Sep 2018: Invited talk at the International Conference on Ternary and Multinary Compounds (ICTMC) in Boulder, CO.

1. Prashun Gorai, Rachel Kurchin, Tonio Buonassisi, Vladan Stevanovic
Colorado School of Mines (CSM), National Renewable Energy Laboratory (NREL)
Massachusetts Institute of Technology (MIT)
Key Structural and Chemical Features of
Defect-Tolerant Semiconductors
GaAs
deep
states
VB
bonding
anti-
bonding
VB
CBCB
MAPbI3
shallow
states
I(p)
As(p)
Pb(p)
Ga(s)
Pb(s)
Defect-intolerant Defect-tolerant

2. Shallow Defect States Reduce Trap-Assisted Recombination
VB
ET
Ei
trap
CB
e-
h+
• Shockley-Read-Hall trap-assisted recombination rate1,2:
shallow traps are desirable for defect tolerance
• Recombination rate increases as ET - Ei decreases
• Other factors: capture cross-section, carrier mobility, trap
density
n, p = electron, hole concentrations, ni = intrinsic concentration
NT = trap density, vth = thermal velocity, 𝜎 = capture cross-section
USRH =
pn n2
i
p + n + 2nicosh Ei ET
kT
NTvth
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1Shockley and Read, Phys. Rev. 87 (1952), 2Hall, Phys. Rev. 87 (1952)
/152

3. Heuristic Guidelines for Defect Tolerance
1Walsh and Zunger, Nat. Mater. 16 (2017); 2Zhang et al., Phys. Rev. B 57 (1998); 3Zakutayev et al., JPC Lett. 5 (2014)
/153
commentary
Instilling defect tolerance in
new compounds
Aron Walshand Alex Zunger
The properties of semiconducting solids are determined by the imperfections they contain. Established
physical phenomena can be converted into practical design principles for optimizing defects and doping
in a broad range of technology-enabling materials.
I
mpurities and defects in solids dictate their
physical properties. Such imperfections
come in a few fundamental flavours:
doping (conductivity-promoting) defects and
impurities can create free carriers that enable
electronics; ‘killer defects’ (deep, charged
recombination centres), on the other hand,
quench transport; and charge scattering
defects reduce mobility. Materials that cannot
be doped (most wide-gap insulators) or that
have vanishing free carrier mobility at room
temperature (many Mott insulators) are not
useful for many electronic and optoelectronic
technologies. Owing to the strong historical
interaction between the theory of defects
and doping of semiconductor-based
technologies — be they microelectronics,
photovoltaics, transparent conductors, light-
emitting diodes (LEDs), or, more recently,
spintronics — a lot has been understood
about the physics and properties of defects in
inorganic semiconductors.
New technologies are focusing attention
on less explored classes of compounds —
such as halide perovskites, metal–organic
frameworks, two-dimensional materials, and
topological insulators — where defects feature
in a leading role. For example, topological
insulators such as Bi2S3 are hardly insulators
because intrinsic defects render them n-type
in the bulk, placing the Fermi level inside the
bulk conduction band. Also, halide perovskite
solar cells have not been effectively doped and
the modern theory of defects in crystalline
solids, based on first-principles electronic
structure techniques, exposes phenomena
that can be converted into practical
approaches for optimizing a broad range of
technology-enabling materials. Calculation
of defect levels based on Greens functions3–5
progressed to supercell treatments including
a complete description of local structure
optimization, chemical potentials and
charge states6,7
. There are many routes
available to instilling defect tolerance in
new compounds, and the specific approach
can be adapted to the target material and
device. For applications that are limited by
electrical conductivity and mobility, including
transparent conductors and thermoelectric
devices, an optimal material would combine
high carrier concentrations with weak carrier
scattering. For light conversion in solar cells
and LEDs, non-radiative recombination
channels must be removed at all costs. In the
new generation of ‘quantum materials’ (such
as topological conductors, Weyl conductors
and high-TC superconductors), control of the
carrier concentrations is key, as the position
of the Fermi level determines whether specific
band structure features are accessible.
Realities of point defect behaviour
All solids in equilibrium contain intrinsic
defects. A compound may also contain
unintentional chemical impurities and
of point defects and their formation energy,
which depends on the parametric Fermi level
(EF) and the external conditions that control
the chemical potentials (μ) of the reactants6–9
.
The formation energies ΔHD,q(μ,EF) of defect
type D (for example, vacancy or interstitial) in
charge state q (donors when q > 0; acceptors
when q < 0) are not material constants but
depend on the growth environment.
Electron-producing donor defects such as
anion vacancies are difficult (easy) to form in
a semiconductor that is already electron-rich
(electron-poor) — that is, n-type (p-type).
In contrast, hole-producing acceptor defects
such as cation vacancies are difficult (easy)
to form in a semiconductor that is already
electron-poor (electron-rich). Likewise,
anion vacancies are difficult (easy) to form
under growth conditions that are anion-rich
(anion-poor), and the opposite holds for
cation vacancies.
These relationships decide if an impurity
contemplated by a researcher will either
successfully substitute a host atom or be
rejected. They determine which of the
possible host crystal sites will be substituted;
whether the impurity will be ionized and
contribute free carriers; if the generated
electrons or holes will be eliminated by
structural rearrangements; and, if charge
carriers survive such compensation, whether
they will be localized or delocalized. Such
physical processes were initially ignored
antimony
Sb3+
tin
Sn2+
indium
In1+
thallium
Tl1+
lead
Pb2+
bismuth
Bi3+
• Presence of partially-oxidized cations - anti-bonding top of valence band1,2,3
• Large dielectric constants - effective screening of charged defects
• Low carrier effective masses - high mobility, small polar formation avoided
heuristic guidelines are qualitative, role of crystal structure is not clear

