Carbon footprint optimization (CFO) is important for sustainable heavy-duty e-truck transportation. We consider the CFO problem for timely transportation of e-trucks, where the truck travels from an origin to a destination across a national highway network subject to a deadline. The goal is to minimize the carbon footprint by orchestrating path planning, speed planning, and intermediary charging planning. We first show that it is NP-hard even just to find a feasible CFO solution. We then develop a $(1+ε_F, 1+ε_β)$ bi-criteria approximation algorithm that achieves a carbon footprint within a ratio of $(1+ε_F)$ to the minimum with no deadline violation and at most a ratio of $(1+ε_β)$ battery capacity violation (for any positive $ε_F$ and $ε_β$). Its time complexity is polynomial in the size of the highway network, $1/ε_F$, and $1/ε_β$. Such algorithmic results are among the best possible unless P=NP. Simulation results based on real-world traces show that our scheme reduces up to 11\% carbon footprint as compared to baseline alternatives considering only energy consumption but not carbon footprint.