Comparative study on the excitons in lead-halide-based perovskite-type crystals CH3NH3PbBr3 CH3NH 3PbI3

Article abstract of DOI:10.1016/S0038-1098(03)00566-0

Optical absorption and magnetoabsorption spectra of the lead-halide-based perovskite-type crystals, CH₃NH₃PbX₃ (X = Br, I) have been investigated. The lowest-energy excitons in these crystals are normal three-dimensional Wannier-type excitons. Bohr radii, binding energies, reduced masses, effective g factors, and oscillator strengths of the excitons have been determined with satisfactory accuracy. A larger bandgap and more tightly bound nature of the excitons in CH₃NH₃PbBr ₃ compared to those in CH₃NH₃PbI₃ are a natural consequence of the halogen substitution.

Full text of DOI:10.1016/S0038-1098(03)00566-0

Solid State Communications 127 (2003) 619–623
www.elsevier.com/locate/ssc
Comparative study on the excitons in lead-halide-based perovskite-
type crystals CH3NH3PbBr3 CH3NH3PbI3
a,c
a,c
a,c
Kenichiro Tanakaa,c, , Takayuki Takahashi , Takuma Ban , Takashi Kondo ,
*
Kazuhito Uchidab, Noboru Miurab
aDepartment of Materials Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 1138656, Japan
bInstitute for Solid State Physics, The University of Tokyo, Kashiwanoha, Kashiwa-shi, Chiba 277-8581, Japan
cCore Research for Evolutional Science and Technology (CREST), Japan Science and Technology Corporation, Japan
Received 25 April 2003; received in revised form 8 June 2003; accepted 1 July 2003 by J. Kuhl
Abstract
Optical absorption and magnetoabsorption spectra of the lead-halide-based perovskite-type crystals, CH3NH3PbX3 (X ¼ Br,
I) have been investigated. The lowest-energy excitons in these crystals are normal three-dimensional Wannier-type excitons.
Bohr radii, binding energies, reduced masses, effective g factors, and oscillator strengths of the excitons have been determined
with satisfactory accuracy. A larger bandgap and more tightly bound nature of the excitons in CH3NH3PbBr3 compared to those
in CH3NH3PbI3 are a natural consequence of the halogen substitution.
q 2003 Elsevier Ltd. All rights reserved.
PACS: 71.35.Cc
Keywords: D. Optical properties; E. Magnetoabsorption
Excitons confined in a low-dimensional structure are
subjects which have been extensively studied because of
their enhanced binding energies, oscillator strength, and
nonlinear optical responses. The large family of the lead-
halide-based perovskite-type crystals has been studied
recently, since these crystals exhibit distinctive optical
properties due to their unique crystal structures. They are
self-organized low-dimensional crystals, where [PbX6]
(X ¼ I, Br) octahedra form zero, one, two, or three-
dimensional (3D) networks [1–3]. Among them, the two-
dimensional (2D) crystal group (R-NH3)2PbI4 has been most
intensely investigated, because these crystals exhibit a
number of fascinating characteristics, such as huge non-
linearity with ultrafast response [4–6], bright electrolumi-
nescence [7], and outstanding scintillation characteristics
[8]. In addition, we have shown recently [9] that the excitons
in a 2D crystal (C6H13NH3)2 are Wannier-type ones with
comparatively strong 2D character, whose binding energies
are enhanced by the spatial confinement and the image
charge effect [10,11].
On the other hand, CH3NH3PbX3 (X ¼ I, Br) are
perovskite-type crystals, where corner-sharing [PbX6]
octahedra form 3D networks. Since they can be regarded
as a 3D analogue of the 2D crystals [12], the knowledge of
their excitonic and electronic properties is necessary for
better understanding of those in lower-dimensional counter-
parts. There have been some reports on their fundamental
optical properties [13–16], and it has been found that their
electronic structures are essentially the same as those of
CsPbX3 [17,18]. On the other hand, there have been a
limited number of reports on their detailed excitonic
parameters such as binding energies, Bohr radii, and
reduced masses [15,16,19,20]. For example, Ishihara
determined the binding energy of the lowest-energy exciton
in CH3NH3PbI3 to be 45 meV from the temperature
dependence of its luminescence intensity [15]. On the
*
Corresponding author. Address: Department of Materials
Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,
Tokyo 1138656, Japan. Tel./fax: þ81-358-417-093.
E-mail address: tanaka@castle.t.u-tokyo.ac.jp (K. Tanaka).
0038-1098/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S0038-1098(03)00566-0

