Quantum dot hetero structures are possible candidate materials for high efficiency solar cells using advanced approaches such as intermediate bands. Lattice mismatch in the epitaxial growth of quantum dot (QD) causes strain in the structure. Here we report the use of the k.p method to calculate the band structure including the effects of strain, and light and heavy holes. With the modified band gaps due to strain, a material search is performed among III-V binaries and ternaries for a high efficiency QD solar cell material with negligible valence band offsets. It is found that the condition of negligible valence band offsets severely limits the choice of materials. The closest to ideal barrier/dot material system found is Al0.57In 0.43As/InP0.87Sb0.13 corresponding to an efficiency of 58% under x1000 solar concentration for AM 1.5 spectrum.