A device comprising a low-resistivity, n-type, Si substrate as a back gate to a p-type (boron), remote-doped, SiGe quantum well has been fabricated and characterized. Reverse and forward voltage biasing of the gate with respect to the two-dimensional hole gas in the quantum well allows the density of holes to be varied from8×1011 cm−2down to a measurement-limited value of4×1011 cm−2. This device is used to demonstrate the evolution with decreasing carrier density of a re-entrant insulator state between the integer quantum Hall effect states with filling factors 1 and 3. ©1997 American Institute of Physics.