Amorphization-induced strong localization of electronic states in CsPbBr3 and CsPbCl3 studied by optical absorption measurements

Article abstract of DOI:10.1103/PhysRevB.58.11401

Optical absorption spectra of amorphous CsPbX₃ films (X=Br,Cl) are characterized by two Gaussian bands near the fundamental edge, with the optical energy gap largely blueshifted and the absorption intensity strongly reduced as compared with the crystalline films. The peak energies of the bands are close to those of the A and C bands of Pb-doped alkali halides. The spectral features are discussed in terms of a molecular orbital theory based on a quasicomplex Pb²⁺(X^-)₆ model similar to the complex model for the doped alkali halides. It is shown that not only Pb²⁺ 6s and 6p extended states near the band edges but also X^- p states contributing to upper valence bands are localized by amorphization. The transitions from the localized Pb²⁺ 6s to 6p states produce the spin-orbit allowed ³P₁ and dipole allowed ¹P₁ states responsible for the two Gaussians. The localized X^- p states lie deeper in energy than the localized Pb²⁺ 6s state and only contribute to higher-energy absorption above the Gaussian bands, giving the reason for the reduced absorption near the fundamental edge. The blueshift of the optical energy gap is attributed to the disappearance of k dispersions for these one-electron states.

Full text of DOI:10.1103/PhysRevB.58.11401

PHYSICAL REVIEW B
VOLUME 58, NUMBER 17
1 NOVEMBER 1998-I
Amorphization-induced strong localization of electronic states in CsPbBr3 and CsPbCl3 studied
by optical absorption measurements
S. Kondo, T. Sakai, H. Tanaka, and T. Saito
Department of Applied Physics, Faculty of Engineering, Fukui University, Bunkyo, Fukui 910, Japan
͑Received 22 December 1997͒
Optical absorption spectra of amorphous CsPbX3 films (XϭBr,Cl͒ are characterized by two Gaussian bands
near the fundamental edge, with the optical energy gap largely blueshifted and the absorption intensity strongly
reduced as compared with the crystalline films. The peak energies of the bands are close to those of the A and
C bands of Pb-doped alkali halides. The spectral features are discussed in terms of a molecular orbital theory
based on a quasicomplex Pb2ϩ(XϪ)6 model similar to the complex model for the doped alkali halides. It is
shown that not only Pb2ϩ 6s and 6p extended states near the band edges but also XϪ p states contributing to
upper valence bands are localized by amorphization. The transitions from the localized Pb2ϩ 6s to 6p states
produce the spin-orbit allowed 3P1 and dipole allowed 1P1 states responsible for the two Gaussians. The
localized XϪ p states lie deeper in energy than the localized Pb2ϩ 6s state and only contribute to higher-energy
absorption above the Gaussian bands, giving the reason for the reduced absorption near the fundamental edge.
The blueshift of the optical energy gap is attributed to the disappearance of k dispersions for these one-electron
states. ͓S0163-1829͑98͒06341-3͔
I. INTRODUCTION
The compounds CsPbX3 (XϭBr,Cl͒ crystallize in a
slightly distorted perovskite structure. Their optical proper-
ties are governed by the octahedral quasicomplex Pb2ϩ(XϪ)6
embedded in a simple cubic matrix of Csϩ ions. The six XϪ
ions are located at the face-centered positions of the cube and
the cation Pb2ϩ is at the cube center. Heidelich et al.16 has
calculated the band structure of the compounds based on an
empirical linear combination of atomic orbitals ͑LCAO͒
method completely neglecting the electronic orbitals of ce-
sium: Upper valence bands are constructed from the Pb2ϩ 6s
and BrϪ 4p or ClϪ 3p orbitals, and lower conduction bands
from Pb2ϩ 6p orbitals; a cationic direct energy gap is located
at the R point in the Brillouin zone due to positive and nega-
tive k dispersions of the uppermost valence and lowermost
conduction bands, respectively, along the ⌫-R direction. The
low-energy optical absorption16–18 and reflection16,19–21
spectra, which are characterized by a sharp first exciton
(R-point exciton͒ peak around 2.3 eV for CsPbBr3 and 3.0
eV for CsPbCl3, have indeed been well explained in the
framework of this model.
