We focused on design of suitable underlying and covering layers of InAs/GaAs quantum dots (QDs) with the aim to increase the carrier extraction rate in the QD solar cell structures. Covering QDs by a GaAsSb strain reducing layer (SRL) with type II band alignment significantly improves photogenerated carrier extraction from InAs QDs. An additional thin InGaAs SRL below InAs QDs further enhances the extraction of photogenerated carriers. Properties of QD structures without any SRL, with GaAsSb covering SRL, and with combination of thin below-QDs InGaAs and GaAsSb covering SRLs are compared and the mechanism of carrier extraction is discussed. We showed that thin below-QDs InGaAs SRL together with increasing profile of antimony concentration in covering GaAsSb SRL can significantly improve the resulting properties of solar cell structures with InAs QDs.