Adaption of Basic Metal–Insulator–Semiconductor (MIS) Theory for Passivating Contacts Within Numerical Solar Cell Modeling

The main goal of a solar cell's contact is to simultaneously minimize the contact resistivity ρ
_cont
and the effective recombination, the latter often expressed via J
_0,cont
. To model the resulting solar cell characteristics, the simplest approach is to use those two measurable quantities as an effective boundary condition. Within crystalline silicon solar cell modeling, this “lumped” modeling approach is well valid for classical contacts, which feature high doping near the surface. Contacts to lowly doped silicon in contrast require a suitable stack of materials deposited onto the absorber surface to simultaneously induce band bending via an electrical barrier (field-effect passivation), provide chemical passivation, and efficiently extract majority carriers. Such “passivating contacts” often show effects not reproducible by the lumped modeling approach, e.g., non-ohmic contact resistivity, injection-dependent recombination, and voltage drops independent of current extraction. In this paper, we explore the suitability of the basic metal-insulator-semiconductor theory, employed as a boundary condition to a numerical model of the semiconductor transport in the absorber, to represent such effects of passivating contacts. We show that with only very few input parameters, several relevant experimental observations can be quantitatively replicated: temperature dependence of the fill factor of solar cells featuring tunnel-oxide passivating contacts, as well as implied versus external open-circuit voltage losses for heterojunction solar cells. While being the focus of this paper, the presented approach is well applicable also beyond crystalline silicon cells.