Supporting Information
Predicting a Quaternary Tungsten Oxide for Sustainable Photovoltaic Application by
Density Functional Theory
Pranab Sarker,1 Mowafak M. Al-Jassim,2 and Muhammad N. Huda1,*
1
Department of Physics, University of Texas at Arlington, Arlington, Texas 76019, USA
2
National Renewable Energy Laboratory, Golden, Colorado 80401, USA
Computational Details
The present DFT calculations were performed within the framework of the standard
frozen-core projector augmented-wave (PAW)1,2 method using DFT as implemented in the
Vienna ab initio simulation package (VASP)3,4 code. Exchange and correlation potentials were
treated in the generalized gradient approximation (GGA) as parameterized by Perdew-BurkeErnzerhof (PBE).5,6 The basis sets were expanded with plane waves with a kinetic-energy cut-off
of 400 eV. The shortcoming of DFT—i.e., the underestimation of electron localization for
systems with localized 𝑑 and 𝑓 electrons7–9—was rectified in terms of two post-DFT methods:
DFT+U7,10,11 and Hybrid functional (HSE0612) (µ=0.2, α=0.25 EXCHF). DFT-HSE06 was
employed to calculate electronic band structure and density-of-states (DOS) calculations of the
pristine unit cell. However, DFT+U was used for optical absorption calculation of pristine
CTTO. The reason for that was having an absorption spectrum of pristine CTTO with detailed
features, which requires a very high K-sampling as well as enough empty bands. Such
requirements could not be achieved with HSE06 for a multi-cations material like CTTO within
our computation resource. In contrast, DFT+U is computationally convenient and hence,
generating a desirable absorption spectrum was possible. Further, a comparison between DFT+U
and HSE06 band structures was made, which exhibited negligible dissimilarity between those
Supporting Information
(see Figure 2 and S2) except the difference in band gaps. So, it was expected that DFT-HSE06
optical absorption will have the same features as does DFT+U except delayed onset. Considering
this fact in conjunction with computational convenience, we were convinced to employ DFT+U
for optical absorption calculations for pristine to all supercells (1x2x2) of CTTO. The unit cell of
CTTO was converged with DFT (or DFT+U) at 7x11x13 k-mesh, and the converged unit cell
was later used for all HSE06 calculations. Although it is better to use a higher K-mesh for DOS
calculation, we had to restrict ourselves to a smaller 3×5×5 Monkhorst–Pack13 K-sampling, in
order to make DFT-HSE06 DOS calculation compatible with our available computational
efficiency. For DFT+U calculations, we used Ueff = 6 eV to the Cu 3d orbital. We chose this
value of Ueff to be consistent with our previous work.14 For the defect calculations, we
constructed a supercell containing 96 atoms. The k-point sampling for all defect-induced
calculations was 5×5×5. For visualization of the crystal structures, we used VESTA
(Visualization for Electronic and Structural Analysis).15,16
Supporting Information
Figures
Figure S1: Evolution of motif structures from existing structures. “nx” (n=2 and 4) indicates that
original structures were doubled and quadrupled to form motif structures. "⨂” corresponds to all
possible different arrangements among the cations in a unit cell.
(a)
Supporting Information
(b)
Figure S2: The DFT+U and DFT-HSE06: a) electronic band structures and b) projector density
of states (p-DOS). The Fermi level was set to 0 eV. The overall features, except the band gap, of
band structures and p-DOS plots in both methods were found to be similar. The difference in
band gap in two post-DFT methods can be attributed to the difference in DFT correction
methodologies employed in those approaches.
Supporting Information
Figure S3: The DFT+U defects formation energy in CTTO at two different growth conditions:
Cu-rich and Cu-poor. See Reference 17 for defects nomenclature and calculation procedure.
Figure S4: The DFT+U electronic band structures of VCu – CTTO: (left) spin up and (right) spin
down. The Fermi level was set to 0 eV. The band features in two channels are barely distinctive.
