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MOS capacitors fabricated on substrates with doping concentrations as high as 10 ^18 cm ^−3 were characterized at 4.2 K. The highly doped substrate exhibited an intrinsic imaginary component of impedance at 4.2 K. The imaginary component is attributed to the time delay induced by hopping phenomena, leading to a decrease in the gate capacitance. Furthermore, we investigated the time constant associated with dopant ionization under depletion conditions and determined it to be 0.35 μ s. An equivalent circuit model of the highly doped substrate at 4.2 K is also shown.