Geometry-Tunable Hybrid Vacuum Transport in Graphene-Silicon Photodetectors via Nanoscale Air Gaps

Hybrid vacuum/solid-state transport enables low-voltage, high-gain optoelectronics, yet wafer-scale implementation remains elusive. Here, we suspend monolayer graphene (Gr) across trenches in lightly doped p-Si; 20-100 nm vacuum gaps are formed by natural sagging, creating a lithography-defined Gr/air/Si-Gr/p-Si heterostructure. Finite element modeling shows field focusing >3 × 10⁶ V cm^-1 at trench shoulders, driving a bias-tunable cascade from ohmic drift to trap-free space-charge-limited conduction (SCLC) and, at higher biases, the Fowler-Nordheim (FN) tunneling. Under a 633 nm illumination (∼1 mW, ∼1 mm² spot), the narrow trenches deliver an ∼0.60 AW^-1 responsivity with an ∼120% external quantum efficiency (EQE) and an ∼180% internal quantum efficiency (IQE) at 3 V, whereas the dark current remains <10 nA at 1 V (ON/OFF > 10⁵). The responsivity is confined to graphene-covered areas yet is uniform across the membrane; ∼15 ns rise and ∼100 ns fall times confirm a nanosecond, photogating-free gain. The broadband responsivity peaks near 800 nm, exceeding that of planar Gr/Si diodes by 2-3×. Regarding the geometry-defined performance, extending the trench perimeter from ∼4 to ∼16 mm lowers V_th from ∼1.26 to ∼0.84 V and shifts the dominant regime from SCLC to FN emission, whereas wide (∼2 mm) trenches show strong SCLC but no FN onset. These results establish trench-suspended graphene as a scalable, lithography-programmable platform for fast, broadband, and energy-efficient hybrid vacuum/solid-state photodetectors.