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Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites

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For a class of 2D hybrid organic-inorganic perovskite semiconductors based on $\pi$-conjugated organic cations, we predict quantitatively how varying the organic and inorganic component allows control over the nature, energy and localization of carrier states in a quantum-well-like fashion. Our first-principles predictions, based on large-scale hybrid density-functional theory with spin-orbit coupling, show that the interface between the organic and inorganic parts within a single hybrid can be modulated systematically, enabling us to select between different type-I and type-II energy level alignments. Energy levels, recombination properties and transport behavior of electrons and holes thus become tunable by choosing specific organic functionalizations and juxtaposing them with suitable inorganic components.
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Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid
Organic-Inorganic Perovskites
Chi Liu,1William Huhn,2Ke-Zhao Du,2Alvaro Vazquez-Mayagoitia,3David Dirkes,4Wei You,4
Yosuke Kanai,4David B. Mitzi,2,1 and Volker Blum2,1
1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
2Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
3Argonne Leadership Computing Facility, 9700 South Cass Avenue, Lemont, Illinois 60439, USA
4Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
(Received 19 March 2018; revised manuscript received 4 August 2018; published 4 October 2018)
For a class of 2D hybrid organic-inorganic perovskite semiconductors based on π-conjugated organic
cations, we predict quantitatively how varying the organic and inorganic component allows control over the
nature, energy, and localization of carrier states in a quantum-well-like fashion. Our first-principles
predictions, based on large-scale hybrid density-functional theory with spin-orbit coupling, show that the
interface between the organic and inorganic parts within a single hybrid can be modulated systematically,
enabling us to select between different type-I and type-II energy level alignments. Energy levels,
recombination properties, and transport behavior of electrons and holes thus become tunable by choosing
specific organic functionalizations and juxtaposing them with suitable inorganic components.
DOI: 10.1103/PhysRevLett.121.146401
Hybrid organic-inorganic perovskites (HOIPs) [1,2],
particularly three-dimensional (3D) HOIPs, are currently
experiencing a strong revival in interest as economically
processable, optically active semiconductor materials with
excellent transport characteristics. Their success is show-
cased most prominently by record performance gains in
proof-of-concept photovoltaic [312] and light-emitting
devices [1320]. The electronic function of 3D HOIPs
can be tuned to a limited extent by manipulating the
inorganic component (from which the frontier orbitals
are derived), but the organic cations are confined by the
3D structure and are thus necessarily small (e.g., methyl-
ammonium [38,1318] and formamidinium [911,
19,21,22]), with electronic levels that do not contribute
directly to the electronic functionality [2328]. However,
the accessible chemical space of HOIPs extends well beyond
the 3D systems [1]. In particular, the layered, so-called two-
dimensional (2D) perovskites do not place a strict length
constraint on the organic cation. In these materials, a much
broader range of functional organic molecules can be
incorporated within the inorganic scaffolds, including com-
plex functional molecules such as oligoacene or oligothio-
phene derivatives [1,2937].Fig.1(a) shows the atomic
structure of a paradigmatic example of such a 2D HOIP with
active organic functionality, bis(aminoethyl)-quaterthio-
phene lead bromide AE4TPbBr4[34]. Similar juxtapositions
of targeted organic and inorganic components give rise to a
vast, yet systematically accessible, space of possible semi-
conductor materials [1,2,3840], including those in which
the molecular carrier levels contribute directly to the low-
lying excitations and carrier levels [1,3032,34,38,39,41].
This large space of conceivable organic-inorganic combina-
tions thus offers the unique opportunity to tailor (ideally with
computational guidance) materials with particularly desir-
able semiconductor properties, by intentionally controlling
the spatial location and character of the electronic carriers and
optical excitations throughout the material.
A key physical prerequisite to manipulate the semi-
conductor properties of layered hybrid materials is to
understand the nature and spatial localization of their
FIG. 1. (a) Structure of AE4TPbBr4, fully relaxed by
DFT-PBE þTS taking the experimental (x-ray diffraction)
structure [34] as the input. (b) Possible energy level schemes
(Ia, Ib, IIa, IIb) for the alternating organic-inorganic perovskite
structure are shown, with the overall band gap indicated by
arrows and dashed lines.
