The efficiency of a solar cell can be substantially increased by opening new energy gaps within the semiconductor band gap. This creates additional optical absorption pathways which can be fully exploited under concentrated sunlight. Here we report a new approach to opening a sizeable energy gap in a single junction GaAs solar cell using an array of InAs quantum dots that leads directly to high device open circuit voltage. High resolution imaging of individual quantum dots provides experimentally obtained dimensions to a quantum mechanical model which can be used to design an optimised quantum dot array. This is then implemented by precisely engineering the shape and size of the quantum dots resulting in a total area (active area) efficiency of 18.3% (19.7%) at 5 suns concentration. The work demonstrates that only the inclusion of an appropriately designed quantum dot array in a solar cell has the potential to result in ultra-high efficiency under concentration.