Heavily-doped strained germanium (Ge) can emit light efficiently thanks to its pseudo direct band gap characteristic. This makes Ge a good candidate for on-chip monolithic light sources in silicon (Si) photonics systems. We propose fin-shaped Ge-Si heterojunction light-emitting diode (LED) with metal gates, which can enhance light emission by coupling with surface plasmon resonant modes and modulate light emission from the LED. We verify these two aspects through numerical analysis and device simulations. We develop the method to find the optimal device structure and specific device dimensions to maximize the spontaneous emission rate enhancement. Also we find that the LED can be modulated by a gate voltage bias.