The Pb atoms in PbX2 (XϭI,Br,Cl,F͒ and CsPbX3 (X
ϭBr,Cl͒ make a dominant contribution to the optical prop-
erties of the compounds in the region near the optical energy
gap. In PbX2, all of which can be amorphized by quench
deposition,1–4 optical absorption near the fundamental edge
is based on Pb 6s to 6p transitions exhibiting a sharp cat-
ionic exciton peak in the crystalline (c) state (PbI2 is an
extensively investigated material both experimentally5 and
theoretically,6 though experimental studies have only been
reported for PbBr2,7–11 and PbCl2 ͑Refs. 7–9, 11, and 12͒; as
to PbF2 only
a
few, but both theoretical13 and
experimental,9,14 works are available in literature͒. In the
amorphous (a) state, their absorption spectra are classified
according to the crystal structure into which the compounds
crystallize. In a-PbI2 ͑which crystallizes into a layer struc-
ture͒, no structure is observed near the fundamental edge,1
while other a-PbX2 with XϭBr, Cl, and F ͑which crystallize
into an orthorhombic structure͒ are characterized by a promi-
nent first absorption band due to Pb 6s to 6p excitation.2–4
According to our line-shape analysis performed on the
absorption spectra of amorphous lead halides,15 a-PbI2 is a
typical material obeying the Tauc law, as in the case of or-
dinary covalent semiconductors. In contrast, the first band of
a-PbX2 with XϭBr, Cl, and F is by no means fitted with any
power law, but instead an excellent fit to the band is obtained
with a Gaussian function. Such a distinct difference between
PbI2 and PbX2 originates in the difference in their electronic
energy band structure. The Gaussian band in a-PbX2 is ex-
plained as being due to localized electronic transitions of
nonexcitonic origin within Pb2ϩ ions affected by inhomoge-
neous, local electric fields in the disordered network. Based
on the obtained fitting parameters, an ‘‘ion-glass’’ model has
been introduced, in which each Pb2ϩ ion is surrounded by
nine neighboring XϪ ions without any well-defined site sym-
metry around it.
The motivation of the present study is based on the as-
sumption that the ion-glass model such as proposed for
a-PbX2 may also be applicable to a-CsPbX3; in a-CsPbX3,
the optical absorption at low photon energies may be caused
by the cationic electronic transitions within Pb2ϩ ions sur-
rounded by ‘‘six’’ ͑instead of ‘‘nine’’ for a-PbX2) neighbor-
ing XϪ ions. It is expected that a distorted ͑due to amor-
phization͒ quasicomplex Pb2ϩ(XϪ)6 embedded in
a
disordered Csϩ-ion matrix leads to enhanced localization of
the cationic electronic transitions ͑within the Pb2ϩ ion͒ due
to intervening Csϩ ions as compared to the case of a-PbX2,
since the electronic orbitals of cesium do not contribute to
the electronic states near the band edges as stated above.
Therefore, it is useful to investigate optical properties of
a-CsPbX3 for obtaining a further clue to the nature of the ion
glass. In the present study, amorphous films have been ob-
0163-1829/98/58͑17͒/11401͑7͒/$15.00
PRB 58
11 401
©1998 The American Physical Society

11 402
S. KONDO, T. SAKAI, H. TANAKA, AND T. SAITO
PRB 58
deposition. The first term in Eq. ͑1͒ corresponds to the opti-
cal density of the film-deposited substrate and the second
term is the optical density of the substrate. Correction for
reflectance at the film surfaces ͑both the substrate/film and
vacuum/film interfaces͒ is involved in the first term. It is
possible to represent Eq. ͑1͒ in terms of quantities indepen-
dent of the characteristics of the two individual detectors
͑such as sensitivity, its wavelength dependence, etc.͒,
1ϪR0Rr
ODϭlog10
,
͑2͒
1ϪR ͒T
͑
0
r
where TrϭI/I0 , RrϭJ/J0 , and R0 is the reflectivity of the
substrate. Then the values of OD can be determined from the
measurements of the intensity ratios (Tr and Rr) of the light
beams irradiating the individual detectors before and after
the film deposition, using the predetermined values of R0.
The OD values thus determined are expected to be very ac-
curate, since the optical configuration is kept unchanged
throughout all the measurements and since all the imbalances
in intensity between the probing and reference light are can-
celled out.
The substrate ͑silica glass with 1 mm thickness͒ was put
on a copper sample holder with a square light path
4ϫ4 mm2, attached to the bottom of a copper vessel in a
cryostat. The vessel was filled with liquid nitrogen, or heated
with a heater to control the temperature of the substrate. This
permits us to measure in situ OD spectra for both the amor-
phous and crystalline phases of the same film and the crys-
tallization temperature as well.
FIG. 1. The schematic view of the light path for in situ mea-
surements of reflection-corrected OD spectra of a film quench de-
posited onto a cooled ͑to 77 K͒ substrate.
tained for CsPbX3 by quench deposition, and their absorp-
tion spectra have been measured in the range up to 6.2 eV.
Based on the line shape analysis of the spectra, we will give
a thorough discussion of the nature of optical absorption and
the related electronic state of a-CsPbX3 including the com-
parison with the a-PbX2 case.
