Perovskites and TMDCs

Novel electronic materials require advanced charge transport modeling and simulation techniques.

For example, perovskite materials are a promising candidate for many semiconductor devices such as lasers, memristors, LEDs and solar cells. Despite being the fastest growing photovoltaic technology, commercialization of perovskite devices faces many challenges which need to be overcome such as degradation of the material. Precise mathematical models and numerical simulations help to advance the technology by understanding how charge carriers move through the device.

Another example are 2D layered transition metal dichalcogenides (TMDCs) such as molybdenum disulfide are promising memristive materials for neuromorphic computing systems as they could solve the problem of the excessively high energy consumption of conventional von Neumann computer architectures. Despite extensive experimental work, the underlying switching mechanisms are still not understood, impeding progress in material and device functionality.

Perovskites and TMDCs share the fact that when simulating charge transport one has to take into account the movement of ions on the crystal lattice. The units cells for both materials are shown in the figure.

Perovskite (left) and molybdenum disulfide unit cell (right).

Contribution from the institute

At WIAS, for perovskite materials we derive new potential-based models which take into account an additional ion species as well as corresponding volume exclusion effects on a perovskite lattice. We compare density-dependent diffusion coefficients with density-dependent mobility coefficients and study the existence of numerical solutions. For the simulation we rely on a stable finite volume discretization, as implemented in our flexible 1D/2D/3D Julia tool ChargeTransport.jl. For more details see Abdel et al, 2021, Abdel et al, 2023 and Abdel et al, 2023.

Similar to perovskites, we identified the dominant role of mobile ion vacancies in the switching dynamics of 2D TMDC materials. The switching process is governed by the formation and annihilation dynamics of a local vacancy depletion zone. Moreover, minor changes in the interface potential barriers cause fundamentally different device behavior previously thought to originate from multiple mechanisms. The key mechanisms are identified with a charge transport model for electrons, holes, and ionic point defects, including image-charge-induced Schottky barrier lowering (SBL). The model is validated by comparing simulations to measurements for various 2D MoS2-based devices, strongly corroborating the relevance of vacancies in TMDC devices and offering a new perspective on the switching mechanisms. The insights gained from this study can be used to extend the functional behavior of 2D TMDC memristive devices in future neuromorphic computing applications. For more details see Spetzler et al, 2023.


  Preprints, Reports, Technical Reports

  • D. Abdel, A. Glitzky, M. Liero, Analysis of a drift-diffusion model for perovskite solar cells, Preprint no. 3073, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3073 .
    Abstract, PDF (541 kByte)
    This paper deals with the analysis of an instationary drift-diffusion model for perovskite solar cells including Fermi--Dirac statistics for electrons and holes and Blakemore statistics for the mobile ionic vacancies in the perovskite layer. The free energy functional is related to this choice of the statistical relations. Exemplary simulations varying the mobility of the ionic vacancy demonstrate the necessity to include the migration of ionic vacancies in the model frame. To prove the existence of weak solutions, first a problem with regularized state equations and reaction terms on any arbitrarily chosen finite time interval is considered. Its solvability follows from a time discretization argument and passage to the time-continuous limit. Applying Moser iteration techniques, a priori estimates for densities, chemical potentials and the electrostatic potential of its solutions are derived that are independent of the regularization level, which in turn ensure the existence of solutions to the original problem.

  • Y. Hadjimichael, Ch. Merdon, M. Liero, P. Farrell, An energy-based finite-strain model for 3D heterostructured materials and its validation by curvature analysis, Preprint no. 3064, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3064 .
    Abstract, PDF (6517 kByte)
    This paper presents a comprehensive study of the intrinsic strain response of 3D het- erostructures arising from lattice mismatch. Combining materials with different lattice constants induces strain, leading to the bending of these heterostructures. We propose a model for nonlinear elastic heterostructures such as bimetallic beams or nanowires that takes into account local prestrain within each distinct material region. The resulting system of partial differential equations (PDEs) in Lagrangian coordinates incorporates a nonlinear strain and a linear stress-strain relationship governed by Hooke?s law. To validate our model, we apply it to bimetallic beams and hexagonal hetero-nanowires and perform numerical simulations using finite element methods (FEM). Our simulations ex- amine how these structures undergo bending under varying material compositions and cross-sectional geometries. In order to assess the fidelity of the model and the accuracy of simulations, we compare the calculated curvature with analytically derived formula- tions. We derive these analytical expressions through an energy-based approach as well as a kinetic framework, adeptly accounting for the lattice constant mismatch present at each compound material of the heterostructures. The outcomes of our study yield valuable insights into the behavior of strained bent heterostructures. This is particularly significant as the strain has the potential to influence the electronic band structure, piezoelectricity, and the dynamics of charge carriers.