Solid-State Physics Perspective on Hybrid Perovskite Semiconductors

TLDR: In this article, the authors examine recent theoretical investigations on 2D and 3D hybrid perovskites (HOPs) that combine classical solid-state physics concepts and density functional theory (DFT) simulations as a tool for studying their optoelectronic properties.

Abstract: In this review we examine recent theoretical investigations on 2D and 3D hybrid perovskites (HOPs) that combine classical solid-state physics concepts and density functional theory (DFT) simulations as a tool for studying their optoelectronic properties. Such an approach allows one to define a new class of semiconductors, where the pseudocubic high-temperature perovskite structure plays a central role. Bloch states and k.p. Hamiltonians yield new insight into the influence of lattice distortions, including loss of inversion symmetry, as well as spin–orbit coupling. Electronic band folding and degeneracy, effective masses, and optical absorption are analyzed. Concepts of Bloch and envelope functions, as well as confinement potential, are discussed in the context of layered HOP and 3D HOP heterostructures. Screening and dielectric confinements are important for room-temperature optical properties of 3D and layered HOP, respectively. Nonradiative Auger effects are analyzed for the first time close to the ele...

Figures

Figure 1. (a) Density of states (DOS) and (b) electronic band dispersion diagram of GaAs in the zinc-blende structure. The energy at the top of the valence band (VB) at Γ point is set to 0 eV. The DOS close to the band gap is mostly associated to hybridized s and p states of the Ga and As atoms. The conduction bands (CB) and VB are represented respectively as red and blue lines in the band dispersion diagram (b). The computation is performed within the GGA with the SIESTA code. Spin-orbit coupling (SOC) is not considered.

Figure 6. (left) Electronic band structure of the layered HOP ([pFC6H5C2H4NH3]2PbI4), (a) without and (b) with SOC at the GGA level of theory with the ABINIT code.61 Energy levels are referenced to the valence band maximum. (right) General schematic representations of a layered HOP electronic band diagram without and with SOC (ΔSO). Δcr represents the anisotropy of the crystal field. This panel includes the a) real and b) imaginary parts of the complex spinorial components of the first and second CBM states with spin up component on top of the spin down component. Reprinted with permission from ref 61. Copyright 2012 American Physical Society.

Figure 11. Comparison of the dielectric constant variation of CH3NH3PbI3 in the cubic phase with (dotted line, BSE calculation) and without (straight line, RPA calculation) the excitonic interaction. Onsets of optical transitions at R and M points are indicated. Reprinted with permission from ref 74. Copyright 2014 John Wiley and Sons.

Figure 10. (a) Representation of the electronic density for the VBM of the short superlattice SL2 containing two CH3NH3PbI3 cells and one CH3NH3PbBr3 cell (Figure 9). (b) Overview of the atomic structure. The diagrams are computed at the DFT level with a GGA exchange-correlation functional. SOC is not considered. (c) Electron (CBM) and hole (VBM) ground state energies as a function of QW thickness computed with effective masses and confinement potentials.

Figure 7. (a) Band structure of the I4cm phase of CH3NH3SnI3 at the LDA level of theory with SOC and zoom close to the critical Γ point, (b) for CH3NH3PbI3 and (c) for CH3NH3SnI3 showing the Rashba-Dresselhaus-like spinor splitting due to the loss of inversion symmetry. Reprinted

Figure 14. (a) Absorbance spectrum of a 50 nm thick (C6H5C2H4–NH3)2PbI4 (PEPI) layer deposited by spin-coating on a glass substrate at T=10K. The peak located at about 2.35-2.40eV correspond to the exitonic resonance, and the band to band absorption edge is located at about

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Solid-State Physics Perspective on Hybrid Perovskite
Semiconductors
Jacky Even, Laurent Pedesseau, Claudine Katan, Mikaël Kepenekian,
Jean-sébastien Lauret, Daniel Sapori, Emmanuelle Deleporte
To cite this version:
Jacky Even, Laurent Pedesseau, Claudine Katan, Mikaël Kepenekian, Jean-sébastien Lauret, et al..
Solid-State Physics Perspective on Hybrid Perovskite Semiconductors. Journal of Physical Chemistry
C, American Chemical Society, 2015, 119 (19), pp.10161-10177. �10.1021/acs.jpcc.5b00695�. �hal-
01138487�

