They could use extra thin paper, like the one found on edible paper on cent wafers for instance.
I'd love to know more about the capacity, as it seems to me that the capacity of these batteries will probably not exceed Cd, Ni or Li-ion batteries for the same size. It'll all depend on how thin they can create this paper.
[citation][nom]pocketdrummer[/nom]interesting, but how are we going to grow trees fast enough to support this technology if it takes off?[/citation]
Faster growing trees like pine and bamboo are already being farmed. It is a renewable resource.