II. EXPERIMENT
As starting materials CsX and PbX2 (XϭBr,Cl͒ of 99.9%
purity were used. For the preparation of the compounds
CsPbX3, stoichiometric amounts of CsX and PbX2 in powder
form were thoroughly mixed together and molten for 15 min
at 690 °C for XϭBr and 600 °C for XϭCl in a silica-tube
container purged with Ar gas. The container was then
quenched in ice water to ensure homogeneity of the resulting
compounds.
Simultaneous measurements of optical absorption and re-
flection were performed in situ on CsPbX3 films quench de-
posited onto silica-glass substrates at 77 K at a rate of about
20 nm minϪ1. The deposition was carried out in a vacuum of
about 9ϫ10Ϫ6 Pa using a tungsten basket heating element
placed 8 cm in front of the substrate. The spectral measure-
ments ͑resolution, 0.2 nm͒ were performed by a double-
beam detection method, using a grating monochromator in
combination with a 150-W xenon lamp as light source.
To measure absorption spectra accurately ͑for the purpose
of performing the line-shape analysis of the resulting spec-
tra͒, we employed an improved optical configuration shown
in Fig. 1 ͑where the reference-light path in the double-beam
detection method is omitted͒. The p-polarized monochro-
matic light is incident on the substrate at an incident angle of
45°. The optical density ͑OD͒ of the film was defined as
III. RESULTS
In Fig. 2 we compare the fundamental absorption spectra
of a quench-deposited CsPbBr3 film ͑upper half͒ with those
of a quench-deposited PbBr2 film ͑lower half, from Ref. 2͒.
Spectra 1 were first measured at 77 K for the as-deposited
films. Then the films were annealed for 10 min at 500 K for
CsPbBr3 and 400 K for PbBr2, and cooled again to 77 K to
measure spectra 2. The as-deposited PbBr2 film is in the
amorphous state and the annealed one is in the crystalline
state.2 In CsPbBr3, spectrum 1 is composed of two broad
bands peaking at 3.87 and 5.23 eV. By annealing the film, a
sharp excitonic peak shows up at 2.357 eV characteristic of
crystalline CsPbBr3,21 as seen from spectrum 2. It should be
noted here that the as-deposited film exhibits a strongly re-
duced optical absorption in comparison to the annealed film.
Furthermore, spectrum 1 has about a 1 eV larger optical
energy gap than spectrum 2. It is interesting to note that the
as-deposited CsPbBr3 film has almost the same optical en-
ergy gap ͑about 3.5 eV͒ as that of the a-PbBr2 film, despite
the large difference in the gap after annealing the films.
Figure 3 shows the change in transmittance at 3.26 eV
during heating of a CsPbBr3 film. In the measurement, the
as-deposited film was heated at a rate of 1 K minϪ1 up to
500 K ͑curve 1͒ and then the film was immediately cooled to
77 K at a rate of 10 K minϪ1 to measure the second curve
͑curve 2͒ at the same heating rate. Curve 1 clearly shows a
drastic change ͑decrease͒ in the transmittance in a narrow
temperature range of 4 K near 298 K, while curve 2 no
longer exhibits such a marked change and was shown to be
DϪJ
DϪJ0
ODϭlog10
Ϫlog10
,
͑1͒
I
I0
where D is the intensity of the incident light, I0 and J0 are
the intensities of transmitted and reflected light, respectively,
from the substrate before the deposition of the film, and I
and J are the corresponding light intensities after the film

PRB 58
AMORPHIZATION-INDUCED STRONG LOCALIZATION . . .
11 403
FIG. 2. Comparison of fundamental absorption spectra of a
FIG. 4. Comparison of fundamental absorption spectra of a
quench-deposited film of CsPbCl3 ͑upper half͒ to those of PbCl2
͑lower half, from Ref. 3͒, measured at 77 K for the as-deposited
͑amorphous, 1͒ and annealed ͑crystalline, 2͒ films.
quench-deposited film of CsPbBr3 ͑upper half͒ to those of PbBr2
͑lower half, from Ref. 2͒, measured at 77 K for the as-deposited
͑amorphous, 1͒ and annealed ͑crystalline, 2͒ films.
Such a drastic change in transmittance as above was also
observed for a-CsPbCl3, leading to a crystallization tem-
perature of 302 K, very close to that of a-CsPbBr3 in con-
trast to the considerably lower crystallization temperature for
PbCl2, 281.5 K,3 than for PbBr2.
reversible ͑below 500 K͒ by measuring a third curve. The
drastic change in curve 1 is very similar in sharpness to
previous results on a-PbBr2,2 and provides evidence of a
well-defined phase transition from amorphous to crystalline
states in the quench-deposited CsPbBr3 film, though struc-
tural studies are necessary for a direct support. ͑It has been
reported for a ternary Ge-Sb-Te solid solution, which is a
promising material for fast phase-change optical disks,22,23
that an abrupt transmittance change during slow heating of
the amorphous film is due to nucleation followed by a fast
grain-growth process resulting in a crystalline film.24͒ The
transition temperature ͑crystallization temperature, Tc),
which we defined here as the onset temperature for the dras-
tic change, was 296 K as compared with 335 K for PbBr2.