4. Broad Search Based on Heuristic Guidelines
• Preliminary search based on heuristic guidelines
identified several candidates1:
• Binary halides: InI, TlI, PbI2, SnI2, SbI3, BiI3
• Chalcohalides: BiOI, BiSI, BiSeI, SbSI, SbSeI, …
Prospective Article
Identifying defect-tolerant semiconductors with high minority-carrier
lifetimes: beyond hybrid lead halide perovskites
Riley E. Brandt, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
Vladan Stevanović, National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401; Colorado School of Mines,
1500 Illinois Street, Golden, Colorado 80401, USA
David S. Ginley, National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, USA
Tonio Buonassisi, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
Address all correspondence to Riley E. Brandt, Tonio Buonassisi at rbrandt@alum.mit.edu; buonassisi@mit.edu
(Received 27 March 2015; accepted 23 April 2015)
Abstract
The emergence of methyl-ammonium lead halide (MAPbX3) perovskites motivates the identification of unique properties giving rise to excep-
tional bulk transport properties, and identifying future materials with similar properties. Here, we propose that this “defect tolerance” emerges
from fundamental electronic-structure properties, including the orbital character of the conduction and valence band extrema, the charge-
carrier effective masses, and the static dielectric constant. We use MaterialsProject.org searches and detailed electronic-structure calculations
to demonstrate these properties in other materials than MAPbX3. This framework of materials discovery may be applied more broadly, to
accelerate discovery of new semiconductors based on emerging understanding of recent successes.
Introduction
Many semiconductors have been studied over the last century for
their possible use in photovoltaics (PVs), light-emitting diodes
(LEDs), computing devices, sensors, and detectors. Of these,
only a select few have achieved sufficient optoelectronic perfor-
mance to transition into industrial manufacturing, and their iden-
tification and development have been slow and mostly empirical.
Recently, high-throughput computation and a deeper under-
standing of the physics-based requirements for high performance
have created the potential for an accelerated identification of
functional materials with manufacturing potential. For example,
materials screening criteria have been proposed to better focus
the search for novel candidate PV materials; they include the op-
tical band-gap energy[1,2]
and abruptness of absorption onset,[3,4]
in addition to boundary conditions of elemental abundance,[5]
and manufacturing cost.[6,7]
However, many materials have
met these criteria and yet have not achieved industrially relevant
conversion efficiencies (in excess of 10–15%) due to low
minority-carrier lifetimes or diffusion lengths, e.g., in the case
of Cu2ZnSn(S,Se)4,[8]
SnS,[9]
and others.[10]
Meanwhile, PV de-
vices have emerged based on methyl-ammonium lead iodide
(MAPbI3) and closely related halides (herein referred to as
MAPbX3). MAPbI3 is a semiconductor, which has demonstrated
exceptional minority-carrier lifetimes of 280 ns (in the mixed
iodide–chloride composition)[11]
and diffusion lengths up to
175 μm,[12]
comparable with the best single-crystal semiconduc-
tors. This, in addition to meeting the criteria above, has resulted
in a dramatic realization of PV conversion efficiencies up to
20.1%[13,14]
in 2015, from <4% in 2009.[15]
This paper examines whether the dramatic success of
MAPbX3 in PVs can be used as a basis to expand design criteria
to identify new potential high-performance optoelectronic ma-
terials. One of the most compelling questions engendered by
MAPbX3 as an optoelectronic material is the degree to which
it is unique, and whether its success can lead to the identifica-
tion of materials with improved stability and lower toxicity, yet
similar high performance. Clearly, as in previous design criteria
the high optical absorption coefficient is important, but also es-
sential are the long carrier diffusion lengths observed in
MAPbX3, enabled by high minority-carrier lifetime (τ) and mo-
bility (μ).[11,16,17]
The importance of τ and μ for device perfor-
mance has been established[18]
for the most highly performing
PV materials, including silicon,[19]
cadmium telluride,[20,21]
copper indium gallium diselenide,[22]
and gallium arsenide.[23]
Oddly, these more direct transport parameters, τ and μ, are
not traditionally considered essential screening criteria for
novel candidate PV materials. This may be partially a conse-
quence of the difficulty in measuring and/or calculating these
parameters. The direct measurement of minority carrier τ and
μ requires ultrafast electronic or optical sensors to capture tran-
sients,[24–27]
or strong steady-state signals,[28,29]
and must be
performed with PV-device-relevant illumination conditions,
