Achieving the energy transition is among global priorities of the 21st century, one key element to success being the development of affordable renewable technology to compete with fossil energy. While technological progress seems already biased in favor of the renewable sector since the 70's, we had to wait until 2005 to observe a sharp increase of its share in the US energy mix. In this paper I develop a theoretical model of energy transition, with exogenously biased technological change,
able to explain this delay through a lasting capital effect in favor of fossil energy. The presence of embodied technical change in the energy sector creates a lasting capital effect in favor of the fossil sector, which slows down the capacity to close polluting units. This mechanism postpones the effect of directed technical change, therefore technological progress by itself is not enough to achieve a quick energy transition unless its rate is really high. I also show that in this framework, the optimal carbon tax is less sensitive to the discount rate.