Inexpensive high-resolution silicon (Si) X-ray detectors are required for on-site surveys of traces of hazardous elements in food and soil by measuring the energies and counts of X-ray fluorescence photons radially emitted from these elements. Gated silicon drift detectors (GSDDs) are much cheaper to fabricate than commercial silicon drift detectors (SDDs). However, previous GSDDs were fabricated from 10-kΩ·cm Si wafers, which are more expensive than 2-kΩ·cm Si wafers used in commercial SDDs. To fabricate cheaper portable X-ray fluorescence instruments, we investigate GSDDs formed from 2-kΩ·cm Si wafers. The thicknesses of commercial SDDs are up to 0.5 mm, which can detect photons with energies up to 27 keV, whereas we describe GSDDs that can detect photons with energies of up to 35 keV. We simulate the electric potential distributions in GSDDs with Si thicknesses of 0.5 and 1 mm at a single high reverse bias. GSDDs with one gate pattern using any resistivity Si wafer can work well for changing the reverse bias that is inversely proportional to the resistivity of the Si wafer.