The irreversible change just above the drastic change ͑300–
420 K in curve 1͒ is considered to be due to crystal growth in
the film.
Figure 4 is a comparison of the fundamental absorption
spectra of a quench-deposited CsPbCl3 film ͑upper half͒ with
those of a quench-deposited PbCl2 film ͑lower half, from
Ref. 3͒ in their amorphous ͑spectra 1͒ and crystalline ͑spectra
2͒ states. These spectra were obtained in the same way as
those of the bromides but with an annealing temperature of
400 K for both CsPbCl3 and PbCl2. As in the case of the
bromides, the spectrum of a-CsPbCl3 is composed of two
broad bands with the peaks at 4.43 and 5.88 eV and exhibits
nearly the same optical energy gap ͑about 4 eV͒ as that of
a-PbCl2; the amorphization is again characterized by a large
blueshift ͑about 1 eV͒ of the fundamental edge and signifi-
cant reduction in the absorption intensity; after crystalliza-
tion, a very sharp exciton peak appears at 3.013 eV.
It is worth noting that the full widths at half maximum
͑FWHM’s͒ of the exciton peaks, 15 meV for c-CsPbBr3 and
14 meV for c-CsPbCl3, are comparable to that of the reflec-
tion spectrum at 4.2 K of a single crystal of CsPbCl3, 12
meV,21 and are much smaller than those of the ‘‘improved’’
films in Ref. 18 ͑where the FWHM’s are, though not explic-
itly given, of the order of 30 meV for both of the CsPbBr3
and CsPbCl3 films as are read from the presented spectra at
77 K͒. This suggests that the process of amorphization and
subsequent heat treatment ͑annealing͒ is favorable for
achieving high-quality polycrystalline films free from strains
and lattice defects.
IV. DISCUSSION
FIG. 3. The change in transmittance at photon energy 3.26 eV
during heating ͑1 K minϪ1), measured for the first ͑1͒ and second
͑2͒ heating cycles of a quench-deposited CsPbBr3 film.
It has been shown15 that the first absorption bands of
a-PbX2 (XϭBr,Cl,F͒ are well fitted to single Gaussian func-

11 404
S. KONDO, T. SAKAI, H. TANAKA, AND T. SAITO
PRB 58
FIG. 5. Line-shape analysis of the absorption spectrum of
FIG. 6. Line-shape analysis of the absorption spectrum (M) of
a-CsPbCl3 similar to that for CsPbBr3, with the same notations for
the resulting curves as in Fig. 5.
a-CsPbBr3. The measured spectrum (M) is decomposed into two
Gaussian bands, the low- (G1) and high- (G2) energy components,
with the remainder (M minus G1 minus G2) as the background
absorption (B).
plexes Pb2ϩ(XϪ)6 without any well-defined site symmetry
around the central Pb2ϩ ion, are embedded in a disordered
Csϩ-ion network. The small differences in magnitude of the
fitting parameters between a-CsPbX3 and a-PbX2 are con-
sidered to be due to the difference in the coordination num-
ber of the quasicomplexes.
A more noticeable result of the spectral decomposition is
that, in contrast to the case of a-PbX2, not only the first
absorption bands but also the second bands of a-CsPbX3 are
well fitted to the Gaussian functions. Therefore, it is plau-
sible to relate both bands to localized excitations of Pb2ϩ
ions. We note here that the values of E2ϪE1, 1.398 eV for
a-CsPbBr3 and 1.460 eV for CsPbCl3, are comparable to the
Pb 6p spin-orbit splitting energy, 1.3 eV.6
tions, as compared to the c-phase excitonic absorption bands
fitted to multiple Lorentzian functions. As mentioned in Sec.
I, the fitting parameters for the Gaussian bands have led to an
‘‘ion-glass’’ model for the amorphous state, in which each
individual Pb2ϩ ion is surrounded ͑and thus localized͒ by
nine negative ions forming the quasicomplex Pb2ϩ(XϪ)9
without any well-defined site symmetry around the central
Pb2ϩ ion.
