Heterogeneously integrated DFB lasers, consisting of thin InP membranes coupled to low loss Si wire waveguides possess several advantages compared to traditional all-InP DFB lasers. The thin membranes give a large optical confinement factor and their small surface area results in relatively small parasitic capacitances. Both properties make these lasers very well suited for high speed direct modulation. The low loss silicon wire waveguides furthermore lend themselves very well for the implementation of low loss external cavities. Coupling membrane DFB lasers to such an external cavity allows exploiting photon-photon resonances in the modulation response. In this paper we report on the high speed modulation results of our heterogeneously integrated DFB laser diodes. Below we mainly focus on results for on-off-keying, but at the conference we will also present eye diagrams and BER curves for duobinary and PAM-4 modulation formats. We also discuss link experiments done with the lasers and some ideas for further improvement. The excellent large signal modulation and transmission results and the potential to integrate them into WDM modules make the laser diodes particularly suited as transmitters for longer distance optical interconnects inside or between data centers.