MAI (Methyl Ammonium-iodide). In all the
geometry optimization for these hybrid structures, the atoms’ positions in the
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bottom two layers of the perovskite were fixed. That’s their coordinates will
not be shifted during optimization iterations. A ‘selective dynamics’ option
is used which is a feature in VASP input files. The lattice mismatch (Lm) is
calculated as (a1 – a2)/a2 x 100% where a1, a2 are lattice parameters of the
material and the perovskite, respectively. The mismatch is about 4.1%
compressive strain in a-direction which is presumed to be negligible in this
study. The following equation was used to calculate the hybrid interface
energies;
……. (7.1)
Where , and are the total energy of the hybrid structure,
and the individual PbO and MAPbI3, respectively275. The characterization of
electron coupling at the hybrid component interface is obtained through
charge density difference in a hybrid system, and is calculated using the
following equation;
(7.2)
Where , and are the total charge density of hybrid
structure, individual PbO and perovskite, respectively. Furthermore, the
quantitative Bader analysis on charge transfer between the
material/perovskite interface was calculated.
7.4.RESULTS AND DISCUSSION
The crystal structures of the inorganic semiconductors considered for this
study are shown in Figure 7.1. The study of hole transportation between the
perovskite surface and the HTM would need the energy positions of the band
edges for the perovskite and the HTMs. The band edge positions of all the
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inorganic semiconductors considered in this study, corrected with the vacuum
potentials, are calculated with HSE06 exchange-correlation functional162.
The HSE06 hybrid functional band structures for the monolayer of the
selected materials are shown in Figure 7.2. The results of vacuum potentials
and the other HSE band structures for different layers are given in electronic
supporting information (ESI).
Figure 7.2: HSE Band structures of (a) PbI2, (b) PbO, and (c) SnO monolayers
It is observed that the PbI2, SnO monolayers resulted in indirect band gaps
(Figure 7.2(a,c)) whereas the PbO monolayer demonstrates a direct bandgap
of 3.35 eV (Figure 7.2(b)). It is also found that the bandgap of SnO is reduced
when the number of layers is increased to two-layers (2L). This feature is in
agreement with the reported results276 and the reason for such a feature is the
interlayer lone pair interactions of divalent Sn2+.
The summary of the band gaps calculated for these materials is given in Table
7.1. The band edge positions thus obtained from the band structures, are then
compared with literature values84 of band positions of MAPbI3, (CBM @ -
3.93 eV and VBM @ -5.43 eV). This comparison is depicted in Figure 7.3.
It is clear from the comparison that a PbO monolayer and a Bi-layered SnO
have their VBM positions at -4.98 eV and -4.81 eV respectively, which are
3.31 eV 3.95 eV 3.35 eV
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more positive than the VBM value of the perovskite and are thus feasible to
support hole transport in PSCs. Further examination of the charge transfer
driving forces shows that the VBM energy of PbO and the bi-layered SnO
are at 0.38 eV and 0.62 eV more positive energy, respectively than that of the
VBM of MAPbI3.
As per the recent study on the effect of interfacial energies between
perovskite and organic hole transfer materials, it is found that a very small
driving force of about 0.07 eV would be enough to achieve efficient hole
transfer and the authors have also suggested a range of this offset as
0<∆E<0.18 eV97.
Figure 7.3: HSE06 Band edge positions (calculated CBM and VBM) of PbI2, PbO and SnO compared with that of MAPbI3 Legend: 1L=monolayer, 2L=bi-layer
Considering this range, we can hereby suggest PbO and SnO-bilayers could
easily transport holes in perovskite solar cells and thus can be used as HTMs.
Further exploration of the charge distribution of one of these material hybrids
was conducted. As a reference, PbO/Perovskite interface structures (Figure
7.4) for both possible surfaces of perovskite (i.e. PbI2 and MAI as top
surfaces) are evaluated. The interaction/binding energies between the
PbO/perovskite interfaces were calculated using equation (1).