In a-CsPbX3 (XϭBr,Cl͒, the absorption spectra are com-
posed of two broad bands ͑Figs. 2 and 4͒, and it is possible to
decompose the spectra into two Gaussian functions. The re-
sults are shown in Figs. 5 and 6. In both figures, the mea-
sured spectra ͑curves M) are nicely decomposed into two
Gaussian bands ͑curves G1 and G2); the difference in inten-
sity between the measured spectrum and the total intensities
of the two Gaussian bands (M minus G1 minus G2, curves
B) is, indeed, almost zero in the photon energy region up to
5.7 eV for a-CsPbBr3 ͑Fig. 5͒ and in the whole measurement
range for a-CsPbCl3 ͑Fig. 6͒. The peak energies (E1 ,E2)
and FWHM’s (⌫1 ,⌫2) of the respective Gaussian bands are
listed in Table I together with the peak energy difference
(E2ϪE1). For comparison, the corresponding values of the
first Gaussian bands previously obtained15 for a-PbBr2 and
a-PbCl2 are also listed in the table.
It is instructive to compare the spectra of a-CsPbX3 with
the absorption spectra25,26 of Pb-doped CsX crystal
(XϭBr,Cl͒. According to Ref. 25, the latter spectra ͑at room
temperature͒ are composed of two Gaussian bands termed A
and C, with a vibration-induced weak subband B between
them. The energy locations (EA ,EC) and FWHM’s (⌫A ,⌫C)
of the main bands A and C are listed in Table II together
with the peak-energy difference (ECϪEA). The two bands A
and C are known to be due to the spin-orbit allowed 1S0
3
1
1
→ P1 and the dipole allowed S0→ P1 transitions, respec-
tively, in the Pb2ϩ ion. As seen from the comparison of
Tables I and II, there exists a close similarity between the
values of EA and E1 for both bromides and chlorides. Fur-
thermore, the values of ECϪEA , which are mainly deter-
mined from the strength of spin-orbit interaction of the Pb
6p electron, are relatively close to those of E2ϪE1 in both
cases of XϭBr and Cl. Therefore, it is useful to discuss the
G1 and G2 bands of a-CsPbX3 on the basis of the physical
model applied to the doped alkali halides. ͑There is no large
difference in the absorption feature between Pb-doped ce-
It is noted that a-CsPbX3 and a-PbX2 have similar values
of E1 and ⌫1 in both halides (XϭBr,Cl͒. This indicates that,
in analogy with the case of a-PbX2, the first absorption
bands of a-CsPbX3 arise from localized, cationic electronic
transitions within Pb2ϩ ions surrounded by six ͑instead of
nine for a-PbX2) XϪ ions; these ions, forming quasicom-
TABLE I. The peak energies (E1 ,E2), their difference (E2
ϪE1), and FWHM’s (⌫1 ,⌫2) of the Gaussian bands (G1 ,G2) of
a-CsPbX3 for XϭBr and Cl in unit of eV. Corresponding values of
the first Gaussian bands of PbX2 from Ref. 15 are also listed.
TABLE II. The peak energies (EA ,EC), their differences (EC
ϪEA), and FWHM’s (⌫A ,⌫C) of the A and C absorption bands of
Pb2ϩ-doped CsX single crystals for XϭBr and Cl in units of eV,
from Ref. 25.
E1
E2
E2ϪE1
⌫
⌫
2
1
a-CsPbBr3
a-PbBr2
a-CsPbCl3
a-PbCl2
3.843
3.700
4.406
4.418
5.241
1.398
0.444
0.400
0.510
0.410
1.533
1.138
EA
EC
ECϪEA
⌫
⌫
C
A
5.866
1.460
CaBr:Pb2ϩ
CsCl:Pb2ϩ
4.00
4.46
5.64
6.20
1.64
1.74
0.32
0.34
0.54
0.57

PRB 58
AMORPHIZATION-INDUCED STRONG LOCALIZATION . . .
11 405
sium halides with bcc lattice and other Pb-doped alkali ha-
lides with fcc lattice, as exemplified in Ref. 25.͒
tion spectra in the region above the excitonic transition en-
ergies exhibit similar features in outline to the a-phase ones
in the same energy region as seen in Figs. 2 and 4 ͑lower
halves͒.
Generally, the absorption spectra of s2-configuration ions
doped in alkali halides are interpreted in terms of a molecu-
lar orbital theory based on a complex model. Bramanti
et al.27 have performed molecular orbital calculations for T1-
doped KCl based on an octahedral T1ϩ͑ClϪ)6 complex
model. Following their model, we take into account the 6s
and 6p orbitals of the central Pb2ϩ ion and the 4p or 3p
orbitals of the XϪ ion to construct molecular orbitals of the
Pb2ϩ(XϪ)6 quasicomplex. From the transformation proper-
ties of these atomic orbitals in the Oh point group (a1g for
In contrast, in CsPbX3 (XϭBr,Cl͒, there occurs a notice-
able change in spectral shape by amorphization ͑Figs. 2 and
4, upper halves͒: i.e., the large blueshift ͑ϳ1 eV͒ of the fun-
damental edge and significant reduction in the integrated ab-
sorption intensity ͑by a factor of ϳ1.6 for XϭBr and ϳ2 for
XϭCl in the measured region͒, giving rise to the two-
Gaussians shape for the spectra. In terms of energy band
structure, these features may be explained as follows.
