This article proposes a silicon-based electrostatic kinetic energy harvester with an ultra-wide operating frequency bandwidth from 1 Hz to 160 Hz. This large bandwidth is obtained, thanks to a miniature tungsten ball impacting with a movable proof mass of silicon. The motion of the silicon proof mass is confined by nonlinear elastic stoppers on the fixed part standing against two protrusions of the proof mass. The electrostatic transducer is made of interdigited-combs with a gap-closing variable capacitance that includes vertical electrets obtained by corona discharge. Below 10 Hz, the e-KEH offers 30.6 nJ per mechanical oscillation at 2 grms, which makes it suitable for powering biomedical devices from human motion. Above 10 Hz and up to 162 Hz, the harvested power is more than 0.5 μW with a maximum of 4.5 μW at 160 Hz. The highest power of 6.6 μW is obtained without the ball at 432 Hz, in accordance with a power density of 142 μW/cm3. We also demonstrate the charging of a 47-μF capacitor to 3.5 V used to power a battery-less wireless temperature sensor node.