Recent evidence suggests a slowdown of economic productivity in major Western and Asian economies. One of the most convincing causes is the slowdown in research productivity in key sectors of the economy, such as low-carbon technologies. The latter trend is particularly worrying as low-carbon technologies play a critical role in keeping global warming well below the 2°C that the Paris Agreement set. We rely on a novel data science method that connects scientific articles with patented technologies. We extract the scientific publications cited in more than 600,000 clean energy technologies (wind, solar, biomass, li-ion) and investigate what determines the diffusion speed between scientific research and patented technologies. We demonstrate that the higher the quality of the scientific article (measured by citations), the lower the distance between scientists and inventors, and the higher the similarity between the content of the scientific article and the patent, the faster the diffusion between research and application. Yet, we also show that while more dissimilar content takes longer to be used in patents, the eventual impact of the patent is greater, possibly because it is more innovative. Our data also reveals that while distance appears to matter for the speed of knowledge diffusion, patents in the four low-carbon technologies on average rely on 81% of foreign sources of science, as scientific knowledge diffuses widely across the world economy. China and the United States play an outsized role as the source of scientific publications used in clean-technology patents globally. Nevertheless, while research is characterised by global spillovers, the application of such knowledge (in a patent) appears to be dominated by national teams, potentially due to greater local spillovers and secrecy issues.