As mentioned in Sec. I, the optical properties of
c-CsPbX3 are governed by the octahedral Pb2ϩ(XϪ)6 quasi-
complex ͑embedded in a simple cubic Csϩ-ion matrix͒: The
band structure calculation16 based on an LCAO method in-
deed shows that upper valence bands are constructed from
the Pb2ϩ 6s and XϪ 4p or 3p orbitals, and lower conduction
bands from Pb2ϩ 6p orbitals; the low-energy absorption
spectra of c-CsPbX3 are well interpreted in the framework of
this band structure. In the present application ͑both the c and
a phases͒, however, a convenient approach to the band struc-
ture may be provided by an LCMO ͑linear combination of
molecular orbitals͒ method based on the quasicomplex as
expected, though it is essentially the same as the LCAO
method.
In the LCMO method, as suggested from the molecular
orbital theory for the doped alkali halides mentioned above,
upper valence bands of c-CsPbX3 may be constructed from
the aa1g and eng orbitals, and lower conduction bands from the
ta1u orbitals. Other molecular orbitals may only contribute to
much deeper valence bands in energy. The cationic nature of
the (R-point͒ exciton transition ͑the LCAO result16͒ is com-
patible with the transition from aa1g-like valence to ta1u-like
conduction bands, since there is almost no contribution of
halogen p orbitals to the aa1g and t1au orbitals. Charge transfer
transition is also expected to occur near the fundamental
edge, owing to ͑positive͒ k dispersion for the eng-orbital en-
ergy ͑of the upper valence bands͒ due to making extended
states. By amorphization, however, there occurs significant
change in the energy band as suggested from the spectral
change. Both the conduction states coming from ta1u and the
valence states coming from aa1g and egn are considered to
converge to their own localized states with particular
eigenenergies. The resulting one-electron localized states
may be of spin-orbit split ⌫Ϫ6 (jϭ1/2) and ⌫8Ϫ (jϭ3/2) char-
acters for ta1u and of ⌫6ϩ(jϭ1/2) character for a1ag in the
double-group notation for Oh , since then it is possible to
produce the spin-orbit allowed 3P1 state and the dipole al-
lowed 1P1 state responsible for the G1 and G2 bands, re-
spectively, from the transitions ⌫ϩ6 →⌫6Ϫ and ⌫6ϩ→⌫8Ϫ, in
the limit of the Russell-Saunders coupling. ͑Strictly speak-
ing, the Oh symmetry of the Pb2ϩ(XϪ)6 quasicomplex is not
well defined in the a phase.͒ On the other hand, the eng lo-
calized states are, like the molecular orbital case for Pb-
doped alkali halides, expected to lie deeper in energy than
the ⌫ϩ6 ͑or aa1g) localized state, and thus their contribution to
the absorption spectra ͑due to transitions to the ⌫Ϫ6 and ⌫8Ϫ
localized states͒ may occur at high energies above the G1
and G2 bands. This is favorable for explaining the signifi-
6s; t1u for 6p; a1g , eg , and t1u for 4p␴ or 3p␴; t1u , t1g
,
t
2u , and t2g for 4p␲ or 3p␲), there arise one occupied
antibonding (aa1g), two occupied bonding (2t1bg), three oc-
cupied nonbonding (eng ,t2nu, and t2ng), and one unoccupied
antibonding (ta1u) molecular orbitals. The transition from aa1g
a
3
1
to t1u produces two allowed states T1u and T1u , which are
responsible for the A and C bands, respectively, of the doped
alkali halides. In the case of Pb-doped alkali halides, it has
been shown from an f-sum measurement28 of the A, B, and
C bands that the contribution of the halogen p states to the
highest occupied aa1g orbital ͑as well as to the unoccupied ta1u
3
1
orbital͒ is very small ͑therefore, the T1u and T1u states are
3
1
denoted as P1 and P1, respectively͒. This is favorable for
relating the G1 and G2 bands of a-CsPbX3 to excitation ͑to
3P1 and 1P1 states, respectively͒ of the central Pb2ϩ ion in
the Pb2ϩ(XϪ)6 quasicomplex; the contribution of halogen p
orbitals to these bands is considered to be negligible. We
note that, in the Pb-doped alkali halides, a higher-energy
absorption band, namely, the D band, has been assigned29,30
as due to charge-transfer transitions from eng to t1au (egn is the
second-highest occupied orbital͒.
As is well known, valence and conduction bands in semi-
conductors retain their meaning even in the amorphous state.
