In response to the climate crisis, there is a need for technological innovations to reduce the escalating CO2 emissions. Two promising semiconductor technologies in this regard, perovskite-based solar cells and memristive devices based on two-dimensional layered transition metal dichalcogenide (TMDC), can potentially contribute to the expansion of renewable energy sources and the development of energy-efficient computing hardware.
Within perovskite and TMDC materials, ions dislocate from their ideal position in the semiconductor crystal and leave void spaces. So far, the precise influence of these vacancies and their dynamics on device performance remain underexplored. Therefore, this thesis is dedicated to comprehensively examining the impact of vacancy-assisted charge transport in innovative semiconductor devices through a theoretical approach by modeling and simulating systems of partial differential equations. We start by deriving drift-diffusion equations using thermodynamic principles, including Maxwell-Stefan diffusion and the grand canonical ensemble of an ideal lattice gas. Particular attention is directed towards accurately limiting vacancy accumulation. Furthermore, we formulate drift-diffusion models to describe charge transport in perovskite solar cells and TMDC memristors. We discretize the transport equations via the finite volume method and establish the existence of discrete solutions using the entropy method. Our study concludes with simulations conducted with ChargeTransport.jl, an open source software tool developed in the programming language Julia. These simulations investigate the large time behavior of discrete solutions for both transport models. Additionally, we explore the influence of volume exclusion effects on charge transport in perovskite solar cells and compare our simulation results with experimental measurements found in literature for TMDC-based memristive devices.
