Abstract
We present analytical relations for the dark recombination current of a pn+ junction with positively charged columnar grain boundaries in the high defect density regime. We consider two defect state configurations relevant for positively charged grain boundaries: a single donor state and a continuum of both acceptors and donors. Compared to a continuum of acceptor+donor states, or to the previously studied single acceptor+donor state, the grain boundary recombination of a single donor state is suppressed by orders of magnitude. We show numerically that superposition holds near the open-circuit voltage Voc , so that our dark J(V) relations determine Voc for a given short circuit current Jsc . We finally explicitly show how Voc depends on the these two grain boundary defect state configurations.