The weak free carrier dispersion effect significantly hinders the adoption of silicon modulators in low-power applications. While various structures have been demonstrated to reduce the half-wave voltage, it is always challenging to balance the trade-off between modulation efficiency and the bandwidth. Here, we demonstrated a slow-wave Michelson structure with 1-mm-long active length. The modulator was designed at the emerging 2-μm wave band which has a stronger free carrier effect. A record high modulation efficiency of 0.29 V·cm was achieved under a carrier depletion mode. The T-rail traveling wave electrodes were designed to improve the modulation bandwidth to 13.3 GHz. Up to 20 Gb/s intensity modulation was achieved at a wavelength of 1976 nm.