A chap by the name of Knut Karlsen has been playing with flexible solar panels, and developed a basic solar-powered rechargeable battery concept. Using some specially cut solar cells, the cells have been wrapped around NiMH rechargeable batteries.
When the batteries are low, you just need to put them in the sun for a bit. The solar cells only act as a trickle charger, and there’s no facility to check when the batteries are full, but the idea is neat and simple. It wouldn’t be too difficult to create batteries with a chip-on-board (COB) circuit that could fit within the casing of the battery. This circuit would then prevent overcharging of the batteries.
However, in the name of efficiency, I think it’d be better to charge the batteries using an external charger. Not only would it be cheaper to make the batteries, but you could optimise the charging time of the batteries. Additionally, what if the solar panel on the battery breaks? That battery would then be useless.