We report GaSb-based laser diodes (LDs) grown on on-axis (001) Si substrates and emitting at 2.3 µm. Two series of LDs were studied and compared. For the first series, a GaAs-based buffer layer was first grown by metal organic chemical vapor deposition (MOCVD) before growing the laser heterostructure by molecular-beam epitaxy (MBE). For the second series, a MOCVD GaSb buffer layer was added between the MOCVD GaAs buffer layer and the MBE laser heterostructure. Both series of LDs exhibited threshold currents in the 50-100 mA range and several mW output power at room temperature. They demonstrated continuous wave operation (CW) up to 70°C (set-up limited) without thermal rollover. Broad area LDs exhibited record threshold-current densities in the 250-350 A.cm-2 range for the second series of LDs, in spite of cracks that appeared during device processing. These results show that the design and fabrication steps of the buffer-layer stacks are critical issues in the epitaxial integration of GaSb-based optoelectronic devices on Si substrates and offer room for much performance improvement.