Spreading Resistance Modeling for Contact Resistivity Extraction in Ohmic Multilayer Structures With Circular Electrodes

Contacts featuring multiple layers of materials in combination with metal electrodes enabled record-high power conversion efficiencies for solar cells in recent years. Minimizing the contact resistivity in these multilayer structures is critical to achieve a high device performance and rapid characterization methods are crucial for the experimental analysis of this aspect. However, commonly used test methods and the associated mathematical formulations to extract contact resistivity are not designed for samples with multiple layers. In this work, we analyze formulations describing the resistance measured in ohmic multilayer test structures, which are used to fit and extract an unknown contact resistivity. We focus on a contacting scheme with circular electrodes, commonly named after Cox and Strack (CS), and analyze a material configuration consisting of a thick Si substrate fully coated with a thin conductive layer (CL). We demonstrate the applicability and accuracy of various spreading resistance models (SRMs) from the literature to calculate the measured resistance and compare the results with those obtained by the finite element method (FEM). Moreover, we present a new SRM with a closed-form expression for the measured resistance, which is computationally more efficient than the existing SRMs. Last, we demonstrate the applicability of this model in experiments with (
${n}$
)c-Si/(
${i}$
)a-Si:H/(
${n}$
)a-Si:H/indium tin oxide (ITO) test structures.