PHYSICAL REVIEW LETTERS 121, 146401 (2018)
0031-9007=18=121(14)=146401(6) 146401-1 © 2018 American Physical Society
carriers and excitations. Specifically, the question of
whether and exactly how one can understand their proper-
ties in analogy to quantum wells with varying confinement
barriers (often assumed [40,4244]) is subject to discussion
in the literature [4548]. Figure 1(b) exemplifies the
principle by comparing four different conceivable quan-
tum-well-like situations: type I,with low-energy elec-
trons and holes localized on the same component (either
organic, Ia, or inorganic, Ib) or type II,with electrons and
holes on different components (holes on inorganic, elec-
trons on organic, IIa, or vice versa, IIb). While some simple
layered HOIPs have been successfully explained in a type-
Ib picture (inorganic band edges with the organic acting as a
quasi-inert screening medium [40,4244,4648]), a fully
quantitative understanding of both band gaps within and
band alignment between the materialscomponents is
essential to recover the larger set of possibilities in
Fig. 1(b). Providing this understanding for the large,
complex crystal structures at hand constitutes a substantial
challenge for current theory, both regarding computational
resources and sufficiently accurate approximations. In this
Letter, we demonstrate that these challenges can now be
met, enabling us to answer questions that are central to
future targeted developments of new HOIP semiconductors:
(1) Can these structures be understood as quantum-well-like
structures with spatially well-separated levels in the organic
vs inorganic components, or will the electronic states be
hybridized and thus delocalized across both components?
(2) What is the spatial nature of electron and hole carriers
within the structure? For instance, do they tend to migrate to
the organic or the inorganic hybrid component in the
lowest-energy configuration, drastically affecting each
carriers transport properties (bandlike inorganic vs hop-
pinglike organic)? (3) To what extent can we rationally tune
the carrier and excitation properties by independently
varying the organic and inorganic components?
Whether we can uncover a new paradigm using 2D
HOIPs as semiconductors on demandwith finely tunable
properties and high-precision crystalline structural control
depends on building a design principle that relates complex
hybrid atomic structures to optoelectronic properties
through answering the questions above. In this Letter, we
do so through a first-principles theoretical examination of a
class of oligothiophene-based 2D HOIPs, expanding on the
AE4TPbBr4compound shown in Fig. 1(a). A practical
challenge for theory is the structural complexity of these 2D
HOIPs for which the unit cells are large. For instance, a
(2×2) lateral supercell of the perovskite layer (Figs. S1S3
in the Supplemental Material [49]) in this and other
structures considered in this Letter is needed to cover the
experimentally correct perovskite layer distortion and
molecular arrangement, leading to 424 atoms in the
simulation cell for AE4TPbBr4. The (2×2) supercell
instead of the experimentally reported (1×2) structure is
necessary with regards to both accessing an energetically
lower structure (Table S1 [49]) and also removing the
disordering in the inorganic and organic structural compo-
nents in the experimental structure. In addition, the two
inorganic layers in the (1×2) relaxed structure have
different Pb-Br-Pb angles, which disagrees with the
experimental structure of AE4TPbBr4(Fig. S4 [49]). For
structure predictions that capture the subtle balance of
different molecular and inorganic bonding contributions,
we use van der Waals corrected semilocal density-func-
tional theory (DFT)i.e., Perdew-Burke-Ernzerhof (PBE)
exchange-correlation functional [55], plus the Tkatchenko-
Scheffler (TS) pairwise dispersion scheme [56]. Electronic
properties require a higher level of theory for qualitatively
correct results, but the most attractive first-principles many-
body approaches such as the GW approximation [57,58]
remain out of reach for structures of this size. For band
structure predictions, we therefore resort to the still
demanding level of hybrid DFT using the Heyd-Scuseria-
Ernzerhof (HSE06) functional [59,60], including spin-orbit
coupling (SOC) [61]. Importantly, and unlike semilocal
DFT, hybrid DFT in principle contains the right physics
[62] to capture the frontier energy levels [valence band
maximum (VBM) and conduction band minimum (CBM)].
Including SOC is critical to capture correctly the qualitative
underlying nature of carriers, changing the nature of the
CBM from organicto inorganicin AE4TPbBr4and
reducing the band gap by 0.3eV (Fig. S5 [49]).
