A theoretical expression for Hooge’s 1/f noise parameter α, for a Schottky barrier field‐effect transistor, which has been biased at a small drain‐source voltage (a gate‐controlled semiconductor resistor), has been derived. The theory is based on the fluctuating occupancy of deep level traps in the depletion region. The theory explains the large variations in the observed values of Hooge’s parameter since the derived expression shows that α varies approximately as n−7/2, where n is the electron density, and that α is sensitive to the trap concentration, the gate (or semiconductor surface) potential, the thickness of the semiconductor conducting layer, and the low‐field electron mobility‐depletion depth profile. Detailed experimental characterization of a semiconductor resistor has been carried out resulting in the accurate determination of α over a range of the applied gate voltage, Vg. We obtain excellent agreement between the theoretical and experimental dependence of α on Vg.