We report on the self-biasing effect of carrier depletion based silicon microring modulators (MRM) by demonstrating that a silicon MRM can generate open eye diagrams for non-return-to-zero (NRZ) on-off keying (OOK) modulation without an external reverse bias supplied to it. Two modulator configurations are investigated namely single-ended drive in a ground-signal-ground and differential drive in a ground-signal-signal-ground pad configurations. The single-ended modulator is designed with an on photonic integrated circuit (PIC) 50 Ω termination. Open eye diagrams are obtained at 25 Gbit/s and 36 Gbit/s NRZ OOK modulations. We carry-out thorough experimental characterization of the self-biasing of single-ended MRM under various operating conditions of input optical power, carrier wavelength, ring quality factor and extinction ratio as well as modulation speeds, driving voltage swing and pattern length. We demonstrate that the self-biasing is robust and works well in almost all tested conditions. The differential drive MRM is designed with a high impedance without an on-PIC 50 Ω termination. Open eye diagrams are obtained at 30 Gbit/s and 60 Gbit/s NRZ OOK modulations for modulating voltage swing of ∼2.5 Vpp. As demonstrated, the self-biasing works well in both single-ended and differential drive configurations as well as for on-PIC 50 Ω terminated and non-terminated MRMs. The electrical passive parts are all co-designed and fabricated on the same silicon chip as the PIC. The reported self-biasing eliminates the need of having bipolar DC biases supplied to the anode and cathode of the differential drive modulator and allows for simpler driver / modulator interfaces without inductive bias tees.