  Graphene-silicon (GS) Schottky junctions have been demonstrated as an
efficient architecture for photodetection. However, the response speed of such
devices for free space light detection has so far been limited to 10's-100's of
kHz for wavelength $\lambda >$ 500nm. Here, we demonstrate graphene-silicon
Schottky junction photodetectors fabricated on a silicon-on-insulator substrate
(SOI) with response speeds approaching 1GHz, attributed to the reduction of the
photo-active silicon layer thickness to 10$\mu$m and with it a suppression of
speed-limiting diffusion currents. Graphene-silicon-on-insulator photodetectors
(GSOI-PDs) exhibit a negligible influence of wavelength on response speed and
only a modest compromise in responsivities compared to GS junctions fabricated
on bulk silicon. Noise-equivalent-power (NEP) and specific detectivity (D$^*$)
of GSOI photodetectors are 14.5pW and 7.83$\times10^{\rm{10}}$ cm
Hz$^{\rm{1/2}}$W$^{\rm{-1}}$, respectively, in ambient conditions. We further
demonstrate that combining GSOI-PDs with micro-optical elements formed by
modifying the surface topography enables engineering of the spectral and
angular response.
