Direct-indirect character of the bandgap in methylammonium lead iodide perovskite.

TL;DR: This work provides a new framework to understand the optoelectronic properties of metal halide perovskites and analyse spectroscopic data and finds that second-order electron-hole recombination of photo-excited charges is retarded at lower temperature.

Abstract: Time-resolved photo-conductance and microwave conductance investigations reveal that methylammonium lead iodide perovskites have an indirect bandgap at temperatures relevant to photovoltaic applications.

Summary

Introduction

• Metal halide perovskites such as methylammonium lead iodide (CH3NH3PbI3) are generating great excitement due to their outstanding optoelectronic properties, which lend them to application in high efficiency solar cells and light-emission devices.
• This unprecedented progress not only makes hybrid perovskites interesting candidates for photovoltaic applications, but also illustrates their fascinating opto-electronic properties.
• For these samples Σμ is proportional to T1.5 down to the phase transition and,16,19,28 apart from small deviations, no abrupt decrease in the mobility is observed below the phase transition.

Discussion

• To briefly summarize their results: at 300 K, the generation yield of free charge carriers in CH3NH3PbI3 is 20% higher for excitation just above the band-gap (at 1.7 eV) than further above the band gap (> 1.8 eV).
• Furthermore, in the tetragonal phase, an energetic barrier exists for second-order band-to-band recombination between mobile CB electrons and VB holes.
• That is, if for instance electrons were immobilized in shallow traps, the generation yield of free mobile CB electrons should be enhanced with (i) increasing temperature and (ii) increasing charge carrier concentration.
• This explanation is corroborated by theoretical work claiming that the fundamental band gap in CH3NH3PbI3 is indirect.
• Due to the limited density of states (DOS) at the CBM, direct transitions might dominate over indirect transitions at excitation densities higher than used in the present work (> 1017 cm-3).16.

Conclusions

• The authors used TRMC and PL to investigate the charge carrier dynamics in tetragonal and orthorhombic CH3NH3PbI3.
• Most importantly, the authors find that in the tetragonal phase, second-order recombination of mobile electrons and holes occurs via a non-allowed transition, reminiscent of a semiconductor with an indirect band gap.
• An activation energy of 47.0 ± 1.2 meV was found, which is on the same order of magnitude as the difference between the direct and indirect band gaps predicted from theoretical calculations of the band structure.
• These effects are not observed in the orthorhombic phase of CH3NH3PbI3, in which the major part of the carriers decays rapidly.
• These insights provide a new framework to understand the optoelectronic properties of metal halide perovskites, rationalize their unique suitability for low-cost photovoltaic and light-emitting devices, and analyze spectroscopic data.

Figures

Figure 5. Proposed band diagrams and activation energy for second order recombination in the CH3NH3PbI3 thin film. a) Proposed band diagram and for the tetragonal phase. Here, the conduction band minimum (CBM) is slightly shifted in k-space with respect to the valence band maximum (VBM), making the fundamental band gap indirect. The local minimum in the CB corresponding to a direct transition is denoted by CBD. b) Arrhenius plot of the pre-factor z (T),43 defined as the ratio between the k2 (T), obtained from fitting the experimental TRMC traces for 160 K < T < 300 K (see Supplementary Figure 12), and the theoretical second order recombination rate B (T).42 The slope of the linear fit (dotted line) indicates that the activation energy for second order recombination is 47 ± 1.2 meV. Therefore, thermal energy (kBT) might assist in the release of electrons from CBM to CBD, which is schematically depicted in (a).

Figure 6). To understand this, we note that at 120 K, the FA spectrum is comprised of the band-to-band continuum and a sharp transition peaking at 1.7 eV that has been attributed to an excitonic feature.8,26 Hence, we conclude that, for excitation wavelengths that coincide with the excitonic transition (1.7 eV), the generation yield of free charges is much lower than for the band-to-band continuum (≥ 1.8 eV). This implies that in the orthorhombic phase, excitons are less likely to dissociate into free charges than in the tetragonal phase. This observation can be understood from the exciton binding energy being ~16 meV in orthorhombic CH3NH3PbI3,24 which is higher than the thermal energy of 10 meV at 120 K. To further investigate the generation and recombination pathways of free charges in the different crystal phases, we measured φΣμ for temperatures ranging from 80 to 340 K using an excitation energy of 2.0 eV, which corresponds to band-to-band excitations in both phases. In the tetragonal (b) phase down to 150 K, φΣμ is enhanced upon cooling (Figure 3). In contrast, if the temperature is further reduced to 90 K and the crystal structure changes from tetragonal to orthorhombic (g), φΣμ decreases substantially.

