One of the authors has proposed a simple-structure silicon X-ray detector (gated silicon drift detector: GSDD), whose structure is much simpler than commercial silicon drift detectors (SDDs). SDDs contain multiple built-in metal-oxide-semiconductor field-effect transistors (MOSFETs) or implanted resistors, whose fabrication processes lower the yield rate of detectors, and also require at least two high-voltage sources. On the other hand, GSDDs do not contain built-in MOSFETs or implanted resistors. Moreover, GSDDs require only one high-voltage source. Therefore, GSDDs greatly reduce the cost of the X-ray detection system. We fabricated prototype GSDDs that contained 0.625-mm-thick Si substrates with an active area of 18 mm<sup>2</sup>, operated by Peltier cooling and a single voltage source. Its energy resolution at 5.9 keV from an <sup>55</sup>Fe source was 145 eV at -38°C and -90°V. Thicker Si substrates are required to enhance its absorption of X-rays. To detect X-ray photons with energies up to 77 keV for X-ray absorbance higher than 15%, we simulate the electric potential distribution in GSDDs with Si thicknesses from 0.625 to 3.0 mm. We obtain an adequate electric potential distribution in the thicknesses of up to 3.0 mm, and the capacitance of the GSDD remains small and its X-ray count rate remain high. The high reverse bias required in the 3-mm-thick GSDD was a third of that in a 3-mm-thick pin diode.