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A deep-red semiconductor monolithic mode-locked laser is demonstrated. Multi-section laser diodes based on an AlGaAs multi-quantum-well structure were passively mode-locked, enabling the generation of picosecond optical pulses at 752 nm, at pulse repetition rates of 19.37 GHz. An investigation of the dependence of the pulse duration as a function of reverse bias revealed a predominantly exponential decay trend of the pulse duration, varying from 10.5 ps down to 3.5 ps, which can be associated with the concomitant reduction of absorption recovery time with increasing applied field. A 30-MHz-tunability of the pulse repetition rate with bias conditions is also reported. The demonstration of such a compact, efficient and versatile ultrafast laser in this spectral region paves the way for its deployment in a wide range of applications such as biomedical microscopy, pulsed terahertz generation as well as microwave and millimeter-wave generation, with further impact on sensing, imaging and optical communications.