We demonstrate for the first time generation of 16-state quadrature amplitude modulation (16QAM) signals at a symbol rate of 40 GBd using silicon-based modulators. Our devices exploit silicon-organic hybrid (SOH) integration, which combines silicon-on-insulator slot waveguides with electro-optic cladding materials to realize highly efficient phase shifters. The devices enable 16QAM signaling and quadrature phase shift keying (QPSK) at symbol rates of 40 GBd and 45 GBd, respectively, leading to line rates of up to 160 Gbit/s on a single wavelength and in a single polarization. This is the highest value demonstrated by a silicon-based device up to now. The energy consumption for 16QAM signaling amounts to less than 120 fJ/bit – one order of magnitude below that of conventional silicon photonic 16QAM modulators.