Waveguide-coupled　Ge/Si　separate　absorption,　charge　and　multiplication　avalanche　photodiodes　(SACM　APDs)　have　shown　significant　potential　as　high-sensitivity,　low-noise,　and　high-speed　photo-detection　for　optical　communications.　Here　we　present　a　nanoscale　single-mode　waveguide-integrated　vertical　Ge　absorption,　lateral　Si　charge　and　single　multiplication　configuration　for　a　waveguide　Ge/Si　SACM　APD.　This　device　can　achieve　90%　absorption　at　1550nm　wavelengths　with　a　10m-long　Ge　layer.　The　device　exhibits　a　seven　times　reduction　in　device　length　compared　to　conventional　waveguide　structures　and　a　29%　increase　compared　to　multi-mode　interference　coupling.　Meanwhile,　a　3-dB　bandwidth　can　achieve　47GHz,　which　is　five　times　higher　than　the　conventional　vertical　Ge　absorption,　lateral　Si　charge　and　multiplication　devices.