All calculations are performed by the
FHI
-
AIMS
code
[57,61,6368], using the ELSI infrastructure [67] and
ELPA eigenvalue solver [69] for massively parallel simu-
lations. For all crystal geometries, we employ full relax-
ation of unit cell parameters and cell-internal atomic
coordinates [70], using the
FHI
-
AIMS
tightnumerical
defaults (Table S2 [49]) and k-point grid settings of
1×2×2(Table S3 [49]). For band structures,
FHI
-
AIMS
intermediatesettings (Table S4 [49]) and dense k-point
grids of 3×3×3are used. The exchange mixing param-
eter in HSE06 was kept at 25% and the screening parameter
at Ω¼0.11 bohr1[71] in order to retain a single con-
sistent base to compare energy band structures across
different materials in this work. We first validate this
approach for the low-temperature orthorhombic phase of
MAPbI3[Fig. S6(a) [49] ]. The lattice parameters predicted
by DFT-PBE þTS agree with the experimental values [72]
to within 1.4% [Fig. S6(b) [49] ]. The HSE06 þSOC
approach predicts a direct band gap of 1.42 eV, which
underestimates the experimental value [1.651.68 eV,
Fig. S6(b) [49] ] by 0.20.3 eV [73,74]. Details of how
we constructed the computational models for all structures
considered in this Letter can be found in the Supplemental
Material, Sec. IX [49].ForAE4TPbBr4[Fig. 1(a)], devia-
tions of any unit cell parameters of the resulting predicted
structure compared to experiment are 1.2% or better; i.e.,
they are in excellent agreement (Table S5 [49]). Finally, a
new crystalline sample of AE4TPbI4was grown and an x-ray
PHYSICAL REVIEW LETTERS 121, 146401 (2018)
146401-2
structure refinement performed (Supplemental Material,
Sec. X [49]), also indicating excellent agreement with the
DFT-predicted structure used in the analyses below
(Table S5 [49]).
Turning first to energy level localization, orbital plots
(see Figs. S9S11 [49] e.g., orbitals of AE4TPbX4,
X¼Cl, Br, I) show that the states associated with
inorganic and organic components are spatially well sepa-
rated, supporting the notion of quantum-well-likestates in
these materials. This answers question (1) above and
validates a discussion in terms of separate inorganic and
organic bands. Even et al. [47,48] have also considered 2D
HOIPs from the perspective of semiconductor quantum
wells, showing that the effective mass model may fail due
to the absence of superlattice coupling and importance of
nonparabolicity. They proposed a computational analysis in
terms of separate, neutralized organic and inorganic layers,
appropriate for type-Ib situations. In the current Letter, we
cover the full set of materials directly, allowing us to assess
band gaps within each component as well as the alignments
of their electronic levels. Knowing the alignments enables us
to assess the full space of possible HOIP semiconductors
(e.g., types I and II), where both the inorganic and the organic
components are electronically active.
The halogen atoms in the inorganic framework offer a
convenient handle for tailoring the associated electronic
structure of the inorganic component by varying it from Br
to Cl and I [34]. Full band structures for the compound
series AE4TPbX4(X ¼Cl, Br, I) are shown in Fig. 2.All
three compounds have a direct band gap at the Γpoint. By
changing the halogen, the dispersive bands originating
from the inorganic component [Pb- and halogen-derived
states, colored lines in Figs. 2(b)2(g)] shift substantially
with respect to the organic bands. In contrast, the organic-
derived bands [black lines in Figs. 2(b)2(g)] vary only
slightly among these three compounds. Full and partial
densities of states for these and other compounds in
Figs. S14S15 (Supplemental Material [49]) corroborate
the chemical makeup shown in the band structures. Band
curvature parameters (Table S6) that correspond to the
diagonal elements of the effective mass tensors [7577]
in the reciprocal-space coordinate system of Fig. 2(a)
confirm some qualitative trends emerging from the band
structures: uniformly flat bands (effective masses >20 me)
perpendicular to the perovskite planes indicate hindered,
nonbandlike transport. Somewhat lower effective mass
tensor elements (2.211.4 me, still higher than in typical
semiconductor materials) emerge for the holes (VBM) on the
organic components parallel to the planes. Low effective
mass tensor elements, 0.20.5me, for the electrons (CBM)
along the inorganic planes, in the range typical of 3D
perovskites [76,77] might, absent other detrimental factors,
indicate relatively easy electron transport.
The trends of the organic and inorganic frontier energy
levels are shown in Fig. 3(a). The average of Pb 1senergy
levels is chosen to formally align energy levels between
different HOIPs in Fig. 3. However, we did not study how
this choice (equivalent to the absence of dipolar fields
between Pb ions across an interface between two different
HOIPs) pertains to real interfaces between HOIPs, and the
conclusions of this Letter do not rely on this convention.