However, a certain amount of the extended states near the
band edges are localized by amorphization. The first absorp-
tion bands of a-PbX2 (XϭBr,Cl͒ have indeed been related to
electronic transitions between localized states,15 i.e., from
the filled localized states just above the mobility edge of the
valence band to the empty ones just below the conduction
mobility edge. The transitions are spatially allowed because
the uppermost valence and the lowest conduction bands are
both cationic (Pb2ϩ 6s- and 6p-like, respectively͒; the os-
cillatorlike character of the first band is attributed to the high
densities of the localized states due to a relatively flat band
structure of PbX2. Furthermore, it has been shown31 from an
‘‘f-sum rule,’’ applied to the Gaussian function for the first
band in the a phase and the multiple Lorentzian functions for
the excitonic absorption band in the c phase, that, by amor-
phization, all the extended states contributing to the c-phase
excitonic transitions are localized and take part in the local-
ized absorption responsible for the Gaussian band. It is there-
fore plausible to assume that the high-energy absorption
above the first band of a-PbX2 corresponds to transitions
related to extended states ͑Pb 6s-like localized to Pb 6p-like
extended, Pb 6s-like extended to Pb 6p-like localized,
and/or Pb 6s-like extended to Pb 6p-like extended states,
with a certain contribution of X 4p- or 3p-like extended
states to the transitions as well͒. Indeed, the c-phase absorp-

11 406
S. KONDO, T. SAKAI, H. TANAKA, AND T. SAITO
PRB 58
cantly reduced absorption intensity in the measurement en-
ergy region, below 6.2 eV. Due to such strong localizations
of the one-electron states as above, the positive and negative
k dispersions that exist in the c phase of the uppermost va-
lence and lowermost conduction bands, respectively, along
the ⌫-R direction in the Brillouin zone, which is responsible
for the very small optical energy gap ͑as well as for the
R-point exciton absorption͒ in the c phase, may disappear
͑the quantity k is no longer well defined for localized states͒,
resulting in the absence of low-energy absorption. This ac-
counts for the large blueshift of the optical energy gap.
doped CsX crystals, respectively. For this reason, an LCMO
band-structure approach starting from the molecular orbitals
of the Pb2ϩ(XϪ)6 quasicomplex similar to the complex
model for the doped alkali halides is used to explain the
spectral change due to amorphization: By amorphization,
both the conduction states coming from ta1u and the valence
states coming from a1ag and eng converge to their own local-
ized states with particular eigenenergies. As a result, the op-
tical absorption associated with the aa1g to t1au transitions is
changed to two discrete absorptions arising from the transi-
tions from the 6s localized state to the spin-orbit split 6p1/2
and 6p3/2 localized states of the Pb2ϩ ion, responsible for the
first and second Gaussians, respectively. The eng localized
states, lying deeper in energy than the Pb2ϩ 6s localized
state, are considered to contribute to higher-energy optical
absorption above the G1 and G2 bands. This accounts for the
reduction of the integrated absorption intensity. On the other
hand, the blueshift of the optical energy gap is attributed to
the disappearance of k dispersions for these one-electron
states.
These considerations are based on an ‘‘ion-glass’’ model,
in which quasicomplexes Pb2ϩ(XϪ)6 without well-defined
site symmetry around the central Pb2ϩ ion are embedded in a
disordered Csϩ-ion matrix, with the Pb2ϩ-ion excitation en-
ergies strongly perturbed ͑Stark effect͒ in different ways due
to different microscopic environments in the individual qua-
sicomplexes. Here the intervening ͑between Pb2ϩ ions͒ Csϩ
ions act as the cause for the stronger electronic-state local-
ization for a-CsPbX3 than for a-PbX2.
V. CONCLUSION
We have obtained amorphous films of CsPbX3 (XϭBr,Cl͒
by quench deposition onto 77-K substrates. Upon slow heat-
ing they show sharp crystallization behavior in a narrow tem-
perature range, exhibiting a well-defined crystallization tem-
perature of 296 K for CsPbBr3 and 302 K for CsPbCl3. The
UV absorption spectra of a-CsPbX3 are composed of two
broad bands ͑first and second bands͒. The first bands are very
similar in shape and energy location to the first absorption
bands of respective a-PbX2 resulting in nearly equal optical
energy gaps between a-CsPbX3 and a-PbX2. It is shown
that in a a-CsPbX3 the spectra are nicely decomposed into
two Gaussian functions, as compared to the case of a-PbX2,
where a nice fit to a Gaussian function is obtained for the
first band, but not for the higher-energy bands. Further, there
exist a noticeable spectral difference between the c- and
a-CsPbX3 in contrast to the case of PbX2, i.e., the
amorphization-induced large ͑ϳ1 eV͒ blueshift of the funda-
mental edge and significant reduction of the integrated ab-
sorption intensity ͑by a factor of about 1.6 for CsPbBr3 and
about 2 for CsPbCl3 in the measured region͒.
