Si and CdTe semiconductor imaging detectors have been developed for use in a Si/CdTe Compton camera. Based on a previous study using the first prototype of a Si/CdTe Compton camera, new detector modules have been designed to upgrade the performance of the Compton camera. As the scatter detector of the Compton camera, a stack of double-sided Si strip detector (DSSD) modules, which has four layers with a stack pitch of 2 mm, was constructed. By using the stack DSSDs, an energy resolution of 1.5 keV (FWHM) was achieved. For the absorber detector, the CdTe pixel detector modules were built and a CdTe pixel detector stack using these modules was also constructed. A high energy resolution (DE=E$1%) was achieved. The improvement of the detection efficiency by stacking the modules has been confirmed by tests of the CdTe stack. Additionally, a large area CdTe imager is introduced as one application of the CdTe pixel detector module.