M = Sn, Ti X = Br, Cl, I
Cs
Seán R. Kavanagh, Christopher N. Savory, Shanti M. Liga,
Gerasimos Konstantatos, Aron Walsh, David O. Scanlon
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Figures: (a) Electronic band structures calculated with hybrid DFT including spin-orbit coupling (HSE06+SOC), alongside charge densities at the (b) CBM and (c) VBM.
Theoretical investigations dramatically and consistently overestimate the
electronic bandgaps of the Cs2
TiX6
family of compounds (X = I, Br, Cl), as well as
incorrectly predicting the relative bandgap trends between Cs2
TiX6
and Cs2
SnX6
– despite accurately predicting the electronic structure of Cs2
SnX6
.
Here we reveal strong excitonic effects as the origin of this major discrepancy
between theory and experiment; a consequence of both low structural
dimensionality and orbital localisation.
@Kavanagh_Sean_
[email protected] Y.-T. Huang, S.R. Kavanagh, D.O. Scanlon, A. Walsh, and R.L.Z. Hoye, Nanotechnology (2021)
B. Cucco, G. Bouder, L. Pedesseau, C. Katan, J. Even, M. Kepenekian, G. Volonakis, Appl Phys Lett (2021)
S.R. Kavanagh, C. N. Savory, S.M. Liga, G. Konstantatos, A. Walsh and D.O. Scanlon (In submission)
Revealing strongly-bound excitons in vacancy-
ordered 5tanium perovskites (Cs2
TiX6
)
L W X
−6
−4
−2
0
2
4
6
Energy (eV)
Total DOS
I (p)
Ti (d)
Ti (s)
a b
c
L W X
−6
−4
−2
0
2
4
6
Energy (eV)
Total DOS
I (p)
Sn (s)
Sn (p)
a b
c
0 1 2 3
h (eV)
(Arbitrary Units)
Hybrid DFT
GW0+BSE
Experiment
Cs
2
TiBr
6
0 1 2 3
h (eV)
(Arbitrary Units)
Hybrid DFT
GW0+BSE
Experiment
Cs
2
TiI
6
E
ex
(dark) E
ex
(dark)
E
ex
(dark)
0 1 2 3 4
h (eV)
2
3
4
5
6
7
8
9
real
0 1
HSE06
GW0
+ BSE
GW0
(RPA)
Cs
2
TiI
6
0 1 2 3 4
h (eV)
(Arbitrary Units)
Cs
2
SnBr
6
Hybrid DFT
GW0+BSE
Experiment
a
0 1 2 3 4 5
h (eV)
(Arbitrary Units)
Hybrid DFT
GW0+BSE
Experiment
Cs
2
SnCl
6
b
E
ex
(dark)
E
ex
(dark)
Beyond-DFT calculations including
electron-hole interactions (GW+BSE) reveal
strong excitonic binding for Cs2
TiX6
, with
band contributions to the exciton
wavefunction across the Brillouin zone.
⬅ Figures left/right ➡
This delocalisation in reciprocal space
corresponds to a strong real-space
localisation, and thus a strongly-bound
charge-transfer Frenkel exciton.
Cs2
SnX6
exhibits opposite behaviour, with
delocalised Wannier-Mott excitons (though
intermediate behaviour for Cs2
SnCl6
).
Exciton binding significantly redshifts the
absorption onset, resolving the discrepancy
between theory/experiment and reproducing
the measured absorption spectra.
⬅ Figures left/right ➡
Cs2
SnI6
Cs2
TiI6
0 1 2 3 4 5
h (eV)
(Arbitrary Units)
Hybrid DFT
GW0+BSE
Experiment
Cs
2
TiCl
6
E
ex
(dark)
Remaining Issues:
- Major overestimation of quasiparticle
bandgaps within GW (Cs2
TiX6
& Cs2
SnX6
)
- Consequence of significant under-
screening within the RPA Coulomb
potential W.
- Known to worsen for localised (e.g. d/f-
orbital) and low-dimensional systems.
- Requires state-of-the-art self-consistent
vertex corrections within the GW
calculation.
M = Sn, Ti X = Br, Cl, I
Cs
Conclusions:
- Strongly-bound, localised excitons are present in Cs2
TiX6
, explaining
long-standing experiment/theory disagreement.
- Strong exciton binding can reduce charge separation and open-circuit
voltages (Voc
) in solar cells, likely a key origin of the poor photovoltaic
performance achieved thus far in this material class.
- Importance of frontier orbital character and structural connectivity &
dimensionality when employing atomic substitution in materials design
strategies -- here resulting in qualitatively different electronic behaviour
despite equal cation valence and similar bandgaps.