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for this to make any economic sense they would have to be pretty cheap per-piece. that is why they should use the simplest possible manufacturing materials, such as doped silicon. we know from solar panels (PV cells) that those that eventually market-matured were using very simple materials (doped silicon) instead of the more rare and difficult-to-get germanium, gallium, etc.
there has been lots of research into more "efficient" (energy efficient) solar panels from german research institute fraunhofer institut, however it turns out that energy efficiency wasn't what eventually made solar panels take off. the chemistry used today is still the simplest chemistry from around 2000, just scaled up enormously to take advantage of economies of scale. i think that peltier devices would have to be similar: simple doped silicon, no germanium etc., just very simple chemistry, mass manufactured to produce a lot of devices with cheap per-piece price, then just take a bunch of them and stack them behind one another to achieve greater energy efficiency.