InP nanowire arrays with axial p-i-n junctions are promising devices for next-generation photovoltaics, with a demonstrated efficiency of 13.8%. However, the short-circuit current in such arrays does not match their absorption performance. Here, through combined optical and electrical modeling, we study how the absorption of photons and separation of the resulting photogenerated electron-hole pairs define and limit the short-circuit current in the nanowires. We identify how photogenerated minority carriers in the top n segment (i.e. holes) diffuse to the ohmic top contact where they recombine without contributing to the short-circuit current. In our modeling, such contact recombination can lead to a 60% drop in the short-circuit current. To hinder such hole diffusion, we include a gradient doping profile in the n segment to create a front surface barrier. This approach leads to a modest 5% increase in the short-circuit current, limited by Auger recombination with increased doping. A more efficient approach is to switch the n segment to a material with a higher band gap, like GaP. Then, a much smaller number of holes is photogenerated in the n segment, strongly limiting the amount that can diffuse and disappear into the top contact. For a 500 nm long top segment, the GaP approach leads to a 50% higher short-circuit current than with an InP top segment. Such a long top segment could facilitate the fabrication and contacting of nanowire array solar cells. Such design schemes for managing minority carriers could open the door to higher performance in single- and multi-junction nanowire-based solar cells.