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A GaSb quantum-well (QW) laser diode grown monolithically on a 5deg miscut Si (001) substrate is presented. The III-Sb epi-structure is grown monolithically on the miscut Si substrate via a thin (50 nm) AlSb nucleation layer. The 13% lattice mismatch between AlSb and Si is accommodated by a self-assembled 2D array of interfacial misfit dislocations (IMF). The 5deg miscut geometry enables simultaneous IMF formation and anti-phase domain suppression. The 1 mm times 100 mum GaSb QW laser diode operates under pulsed conditions at 77 K with a threshold current density of 2 kA/cm2 and a maximum peak power of ~20 mW. Furthermore, the device is characterised by a 9.1 Omega forward resistance and a leakage current density of 0.7 A/cm2 at -5 V.