1
A Solid State Physics Perspective on Hybrid
Perovskite Semiconductors
Jacky Even,*
†
Laurent Pedesseau,
†
Claudine Katan,
‡
Mikaël Kepenekian,
‡
Jean-Sébastien
Lauret,
¥
Daniel Sapori,
†
and Emmanuelle Deleporte
¥
†
Fonctions Optiques pour les Technologies de l'Information, FOTON UMR 6082, CNRS, INSA
de Rennes, 35708 Rennes, France
‡
Institut des Sciences Chimiques de Rennes, ISCR UMR 6226, CNRS, Université de Rennes 1,
35042 Rennes, France
¥
Laboratoire Aimé Cotton, Ecole Normale Supérieure de Cachan, CNRS, Université Paris-Sud,
Bât, 505 Campus d’Orsay, 91405 Orsay, France
Corresponding Author
*Email: Jacky.Even@insa-rennes.fr Tel: +33 (0)2 23 23 82 95
TOC GRAPHICS
KEYWORDS Photovoltaics, optoelectronics, exciton, Bloch function, band folding, Auger
effect
J. Phys. Chem. C, 2015, 119 (19), pp 10161–10177 DOI: 10.1021/acs.jpcc.5b00695

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Biography:
Jacky Even
Jacky Even is full Professor at INSA Rennes engineering school since 1999. He received a PhD
in Physics from the University of Paris VI in 1992. He was assistant professor at the Physics
Department of Rennes University (1992-1999), where he gained broad experience in phase
transitions and solid-state chemical reactions in molecular materials, using theoretical and
experimental approaches: neutron and X-ray scattering, Raman/FTIR spectroscopy, calorimetry,
among others. In 1999, he created FOTON laboratory’s simulation team, to address fundamental
questions on semiconductors at the atomistic level as well as to perform optoelectronic device
simulation. Besides hybrid perovskite materials and colloidal nanoplatelets, his theoretical
activity is now dedicated to semiconductor nanostructures, photovoltaic and light emitting (LED,
laser, …) devices for silicon photonics and optical telecommunication.
Laurent Pedesseau
Born March 12, 1975, Laurent Pedesseau obtained his MSc in condensed matter from the
University of Montpellier in 2001. In 2004, he received his PhD in physics from the University
of Toulouse for atomistic empirical simulations applied to Civil Engineering materials. In 2013,
he was appointed as assistant-professor at FOTON laboratory (INSA Rennes) to work on III-V
semiconductor nanostructures for silicon photonics, hybrid-perovskites for photovoltaics and
optoelectronic device simulations for optical telecommunication.
Claudine Katan
Dr. Claudine Katan, born Hoerner, received a PhD in Physics from the University of Strasbourg
in 1992, working with Pr. Albert Villaeys and Dr. Jean-Pascal Lavoine on dephasing effects in
four-wave mixing experiments studied using density matrix formalism. She subsequently served
J. Phys. Chem. C, 2015, 119 (19), pp 10161–10177 DOI: 10.1021/acs.jpcc.5b00695

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as lecturer in physics at the University of Rennes before being appointed as a CNRS Research
Investigator in the Physics department in 1993. Until 2003, her research interests mainly focused
on the properties of molecular charge-transfer crystals and topology of electron densities. She
then joined the Chemistry department, interspersed by a two years stay at FOTON-OHM. Her
current research at ISCR is devoted to theoretical approaches from modeling to state-of-the-art
electronic structure calculations for structural, electronic and linear/non-linear optical properties
(e.g. two-photon absorption) of molecular chromophores, but also of hybrid perovskites for light
emission and photovoltaic technologies. Her theoretical research is usually conducted in close
collaboration with experimentalists.
Mikaël Kepenekian
Dr. Mikaël Kepenekian graduated from the ENS de Lyon in Chemistry with a thesis work on
molecular magnetism. After a PhD on bistable molecular materials conducted at ENS Lyon and
CEA Grenoble under the direction of Dr. Pascale Maldivi and Prof. Vincent Robert, he joined
the Centro de Investigación en Nanociencia y Nanotecnología (CIN2) in Bellaterra, Spain
working with Prof. Nicolás Lorente on density functional theory applied to electron transport
calculations using the non-equilibrium Green's functions formalism. In 2013, he was appointed
as a CNRS Researcher at ISCR. His research is devoted to the simulation of semiconductors and
interfaces such as molecules supported on surfaces.
Jean-Sébastien Lauret
After a PhD on the optical properties of carbon nanotubes and a post doc on boron nitride, he
was appointed as assistant professor at ENS Cachan. There, he developed activities on the optical
properties of 2D hybrid organic perovskites. He has also an activity on carbon nanostructures.
J.S. Lauret is now professor at Ecole Normale Supérieure de Cachan.
Daniel Sapori
Born on November 28th, 1991, Daniel Sapori graduated from the engineering school CPE Lyon
in chemistry and chemical engineering and also obtained an MSc in nanotechnology. Now, he is
a PhD student in the simulation group of the FOTON laboratory (INSA Rennes) working on
electronic and optical properties of hybrid perovskites under the supervision of Jacky Even.
Emmanuelle Deleporte
Emmanuelle Deleporte is Professor at Ecole Normale Supérieure de Cachan, head of the Physics
Department since 2006. Her research activites are conducted in Laboratoire Aimé Cotton. She is
a specialist in optical properties of semiconductors (SCs): semimagnetic SCs, II-VI and III-V
SCs, heterostructures such as quantum wells and quantum dots, hybrid perovskites. Her main
interests are the study of the excitonic effects, the relaxation dynamics of the carriers, the
exciton-phonon interaction and the light-matter interaction, in the framework of opto-electronics:
lasers, electroluminescent diodes and photovoltaïc systems.
J. Phys. Chem. C, 2015, 119 (19), pp 10161–10177 DOI: 10.1021/acs.jpcc.5b00695

