The deliverable D3.4

# Materials for Energy

**Introduction**

Computational materials modelling plays a crucial role in the design of devices for efficient low cost energy generation and storage by allowing the characterization of materials down to the atomic scale. The accuracy of predicted macroscopic quantities depends on the atomic scale models describing the interatomic forces and how they are implemented on larger length and time scales. Despite its large demand on computer resources, materials modelling has a considerable impact in research and industry areas. Applications, for example inorganic and organic photovoltaics (PV), supercapacitors and batteries, benefit from atomic and meso scale design to understand and improve charge transfer at molecular level. The main objectives are:

- To provide a set of computational routines for morphology, electronic structure and transport properties of energy-related materials for PV, batteries and supercapacitors;
- To set up a screening methodology for designing materials for PV, rechargeable batteries and supercapacitors with optimal energy conversion and storage capabilities;
- To demonstrate how the computing infrastructure can address challenging problems in the field of energy by focussing on their atomic scale origin.

WP3 is divided in 5 Tasks. Task 3.1 (Leader: CEA) is about the developments of models and numerical approaches for the atomic-scale description of materials for energy. This task is already finished. The core of the remaining work package is in Tasks 3.2, 3.3 and 3.4. Task 3.2 (Leader: CEA) is about the development of new methods for the ab-initio characterization of both the electronic and photonic properties. Task 3.3 (Leader: CEA) is devoted to the dynamical properties of materials , Task 3.4 (Leader: UBAH) concerns continuum models. Task 3.5 (Leader: JUELICH) providing tools for applications is reported on at length here.

To fulfil the WP objectives three application lines have been set up as part of Task 3.5. An application line is a WP3 transversal activity that composes the available numerical methods and models to better address a full characterization of a technological application (in this project PV, batteries and supercapacitors). The development of the application line approach will allow to extend this methodology to other energy technologies.

WP3 activities are reported in several papers and communications to congresses. The complete list can be found here.

**Application line: inorganic PV (task 3.5).**

The silicon hetero-junction (SHJ) technology for inorganic photovoltaic solar cells has achieved efficiency as high as 26.3% and shows great potential to become a future industrial standard for high-efficiency crystalline silicon (c-Si) cells. One of the key features of the technology is the passivation of contacts by thin films of hydrogenated amorphous silicon (a-Si:H). The a-Si:H/c-Si interface, while central to the technology, is still not fully understood in terms of charge carrier transport and recombination across this nanoscale region and its impact on the overall efficiency of the cell. The difficulty of modeling an interface arises from the consideration that it should be large enough to take into account all the amorphous surface peculiarities. Moreover on both sides of the interface several planes of atoms are needed to mimic the behaviour of bulk materials. Thus a reliable picture of the charge carrier dynamics at the interface implies the simulation of a very large number of atoms with the accuracy of quantum approaches to take into account properly the electronic properties.

** **An ENEA - Jülich collaboration, supported by the computational expertise available in the Center of Excellence EoCoE, has designed a new procedure to model the SHJ solar cell from the atomic-scale material properties to the macroscopic device characteristics. The atomic scale configurations have been designed by performing highly accurate quantum simulations by using the ab-initio electronic structure package Quantum ESPRESSO (QE). Then larger systems have been generated by exploiting the linear scaling of the quantum package CP2K. Dedicated evaluation sessions on the CP2K code have been performed to optimize its performance for the simulation of the interface. Both the optimization of the code and the right design of the material allow for upscaling of the performance for the simulation of large interfaces. This approach opens the way to the simulation of very large interfaces fully exploiting the power of HPC infrastructures. As shown Figure C1, given a reliable atomic-scale model a full electronic characterization allows to understand the effect of the atomic-scale chemical disorder on the electronic structure. The black arrow in Figure indicates the position of the interface. The atomic structure of the a Si:H/c-Si interface was used to determine the electronic states of the structure via the DFT code QE.

Special consideration was given to the analysis of localized states in the vicinity of the interface, which can act as recombination centers. An insightful method based on the wave function localization (spread) was developed to assess the electronic quality of the interface in view of transport and recombination [“Towards a multi-scale approach to the simulation of silicon heterojunction solar cells“. U.Aeberhard et al. Journal of Green Engineering 5, 11-32 (2016)]. A step further toward the complete characterization of the solar cell is given by the implementation of a massively parallel Discontinuous Galerkin Maxwell solver (WP1-WP3 collaboration) for light propagation and absorption that uses data structures defined by Jülich. The efficient parallelization on INRIA supercomputers will allow to model light trapping architectures in silicon heterojunction solar cells with realistic multi-scale textures for anti-reflection and light incoupling.