ACKNOWLEDGMENTS
This work was partly supported by The Hokuriku Indus-
trial Advancement Center and partly by a Grant-in-Aid for
Scientific Research from the Ministry of Education, Science,
Sports and Culture in Japan.
The peak energies of the first and second Gaussians of
a-CsPbX3 are close to those of the A and C bands of Pb-
1 S. Kondo, M. Shiraki, and T. Saito, Jpn. J. Appl. Phys., Part 1 31,
3399 ͑1992͒.
13 B. Velicky and J. Masek, Solid State Commun. 58, 663 ͑1986͒.
14 D. L. Alov and S. I. Rybchenko, J. Phys.: Condens. Matter 7,
1475 ͑1995͒.
2 S. Kondo, T. Arakawa, and T. Saito, Jpn. J. Appl. Phys., Part 1
32, 4511 ͑1993͒.
15 S. Kondo, Phys. Status Solidi A 153, 529 ͑1996͒.
16 K. Heidelich, H. Kunzel, and J. Treusch, Solid State Commun.
25, 887 ͑1978͒.
3 S. Kondo, H. Maruyama, and T. Saito, Phys. Status Solidi A 147,
453 ͑1995͒.
4 S. Kondo, M. Itoh, and T. Saito, Phys. Status Solidi A 154, 591
͑1996͒.
17 H. Ito, H. Onuki, and R. Onaka, J. Phys. Soc. Jpn. 45, 2043
͑1978͒.
5 For example, Le Chi Thanh, C. Depeursinge, F. Levy, and E.
18
¨
D. Frohlich, K. Heiderich, H. Kunzel, G. Trendel, and J. Treush,
Mooser, J. Phys. Chem. Solids 36, 699 ͑1975͒.
6
J. Lumin. 18/19, 385 ͑1979͒.
¨
¨
For example, I. Ch. Schluter and M. Schluter, Phys. Rev. B 9,
1652 ͑1974͒.
19 B. A. Belikovich, I. P. Pashchuk, and N. S. Pidzyrailo, Opt. Spec-
trosc. 42, 62 ͑1977͒.
7 W. C. De Gruijter, J. Solid State Chem. 6, 151 ͑1973͒.
8 A. F. Malysheva and V. G. Plekhanov, Opt. Spectrosc. 34, 302
͑1973͒.
20 L. N. Amitin, A. T. Anistratov, and A. I. Kuznetsov, Sov. Phys.
Solid State 21, 2041 ͑1979͒.
9 V. G. Plekhanov, Phys. Status Solidi B 57, K55 ͑1973͒.
10 A. J. H. EIjkelenkamp and K. Vos, Phys. Status Solidi B 76, 769
͑1976͒.
21 I. P. Pashuk, N. S. Pidzyrailo, and M. G. Matsko, Sov. Phys.
Solid State 23, 1263 ͑1981͒.
22 J. H. Coombs, A. P. J. M. Jongenelis, W. Van Es-Spiekman, and
B. A. J. Jacobs, J. Appl. Phys. 78, 4906 ͑1995͒.
23 J. H. Coombs, A. P. J. M. Jongenelis, W. Van Es-Spiekman, and
B. A. J. Jacobs, J. Appl. Phys. 78, 4918 ͑1995͒.
24 N. Ohshima, J. Appl. Phys. 79, 8357 ͑1996͒.
11 M. Fujita, H. Nakagawa, K. Fukui, H. Matsumoto, T. Miyanaga,
and M. Watanabe, J. Phys. Soc. Jpn. 60, 4393 ͑1991͒.
12 J. Kanbe, H. Takezoe, and R. Onaka, J. Phys. Soc. Jpn. 41, 942
͑1976͒.

PRB 58
AMORPHIZATION-INDUCED STRONG LOCALIZATION . . .
11 407
25 S. Radhakrishna and K. P. Pande, Phys. Rev. B 7, 424 ͑1973͒.
26 M. Nikl, K. Nitsch, and K. Polak, Phys. Rev. B 51, 5192 ͑1995͒.
27 D. Bramanti, M. Mancini, and A. Ranfagni, Phys. Rev. B 3, 3670
͑1971͒.
28 P. R. Collins and W. J. Fredericks, J. Phys. Chem. Solids 47, 529
͑1986͒.
29 T. Tsuboi, Physica B 96, 341 ͑1979͒.
30 S. Hashimoto and Y. Ohiwa, J. Phys. Soc. Jpn. 48, 1655
͑1980͒.
31 S. Kondo, H. Maruyama, and T. Saito, Phys. Status Solidi A 158,
529 ͑1996͒.