We demonstrate electrically pumped two-section mode locked quantum well lasers emitting at the L-band of telecommunication wavelength on silicon utilizing die to wafer bonding techniques. The mode locked lasers generate pulses at a repetition frequency of 30 GHz with signal to noise ratio above 30 dB and 1 mW average output power per facet. Optical injection-locking scheme was used to improve the noise properties of the pulse trains of passively mode-locked laser. The phases of the mode-locked frequency comb are shown to be coherent with that of the master continuous-wave (CW) laser. The radio-frequency (RF)-line-width is reduced from 7.6 MHz to 150 kHz under CW optical injection. The corresponding pulse-to-pulse jitter and integrated RMS jitter are 29.7 fs/cycle and 1.0 ps, respectively. The experimental results demonstrate that optical injection can reduce the noise properties of the passively mode locked III-V/Si laser in terms of frequency linewidth and timing jitter, which makes the devices attractive for photonic analog-to-digital converters and clock generation and recovery.