Analytical Model of Leakage Currents in Contact Resistivity Measurements on Silicon Solar Cells

We derive an analytical description of leakage currents in an ohmic system of two conductive layers, with current in- and outflow at two line contacts on the first layer, and current flow in the second layer induced over a resistive interface. Examples of such interfaces in the photovoltaic context include the tunnel interface of TOPCon solar cells, the high-low junction of silicon heterojunction (SHJ) solar cells, and p-n junctions for low current densities. Experimentally the modeled leakage currents are observed in measurements of transfer length method (TLM) samples of SHJ solar cells due to the finite shunt resistivity of the p-n junction. Using the new model, we find that for a typical TLM-setup with a contacting distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{\text{c}}=\text{1 cm}$</tex-math></inline-formula>, apparent sheet resistance reductions of 0.3, 2.6, and 9.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Omega$</tex-math></inline-formula> for a top layer of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{1}=\text{100}\;{\Omega }$</tex-math></inline-formula> occur for interface resistivities <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rho _{\text{c}}$</tex-math></inline-formula> of 100, 10, and 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{k}\Omega \text{cm}^{2}$</tex-math></inline-formula>, respectively. Evaluating the measurement example by the commonly used linear regression, a twice higher contact resistivity is found in comparison to a numerical least square fit of the new model. Similar results are obtained in a synthetic data study using the solar cell simulation software Quokka3, with contact resistivity deviations of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{10 m} \Omega \text{cm}^{2}$</tex-math></inline-formula> for the linear regression evaluation. By evaluating the same data with the new analytical model, the original simulation parameters of contact resistivity and sheet resistance are recovered with relative deviations below 0.2%.