Replacing Br by Cl increases the overall computed band
gap from 1.88 to 2.12 eV, whereas the substitution by I
decreases the energy gap value to 1.84 eV. While the
inorganic energy gap changes drastically from 2.70 to
3.32=2.11 eV for Cl=I substitutions (Fig. 3), the associated
change in the organic energy gap is negligibly small
(0.1eV). However, a drastic change evident from both
Figs. 2and 3(a) is the ordering of the levels, particularly the
electronlike (CBM) states when going from Cl to Br and I.
FIG. 2. Band structures of AE4TPbX4(X ¼Cl, Br, I) calculated by DFT-HSE06 þSOC with the states of Pb (b)(d) and halogen (e)
(g) identified by projected density of states onto different species. The Kpath in the reciprocal space is shown in (a). The energy zero in
(b)(g) is set equal to the valence band maximum [for internal alignments relative to Pb 1slevels, see Fig. 3(a)].
PHYSICAL REVIEW LETTERS 121, 146401 (2018)
146401-3
For Br and I, the band structures indicate type-IIb
[Fig. 1(b)] quantum-well-like behavior; i.e., electrons
and holes are expected to be spatially well separated on
the inorganic and organic components, respectively. In
contrast, the organic and inorganic CBM levels are pre-
dicted to lie within a few tens of meV for the Cl-substituted
compounds; i.e., they are essentially degenerate within the
uncertainties of the HSE06 þSOC treatment employed
here. AE4TPbCl4is thus between types Ia and IIb in
Fig. 1(b) and would allow electrons to travel to either
component with reasonable ease at finite temperature. This
difference would have profound implications for the
expected carrier recombination properties of all three com-
pounds, as evidenced, e.g., in photoluminescence (PL). In
fact, strong quaterthiophene PL emission at 540 nm
(2.30 eV) was experimentally observed for X ¼Cl [34],
whereas the analogous PL features are substantially
quenched for X ¼Br, I. Our present computational result
agrees with and explains this experimental observation.
While the X ¼Cl compound displays a near type-Ia band
alignment, the X ¼Br, I compounds are clearly type IIb. In
the latter two compounds, the energy level alignment there-
fore effectively impedes the electron-hole recombination
since the electrons and the holes are preferentially located
across the interface in the inorganic and organic hybrid
components, respectively, i.e., addressing question (2) from
the Introduction.
The importance of a fully predictive, quantitative theo-
retical treatment is further underscored by the fact that a
discussion based on qualitative factors in 1999 led to the
different conclusion of type-IIa, not type-IIb, alignment for
this compound [34]. We note that optical excitations in
absorption or emission cannot be expected to be captured
based on the band structures derived in this work alone,
since the typically strong excitonic effects are not included.
For instance, exciton binding energies of up to 540 meV
have been reported for 2D organic-inorganic perovskites
[1,78] and an exciton binding energy of 0.4 eV has been
reported in organic (not hybrid) sexithiophene thin films
[79]. However, the qualitative localization of carriers
prior to recombination (discussed above) still provides
valuable insights into their expected recombination proper-
ties. We also note the potential implications of being able to
tune levels on the organic and inorganic components
independently, beyond optical properties, affects (e.g.)
transport properties, dopability, and/or band offsets (and
thus potential energy losses in devices) between the
components.
We finally consider the ability to tune the band gap and
quantum-well nature of the structure by varying the organic
component, changing the conjugation length of the oligo-
thiophene molecules. As shown in Fig. 3(b), we substitute
the all-anticonfiguration (successive S atoms on alter-
nating sides) of bis-ethylamine terminated oligothiophene
AEnT[n¼15, Fig. 3(c)] into the scaffold of AE4TPbBr4.
