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Anharmonicity and Disorder in the Black Phases of
Cesium Lead Iodide used for Stable Inorganic Perovskite
Solar Cells
Arthur Marronnier, Guido Roma, Soline Boyer-Richard, Laurent Pedesseau,
Jean-Marc Jancu, Yvan Bonnassieux, Claudine Katan, Constantinos C
Stoumpos, Mercouri G Kanatzidis, Jacky Even
To cite this version:
Arthur Marronnier, Guido Roma, Soline Boyer-Richard, Laurent Pedesseau, Jean-Marc Jancu, et
al.. Anharmonicity and Disorder in the Black Phases of Cesium Lead Iodide used for Stable Inor-
ganic Perovskite Solar Cells. ACS Nano, American Chemical Society, 2018, 12 (4), pp.3477-3486.
�10.1021/acsnano.8b00267�. �hal-01741313�
Anharmonicity and Disorder in the Black
Phases of Cesium Lead Iodide used for Stable
Inorganic Perovskite Solar Cells
Arthur Marronnier,
∗,†
Guido Roma,
‡
Soline Boyer-Richard,
¶
Laurent Pedesseau,
¶
Jean-Marc Jancu,
¶
Yvan Bonnassieux,
†
Claudine Katan,
§
Constantinos C.
Stoumpos,
∗,k
Mercouri G. Kanatzidis,
k
and Jacky Even
∗,¶
†LPICM, CNRS, Ecole Polytechnique, Université Paris-Saclay, 91128 Palaiseau, France
‡DEN - Service de Recherches de Métallurgie Physique, CEA, Université Paris-Saclay,
91191 Gif sur Yvette, France
¶Univ Rennes, INSA Rennes, CNRS, Institut FOTON — UMR 6082, F-35000 Rennes,
France
§Univ Rennes, ENSCR, INSA Rennes, CNRS, ISCR (Institut des Sciences Chimiques de
Rennes) – UMR 6226, F-35000 Rennes, France
kDepartment of Chemistry and Argonne-Northwestern Solar Energy Research (ANSER)
Center, Northwestern University, Evanston, Illinois 60208, United States
E-mail: arthur.marronnier@polytechnique.edu; konstantinos.stoumpos@northwestern.edu;
jacky.even@insa-rennes.fr
1
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Abstract
Hybrid organic-inorganic perovskites emerged as a new generation of absorber ma-
terials for high-efficiency low-cost solar cells in 2009. Very recently, fully inorganic
perovskite quantum dots also led to promising efficiencies, making them a potentially
stable and efficient alternative to their hybrid cousins. Currently, the record efficiency
is obtained with CsP bI
3
whose crystallographical characterization is still limited. Here
we show through high resolution in-situ synchrotron XRD measurements that CsP bI
3
can be undercooled below its transition temperature and temporarily maintained in
its perovskite structure down to room temperature, stabilizing a metastable perovskite
polytype (black γ-phase) crucial for photovoltaic applications. Our analysis of the
structural phase transitions reveals a highly anisotropic evolution of the individual lat-
tice parameters versus temperature. Structural, vibrational and electronic properties
of all the experimentally observed black phases are further inspected based on sev-
eral theoretical approaches. While the black γ-phase is shown to behave harmonically
around equilibrium, for the tetragonal phase density functional theory reveals the same
anharmonic behavior, with a Brillouin zone-centered double-well instability, as for the
cubic phase. Using total energy and vibrational entropy calculations, we highlight the
competition between all the low-temperature phases of CsP bI
3
(γ, δ, β) and show that
avoiding the order-disorder entropy term arising from double-well instabilities is key in
order to prevent the formation of the yellow perovskitoid phase. A symmetry-based
tight-binding model, validated by self-consistent GW calculations including spin-orbit
coupling, affords further insight into their electronic properties, with evidence of Rashba
effect for both cubic and tetragonal phases when using the symmetry breaking struc-
tures obtained through frozen phonon calculations.
Keywords
inorganic perovskite solar cells, anharmonicity, cesium, phonons, DFT, SXRD, Rashba
2
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The interest of the photovoltaics community for hybrid perovskite solar cells (PSCs) has
been growing rapidly since the first demonstration in 2009,
1
mainly because PSCs combine
ease and low-cost fabrication of organic electronics with efficiencies which compete with
those of traditional sectors, considering the highest certified efficiency of 22.7%.