Figure 2. Photo-conductance for a CH3NH3PbI3 thin film. Photo-conductance as function of time after excitation at 1.65 eV (l = 753 nm) and 2.00 eV (l = 621 nm) for the tetragonal phase at 300 K for an absorbed photon fluence of 8 x 108 cm-2 per pulse (a). Photo-conductance as function of time after excitation at 1.70 eV (l = 730 nm) and 2.00 eV (l = 621 nm) for the orthorhombic phase at 120 K for an incident photon fluence of 2 x 1010 cm-2 per pulse (c). Comparison of maximum photo-conductance (ηΣμ, circles) to fraction of absorbed photons at 300 K (b) and 120 K (d), where the absorbed photon fluences are 8 x 108 cm-2 per pulse for T = 300 K and on the order of 109 cm-2 per pulse for 120 K. For each excitation wavelength, the photo-conductance was averaged over at least 200 laser pulses and error bars were calculated based on the inaccuracy in the laser intensity I0 .

Full text

Delft University of Technology
Direct-indirect character of the bandgap in methylammonium lead iodide perovskite
Hutter, Eline M.; Gélvez-Rueda, María C.; Osherov, Anna; Bulović, Vladimir; Grozema, Ferdinand C.;
Stranks, Samuel D.; Savenije, Tom J.
DOI
10.1038/nmat4765
Publication date
2017
Document Version
Accepted author manuscript
Published in
Nature Materials
Citation (APA)
Hutter, E. M., Gélvez-Rueda, M. C., Osherov, A., Bulović, V., Grozema, F. C., Stranks, S. D., & Savenije, T.
J. (2017). Direct-indirect character of the bandgap in methylammonium lead iodide perovskite.
Nature
Materials
,
16
(1), 115-120. https://doi.org/10.1038/nmat4765
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!
1!
Direct-Indirect Character of the Band Gap in Methylammonium
Lead Iodide Perovskite
Eline M. Hutter
1
, María C. Gélvez-Rueda
1
, Anna Osherov
2
, Vladimir Bulović
2
,
Ferdinand C. Grozema
1
, Samuel D. Stranks
2,3*
, and Tom J. Savenije
1*
1
Opto-electronic Materials Section, Department of Chemical Engineering, Delft University of
Technology, van der Maasweg 9, 2629 HZ Delft, The Netherlands
2
Research Laboratory of
Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139,
U.S.A
3
Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
*e-mail: sds65@cam.ac.uk
*e-mail: T.J.Savenije@tudelft.nl
Abstract
Metal halide perovskites such as methylammonium lead iodide (CH
3
NH
3
PbI
3
) are generating
great excitement due to their outstanding optoelectronic properties, which lend them to
application in high efficiency solar cells and light-emission devices. However, there is
currently debate over what drives the second order electron-hole recombination in these
materials. Here, we propose that the band gap in CH
3
NH
3
PbI
3
has a direct-indirect character.
Time-resolved photo-conductance measurements show that generation of free mobile charges
is maximized for excitation energies just above the indirect band-gap. Furthermore, we find
that second-order electron-hole recombination of photo-excited charges is retarded at lower
temperature. These observations are consistent with a slow phonon-assisted recombination
pathway via the indirect band-gap. Interestingly, in the low-temperature orthorhombic phase,
fast quenching of mobile charges occurs independent of the temperature and photon
excitation energy. Our work provides a new framework to understand the optoelectronic
properties of metal halide perovskites and analyze spectroscopic data.

!
2!
Solar cells based on the metal halide perovskite family of materials including CH
3
NH
3
PbI
3
have been rapidly developed in the past few years, reaching record power conversion
efficiencies exceeding 22%.
1–3
This unprecedented progress not only makes hybrid
perovskites interesting candidates for photovoltaic applications, but also illustrates their
fascinating opto-electronic properties. The outstanding photovoltaic performance of
CH
3
NH
3
PbI
3
is mainly due to (i) the high absorption coefficient (ii) high yield of free
electrons and holes upon photo-excitation and (iii) excellent charge transport properties.
4,5
6,7
Although substantial progress has been made in modeling the dynamics of photo-excited
charge carriers in CH
3
NH
3
PbI
3
,
8,9
we are yet to fully understand what drives the second order
electron-hole recombination in this material. Currently, the conventional idea is that
CH
3
NH
3
PbI
3
behaves as a direct band gap semiconductor, where the absorption and emission
of photons occur via allowed transitions. This is fundamentally different from indirect band
gap semiconductors such as silicon in which both absorption and recombination involve not
only photons, but also phonons. This results in lower absorption coefficients than in direct
semiconductors,
10
but at the same time recombination is much slower.
11
Recent theoretical calculations of the band structure of CH
3
NH
3
PbI
3
suggest that the
conduction band minimum (CBM) is slightly shifted in k-space with respect to the valence
band maximum (VBM), making the fundamental band gap indirect.
12–15
Nevertheless, to date,
there are no reports of experimental evidence for the presence of an indirect band gap in
CH
3
NH
3
PbI
3
or in any other metal halide perovskite. Furthermore, it remains controversial to
what extent the temperature and the crystal phase affects the photo-physics in CH
3
NH
3
PbI
3
.
16–
18
Finally, most temperature-dependent spectroscopic studies monitor the charge carrier
dynamics at relatively high excitation fluences (i.e., in excess of 1 μJ/cm
2
), whereas most
processes relevant to solar cell operation happen at much lower illumination intensities.
In this work, we use temperature-dependent Time-Resolved Photoluminescence (TRPL) and
Microwave Conductance (TRMC) techniques to study the dynamics of optically-excited
charge carriers in CH
3
NH
3
PbI
3
at charge densities comparable to AM 1.5 excitation (see