electrical fields, and transport directions. Calculating τ and μ
from first-principles is even more challenging, given the lack
of well-established and high-throughput methods to directly
calculate electron–phonon interactions and/or trap capture
cross-sections. Although it is possible to obtain some informa-
tion about carrier mobility from effective masses, and
MRS Communications (2015), 5, 265–275
doi:10.1557/mrc.2015.26
MRS COMMUNICATIONS • VOLUME 5 • ISSUE 2 • www.mrs.org/mrc ▪265
1Brandt et al., MRS Comm. 5 (2015); 2Brandt et al., Chem. Mater. 29 (2017)
Searching for “Defect-Tolerant” Photovoltaic Materials: Combined
Theoretical and Experimental Screening
Riley E. Brandt,*,†
Jeremy R. Poindexter,†
Prashun Gorai,‡,§
Rachel C. Kurchin,†
Robert L. Z. Hoye,†,@
Lea Nienhaus,†
Mark W. B. Wilson,†,#
J. Alexander Polizzotti,†
Raimundas Sereika,∥
Raimundas Žaltauskas,∥
Lana C. Lee,⊥
Judith L. MacManus-Driscoll,⊥
Moungi Bawendi,†
Vladan Stevanović,‡,§
and Tonio Buonassisi†
†
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
‡
Colorado School of Mines, Golden, Colorado 80401, United States
§
National Renewable Energy Laboratory, Golden, Colorado 80401, United States
∥
Faculty of Science and Technology, Lithuanian University of Educational Sciences, Vilnius 08106, Lithuania
⊥
Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FE, United Kingdom
*S Supporting Information
ABSTRACT: Recently, we and others have proposed screening criteria for
“defect-tolerant” photovoltaic (PV) absorbers, identifying several classes of
semiconducting compounds with electronic structures similar to those of
hybrid lead−halide perovskites. In this work, we reflect on the accuracy and
prospects of these new design criteria through a combined experimental and
theoretical approach. We construct a model to extract photoluminescence
lifetimes of six of these candidate PV absorbers, including four (InI, SbSI,
SbSeI, and BiOI) for which time-resolved photoluminescence has not been
previously reported. The lifetimes of all six candidate materials exceed 1 ns, a
threshold for promising early stage PV device performance. However, there
are variations between these materials, and none achieve lifetimes as high as
those of the hybrid lead−halide perovskites, suggesting that the heuristics for
defect-tolerant semiconductors are incomplete. We explore this through first-
principles point defect calculations and Shockley−Read−Hall recombination
models to describe the variation between the measured materials. In light of these insights, we discuss the evolution of screening
criteria for defect tolerance and high-performance PV materials.
■ INTRODUCTION
Thin-film polycrystalline photovoltaic (PV) materials offer the
potential for lower-capital intensity manufacturing relative to
crystalline silicon PV, but only if they can achieve high PV
conversion efficiencies in excess of 20%.1,2
Long minority-
carrier lifetimes are necessary to achieve high efficiency, yet to
date, there have been only a few classes of polycrystalline
semiconductors that have demonstrated minority-carrier life-
times in excess of 1 ns.3
Three classes of thin-film PV absorbers
have achieved bulk lifetimes in excess of 100 ns, and they
materials: it allows power conversion efficiencies on the order
of 10% in materials with strong optical absorption and suggests
the potential for further improvements.3
Including InP and
other III−V materials, as well as the Cu2ZnSn(S,Se)4 family of
materials14
in addition to CIGS, CdTe, and LHPs, there are
several additional classes of thin-film inorganic (or hybrid
organic−inorganic) polycrystalline semiconductors that are
known to exceed this 1 ns threshold.
In prior work, we hypothesized that a promising path to
achieving these long lifetimes is through defect-tolerant
Article
pubs.acs.org/cm
• Candidates exhibit lifetimes >1 nanosecond2
but not comparable to MAPbI3:
■ RESULTS
Photoluminescence Lifetime. TRPL data for all six
materials are plotted in Figure 1. There is a clear variation in
the TRPL behavior across the materials tested, with
(CH NH ) Bi I and InI demonstrating the slowest decay,
however, all effective lifetimes as well as “slow” expo
time constants exceed 1 ns.
Defect Calculations. Figure 2 shows calculated
formation enthalpies as a function of Fermi level for I
Figure 1. TRPL decay curves of all six materials measured. Dashed gray lines represent biexponential fits to the data, while solid black lines
using a numerical model incorporating both Shockley−Read−Hall and radiative recombination (see the Supporting Information for det
estimated parameters). The fluence used was 20 nJ/cm2
for all traces except for those of (CH3NH3)3Bi2I9 (approximately 1 nJ/cm2
) and S
nJ/cm2
). Data for (CH3NH3)3Bi2I9 were reproduced with permission from ref 33.
Chemistry of Materials A
defect calculations can reveal the nature of defects
/154

