An information picture of the Coulomb interaction between localized charge carriers

Electrostatic interactions between charge carriers strongly impact the dynamics and fundamental microscopic as well as macroscopic properties such as charge carrier recombination and mobility, respectively. Within amorphous materials of low dielectric constants, such as organic semiconductors (OS), charge carriers are strongly localized, and the Coulomb interaction is weakly screened. To access the connection between the Coulomb interaction and the charge transport in OS, numerical simulations such as kinetic Monte Carlo (kMC) simulations of high computational cost need to be performed [1]. Analytical theories of charge transport in OS are based on the concept of the transport energy, which depends on the charge carrier density while neglecting the detailed distribution of charge carriers [2]. However, these theories are not directly applicable to systems of bipolar charge carriers, such as within LEDs or solar cells, where strongly bound electron-hole pairs are generated upon light absorption. In this work, we analyze the Coulomb interaction of an electron-hole pair within organic semiconductors from an information perspective. A measure of the correlation between two probability variables x and y is given by the mutual information I(x,y)=ln(p(x,y)/p(x)p(y)) [3], with the joint probability distribution p(x,y). In the disordered OS, the molecular orbital energies are disordered following a Gaussian distribution. We take the energy of the electron and the hole as our probability variables x and y, respectively. We study the mutual information of the electron-hole energy probabilities by (i) computing p(x) and p(y) when Coulomb interaction is neglected, and (ii) p(x,y) considering the Coulomb interaction using kMC. We analyze the mutual information for test cases in several dimensions (1D to 3D), and different energetic disorders and provide a comparison with kMC. This study allows shedding light on the connection between the mutual information and the thermalization of an electron-hole pair within a disordered system [4]. [1] W. Kaiser et al. Phys. Chem. Chem. Phys. (2018): 20.13: 8897-8908. [2] S. Baranovskii. Physica Status Solidi (a) 215.12 (2018): 1700676. [3] J. Parrondo et al. Nature Phys. 11.2 (2015): 131. [4] S. Roland, J. Phys. Chem. Lett. (2019) DOI:10.1021/acs.jpclett.9b00516     «

Electrostatic interactions between charge carriers strongly impact the dynamics and fundamental microscopic as well as macroscopic properties such as charge carrier recombination and mobility, respectively. Within amorphous materials of low dielectric constants, such as organic semiconductors (OS), charge carriers are strongly localized, and the Coulomb interaction is weakly screened. To access the connection between the Coulomb interaction and the charge transport in OS, numerical simulations s...     »