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Figure 7.4 : The top and side view hybrid structures of PbO/PbI2 and PbO/MAI terminated hybrid structures respectively.
The binding energy between PbO/perovskite (i.e. PbI2 and MAI surface
perovskite) interfaces is -3.66 eV and -4.52 eV, respectively. Thus, the
PbO/MAI-terminated perovskite interface is more stable. The charge density
difference between the hybrid and pristine components of the system are
calculated using equation (2). The results are pictorially shown in the three-
dimensional (3D) graphic in Figure 7.5.
Table 7.1: Bandgaps of the materials calculated with HSE06 functional
Band Gap / eV
Monolayer Bilayer Tri-layer
PbI2 3.31 3.19 3.11
PbO 3.35 2.95 -
SnO 3.95 1.62 0.93
It is clear from the 3D graphic that the charge depletion region is observed
in the (Figure 7.5 (a)) PbO layer. Similarly, the other materials can also be
subjected to such studies to prove their potential usage as declared in this
study.
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Figure 7.5: The side view of the charge density difference at an iso-value of 0.003 e Å-3, between the two interface systems (a) PbO/PbI2, and (b) PbO/MAI. The Yellow and Cyan iso-surface profiles represent electron accumulation and depletion in 3D space. The atom positions in dotted region i.e. bottom two layers was fixed during geometry optimisation (Inset: Color Code of atoms)
In addition, the Bader analysis277-280 has been conducted on these two
selected systems, to further assess the actual charge transfer that takes place
in the two material interfaces. It is found that there is charge depletion of
0.340e (0.009 e/atom) and of 0.084e (0.0023 e/atom) in two PbO/PbI2-
teriminated perovskite and PbO/MAI-terminated surface interfaces,
respectively, in this system. Thus, it is predicted that PbO can be used as
HTM in PSCs. Similar charge transfer phenomenon is anticipated for the
other materials as per the band edge positions and can be used for the
predicted purposes, as discussed.
7.5.CONCLUSIONS
A density functional theory (DFT) study was conducted on different
inorganic materials PbI2, PbO, SnO for their suitability for hole transport in
Perovskite Solar Cells where the band edge positions of these materials were
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calculated. Further examination of the charge density difference between the
interfaces of selected materials and the corresponding quantitative Bader
analysis of charge transfer was also conducted for PbO/perovskite interfaces.
We also determined the potential driving force values for charge transfer
between the perovskite-HTM interfaces. It is found that a PbO monolayer
and Bi-layered SnO could be potential hole transport materials in PSCs.
Bader analysis on the two interfaces systems quantified the charge depletion
of 0.009 e/atom and 0.0023 e/atom in PbO/PbI2 and PbO/MAI interface
structures, respectively. This has indicated a new set of possible materials
that can be used in a PSC configuration and paves the way for further
experimental scrutiny.
Conflicts of interest
There are no conflicts to declare.
Acknowledgments
A.D acknowledges the financial support by Australian Research Council
under Discovery Project (DP170103598) and computer resources provided
by high-performance computer time from computing facility at the
Queensland University of Technology, NCI National Facility, and The
Pawsey Supercomputing Centre through the National Computational Merit
Allocation Scheme supported by the Australian Government and the
Government of Western Australia.
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7.6.SUPPORTING INFORMATION
Band alignment investigation of multi-layered Lead Iodide, Lead
monoxide and Tin monoxide: Inorganic Hole-transport materials for
Perovskite Solar Cells
Sri Kasi Mattaa, Chunmei Zhanga, Anthony O’Mullane a and Aijun Du*, a
a School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Gardens Point Campus, QLD 4001, Brisbane, Australia.