5. First-principles Calculation of Defect Levels
∆HD,q
Fermi energy (EF
)
VBM
CBM
0 Eg
q=0
-2
shallow
+1
acceptor
donor
deep acceptor
donor
• Supercell approach with finite size corrections and GW-corrected band edges1
HD,q = ED,q Ehost +
X
i
niµi + qEF + Ecorr
1Lany and Zunger, Phys. Rev. B 78 (2008)
/155

6. Breakdown of the Heuristic Description in Binary Halides
Kurchin, Gorai, Buonassisi, Stevanovic, Chem. Mater. 30 (2018)
VI
VIn
InI
IIn
InI
-1
+1
-1
+2
-3
-2
0
1
2
3
0 1.0 2.0
VI
VTl
TlI
ITl
TlI
-1
+1
+1
-1
-2
-1
0
1
2
3
4
0 1.0 2.0
VI
VSn
ISn
SnI
-2
+1
-3
-2
-3
+3
-1
0
1
2
3
4
0 1.0 2.0
VI
VPb
PbI
IPb
-2
+1
+3
-3
-1
0
1
2
3
4
5
0 1.0 2.0
VI
VBi
BiI
IBi
-3+1
-1
+1
+3
-1
0
1
2
3
4
0 1.0 2.0
SnI2
PbI2
BiI3
EF
(eV) EF
(eV) EF
(eV)
∆HD,q
(eV)∆HD,q
(eV)
VI
VSb
+1
-3
ISb
SbI
-1
+1
-1
0
1
2
3
4
5
0 0.5 1.0 1.5 2.0
SbI3
deep defects are present in all the candidate materials
/156

7. Refined Understanding
/157
• Existing guidelines are based on chemistry - does not account for interactions of dangling bonds or
structural relaxation upon defect formation
prior understanding refined understanding
cation vacancy
A(p) A(p)-nn
VC states
deep
C(p)
C(s)
A(s)
A(p)
band gap
C(p)
C(s)
A(s)
VC states
shallow
orbital chemistry and structure likely play a role in defect tolerance
Kurchin, Gorai, Buonassisi, Stevanovic, Chem. Mater. 30 (2018)

8. Role of Orbital Alignment
/158
A(p)
C(p)
C(s)
A(p)-nnresonant
VC states
A(p) A(p)-nn
VC states
deep
C(p)
C(s)
A(s) A(s)
bad alignment better alignment
• Good energy alignment of anion (p) and cation (s) will push valence band maxima to higher energies
• Better alignment in InI, TlI: cation vacancies are shallow
partially oxidized cation + good energy alignment = shallow cation vacancies
Kurchin, Gorai, Buonassisi, Stevanovic, Chem. Mater. 30 (2018)

9. Role of Crystal Structure: Symmetry
/159
1Shi and Du, Phys. Rev. B 90 (2014); 2Kurchin, Gorai, Buonassisi, Stevanovic, Chem. Mater. 30 (2018)
• Crystal site symmetry can promote shallow anion vacancies e.g. CsCl structure type1,2
TlBr: conduction band edge
Tl
Br
• Anion vacancy is deep in rocksalt TlBr1 but shallow in CsCl structure
VBr
VTl
TlBr
BrTl
-1
+1
+2-2
HD,q(eV)
0
1
2
3
4
EF (eV)
0 1.0 2.0 3.0
TlBr (CsCl structure): I-rich
TlBr (CsCl structure)