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K. Tanaka et al. / Solid State Communications 127 (2003) 619–623
other hand, Hirasawa et al. reported the optical and
magnetoabsorption (MA) study of CH3NH3PbI3 [19,20],
and estimated the binding energy, Bohr radius and reduced
analyzed in terms of group theoretical considerations (see
Fig. 2). A first-principles band calculation [21] shows
that the sixfold conduction band is mainly composed of
Pb 6p orbitals (with a small amount of contribution from
I 5s (Br 4s) orbitals), whereas the valence band is the Pb
6p–I 5p (Br 4p) antibonding state. The direct bandgap is
located at the R½111Š point, where the conduction band
and valence band have G24 ðp-likeÞ and G1þðs-likeÞ
symmetry, respectively. After introducing the spin–
orbital interactions, the valence band transforms as
Gþ6 ðJ ¼ 1=2Þ; while the sixfold conduction band splits
into the fourfold G82 state ðJ ¼ 3=2Þ and the twofold G62
state ðJ ¼ 1=2Þ; respectively. Here J represents the total
angular momentum. The absorption peaks I correspond to
the excitons which come from the Gþ6 ! G62 space
transition at the R point. The direct product Gþ6 £ G62
transforms according to G21 þ G42 representations, where
the sixfold G24 ðJ ¼ 1Þ is dipole allowed, while the
twofold G21 ðJ ¼ 0Þ is a spin triplet and thus dipole
forbidden; the observed lowest-energy excitons I are
attributed to G24 excitons. On the other hand, the
absorption peaks II correspond to a Gþ6 ! G82 transition
at the R point (spin–orbit split-off band). Higher energy
structures III are associated with the interband transition
at the M½110Š point [19,21]. The energy difference
between these structures of CH3NH3PBr3 and CH3NH3-
PbI3 is a direct consequence of the halogen substitution.
Replacement of I with Br shifts the Gþ1 valence band to
lower energies thus resulting in the increase in the
bandgap.
˚
mass of its lowest-energy excitons to be 37 meV, 28 A and
0:12m0; respectively. However, Hirasawa’s values seem
rather unreliable, because their MA spectra taken on
microcrystalline samples suffer from magnetic-field-
induced photoluminescence which apparently shifts exciton
absorption peaks to the higher energy side. We have
remeasured MA spectra of CH3NH3PbI3 with much
improved accuracy, and compared with those in CH3NH3-
PbBr3 in order to clarify the effects of halogen substitution.
Samples used in our MA study were randomly oriented
polycrystalline thin films prepared by simultaneous depo-
sition of CH3NH3I(Br) and PbI2(Br2) on quartz substrates.
We have confirmed that optical properties of the samples are
almost identical with those of single crystals. Optical
absorption spectra of CH3NH3PbBr3 were obtained by
transforming reflection spectra of a single-crystalline
sample using the Kramers–Kronig relation. A single crystal
of CH3NH3PbBr3, 5 £ 5 £ 3 mm3 in size, were grown by
slow evaporation from a dimethylformamide solution where
stoichiometric amounts of PbBr2 and CH3NH3Br were
dissolved.
Fig. 1 shows the optical absorption spectrum of
CH3NH3PbBr3 at 5 K. Rather sharp excitonic lines are
located at 2.258 eV(I), 3.329 eV(II), and around 3.9 eV(III).
We have measured the temperature dependence of its
optical absorption spectrum. The lowest-energy exciton line
(I) shifts to higher energy as the temperatures increase, and
it is located at 2.337 eV at room temperature. The observed
exciton peak energy at room temperature agrees well with
that in the previous report [13,14]. These excitonic
structures (I–III) are similar to the absorption spectrum of
CH3NH3PbI3 (1.633 eV(I), 2.8 eV(II), 3.6 eV(III) [19]),
indicating that fundamental electronic structures of both
crystals are essentially the same. Blue shift of the whole
structures in CH3NH3PbBr3 as compared to CH3NH3PbI3 is
due to the halogen substitution.
MA measurements have been carried out on
Electronic structures of the 3D crystals have been
Fig. 2. Schematic energy diagram of 3D crystals at the R½111Š point
of the Brillouin zone. (a) The conduction band and valence band
have G24 and Gþ1 symmetry, respectively. (b) With the spin–orbit
interaction, the conduction band splits into fourfold G28 and twofold
G26 states, while the valence band transforms as twofold Gþ6 in
double representation. (c) The lowest-energy exciton is split by the
Coulomb and exchange interactions into sixfold G24 and twofold G12
states and transitions to these states are optically allowed and
forbidden, respectively.
Fig. 1. Optical absorption spectrum of CH3NH3PbBr3 at 5 K.

