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We report the formation and growth characteristics of an interfacial misfit (IMF) array between AlSb and Si and its application to III-Sb-based quantum-well broad-area edge-emitting laser diodes monolithically grown on an Si (001) substrate. A 13% lattice mismatch between AlSb and Si is accommodated by using the IMF array. A use of 5deg miscut Si substrates enables simultaneous IMF formation and suppression of an antiphase domain, resulting in a drastic suppression of dislocation density over the III-Sb epilayer and realization of electrically injected laser diodes operating at 77 K. The current-voltage characteristics indicate a diode turn-on of 0.7 V, which is consistent with a theoretical built-in potential of the laser diode. This device is characterized by a 9.1-Omega forward resistance and a leakage current density of 0.7 A/cm2 at -5 V and 46.9 A/cm2 at -15 V.