The purpose of this work was to evaluate potential advantages and limitations of CZT detectors used in surface-on, edge-on, and tilted angle irradiation geometries. Simulations and experimental investigations of the energy spectrum measured by a CZT detector have been performed using different irradiation geometries of the CZT. Experiments were performed using a CZT detector with 10 x 10 mm2 size and 3 mm thickness. The detector was irradiated with collimated photon beams from Am-241 (59.5 keV) and Co-57 (122 keV). The edge-scan method was used to measure the detector response function in edge-on illumination mode. The tilted angle mode was investigated with the radiation beam directed to the detector surface at angles of 90 degrees, 15 degrees, and 10 degrees. The Hecht formalism was used to simulate theoretical energy spectra. The parameters used for simulations were matched to experiment to compare experimental and theoretical results. The tilted angle CZT detector suppressed the tailing of the spectrum and provided an increase in peak-to-total ratio from 38% at 90 degrees to 83% at 10 degrees tilt angle for 122 keV radiation. The corresponding increase for 59 keV radiation was from 60% at 90 degrees to 85% at 10 degrees tilt angle. The edge-on CZT detector provided high energy resolution when the beam thickness was much smaller than the thickness of CZT. The FWHM resolution in edge-on illumination mode was 4.2% for 122 keV beam with 0.3 mm thickness, and rapidly deteriorated when the thickness of the beam was increased. The energy resolution of surface-on geometry suffered from strong tailing effect at photon energies higher than 60 keV. It is concluded that tilted angle CZT provides high energy resolution but it is limited to a 1D linear array configuration. The surface-on CZT provides 2D pixel arrays but suffers from tailing effect and charge build up. The edge-on CZT is considered suboptimal as it requires small beam thickness and also suffers from charge buildup.