The topmost valence bands are partially occupied along Г-Z and at Y in spin-up channel and
along Г-Z, C-Y in spin-down channel, giving rise to p-type activity in CTTO.
Supporting Information
Figure S5: The DFT+U optical absorption spectra of pristine and defect-induced CTTO. It is
seen that the absorption spectra of pristine and defects-induced CTTO have similar features
except the very early absorption in SnCu-CTTO. The first two early rises in the SnCu absorption
spectrum correspond to the transition between occupied and unoccupied states around the
conduction band edge, which do not contribute to PV efficiency. A 7×13×15 K- point sampling
was used to produce the absorption spectrum of pristine CTTO, while it was 5×5×5 for those of
defect-induced CTTO.
Supporting Information
Equations
A chemical potential landscape (CPL), wherein the desired material is thermodynamically stable,
can be defined as a region spanned by chemical potentials of the constituent atomic species of
that material.17At thermodynamic equilibrium, the necessary growth condition for the stable
formation of CTTO is
∆μCu + ∆μSn + 2∆μW + 8∆μO = ∆Hf,CTTO = -21.45 eV
(SE A)
Where ∆Hf,CTTO is the formation enthalpy per formula unit of CTTO computed using the
following equation:14,17
bulk/molecule
∆Hf,CTTO = ECTTO − ni ∑αi Eαi
bulk/molecule
Where ECTTO is the Gibbs free energy of CTTO; Eαi
represents the energy per atom of
bulk
a constituent species α in its standard elemental phase. For example, ECu
and EOmolecule
corresponds to the energy per atom with respect to FCC phase of Cu and O2, respectively.αi
represent different atomic species that constitute CTTO and 𝑛𝑖 is the number of atoms of species
‘αi ’ in the CTTO unit cell. ∆μα (α = Cu, Sn, W, and O) represent chemical potential (growth
condition) of a species α. The upper and lower bounds of ∆μα for each atomic species in CTTO,
satisfying Equation (SE A), are (see Ref. 17 for further details)
21.45 eV ≤ ∆μCu ≤ 0 eV,
(SE A1)
21.45 eV ≤ ∆μSn ≤ 0 eV,
(SE A2)
10.72 eV≤ ∆μW ≤ 0 eV,
(SE A3)
2.68 eV ≤ ∆μO ≤ 0 eV.
(SE A4)
Supporting Information
These sets of growth conditions in SE A1-A4 could facilitate the formation of secondary phases,
with CTTO as well. To avoid the occurrence of secondary phases at thermodynamic equilibrium,
the following conditions need to be further satisfied:17
∑lβ=1 nβ ∆μβ < ∆Hf,s
(SE B)
where ∆Hf,s is the formation enthalpy of a secondary phase (here the subscript ‘s’ refers to
‘secondary’); β corresponds to different atomic species in a secondary phase; nβ is the number of
atoms of the species  for each secondary phase. For CTTO, the following secondary phases are
highly probable, and the required conditions to avoid them, in according to SE B, are
α-SnWO4 (L1): ∆μSn +∆μW +4∆μO < ∆Hf,SnWO4 = -11.51 eV,
(SE B1)
CuWO4 (L2): ∆μCu +∆μW +4∆μO < ∆Hf,Cu2 WO4 = -10.20 eV,
(SE B2)
Cu2WO4 (L3): 2∆μCu +∆μW +4∆μO < ∆Hf,Cu2WO4 = -9.03 eV,
(SE B3)
WO3 (L4): ∆μW +3∆μO < ∆Hf,WO3 = -8.56 eV,
(SE B4)
SnO (L5): ∆μSn + ∆μS < ∆Hf,SnO = -2.76 eV,
(SE B5)
SnO2 (L6): ∆μSn + 2∆μS < ∆Hf,SnO2 = -5.18 eV,
(SE B6)
CuO (L7): ∆μCu + ∆μS < ∆Hf,CuO = -1.53 eV,
(SE B7)
Cu2O (L8): 2∆μCu + ∆μS < ∆Hf,Cu2 O = -1.60 eV.
(SE B8)
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Supporting Information
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