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A class of electro-optically tunable metamaterial absorbers is designed and theoretically investigated in the infrared regime towards realizing free-space amplitude modulators. The spacer between a subwavelength metallic stripe grating and a back metal reflector is occupied by a bilayer of indium tin oxide (ITO) and hafnium oxide (
HfO
2
). The application of a bias voltage across the bilayer induces free-carrier accumulation at the
HfO
2
/ITO interface that locally modulates the ITO permittivity and drastically modifies the optical response of the absorber owing to the induced epsilon-near-zero (ENZ) effect. The carrier distribution and dynamics are solved via the drift–diffusion model, which is coupled with optical wave propagation studies in a common finite-element method platform. Optimized structures are derived that enable the amplitude modulation of the reflected wave with moderate insertion losses, theoretically infinite extinction ratio, sub-picosecond switching times and low operating voltages.