Corresponding Author
Figure 7.S1. Vacuum potential obtained from HSE06 method for PbO (a) mono, and (b) bi-layers
Figure 7.S2. Vacuum potential obtained from HSE06 method for PbI2 (a) mono, (b) bi-, and (c) tri-layers
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Page 139 of 163 Chapter-7: Inorganic 2D materials for charge transport in Perovskite Solar Cells
Figure 7.S3. Vacuum potential obtained from HSE06 method for SnO (a) mono layer, (b) bi-layer, and (c) Tri layers
Figure 7.S4. Band Structures calculated from HSE06 method for PbO (a) Mono, and (b) Bi layers
Figure 7.S5. Band Structures calculated from HSE06 method for PbI2 (a) Mono, (b) Bi-, and (c) Tri layers
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Figure 7.S6. Band Structures calculated from HSE06 method for SnO (a) Mono, (b) Bi-, and (c) Tri-layers
Table 7.S1. Bandgaps, CBM and VBM obtained from HSE06 method
PbI2 PbO SnO
Mono layer
Bi layer
Tri layer
Mono layer
Bi layer
Mono layer
Bi layer
Tri layer
Bandgap /eV 3.31 3.19 3.11 3.35 2.95 3.95 1.62 0.93
CBM* /eV -3.62 -3.68 -3.72 -1.64 -1.77 -2.00 -3.19 -3.53
VBM* /eV -6.93 -6.87 -6.83 -4.98 -4.72 -5.95 -4.81 -4.46
* Corrected w.r.t Vacuum potential
Note: Some data are repeated in this Table from the main article text for the sake of uniformity.
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Page 141 of 163 Chapter 8: Conclusions
Chapter 8: Conclusions
The primary aim of the research study i.e. theoretical exploration of various Two-
dimensional (2D) semiconducting materials for use in different solar energy
applications has been successfully completed. Inorganic layered compounds formed
from Group IV-V elements that are less studied and some innovative organic carbon
quantum dots were considered for this investigation. The photocatalytic water
splitting, photovoltaic applications and perovskite solar cells were the main solar
technologies considered in this first-principles Density Functional Theory (DFT)
exploration. The fundamental properties viz. light harvesting capability, bandgap and
band edge positions are among the parameters that were explored here in this study.
Regarding water splitting and photovoltaic applications, the exciton binding energies
were considered for discussion. The type of interfacial charge transfer between
perovskite (MAPbI3) and the materials under investigation was also investigated as
well as the charge density differences in the hybrid structures. The perovskite/carbon
dot and perovskite/inorganic semiconductor hybrid structures were studied to check
the type of transfer i.e. either electron or hole transport.
The photocatalytic analysis on the materials revealed that 2D SiP2 can be obtained
by mechanical cleavage and its phonon spectrum predicts dynamic stability. It has
a direct bandgap of 2.25 eV which is comfortably higher than the threshold bandgap
of 1.23 eV for the material to demonstrate water-splitting capability. Furthermore,
the band edge positions perfectly encompassed the redox potentials of water which
indicates great potential for this material for use in photocatalytic water splitting.
The results highlight a new two-dimensional (2D) photocatalyst for overall water
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Page 142 of 163 Chapter 8: Conclusions
splitting and it is expected to guide future experiments to produce H2 and O2 with
high-efficiency based on this material.
Photovoltaic application feasibility was explored for two other single-layer
materials, SiAs2 and GeAs2. It was found that exfoliation is highly feasible for these
materials and thus experimental mechanical cleavage is predicted to be possible.
Monolayers of SiAs2 and GeAs2 possess a bandgap of 1.91 and 1.64 eV,
respectively, which is excellent for sunlight harvesting and furthermore band-gap
tuning is possible by application of tensile strain. The SiP2 monolayers also show
bandgap tuning by applying tensile strain. In all three materials HSE06 (Wannier90)
band structures were explored and discussed. The exciton binding energies of these
materials was found to be 0.25 and 0.14 eV, respectively. The results highlight a
new family of 2D materials with great potential for photovoltaic applications.
