We discuss the design of mid-infrared quantum cascade lasers in which the emission frequency can be rapidly modulated by applied bias voltage. The devices are based on integrating a layer with voltage-variable refractive index, based on Stark-tunable inter-sub-band transitions, below the laser active region. A three-terminal configuration is used to independently bias the laser active region and the refractive index variation layer. The ultimate performance of the proposed scheme is analyzed theoretically and proof-of-principle devices are demonstrated experimentally. Experimentally, λ ≈ 10 μm lasers demonstrate up to 4.5-GHz frequency tuning at a temperature of 80 K.