Seán R. Kavanagh*, Christopher N. Savory, Shanti M. Liga,
Gerasimos Konstantatos, Aron Walsh*, David O. Scanlon*
Scan me for the paper and a YouTube talk on this study!
Figure 1: (Left) Band structures from hybrid DFT including spin-orbit coupling (HSE06+SOC). (Right) Band contributions to the lowest-energy bright exciton (GW+BSE)
Theoretical investigations dramatically and consistently overestimate the
electronic bandgaps of vacancy-ordered perovskites: Cs2
TiX6
(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
.
We reveal ultra-strong excitonic effects (Eb
>1 eV), despite relatively small
bandgaps (1-3 eV), as the origin of this major experiment-theory discrepancy; a
consequence of both low structural dimensionality and band localization.
@Kavanagh_Sean_
[email protected] S.R. Kavanagh, C. N. Savory, S.M. Liga, G. Konstantatos, A. Walsh and D.O. Scanlon J Phys Chem Lett (2022)
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)
Frenkel Excitons in Vacancy-Ordered
Perovskites (Cs2
MX6
)
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 (Figure 1).
This delocalisation in reciprocal space corresponds to a strong real-space
localisation, and thus a strongly-bound charge-transfer Frenkel exciton. Exciton
binding significantly redshifts the absorption onset, resolving the discrepancy
between theory/experiment and reproducing the measured absorption spectra:
Cs2
SnX6
Cs2
TiX6
Conclusions:
Highly localised, isolated MX6 octahedra yield ‘molecular salt’ behaviour:
- Strongly-bound, localised Frenkel excitons with enormous binding energies
revealed in Cs2
TiX6
, explaining long-standing experiment-theory disagreement.
- Strong van der Waals dispersion interactions are found in these vacancy-
ordered compounds, decreasing volumes by >10% with ΔEg
~ 0.1-0.3 eV.
- 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.
El o (Ti )
p
Ho (
F e e Exc d
0 1 2 3 4
(Arbitrary Units)
hν (eV)
Hybrid DFT
G0W0+BSE
Experiment
Cs
2
TiI
6
E
ex
(dark) E
ex
(dark)
E
ex
(dark)
(Arbitrary Units)
Hybrid DFT
G0W0+BSE
Experiment
Cs
2
TiBr
6
0 1 2 3 4
hν (eV)
Hybrid DFT
G0W0+BSE
Experiment (This Work)
Experiment (Grandhi et al.)
Cs
2
TiCl
6
0 1 2 3 4 5
(Arbitrary Units)
hν (eV)
E
ex
(dark) E
ex
(dark)
0 1 2 3 4
(Arbitrary Units)
hν (eV)
Hybrid DFT
G0W0+BSE
Experiment
Cs
2
SnI
6
0 1 2 3 4 5 6
(Arbitrary Units)
hν (eV)
Hybrid DFT
G0W0+BSE
Experiment (This Work)
Experiment (Karim et al.)
(hν - 0.5 eV)
Cs
2
SnCl
6
0 1 2 3 4
(Arbitrary Units)
Cs
2
SnBr
6
Hybrid DFT
G0W0+BSE
Experiment
hν (eV)
E
ex
(dark)
E
ex
(dark) E
ex
(dark)
L W X
−6
−4
−2
0
2
4
6
Energy (eV)
Total DOS
I (p)
Ti (d)
Ti (s)
a b
L W X
−6
−4
−2
0
2
4
6
Energy (eV)
Total DOS
I (p)
Sn (s)
Sn (p)
a b
Ti d
I p I p
Sn s - I p
t2g
eg
Exciton binding
Cs2
SnX6
exhibits opposite behaviour, with delocalised Wannier-Mott excitons
(though intermediate behaviour for Cs2
SnCl6
).
Figure 2: Optical absorption spectra of Cs2
TiX6
, calculated with hybrid DFT (no
exciton binding), G0
W0
+BSE (exciton binding) and compared to experiment.
Figure 3: Optical absorption spectra of Cs2
SnX6
, calculated with hybrid DFT (no
exciton binding), G0
W0
+BSE (exciton binding) and compared to experiment.
Table 1: Calculated electronic bandgaps Eg
(lowest energy vertical excitations),
using G0
W0
with and without solving BSE (exciton binding). Formally the
difference Δ|EGW
– EGW+BSE
| is defined as the exciton binding energy Eb
.
J. Phys. Chem. Lett. 2022, 13, 10965–10975