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COVER ART
J. Phys. Chem. C, 2015, 119 (19), pp 10161–10177 DOI: 10.1021/acs.jpcc.5b00695

Frequently asked questions

Q1. What are the main effects of the spin-orbit coupling?

Lattice distortions,including loss of inversion symmetry, as well as spin-orbit coupling have a strong impact on theelectronic band structure, in particular regarding folding, degeneracy, effective masses andoptical absorption. 

Q2. What have the authors contributed in "Solid-state physics perspective on hybrid perovskite semiconductors" ?

Even et al. this paper presented an open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. 

Q3. What is the effect of the interaction of the electron-hole pairs with neighboring molecules?

In the low temperature range, the interaction of theelectron-hole pairs with neighboring molecules is expected to yield bound excitons with longlifetime in 3D HOP as shown by recent experimental studies. 

Q4. What is the value of the exciton binding energy at roomtemperature?

The value of the exciton binding energy being smaller than kT (~26meV) at roomtemperature, the authors may infer that most electron-hole pairs are ionized yielding free carriers. 

Q5. What are the main effects of a loss of symmetry in a semiconductor?

For zinc-blende and würtzite structures, many of the structural properties aresimilar to that of diamond and graphite, but loss of inversion symmetry has a subtle impact onthe optoelectronic and piezoelectric properties of the crystal. 

Q6. What is the dominant effect of Auger relaxation in n-type III-V semiconductors?

in quantumdots, carrier assisted (Auger relaxation) is the dominant effect in the high injection regime,yielding very fast carrier relaxation. 

Q7. What is the asteep value of the exciton binding energy?

The low frequency value (~1KHz) undergoes asteep increase above the critical temperature Tc,132 and amounts to about 60 at room temperature. 

Q8. What is the role of the pseudocubic perovskite structure in this approach?

The pseudocubic perovskite structure plays a central role in this approach, allowing to definereference Bloch states and k.p Hamiltonians close to the electronic band gap. 

Q9. What is the effective mass approximation for electrons and holes?

The effective mass approximationworks well close to the bandgap in 3D HOP both for electrons and holes, thanks to the giantSOC in the CB leading to a non-degenerate band instead of a triply degenerate one obtainedwithout SOC. 

Q10. What is the way to simulate exciton screening?

A convenient way to simulate exciton screening is to consider a two-particle wavefunction ( )he rr ,ψ , where er ( hr ) is the electron (hole) position. 

Q11. How did the transition from materialschemistry to solid state physics occur?

since the initial use of 3D HOP as the sensitizer in conventional DSSC, technologicaldevelopments have simultaneously led to a gradual shift of fundamental issues from materialschemistry to solid-state physics. 

Q12. What is the important transformation of the diagram?

This procedure reveals that, besides electronic bandfolding effect, the most important transformation of the diagram is due to atomicdisplacements. 

Q13. How many HOP are very large systems for DFT simulations?

126,127 HOP are very large systems for DFT simulations, and may not be readilysimulated due to computational resources limitations. 

Q14. What is the way to capture the electronic properties of the cubic phase of the prototype HOP?

Electronic properties of the cubic phase of theprototype HOP CH3NH3PbI3 are best captured taking its all-inorganic analog, CsPbI3. 

Q15. Why is the situation more complicated in 3D HOP than in semiconductors?

However the situation is more complicated in 3D HOP than in semiconductors like GaAs, due toorientational disorder of the organic cation. 

Q16. How can the authors reconstruct the whole Hartreepotential profile of layered HOP?

This analysis shows that layered HOP can be considered as composite materials withvery weak interactions between the inorganic layers, with a reconstruction of the whole Hartreepotential profile by pieces. 

Q17. How does the energy of the spinor state at R differ from that of GaAs?

In terms of Kane energy, it drops to ca 6eV which is about four times smaller than that of GaAs, thus evidencing an additional differencebetween HOP and conventional semiconductors. 

Q18. What is the effect of Auger on the performance of 3D hybrid perovskites?

As an example, the detrimental non-radiative Auger effect close to the electronic bandgap of 3D hybrid perovskites, is expected to have a moderate influence on the performances ofoptoelectronic devices.