While the quaterthiophene molecule in experimental
AE4TPbBr4(Fig. 1) adopts a syn-anti-syn configuration
[34], this configuration cannot be adopted by all AEnT
(n¼15) oligothiophenes. For the purpose of having a
systematic assessment, we thus restrict this part of our
study to the all-anti configuration. Note, however, that the
predicted electronic properties are only expected to be
insignificantly affected by this conformational change as
shown by the additional symbols corresponding to the syn-
anti-syn conformation for n¼4[Fig. 3(b)]. The electronic
band structures reveal direct gaps for all considered
conjugation lengths of AEnTPbBr4(Fig. S12 [49]) and
band curvature trends (Table S7) are broadly consistent
with those discussed for AE4TPbX4above. The overall
band gap decreases as nincreases, i.e., 2.66, 2.54, 1.98,
1.73, and 1.63 for n¼15, respectively. The predicted
AEnTPbBr4compounds for n¼25yield type-IIb level
alignments. However, the n¼1compound reveals a type-
Ib alignment (both CBM and VBM derived from the
inorganic component). This behavior (type Ib) is consistent
with other 2D perovskites with smaller organic function-
ality, in which carriers or excitons are mainly funneled onto
the inorganic subcomponent [4648,80]. We thus affirma-
tively answer question (3) abovei.e., the carrier nature
and neutral excitation properties and overall gap can be
varied rationally by changing the organic component or the
inorganic component in 2D HOIPs independently.
In summary, our results show that the quantum-well
model can be used for conceptual understanding and as a
useful starting point as a design principle for the layered
HOIP family of hybrid materials. The tunability of elec-
tronic properties, exemplified by the materials studied in
FIG. 3. (a) Frontier energy levels of the organic and inorganic
components at the Γpoint among the series of AE4TPbX4
(X ¼Cl, Br, I). (b) Frontier energy levels at the Γpoint among
the series of AEnTPbBr4(n¼15). Stars and diamonds indicate
the energy levels of syn-anti-syn AE4TPbBr4for n¼4. The
average of Pb 1senergies is chosen to align the energy levels of
different compounds. (c) Oligothiophene-based organic mole-
cules considered in the all-anti configuration for varying the
number n.
PHYSICAL REVIEW LETTERS 121, 146401 (2018)
146401-4
this Letter, opens up the possibility to computationally
predict and tailor nanoscale charge separation or recombi-
nation, as well as spatially separated charge transport
within the much larger overall class of hybrid crystalline
materials. Clearly, significant challenges would remain if
theory were applied in isolation. For example, capturing all
structural subtleties of complex 2D HOIP arrangements is
nontrivial, as is predicting fundamental gaps with an
accuracy of better than a few tenths of an eV (the accuracy
expected from the unmodified HSE06 þSOC functional
[71], as used in this Letter, for typical semiconductors
[75,81,82]) for structures of this size. Excitingly, the
combination of such predictions with subsequent targeted
experimentalsyntheses overcomes these challenges, creating
enormous possibilities to identify and fine-tune entirely new
layered crystalline organic-inorganic semiconductors with
deliberately selected optoelectronic or electronic properties.
This work was financially supported by the NSF under
Awards No. DMR-1729297 and No. DMR-1728921, as
well as through the Research Triangle MRSEC (DMR-11-
21107). Computer time was provided by the Innovative and
Novel Computational Impact on Theory and Experiment
(INCITE) program and the Theta Early Science Program
(ESP). This research used resources of the Argonne
Leadership Computing Facility (ALCF), which is a DOE
Office of Science User Facility supported under Contract
No. DE-AC02-06CH11357.
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PHYSICAL REVIEW LETTERS 121, 146401 (2018)
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The formation of a dense and uniform thin layer on the substrates is crucial for the fabrication of high-performance perovskite solar cells (PSCs) containing formamidinium with multiple cations and mixed halide anions. The concentration of defect states, which reduce a cell’s performance by decreasing the open-circuit voltage and short-circuit current density, needs to be as low as possible. We show that the introduction of additional iodide ions into the organic cation solution, which are used to form the perovskite layers through an intramolecular exchanging process, decreases the concentration of deep-level defects. The defect-engineered thin perovskite layers enable the fabrication of PSCs with a certified power conversion efficiency of 22.1% in small cells and 19.7% in 1-square-centimeter cells.
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The past two years have witnessed heightened interest in metal-halide perovskites as promising optoelectronic materials for solid-state light emitting applications beyond photovoltaics. Metal-halide perovskites are low-cost solution-processable materials with excellent intrinsic properties such as broad tunability of bandgap, defect tolerance, high photoluminescence quantum efficiency and high emission color purity (narrow full-width at half maximum). In this review, the photophysical properties of hybrid perovskites, which relates with light-emission, such as broad tunability, nature of the recombination processes and quantum efficiency are examined. The prospects of hybrid perovskite light-emitting diodes and lasers, and their key challenges are also discussed.