Measurements have been made of the efficiency in detecting gamma rays of a 0.3-mm-, 3-mm-, and 5-mm-thick silicon detector covered with different absorbers. Calibrated sources over the range from 279 keV to 2.75 MeV were used. The need for the absorbers to obtain meaningful results and their contribution to the response of the detectors at electron biases from 50 to 200 keV are discussed in detail. It is shown that the results are virtually independent of the atomic number of the absorber. In addition, the role of the absorber in increasing the efficiency with increasing photon energy for low bias settings is demonstrated for the 0.3-mm crystal. Qualitative explanations are given for the shapes of all curves of efficiency versus energy at each bias.