The in-house developed NEGF code PVnegf, which is one of the codes assessed in WP1, is adapted to the simulation of hole flow across the a-Si:H/c-Si heterointerface. This includes in a first stage the complex scattering processes for photogeneration and relaxation of charge carriers in Si. Next, a phenomenological defect channel will be added. Finally, connection will be made to the realistic electronic structure via use of a localized orbital basis (Wannier formalism).

**Application line: organic - inorganic PV (perovskite)**

The need for an accurate ab initio description of the electronic and optical properties of the “active” part of organic and hybrid systems in perovskite solar cells has resulted in effort linked to Task 3.1. The methodology used is the same as for batteries. The long term stability of hybrid organic inorganic perovskites (HOIP), APbI3, where A is an organic cation, is a barrier to commercialization of perovskite cells. Recently, a mixture of formamidinium (H2NCH-NH2+, FA), methylammonium (CH3NH3+, MA), ceasium (Cs+), rubidium (Rb+) cations in the A position of the HOIP has been shown to exhibit improved thermodynamic and photo-stability, crystal quality and electronic properties. However, the atomistic origin of the enhanced performance is poorly understood. Here, performing ab initio molecular dynamics, AIMD, simulations, UBAH has predicted dynamical structure-property relations of these recently synthesized mixed A-cation perovskites. These simulations were made with the CP2K package for 768 atoms. UBAH has shown that at ambient conditions, incorporation of small A-cations results in an enhanced hydrogen bond mediated interaction between the A-cations and the inorganic framework. These strengthened interactions are the cause of the increased phase-stability in these materials. The UBAH study also demonstrates a significant change in dynamical motions of organic cations inside the inorganic cages with A-cation mixing, indicating quite distinct optoelectronic properties of these lattices compared to the parent host perovskite.

These results provide an improved understanding of the unusual optoelectronic properties of mixed A-cation perovskites and are being submitted for publication. UBAH is also looking at the phase stability and defect motion in the all inorganic perovskite CsPbI3 with the same modelling approach. UBAH has applied for PRACE time to extend our work to large supercells, so we can reduce finitesize effects which reduce our ability to interpret experimental observations. With HPC resources from PRACE and/or the UK National facility, Archer, we will explore a large compositional space in terms of type of cation and anions and their concentrations. The knowledge of exact mechanism of the ion-migration at ambient condition can eventually stabilize the device structure as well as increase the efficiency of conversion processes. Using AIMD simulations, we intend to explore the atomistic process of ion-migration that we have shown to be a source of current-voltage hysteresis affecting device performance.

In the UBAH simulations of the FAPI structure (Fig. C2), vibrational modes and tumbling motions can be identified. As the cations move, bonds between the I and Pb ions change as the cell distorts to accomodate the FA cation motion. Bond changes affect the electronic structure of the cell so alter charge recombination rates. The real-space formulation of coupled electronic-atomic structure provides electron and hole hopping rates required for the mesoscale analysis. A kinetic Monte Carlo, KMC, code for simulating perovskite layers that includes the effects of ion motion is being developed. This code will use ion diffusion coefficients and electron and hole hopping rates from Marcus theory using transfer integrals from the atomic scale model.

A drift-diffusion model has been developed for perovskite cells that includes coupled electron-ion motion. This activity is linked to WP1 task in which continuum models based on drift diffusion, DD, predict photovoltaic device characteristics, using input parameters taken from KMC, MD and DFT codes have been developed. Partial differential equation solvers based on methods developed in WP1 have been used and input parameters taken from the mesoscopic and microscopic models. DD models solve the continuity equations for electron and hole densities and the Poisson equation relating the electrostatic potential to the charge–carrier densities. A DD model that predicts device characteristics of perovskite solar cells allowing for ion vacancy motion has been developed from DD solvers used to predict the electrical output of batteries. This model has been validated against experimental measurements on cells designed to exaggerate hysteresis. It has been extended to multilayer systems and to other perovskites with the aid of parameter values from the atomic scale model.

**Application line: supercapacitors**

Batteries and supercapacitors play complementary roles in the field of energy storage. While the former are characterized by large energy densities, which makes them suitable for many applications such as in electric vehicles, supercapacitors show better power densities and are therefore used when fast charges/discharges are needed. Both devices would highly benefit for a better understanding of the atomic structure of the solid materials and of the liquid electrolytes which are involved. In this project, we focus on the family of LLZO solid electrolytes for Li-ion batteries and on the study of nanoporous carbon-based electrodes for supercapacitors.

