The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of \textit{ab initio} calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to \emph{ab initio} methods, \emph{i.e.} nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost.

Machine Learning of Molecular Electronic Properties in Chemical Compound Space

Statistical learning of materials properties or functions so far starts with a largely silent, nonchallenged step: the choice of the set of descriptive parameters (termed descriptor). However, when the scientific connection between the descriptor and the actuating mechanisms is unclear, the causality of the learned descriptor-property relation is uncertain. Thus, a trustful prediction of new promising materials, identification of anomalies, and scientific advancement are doubtful. We analyze this issue and define requirements for a suitable descriptor. For a classic example, the energy difference of zinc blende or wurtzite and rocksalt semiconductors, we demonstrate how a meaningful descriptor can be found systematically.

Big Data of Materials Science -- Critical Role of the Descriptor

The performance of organometallic perovskite solar cells has rapidly surpassed those of both traditional dye-sensitized and organic photovoltaics, e.g. solar cells based on CH3NH3PbI3 have recently reached 18% conversion efficiency. We analyze its electronic structure and optical properties within the quasiparticle self-consistent GW approximation (QSGW ). Quasiparticle self-consistency is essential for an accurate description of the band structure: bandgaps are much larger than what is predicted by the local density approximation (LDA) or GW based on the LDA. Several characteristics combine to make the electronic structure of this material unusual. First, there is a strong driving force for ferroelectricity, as a consequence the polar organic moiety CH3NH3. The moiety is only weakly coupled to the PbI3 cage; thus it can rotate give rise to ferroelectric domains. This in turn will result in internal junctions that may aid separation of photoexcited electron and hole pairs, and may contribute to the current-voltage hysteresis found in perovskite solar cells. Second, spin orbit modifies both valence band and conduction band dispersions in a very unusual manner: both get split at the R point into two extrema nearby. This can be interpreted in terms of a large Dresselhaus term, which vanishes at R but for small excursions about R varies linearly in k. Conduction bands (Pb 6p character) and valence bands (I 5p) are affected differently; moreover the splittings vary with the orientation of the moiety. We will show how the splittings, and their dependence on the orientation of the moiety through the ferroelectric effect, have important consequences for both electronic transport and the optical properties of this material.

http://absimage.aps.org/image/MAR15/MWS_MAR15-2014-020499.pdf

Electronic structure of hybrid halide perovskite photovoltaic absorbers

Materials for organic electronics are presently used in prominent applications, such as displays in mobile devices, while being intensely researched for other purposes, such as organic photovoltaics, large-area devices, and thin-film transistors. Many of the challenges to improve and optimize these applications are material related and there is a nearly infinite chemical space that needs to be explored to identify the most suitable material candidates. Established experimental approaches struggle with the size and complexity of this chemical space. Herein, the development of simulation methods is addressed, with a particular emphasis on predictive multiscale protocols, to complement experimental research in the identification of novel materials and illustrate the potential of these methods with a few prominent recent applications. Finally, the potential of machine learning and methods based on artificial intelligence is discussed to further accelerate the search for new materials.

/pdf/toward-design-of-novel-materials-for-organic-electronics-1mwp1lzhpc.pdf

Toward Design of Novel Materials for Organic Electronics.

The conductivity of an $n$-type semiconductor has been calculated in the region of low-temperature $T$ and low impurity concentration ${n}_{D}$. The model is that of phonon-induced electron hopping from donor site to donor site where a fraction $K$ of the sites is vacant due to compensation. To first order in the electric field, the solution to the steady-state and current equations is shown to be equivalent to the solution of a linear resistance network. The network resistance is evaluated and the result shows that the $T$ dependence of the resistivity is $\ensuremath{\rho}\ensuremath{\propto}\mathrm{exp}(\frac{{\ensuremath{\epsilon}}_{3}}{\mathrm{kT}})$. For small $K$, ${\ensuremath{\epsilon}}_{3}=(\frac{{e}^{2}}{{\ensuremath{\kappa}}_{0}}){(\frac{4\ensuremath{\pi}{n}_{D}}{3})}^{\frac{1}{3}}(1\ensuremath{-}1.35{K}^{\frac{1}{3}})$, where ${\ensuremath{\kappa}}_{0}$ is the dielectric constant. At higher $K$, ${\ensuremath{\epsilon}}_{3}$ and $\ensuremath{\rho}$ attain a minimum near $K=0.5$. The dependence on ${n}_{D}$ is extracted; the agreement of the latter and of ${\ensuremath{\epsilon}}_{3}$ with experiment is satisfactory. The magnitude of $\ensuremath{\rho}$ is in fair agreement with experiment. The influence of excited donor states on $\ensuremath{\rho}$ is discussed.

