This document summarizes research on tuning the electronic structure of tin and lead halide perovskites through atomic layering, epitaxial strain, and structural distortions. Key findings include: 1) Atomic layering of perovskites, either through organic linkers or in Ruddlesden-Popper phases, increases band gap due to quantum confinement effects. 2) Epitaxial strain of up to 3% and induced structural distortions can modify electronic structure and shift band gaps by over 1eV. 3) Atomic layering, strain, and distortions effectively tune band gaps throughout the visible spectrum for applications in solar cells.

1. Tuning the electronic structure of tin and lead halide perovskites
through layering, strain, and distortion
Christopher Grote, Bradley Ehrlich, and Robert F. Berger
Department of Chemistry, Western Washington University
• Perovskite compounds with lead or tin at the B site are of interest as light
absorbers for dye-sensitized solar cells [1-3].
• It is therefore desirable to better understand and predict achievable ways to
tune their electronic structure and band gap.
• Changes in atomic layering (Fig. 2), either through structural templating with
organic linkers [4] or growth of layered compounds such as the Ruddlesden-
Popper series (An+1BnX3n+1), [5-6] tune electronic properties.
• Epitaxial strain [7] and structural distortions also modify electronic structure.
Effects of Atomic Layering on Band Gap
• All structures considered (A= Cs+, CH3NH3
+, B=Pb2+, Sn2+ and X= Cl-, Br-, I-)
have been shown to be cubic at or near room temperature.
• Ruddlesden-Popper phases and layered hybrid compounds have larger gaps
than parent perovskites due to quantum confinement. [8]
Computational Methods
Layered Heterostructures
• Compounds with similar lattice
parameters can often be grown
epitaxially. By varying the ratio
of Sn and Pb, a range of band
gaps between the two
compounds can be achieved.
• Band gap trends can again be
explained by quantum
confinement (Fig. 5).
Introduction
Figure 1: Crystal structure of
a cubic perovskite ABX3.
Figure 4: DFT-PBE band gaps of perovskite
compounds layered in the ⟨100⟩ direction: a)
Ruddlesden-Popper phases (A=Cs+) b) hybrid organic-
inorganic perovskites (A’=C3H7NH3
+, A=CH3NH3
+). Line
style indicates the B-site element and marker shape
and color indicate the X-site element.
Figure 2: Two examples of
perovskite compounds
layered in the ⟨100⟩
direction, a) the hybrid
organic-inorganic phase
(C3H7NH3)2BX4 (hydrogen
atoms not shown) and b) the
inorganic Ruddlesden-
Popper phase Cs2BX4.
Figure 6 (below): DFT-PBE band gaps of perovskite
compounds layered along a) ⟨110⟩ and b) ⟨111⟩. The A
site is occupied by Cs+ in all cases, while the A’ site in
⟨111⟩ layered structures is occupied by Ba2+.
Figure 7 (above): Perovskite compounds layered
along a) ⟨100⟩ b) ⟨110⟩, and c) ⟨111⟩, The values of n,
m, and q in these pictures are all equal to 2.
Figure 5: a) Atomic structure and b) DFT-PBE band gaps of layered (CsSnI3)n(CsPbI3)m
heterostructures. Band gaps are computed only at integer values of n and m and are
interpolated as a continuous function for clarity. The red and blue regions are meant to
represent band gaps red- and blue-shifted relative to each other.
[1] A. Kojima et al. J. Am. Chem. Soc. 2009, 131, 6050-6051. [2] M.M. Lee et al. Science 2012, 338, 643-647.
[3] P.P. Boix et al. Mater. Today 2014, 17, 16-23. [4] D.B. Mitzi. J. Chem. Soc., Dalton Trans. 2001, 2001, 1-12.
[5] S.N. Ruddlesden and P. Popper. Acta Cryst. 1957, 10, 538-539. [6] S.N. Ruddlesden and P. Popper. Acta Cryst. 1958, 11, 54-55.
[7] Schlom, D. G., et al. (2007). Annu. Rev. Mater. Res., 37, 589-626.
• Structures can often be strained up to 3% from the relaxed lattice parameter
via epitaxial growth[9].
• Strain can lead to octahedral rotations, resulting in lower symmetry tetragonal
and orthorhombic phases.
• Total energies of the phases were compared under strain (Fig. 10).
• Changes in band gap can be trace to changes in band edge orbitals
Conclusions
• Atomic layerin, epitaxial strain, and structural distortions can be used to tune the
gap by ~1eV throughout the visible region of the solar spectrum.
• Atomic layering can be achieved by multiple means of separation and along
different crystallographic directions with similar effects on electronic structure
Figure 3 : Electronic band structure of CsPbI3. The red dots
indicate the valence band maximum and conduction band
minimum bracketing the direct band gap.
Figure 8 (left): Isosurfaces of
the computed electron
densities of the valence band
maximum (VBM) and
conduction band minimum
(CBM) of CsSnI3.
• Plane-wave density functional theory
(DFT) using the VASP code and Perdew-
Burke-Ernzerhof (PBE) functional
• 6x6x6 k-point mesh for 5-atom perovskite
unit-cell
• DFT-PBE typically underestimates band
gaps but reliably captures trends
• Band edges calculated with 15Å vacuum.
The Effects of Strain and Distortion
Band Edge Calculations in Vacuum
-4 -2 0 2 4
-5.4
-5.2
-5.0
-4.8
-4.6
-4.4
-4.2
Energylevel
Strain (%)
VB
CB
• For strained structures, band edges are computed relative to the vacuum level
• Valence band maximum is tuneable over a wider range due to the changes in
antibonding interactions between B-site s and X-site p orbitals
Figure 9 (right): Energy levels
or the conduction and valence
bands of undistorted CsSnI3
relative to vacuum energy
levels. The VBM changes by
nearly 1 eV for realistic strains
while the CBM only changes
by about 0.1 eV.
Figure 10: Computed total energies of a variety of
undistorted phases of CsSnI3 the z acis is defined as
perpendicular to the plane of epitaxial strain,
Figure 11: Computed band gaps of the same set of strained
phases of CsSnI3.
• Similar atomic layering calculations to those done along the ⟨100⟩ direction were
repeated along the ⟨110⟩ and ⟨111⟩ directions.
The Effects of Crystallographic Direction
[8] C. Grote, B. Ehrlich, B & R.F. Berger. Phys Rev B. 2014 90(20), 205202.
-2 0 2
-14.10
-14.05
-14.00
-13.95
Bandgap(eV)
Strain (%)
No distort
Tetragonal Z
Tetragonal Y
Orthorhombic Z
Orthorhombic Y
-3 -2 -1 0 1 2 3
0.0
0.2
0.4
0.6
0.8
Bandgap(eV)
Strain (%)
Cubic
Tetragonal Z
Tetragonal Y
Orthorhombic Z
Orthorhombic Y
CsSnI3
Strain vs Band Gap
[9] Schlom et al, Annu. Rev. Mater. Res. 37, 589-626 (2007).