Thermal noise of highly reflective mirror coatings is a major limit to the sensitivity of many precision laser experiments with strict requirements such as low optical absorption. Here, we investigate amorphous silicon and silicon nitride as an alternative to the currently used combination of coating materials, silica, and tantala. We demonstrate an improvement by a factor of ≈55 with respect to the lowest so far reported optical absorption of amorphous silicon at near-infrared wavelengths. This reduction was achieved via a combination of heat treatment, final operation at low temperature, and a wavelength of 2 μm instead of the more commonly used 1550 nm. Our silicon-based coating offers a factor of 12 thermal noise reduction compared to the performance possible with silica and tantala at 20 K. In gravitational-wave detectors, a noise reduction by a factor of 12 corresponds to an increase in the average detection rate by three orders of magnitude (≈12^{3}).