Impurity Conduction at Low Concentrations.

In this paper, we present our generalized kinetic Monte Carlo (kMC) framework for the simulation of organic semiconductors and electronic devices such as solar cells (OSCs) and light-emitting diodes (OLEDs). Our model generalizes the geometrical representation of the multifaceted properties of the organic material by the use of a non-cubic, generalized Voronoi tessellation and a model that connects sites to polymer chains. Herewith, we obtain a realistic model for both amorphous and crystalline domains of small molecules and polymers. Furthermore, we generalize the excitonic processes and include triplet exciton dynamics, which allows an enhanced investigation of OSCs and OLEDs. We outline the developed methods of our generalized kMC framework and give two exemplary studies of electrical and optical properties inside an organic semiconductor.

https://www.mdpi.com/1999-4893/11/4/37/pdf

Generalized Kinetic Monte Carlo Framework for Organic Electronics

Insight into the relation between morphology and transport properties of organic semiconductors can be gained using multiscale simulations. Since computing electronic properties, such as the intermolecular transfer integral, using quantum chemical (QC) methods requires a high computational cost, existing models assume several approximations. A machine learning (ML)–based multiscale approach is presented that allows to simulate charge transport in organic semiconductors considering the static disorder within disordered crystals. By mapping fingerprints of dimers to their respective transfer integral, a kernel ridge regression ML algorithm for the prediction of charge transfer integrals is trained and evaluated. Since QC calculations of the electronic structure must be performed only once, the use of ML reduces the computation time radically, while maintaining the prediction error small. Transfer integrals predicted by ML are utilized for the computation of charge carrier mobilities using off‐lattice kinetic Monte Carlo (kMC) simulations. Benefiting from the rapid performance of ML, microscopic processes can be described accurately without the need for phenomenological approximations. The multiscale system is tested with the well‐known molecular semiconductor pentacene. The presented methodology allows reproducing the experimentally observed anisotropy of the mobility and enables a fast estimation of the impact of disorder.

Machine Learning–Based Charge Transport Computation for Pentacene

Low charge carrier mobility is one key factor limiting the performance and applicability of devices based on organic semiconductors. Theoretical studies on mobility using the kinetic Monte Carlo or master equation are mainly based on a Gaussian energetic disorder and regular cubic lattices. The dependence of mobility on the electric field, temperature and charge carrier density is well studied for the Gaussian disorder model. In this work, we investigate the influence of spatially correlated site energies and spatial disorder in the lattice sites on the mobility using kinetic Monte Carlo simulations. Our analysis is based on both a regular cubic and a non-cubic Voronoi lattice. The latter is used to include spatial disorder in order to study its influence on the mobility for amorphous organic materials. Our results show that charge carrier mobility is strongly influenced by correlations in the site energies. Strong correlations even invert the field dependence of the mobility as observed experimentally in semi-crystalline polymers such as P3HT. Evaluation of local currents between localized states reveals the formation of current filaments with increasing correlation. Furthermore, the influence of the electric field and the energy landscape on the transport energy is studied by evaluation of active sites. A strong correlation between the transport energy, filaments in the local currents and the charge carrier mobility is observed. Our studies on the spatial disorder model do not indicate an inversion of the field dependence as observed by other researchers. The negative field-dependence in semi-crystalline materials may be explained by a higher correlation in the site energies as shown in a strongly correlated energetic landscape.

Charge carrier mobility of disordered organic semiconductors with correlated energetic and spatial disorder

Gaining insight into structure–property relations is a key factor for the development of organic electronics. We present a multiscale framework for charge carrier mobilities in organic thin films e...

Machine-Learned Charge Transfer Integrals for Multiscale Simulations in Organic Thin Films

One major factor limiting the efficiency in organic solar cells (OSCs) is the low open-circuit voltage (Voc). Existing theoretical studies link the Voc with the charge transfer (CT) state and nonra...

Waldemar Kaiser

Papers

Generalized Kinetic Monte Carlo Framework for Organic Electronics

Machine Learning–Based Charge Transport Computation for Pentacene

Charge carrier mobility of disordered organic semiconductors with correlated energetic and spatial disorder

Machine-Learned Charge Transfer Integrals for Multiscale Simulations in Organic Thin Films

Kinetic Monte Carlo Study of the Role of the Energetic Disorder on the Open-Circuit Voltage in Polymer/Fullerene Solar Cells.