The impact of using thin GaAs(Sb)(N) capping layers (CLs) on InAs/GaAs quantum dots (QDs) is investigated for their application in solar cell devices. We demonstrate the ability to combine strain-balancing techniques with band engineering approaches through the application of such CLs. Extended photo-response is attainable by means of an independent tunability of the electron and hole confinements in the QD. Moreover, the CL acts itself as a quantum well (QW), providing an additional photoresponse, so that the devices work as hybrid QD-QW solar cells. The use of a GaAsSb CL is particularly beneficial, providing devices with efficiencies under AM1.5 conditions 20% higher than standard GaAs-capped QDs. This is mainly due to a significant increase in photocurrent beyond the GaAs bandgap, leading to an enhanced short-circuit current density (J(sc)). The addition of N to the CLs, however, produces a strong reduction in J(sc). This is found to be related to carrier collection problems, namely, hindered electron extraction and retrapping in the CLs. Nevertheless, the application of reverse biases induces a release of the trapped carriers assisted by a sequential tunneling mechanism. In the case of GaAsN CLs, this leads to a complete carrier collection and reveals an even higher QD-QW-related photocurrent than when using a GaAsSb CL. The hindered carrier collection is stronger in the case of the quaternary CLs, likely due to the faster recombination rates in the type-I GaAsSbN/GaAs QW structure as compared to the type-II ternary counterparts. Nevertheless, alternative approaches, such as the use of a thinner CL or a short-period superlattice CL, lead to significant improvements, demonstrating a great potential for the quaternary CLs under a proper device design.