The current climate and energy crisis urgently needs solar cells with efficiencies above the 29% single junction efficiency bottleneck. Silicon/perovskite tandem solar cells are a solution, which is attracting much attention. While silicon/perovskite tandem cells in 2-terminal and 4-terminal configurations are well documented, the three-terminal concept is still in its infancy. It has significant advantages under low light intensities as opposed to concentrated sunlight, which is the critical factor in designing tandem solar cells for low-cost terrestrial applications. This study presents novel studies of the sub-cell performance of the first three-terminal perovskite/silicon selective band offset barrier tandem solar cells fabricated in an ongoing research project. This study focuses on short circuit current and operating voltages of the sub-cells under light intensities of one sun and below. Lifetime studies show that the perovskite bulk carrier lifetime is insensitive to illumination, while the silicon cell's lifetime decreases with decreasing light intensity. The combination of perovskite and silicon in the 3T perovskite-silicon tandem therefore reduces the sensitivity of V-OC to light intensity and maintains a relatively higher V-OC down to low light intensities, whereas silicon single-junction cells show a marked decrease. This technological advantage is proposed as a novel advantage of three-terminal perovkite/silicon solar cells for low light intensities of one sun or less.