![](https://csdnimg.cn/release/download_crawler_static/15133099/bg3.jpg)
the 3D perovskite framework and solve above problems, which we
will discuss later.
Besides tolerance factor t, the octahedral factor
m
, which is
additional semiempirical geometric parameter, is used to evaluate
the octahedral stability [83]. The
m
is defined as
m
¼ r
B
=r
X
(2)
The range of
m
between 0.442 and 0.895 would be beneficial for
the stable [BX
6
]
4-
octahedral. We compile the
m
value of B-site and
doping B-site (applied in perovskite NCs)erelated octahedron in
Fig. 2b. The choice of B-site cation not only has to satisfy the range
of tolerance factor t but also needs to meet the requirements of
octahedral factor
m
. Although a fair amount of efforts has been
made to explore the substitution of Pb, few fungible B-site cations
are available for 3D LHP structures. Apart from the structure sta-
bility, the luminescence characteristics and electronic structure
change a lot owing to the alteration of B-site cations [84e89].Upto
now, lead-free perovskites have not exhibited satisfactory proper-
ties. On the contrary, incorporation of a small of dopants would not
alter the basic characteristics of host LHPs but could remarkably
improve their stability or optical properties. Over the past years,
various metal ions, including Sn
2þ
,Bi
3þ
,Mn
2þ
, and RE ions (e.g.,
Ce
3þ
,Tb
3þ
,Eu
3þ
), have been doped into halide perovskites, and a
broad range of exotic properties have been imparted to this
prominent materials [67,90].
The unsteadiness of phase structure is severer in the I-based
perovskite than in the Br-based and Cl-based perovskite. It is
known that
a
-APbI
3
(cubic) is desirable for superior applications in
light absorption, luminescence, and optoelectronic devices. How-
ever, APbI
3
(with monotypic A-site cation, such as FA, MA or Cs) is
more stable in
d
phase that exhibits hexagonal for larger tolerance
factor (FA) and orthorhombic for small tolerance factor (Cs) [41,42].
Fig. 3a presents the structure and lattice parameters of
a
-phase and
hexagonal
d
-phase. Compared with
a
-phase,
d
-phase owns the
face-sharing [PbI
6
]
4-
octahedron alignment rather than corner
sharing; this results in the change of lattice distance. Take FAPbI
3
as
an example [41], too large FA cation causes a highly anisotropic
strain of cubic phase lattice (Fig. 3b), leading to the deviation from
the equilibrium interplanar distances, whereas the lattice strain
could be relaxed by alloying smaller MA cation. In a similar way,
double or triple cations of (Cs, FA)PbI
3
or (Cs, MA, FA)PbI
3
show the
same achievements [34,36,43,91,92] in better stability. A-site
doping indeed has revealed a feasible strategy for improving the
stability of phase structure.
In contrast to the A-site, B-site doping faces more challenges
into perovskite lattice, and they also play a big role in phase sta-
bility. On the contrary, most of discussion focused on the cases
whether dopants were introduced into the matrices of LHPs. The
phase structure of doped perovskite does not change generally after
replacing a tiny amount of Pb with Mn, Bi, or other B-site dopants
but may induce the lattice contraction/expansion or change the size
of crystal particles [46,60,61,93e95]. Zou et al [48] reported that
doping traces of Mn
2þ
(with an actual concentration of 2.08 mol %)
brought about the lattice contraction in CsPbBr
3
QDs. They calcu-
lated the three-dimensional stacking diagram of the CsPbBr
3
:Mn
crystal by density functional theory (DFT) (Fig. 3c); the much
shorter Mn-Br bonds compared with Pb-Br bonds were responsible
for the lattice distortions. They thought such kind of lattice con-
tractions are favorable for better thermal stabilities of perovskite
QDs. Similar results were also found by Akkerman et al [96] in Mn-
doped CsPbI
3
(inset of Fig. 3d); the metal-I bonds decreased from
3.14 Å (Pb-I) to 2.97 Å (Mn-I), which contributed to the cell
contraction. DFT (Fig. 3d) was also used to demonstrate the lattice
contraction as well as the negligible variation of the electronic
structures at the band edges. These changes in phase structure
induced by introduced dopants also verify the success incorpora-
tion of them into the perovskite lattice in turn.
3. Doping induced optoelectronic properties
3.1. Bandgap
The quintessential effects of doping to perovskite are on their
tunable bandgap and luminescence based on adjustable compo-
nents. Generally, A-site doping will slightly increase or decrease the
bandgaps depending on the size of the introduced cations. Taking
CsPbX
3
as the host, incorporation of larger impurities (such as FA or
MA) will decrease the bandgap, whereas smaller (such as Rb or K)
dopants will increase the bandgap (Fig. 4a). Meanwhile, partial
replacement of Cs
þ
by these doping cations will not alter their
phase structure of the initial CsPbX
3
NCs [97], which is of great
significance to the applications of photoelectric devices. Chen et al
[28] demonstrated that the bandgap of Cs
x
FA
1-x
PbBr
3
QDs gradu-
ally decreased with the increasing ratio of FA, reflected in the UV
spectra (Fig. 4b). The effect on bandgap is due to the altered Pb-Br
bond lengths and angles in the [PbX
6
]
4-
caused by the incorporation
of larger FA
þ
. The same trend has been found in Cs
x
MA
1-x
PbBr
3
and
Cs
x
FA
1-x
PbI
3
system [98]. The opposite trend has been observed
when smaller cations are introduced. For example, Amgar et al [27]
synthesized Rb
x
Cs
1-x
PbX
3
QDs with blue-shifting absorption band
edge with the increasing ratio of Rb (Fig. 4c). Similarly, other re-
ports [33,99] about incorporation of K
þ
into CsPbBr
3
and CsPbCl
3
QDs brought in the blue shift of absorption spectrum. Overall,
doping to A-site adjusts the bandgap of perovskite in a tiny range
(within 0.1 eV) owing to the altered Pb-X band lengths and angles
in the [PbX
6
]
4-
octahedron caused by the impurities size.
Fig. 2. Perovskite structures and structure factors. (a) Breakdown diagram of perovskite structure. (b) The tolerance factor of 3D lead halide perovskite with general A-site cations,
X-site anions, and octahedral factor of [BX
6
]
4-
octahedra with possible B-site cations.
L. Xu et al. / Materials Today Nano 6 (2019) 100036 3