a Schematic of our designed normal-incident GeSn p-i-n diode on (001) silicon for optical modulation (not to scale). The mid-infrared (MIR) light beam is incident on the top of the device and transmitted through the GeSn active layer. AC bias voltage is applied to the p-i-n diode to modulate the MIR light based on the Franz–Keldysh effect. b Schematic band diagram of Ge/GeSn/Ge heterojunction with an applied electric field. The compressive strain in the GeSn active layer splits the valence band. c Evolution of the lowest direct-gap transition energy (from the heavy-hole (HH) to Γ-conduction band) and indirect-gap transition energy (from HH to L-conduction band) for pseudomorphic GeSn on Ge at 300 K as a function of Sn composition calculated using deformation potential theory. The epitaxially grown GeSn heterostructure samples N1 and N2 are indicated by the dashed lines. d Current–voltage characteristics of the fabricated GeSn p-i-n diodes with D = 250 μm using samples N1 (solid blue line) and N2 (dashed red line). The inset shows a top-view scanning electron microscopy (SEM) image of the fabricated diode.