Materials for facilitating Electron or Hole transport in Perovskite solar cells were
explored. Innovative Carbon quantum dot structures including functional moieties
viz. −OH, and −COOH was designed and investigated. The simple hexagonal
structured C‐dots functionalised with −OH and −COOH groups have suitable
valance band maximum (VBM) positions, compared with that of MAPbI3, so that
hole transport from the perovskite is feasible. More C‐dot structures with
functionalisation of -OH and -COOH groups were also identified as potential hole
transfer materials for perovskite solar cells. It was also determined that the
functional groups’ bonding position on the C‐Dot would impact the bandgap and
band edge positions. This reveals an excellent method of tuning the band positions
of C‐dots to the desired value. The typical charge transfer study through charge
density difference assessments also corroborates the fact of hole transport in the
selected C-dots. A small variation in charge transfer between the C‐Dot/PbI2
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Page 143 of 163 Chapter 8: Conclusions
system interfaces compared to that of C‐Dot/MAI system interfaces was observed.
Thus, C‐dots can be potential hole transport materials that may be cost-effective to
produce. In addition, this would have a future scope for experimental studies for
testing the predictions made here due to their non‐toxicity and environmentally
friendly characteristics, compared with other conventional organic HTMs.
Further study on inorganic 2D materials for HTLs in PSCs was conducted on
layered crystal structures of post-transition metal halides and oxides (lead iodide
(PbI2), lead monoxide (PbO), tin-oxide (SnO)). The CBM and VBM positions and
HSE06 band structures were analysed and summarised to discuss the type of charge
transport that would be feasible with these materials. Further examination of the
charge density difference in the interfaces of perovskite/ HTL for PbO monolayer
and the corresponding quantitative Bader analysis was also discussed. It was
determined that a PbO monolayer and Bi-layered SnO could be potential hole
transport materials in PSCs. A predicted sample values of charge transfer obtained
through Bader analysis for the charge depletion of 0.009 e/atom and 0.0023 e/atom
in PbO/PbI2 and PbO/MAI interface structures, respectively. This study has
therefore identified a new set of possible charge transport materials for PSCs and
paves the way for further experimental work to validate this prediction.
Finally, the research study reveals a few innovative 2D materials for various solar
energy applications and provides scope for further study both theoretically and
experimentally.
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Page 145 of 163 Chapter 9: Future work
Chapter 9: Future work
Based on the research study presented here, we anticipate more insights for the lab-
scale realisation of these new and innovative 2D materials.
9.1 THEORETICAL
The materials explored in this research were less explored computationally and to
some extent, have limited experimental data or no data. This pave the way for future
theoretical exploration of detailed study on the inorganic charge transport materials
PbO, SnO-bi layer for their hole carrier mobilities. Similarly the newly designed
organic C-dots need additional studies of such carrier mobilities and stress and strain
impacts on bandgap variation. As these organic C-dots are simple structured, it might
be possible to conduct experimental studies in parallel to theoretical investigations.
9.2 EXPERIMENTAL WORK
This might take the form of collaboration with experimental scientists from QUT or
might be with universities in Australia or even abroad. In the light of the fast-growing
emerging Perovskite Solar Cell technology research, the HTM studied here in this
research viz. Carbon dots would surely attract attention from the experimentalists and
theoretical physics researchers for the further construction of new models and
analysis for various applications. Some of the materials studied in this research have
good feasibility of producing mono layered crystals, hence there is a quite good scope
for future experimental work. Also, the band-gap tuning possibility with applied
stress or strain can collaborate with experimental physicists in lab-scale studies. The
possibility of applying stress by bending apparatus as described in H.J. Conley et
al.181, or applying external load as explained in J. Feng et al.182 could be explored.
Another method that was referred to, for inducing the strain in crystals, in the main
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research chapters is lattice-mismatch. Experimentally this can be done by carefully
selecting a suitable substrate which has a lattice mismatch with that of layered
material that is to be grown on the substrate. Depending on the lattice-mismatch
between the substrate and the material there would be an intrinsic strain in the crystal
formed on the substrate. An example of this method is growing an epitaxial
monolayer of MoS2 on mica as substrate as reported by Q. Ji et al. 183
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