3D Finite Element Modelling of Micro Transfer Length Measurements in Contact Layers for Silicon Solar Cells Using Multiphysics Simulation

Carrier-selective contacts with low minority carrier recombination and efficient majority carrier transport, i.e. low contact resistivity, play a decisive role in next generation solar cell technologies like silicon heterojunction technology (SHJ), tunnel-oxide passivated contacts (TOPCon), perovskite solar cells or tandem devices thereof. Assessing the contact resistivities between transport layers in thin film systems poses a challenge due to high differences of conductivities of involved layers. The micro transfer length measurement method (µ-TLM) is employed to extract even smallest contact resistivities and also sheet resistances of buried layers in multilayer systems. However, the TLM measurements are not straight forward due to non-homogeneous current densities at the contact pads and within the layers, i.e. current crowding and spreading effects. In this work, we present a finite element model to accurately simulate the current flow in three dimensions. We validate the simulation model by comparison with the analytical model of an ideal single layer system with 1D current flow, where excellent agreement is achieved. Inhomogeneous current injection at the metal pad contacts is studied and deviations of the analytical correction factors accounting for 2D current flow are identified from the simulation, when low contact resistivities on highly conductive substrates are involved and the geometries are not chosen appropriately. Horizontal current spreading due to finite mesa edge insulation is investigated. The simulation model is able to not only qualitatively describe the observed non-linear resistance-distance behavior in SHJ-based µ-TLM samples with insufficient pattern insulation, it can also be used for a simulation-assisted extraction of contact resistivities in an inverse modelling approach even with full 3D current flow. The findings help to understand limitations of TLM and finally allow the evaluation and interpretation of TLM measurements at multilayer stacks with a wide range of geometries and resistivities.