10. Role of Crystal Structure: Symmetry
/1510
1Shi and Du, Phys. Rev. B 90 (2014); 2Kurchin, Gorai, Buonassisi, Stevanovic, Chem. Mater. 30 (2018)
suitable crystal site symmetry promotes shallow anion vacancies
• Crystal site symmetry can promote shallow anion vacancies e.g. CsCl structure type1,2
• Anion vacancy is deep in orthorhombic InI but shallow in CsCl structure
InI (hypo-CsCl structure)
VI
VIn
InI
IIn
-1
+1
+2
-2
ΔHD,q(eV)
−1
0
1
2
3
4
EF (eV)
0 0.5 1.0 1.5
VIVIn
InIIIn
-1
+1
-1
ΔHD,q(eV)
−1
0
1
2
3
4
EF (eV)
0 0.5 1.0 1.5 2.0
InI (orthorhombic)

11. Role of Crystal Structure: Coordination
/1511
• Low anion coordination + large cations promote shallow anion vacancies by creating spatial separation
• Hypothetical PbI2 in a Cu2O structure (2-fold coordinated I) has shallow iodine vacancies
HD,q(eV)
0
1
2
3
4
VI
VPb
IPb
-2
+1
-3
EF (eV)
0 0.5 1.0 1.5
PbI2 (hypo-Cu2O structure) conduction band edge
I
Pb
low anion coordination promotes shallow anion vacancies
Kurchin, Gorai, Buonassisi, Stevanovic, Chem. Mater. 30 (2018)
VI
VPb
PbI
IPb
-2
+1
+3
-3
-1
ΔHD,q(eV)
0
1
2
3
4
EF (eV)
0 0.5 1.0 1.5 2.0
PbI2 (native structure)

12. Tradeoffs and Other Features
/1512
• Chemical and structural features appear to operate
independently
• InI, TlI: ns2 cation, bad structure - shallow cation but deep
anion vacancies
• WO3: ns2 cation absent, good structure - deep cation
vacancies but shallow anion vacancies
VO
WO
OW
VW
WO3: O-rich
+2
-2
-3
-6
-1
-3
W
O
ΔHD,q(eV)
0
2
4
6
8
EF (eV)
0 0.5 1.0 1.5 2.0
Kurchin, Gorai, Buonassisi, Stevanovic, Chem. Mater. 30 (2018)
TlBr (225)
TlBr (221)
TlI (63)
TlI (221)
InI (63)
InI (221)
intolerant
tolerant
E-Evacuum(eV)
−8
−6
−4
−2
0
• Absolute band edge positions: CB edge lower in
defect-tolerant structures with shallow anion
vacancies

13. Defect-Tolerance in Ternary Semiconductors: MAPbI3
/1513
• Pseudo-binary: No MA contribution to band edges
1Miyata et al., Nature Physics 11 (2015)
• Heuristic guidelines:
Partially-oxidized cation: Pb2+
Large dielectric constants: MA dipole contributes
Low effective masses1: ~0.1 me
• Refined guidelines:
Orbital alignment sub-optimal: Pb(6s) and I(5p) but ..
Desirable structure: low anion coordination
Does MAPbI3 fair well within these refined guidelines?
VB
CB
MAPbI3
I(5p)
Pb(6p)
Eg
Pb(6s)
ternary and multinary semiconductors offer more tunability to satisfy these criteria

14. Extending the Refined Guidelines to Ternary Semiconductors
/1514
refined guidelines need to be further refined!
PbTlI3
Pb
Tl
I
• Preliminary search based on presence of ns2 cation and low anion coordination
VI
VTl
PbTlI3: I-rich
VPb
ΔHD,q(eV)
−1
0
1
2
3
EF (eV)
0 1 2
• PbTlI3: anion is 3-fold coordinated
• Iodine vacancies: states ~200 meV from band edges but low concentrations
• Conduction band: not just p states of ns2 cation - also I(p) states

15. Outlook
Funding and Computational Resources
National Science Foundation - SusChem
DOE Energy Frontier Research Center CNGMD
NREL High Performance Computing (HPC)
• A refined understanding of the chemical and structural features for defect tolerance
• Shallow cation vacancies: partially-oxidized cation + good energy alignment
• Shallow anion vacancies: suitable crystal site symmetry or low anion coordination
• Additional factors for defect tolerance to interstitials
• Extension of guidelines to ternary chemistries needs careful consideration