Conventional lithium-ion batteries rely on unstable liquid-organic polymer electrolytes, which pose practical limitations in terms of ammability, miniaturization, and safe disposal. A possible solution is to replace liquid electrolytes with inorganic ceramics that are electrochemically stable and nonammable. The family of garnet-like oxides with general formula LixM3M’2O12, where M= La and M0= Nb, Ta or Zr, have attracted significant attention in this regard due to their high lithium-ion conductivity, high electrochemical stability window, and chemical stability with respect to metallic lithium. The highly studied garnet Li7La3Zr2O12 (LLZO) is the most studied member of this family, and can be considered prototypical. LLZO exhibits two phases with strikingly different ionic conductivities: a cubic phase (c-LLZO) that is adopted at high temperature (>600 K) or stabilized by doping, and a tetragonal (t-LLZO) phase with that is favoured in the pure system at ambient

temperature. In order to study the structure of these systems, we have performed molecular dynamics simulations of various garnets using the Metalwalls code. A 2x2x2 supercell containing 1536 atoms was used for pure LLZO, and the number of atoms was modified to give the corresponding compositions for the doped structures. The optimization of carbon-based supercapacitors is of fundamental importance for electrical energy storage. In order to achieve supercapacitors high-performance, it is necessary to understand the molecular mechanism of adsorption of ions inside the pores of the carbon electrodes. With the purpose of overcoming the limits of classical graphene and obtaining increased energy per unit of volume, we analyzed systems consisting of perforated graphene, which allows the diffusion of the

ions between the sheets and provides us with fast charging and discharging rates, and an ionic liquid electrolyte. We performed classical molecular dynamics simulations with the Metalwalls code – Fig.C3. The two main characteristics of these simulations consist, on one hand, in the possibility of maintaining the electrodes (each one composed of 10627 carbon atoms distributed among 6 perforated graphene planes) at constant potential by allowing the charge of the carbons of the electrode (represented by Gaussian distributions centered on the atom) to fluctuate at each time step, which is essential to obtain a realistic behavior of the ionic liquid/electrode interface. In parallel, several numerical tools are being developed in order to perform large scale characterizations to compute physical quantities of interest for real applications.

**Tools (Tasks 3.2, 3.3)**

In parallel, several numerical tools are being developed in order to perform large scale characterizations to compute physical quantities of interest for real applications.

*Methods for supercapacitor characterization, code interfacing (CNRS)*

MDFT code has been evaluated during the second performance evaluation session at MDLS, Saclay (France). Characteristic and target test cases have been defined and all HPC metrics (for instance memory consumption, CPU time, parallel performance) have been extracted with the help of an HPC expert, Matthieu Haefele (EoCoE WP1). Thanks to the code developments described above in

EoCoE, MDFT is now able to tackle the large dimensions of the supercapacitors model used by METALWALLS. The external potential corresponding to the constant charge electrodes of Metalwalls is now implemented in MDFT. For the MDFT theory, the sole input to fully characterize the solvent is the spatial and angular dependent direct correlation function of the bulk, homogeneous, solvent.

*Development and porting of methods for force-field parametrization (CEA)*

Development and porting of methods via charge analysis to facilitate the parametrization of the force fields using DFT. This will be applied to organic ions and also to batteries (interaction between graphite-like electrode and the electrolyte). The linear scaling version of BigDFT builds an optimized localized atom-centered basis set for each atom expressed on Daubechies wavelets basis sets. Then the Hamiltonian, the overlap matrix and the density matrix can be expressed in this optimized localized basis set, and are sparse reducing considerably the cost of calculations. We can, actually, use this minimal basis set to express other quantities and doing, for instance, a charge analysis which is the natural way to compare with polarizable force fields. Charge analysis is the key quantity to perform QM/QM or QM/MM calculations using a polarizable force field.

*Methods to characterize oPV (CEA)*

A validation scheme devoted to providing reference electronic properties data on few hundred atom systems (e.g. a dopant with its first shell of neighbors) has been set-up, combining state-of-the-art many-body perturbation theory for _nite size systems (the GW and Bethe-Salpeter formalisms, as implemented in the FIESTA package), with an accurate micro-electrostatic approach (the MESCAL package) allowing to account for the electrostatic and polarization effects generated by the environment. The goal is to validate, with one of the most accurate methodology for systems of that size, the larger scale approaches (constrained-DFT, microelectrostatic techniques, etc.) that will be used in production modes on the atomic scale structures. The GW and BSE (Bethe-Salpeter Equation) methods are widely used to calculate spectroscopy of molecules and solids. They are based on many-body perturbation theory. Fiesta was developed by CEA and CNRS to study the organic molecules used in OLEDS and organic photovoltaics. This code is based on Gaussian basis set which has the advantage to have many robust recipes to build the localized basis sets and many Gaussian codes can be used to calculate the Kohn-Sham orbitals. Resolution of identity is an important techniques to decrease considerably the cpu time but also having a robust solution. The next step is to use a new resolution of identity based on real space. Then it is possible to have a product of 1D integral for any 3D integral and decreasing considerably the cpu time for the calculation of the susceptibility term (linear response) in the GW formalism. Another advantage will be the better parallelisation of the code.