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Terahertz quantum cascade laser sources based on intra-cavity Cherenkov difference-frequency generation in dual-wavelength mid-infrared quantum cascade lasers are currently the only monolithic semiconductor laser technology that can deliver continuous-wave coherent terahertz output at room temperature. Because the Cherenkov difference-frequency generation process enables terahertz radiation generation and extraction across a wide range of frequencies, it is often assumed that phase-matching conditions for this process are automatically fulfilled. We theoretically analyze and experimentally demonstrate that phase-matching plays an important role in these devices, and significant improvements in terahertz power output can be achieved by adjusting the waveguide configuration of the quantum cascade lasers to provide better phase-matching.