We have grown CdTe (111) on oriented and misoriented GaAs (100) and have characterized the layers by photoluminescence microscopy (PLM) and transmission electron microscopy (TEM). Photoluminescence microscopy showed a totally different type of defect structure for the oriented substrate than for the misoriented substrates. The CdTe grown on the misoriented substrates exhibited only threading dislocations. The CdTe grown on oriented GaAs showed fewer threading dislocations but exhibited a random structure of loops. The loop structure observed by PLM has been identified by TEM as the boundary between twinned crystallites which extend from the CdTe/GaAs interface to the CdTe surface. When viewed along the growth axis, these boundaries between the columnar twins appear as loops and segments. Surface roughness of the GaAs substrate contributes to the initial growth of twinned material. This leads to competitive growth between the twins and the creation of the observed columnar twins. We present for the first time the growth of CdTe on patterned GaAs substrates. By growing on oriented GaAs(100) substrates that had been patterned prior to growth with 12 μm mesas, it is possible to grow material on the mesa top that is twin free and has a low dislocation density.