!
3!
Figure 1). Both techniques show that second order electron-hole recombination is a
thermally-activated process for T > 160 K.
7,19
These results are explained by proposing that
photo-excited carriers undergo slow phonon-assisted recombination from the CBM. In the
orthorhombic phase (T < 160 K), fast quenching of mobile charges is observed. Finally, we
find that this behavior is general for solution-processed perovskite films with a planar or
meso-structured morphology and independent of the lead precursor used in the fabrication.
Figure 1: Representation of time-resolved photoluminescence (TRPL) and microwave conductance (TRMC)
measurements on a thin film of CH
3
NH
3
PbI
3
. In both techniques, electrons (closed circles) are excited to the
conduction band by a short laser pulse, leaving mobile holes (open circles) in the valence band. TRMC is used to
measure the photo-conductance (
D
G), which scales with the time-dependent concentration and mobility,
µ
of free
electrons and holes. The blue sinusoidal line represents the magnitude of the microwave electric field as it passes
through the sample. The radiative recombination of these mobile electrons and holes is probed by TRPL, which is
a function of the concentrations of electrons (n
e
(t)) and holes (n
h
(t)).
Thin (~250 nm), polycrystalline CH
3
NH
3
PbI
3
films were solution-processed on quartz
substrates using an acetate-based precursor solution (see Supplementary Figure 1).
20
The
TRMC technique was used to measure the photo-conductance ΔG, i.e. the difference in
conductance of CH
3
NH
3
PbI
3
between dark and after pulsed illumination, which scales with
the product of the concentration and mobility of photo-generated free electrons (μ
e
) and holes
(μ
h
) (see Figure 1). Figures 2a and 2c show ΔG as function of time after excitation of
CH
3
NH
3
PbI
3
Laser
)()( tntnPL
heBtoB
µ
Photoluminescence
hn
microwave
power
P
hhee
tntntG
P
tP
µµ
)()()(
)(
+µDµ
D
P -
D
P
Microwave conductance

!
4!
tetragonal (T = 300 K) and orthorhombic (T = 120 K, see also Supplementary Figure 2)
CH
3
NH
3
PbI
3
, respectively. Directly after photo-excitation (t = 0), ΔG increases due to the
formation of free mobile charge carriers. Since no electrodes are attached to the sample, the
decrease of the signal over time can only be due to immobilization of charges by trapping or
recombination. Hence, such measurements yield information on the decay processes in
CH
3
NH
3
PbI
3
similar to a device under open-circuit conditions. Interestingly, in the tetragonal
phase at T = 300 K, the signal observed on excitation at 1.65 eV is significantly higher than at
2.00 eV, while the opposite is true in the orthorhombic phase at T = 120 K.
Figure 2. Photo-conductance for a CH
3
NH
3
PbI
3
thin film. Photo-conductance as function of time after
excitation at 1.65 eV (
l
! =! 753 nm) and 2.00 eV (
l
! =! 621 nm) for the tetragonal phase at 300 K for an absorbed
photon fluence of 8 x 10
8
cm
-2
per pulse (a). Photo-conductance as function of time after excitation at 1.70 eV (
l
! =!
730 nm) and 2.00 eV (
l
! =! 621 nm) for the orthorhombic phase at 120 K for an incident photon fluence of 2 x 10
10
cm
-2
per pulse (c). Comparison of maximum photo-conductance (ηΣμ, circles) to fraction of absorbed photons at
300 K (b) and 120 K (d), where the absorbed photon fluences are 8 x 10
8
cm
-2
per pulse
for T = 300 K and on the
order of 10
9
cm
-2
per pulse
for 120 K. For each excitation wavelength, the photo-conductance was averaged over at
least 200 laser pulses and error bars were calculated based on the inaccuracy in the laser intensity I
0
.
The ratio between the number of light-induced free charge carriers and the number of incident
photons is defined as the incident yield
h
. The product of
h
and the summation of the electron

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Direct-indirect character of the band gap in methylammonium lead iodide perovskite" ?

Here, the authors propose that the band gap in CH3NH3PbI3 has a direct-indirect character. Furthermore, the authors find that second-order electron-hole recombination of photo-excited charges is retarded at lower temperature. 

Q2. What future works have the authors mentioned in the paper "Direct-indirect character of the band gap in methylammonium lead iodide perovskite" ?

It is likely that more stabilized and higher quality embodiments will emerge in the near future to allow for further investigation. The precise influence of shallow or deep intra-band traps, and their relative competition or synergy with the direct-indirect bandgap character, will be the subject of important future work within the community. In any case, in both theoretical scenarios, the band diagrams suggest that the CBM is only slightly shifted in k-space, resulting in a manifold of momentum-allowed ( direct ) transitions for excitation energies close to the absorption onset. To further investigate the thermal activation barrier for second order recombination in CH3NH3PbI3, the authors constructed an Arrhenius plot of the pre-factor z ( T ) ,43 which is defined as the ratio between k2 ( T ) and B ( T ).