K. Tanaka et al. / Solid State Communications 127 (2003) 619–623
621
Fig. 3. Magnetoabsorption spectra of (a) CH3NH3PbBr3 and (b) CH3NH3PbI3 in the Faraday configuration at 4.2 K. The spectra are shown for
sþ polarization (solid lines) and s2 polarization (dashed line).
CH3NH3PbI3 and CH3NH3PbBr3 at 4.2 K in pulsed
magnetic fields up to 45 T in the Faraday configuration
ðkkBÞ; where k is the direction of the incident light and B is
the magnetic field. The samples were both 1-mm-thick films
deposited on 4-mm-diameter quartz substrates. They were
immersed in liquid helium in a specially designed cryostat
where a coil made of Nb/Ti superconducting wires was
installed in a liquid–nitrogen bath. Magnetic fields up to
45 T were generated by discharging a condenser bank into
the coil. The light from a xenon lamp was introduced into
the sample through an optical fiber, a polarizer and a
quarter-wavelength plate. The light transmitted through the
sample was guided through another optical fiber to an
optical multichannel analyzer (OMA). The xenon flash
started at almost the same time the gate of the OMA was
opened. MA spectra were taken while the gate of the OMA
was open, for about 1 ms, when the magnetic field reached
its peak value.
lowest-energy excitons of CH3NH3PbBr3 and CH3NH3PbI3,
respectively, in the Faraday configuration for the left-
handed circular (sþ) polarization. The MA spectra for the
right-handed circular (s2) polarization are displayed only
for the highest magnetic field by dashed lines for
comparison. Note that no magnetic-field-induced photo-
luminescence is observed for both samples. The peak
energies of the absorption lines are plotted as functions of
the magnetic field, by closed circles for sþ, and open circles
for s2 polarizations in Fig. 4. The solid lines in Fig. 4 are
theoretical curves fitted with the method of least-squares by
the formula
1
E ¼ E0 ^ g’mBB þ c0B2;
ð1Þ
2
where E0; the energy of the absorption line at B ¼ 0; g’; the
effective g factor, c0; the diamagnetic coefficient, and mB;
the Bohr magneton. The second term in Eq. (1) is the
Zeeman term and the third term the diamagnetic shift. The
Fig. 3(a) and (b) shows the MA spectra around the
Fig. 4. Energy shifts as functions of the magnetic field in the Faraday configuration for (a) CH3NH3PbBr3 and (b) CH3NH3PbI3. Closed circles
and open circles represent the experimental values for sþand s2 polarization, and solid lines show the theoretical fitting with the method of
least-squares.

