High-resolution X-ray detectors can be used to detect traces of hazardous or radioactive elements in food, soil, and the human body by measuring the energies and counts of emitted X-ray fluorescence photons. We have simulated the electric potential distributions in gated silicon drift detectors (GSDDs) with an active area of 18 mm2 and a Si thickness between 0.625 and 1.5 mm. A GSDD gate pattern was designed for each Si thickness and for various oxide charge densities in the SiO2 passivating layer near the SiO2/Si interface. The simulated GSDDs required approximately half the reverse bias voltage required by Si pin detectors. Our detector design could improve the absorption of Cd or Cs X-ray fluorescence photons and would reduce the cost of X-ray detection systems.