2
In the
race to commercialization, the methylamonium-based perovskite CH
3
NH
3
P bI
3
(MAP bI
3
or "MAPI") will probably be outpaced by more stable perovskite structures because of
its poor stability.
3
Several strategies are currently being explored, such as mixed cation
recipes,
4
layered-perovskites,
5
and nano-structures such as quantum dots.
6
In fact, after
Eperon et al. found in 2015 a new experimental method in order to maintain CsP bI
3
stable
in its black phase at room temperature and realized the first working cesium lead iodide
solar cell,
7
a cell exceeding 10% efficiency was reported in 2016.
8
It was also shown
9
that
adding a small quantity of EDAP bI
4
(EDA = ethylenediamine) prevents the formation of the
nonperovskite yellow phase of CsP bI
3
and leads to a reproducible efficiency of 11.8%. The
recent report of a 13.4% efficient cesium lead iodide perovskite quantum dot solar cell
6
has
demonstrated that purely inorganic perovskite solar cells have definitively become a stable
and efficient alternative to their hybrid cousins. Besides, a four-terminal tandem cell using
the formamidinium organic cation along with a small fraction of cesium as well as halogen
alloying, in order to be able to tune the band gap, has reached more than 25% efficiency.
10
It is currently well-known that the crystal structure has a direct impact on device per-
formance and it is thus of crucial importance to have high-quality crystallographic data so
as to obtain valuable references for structural characterization of thin films or quantum dots
used in those devices. So far, the structure of CsP bI
3
has mainly been studied through
its similarities with the lead-free perovskite CsSnI
3
. In fact, the structure of the black or-
thorhombic γ-phase of CsSnI
3
was experimentally measured in 1991,
11
and twenty years
later all its crystallographic phases have reached a comprehensive understanding (experi-
mental and theoretical).
1,12–16
For CsMI
3
(M=Pb, Sn), four phases are expected:
12,17
cubic
(α), tetragonal (β), and two orthorhombic phases (a black γ and a non-perovskite yellow
3
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δ-phase), thus including transitions between perovskite phases and non-perovskite polytypes
(perovskitoids)
18
at low temperature. All the phases of CsSnI
3
have been thoroughly char-
acterized,
12,19
as well as the room temperature δ-phase of CsP bI
3
.
17,19,20
More recently, some
of us investigated the temperature dependence of CsP bI
3
’s band gap and how reversible the
non-perovskite to perovskite structural transformations at high temperature
21
can be. It
was shown that, after heating the samples above 360
◦
C, the room temperature δ-phase
(yellow) converts to the black perovskite α-phase . At variance, during the cooling step, the
perovskite structure converts at 260
◦
C to the β-phase and at 175
◦
C to the γ-phase; both
these phases are black. Only after a few days the yellow δ-phase is obtained again. This
work was the first report on the black orthorhombic γ-phase that is crucial in the context of
photovoltaics applications.
In addition, vibrational properties of cesium halide perovskites have proven to be a key
factor in determining the stability of phases with temperature. In CsP bCl
3
the role of
phonons in phase transitions was pointed out already in the seventies.
22
Recently, first prin-
ciples calculations on CsSnI
3
revealed soft phonon modes and strong anharmonicity.
23,24
Conversely, in the case of CsP bI
3
(and RbP bI
3
), the role of vibrational properties in de-
termining the phase stability is still under-studied, although large values of Born effective
charges hinted towards possible structural instabilities.
25
Very recently, some of us evidenced
unexpected anharmonic features in the form of Brillouin zone-centered double-well instabil-
ity for both the cubic α-phase and the yellow orthorhombic δ-phase of CsP bI
3
,
26
but due
to lack of experimental data on the other phases, our understanding remained incomplete.
As for hybrid perovskites, several groups
27,28
revealed small lifetimes for the phonons, a
consequence of double-well potential energy profiles at M and R points in the BZ of cubic
CH
3
NH
3
P bI
3
. These structural effects in hybrid organic-inorganic perovskites, complicated
by the rotational motion of the cation, have an influence on the optoelectronic properties.
For instance, octahedral tilting has been shown to have a direct impact on the continuum
band gap.
29,30
This was further investigated by Yang et al.
31
who considered the influence of
4
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