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K. Tanaka et al. / Solid State Communications 127 (2003) 619–623
Table 1
Determined exciton parameters of the three-dimensional crystals CH3NH3PbBr3 and CH3NH3PbI3. Previously reported data are included in
parentheses
CH3NH3PbBr3
CH3NH3PbI3
20 (14.5a)
76 (150a)
0:13m0 (0:12m0
2.03
22 (28b)
˚
Bohr radius aB (A)
Binding energy Eb (meV)
Reduced mass m
50 (37b, 45c)
0:15m0 (0:09m0a, 0:12m0
1.72
a
)
b
)
Effective g factor g’
Oscillator strength f
0.03
(0.02c)
a
Koutselas et al. [16].
b
Hirasawa et al. [20].
c
Ishihara et al. [15].
fitting was quite satisfactory. The values of g’ and c0
of CH3NH3PbI3 were determined to be 1.72 and
1.35 £ 1026 eV/T2, respectively; those of CH3NH3PbBr3
are obtained to be g’ ¼ 2:03; c0 ¼ 1:28 £ 1026 eV/T2,
respectively. We believe the obtained diamagnetic coeffi-
cient c0 of the excitons in CH3NH3PbI3 is more accurate
than the previously reported value [19].
to those in CH3NH3PbI3 are quite natural results of the lower
dielectric constant which reduces dielectric screening of
the Coulomb interaction between the electrons and holes.
Undoubtedly, the lower dielectric constant in CH3NH3-
PbBr3 comes from the larger bandgap energy. Smaller
extent of the exciton wave function is, in turn, reflected in
larger oscillator strength and larger effective g factor.
In summary, we have measured the optical absorption
spectrum of CH3NH3PbBr3 and MA spectra of CH3NH3-
PbBr3 and CH3NH3PbI3 in order to compare the electronic
structures and excitonic properties of the two 3D crystals.
The electronic structure of CH3NH3PbBr3 is qualitatively
the same as that of CH3NH3PbI3 except that the former
possesses a larger bandgap than the latter as a result of the
halogen substitution. The G24 lowest-energy excitons are of
normal 3D Wannier-type characters. The smaller dielectric
constant associated with the larger bandgap in CH3NH3-
PbBr3 results in larger binding energy, smaller Bohr radius,
larger effective g factor, and larger oscillator strength of the
lowest-energy excitons in CH3NH3PbBr3 compared to those
in CH3NH3PbI3.
Since the excitons in both crystals are considered to be
3D Wannier excitons, we can express
ꢀ
ꢁ
ꢀ
ꢁ
1=3
1=3
aB
aH
c0
EB
Ry
1
¼
¼
1
;
¼
;
14ðc0=cHÞ
cH
ð2Þ
!
1=3
m
12
;
m0
c0=cH
respectively, assuming simple 3D hydrogenic envelope
functions and isotropic media. In these equations,
2
cH ¼ 1:23 £ 10210 eV/T , aH ¼ 0:53 A, and Ry ¼ 13:6 eV
˚
are the diamagnetic shift, Bohr radius, and Rydberg constant
of the hydrogen atom, respectively, and m0 is the free
electron mass. From these equations, we determined the
Bohr radii aB; binding energies Eb; and reduced masses m of
the excitons of the 3D crystals, which are summarized in
Table 1. Here, the dielectric constant of CH3NH3PbI3 is
assumed to be 6.5 [20], while that of CH3NH3PbBr3 (4.8) is
obtained from the absolute reflectivity in the transparent
region. Oscillator strengths of the excitons deduced from the
longitudinal–transverse splitting and effective g factors are
also included in Table 1. Relatively large Bohr radii justify
the assumption of Wannier excitons. For comparison, the
previously reported data are included in the parentheses in
Table 1. It is found that the obtained exciton binding energy
in CH3NH3PbI3 agrees well with the reported value obtained
from the temperature dependence of its luminescence
intensity [15]. We also notice that the obtained exciton
binding energy in CH3NH3PbBr3 is much smaller than the
value Koutselas et al. reported, because we have used a
larger 1 than they had in their calculations [16]. We believe
that our data is more reliable because our 1 has been
determined experimentally. Smaller Bohr radius and larger
binding energies of the excitons in CH3NH3PbBr3 compared
Acknowledgements
We wish to thank Professor Era of Saga University for
beneficial advice on sample preparation.
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