Increasing the modulation speed of semiconductor lasers has attracted much attention from the viewpoint of both physics and the applications of lasers. Here we propose a membrane distributed reflector laser on a low-refractive-index and high-thermal-conductivity silicon carbide substrate that overcomes the modulation bandwidth limit. The laser features a high modulation efficiency because of its large optical confinement in the active region and small differential gain reduction at a high injection current density. We achieve a 42 GHz relaxation oscillation frequency by using a laser with a 50-μm-long active region. The cavity, designed to have a short photon lifetime, suppresses the damping effect while keeping the threshold carrier density low, resulting in a 60 GHz intrinsic 3 dB bandwidth (f3dB). By employing the photon–photon resonance at 95 GHz due to optical feedback from an integrated output waveguide, we achieve an f3dB of 108 GHz and demonstrate 256 Gbit s−1 four-level pulse-amplitude modulations with a 475 fJ bit−1 energy cost of the direct-current electrical input.Directly modulated membrane distributed reflector lasers are fabricated on a silicon carbide platform. The 3 dB bandwidth, four-level pulse-amplitude modulation speed and operating energy for transmitting one bit are 108 GHz, 256 Gbit s−1 and 475 fJ, respectively.