Ternary , hybrid and perovskite solar cells are the new generation (4th generation) of these kinds of semiconductor devices and usually the materials used to fabricate them are also new.
Adding to Mehrdad, my opinion is that the perovskites are promising materials for new solar cells. They are characterized by high efficiency with economical retaliation as they are thin film fabricated at low temperature. At the second place comes the organic semiconductors. The efficiency of their solar cells is smaller than that of perovskite. They still suffer from long term stability.
In parallel there is the thin film single crystal silicon solar cell with amorphous silicon emitter and back surface field. High efficiency can be realized with such structures. They have good stability inherited from silicon.They are also economical.
CuO2 due to a different band gap absorption than Silicon, so that they can be used in tandem.
ZnO for the same reasoning as above.
Quantum dots made of different materials.
Perovskites is the new craze at different research institutes due to a high theoretical maximum efficiency (meaning the amount of photoelectrons produced from photons incident on material) and the usefulness of the material. Perovskites can stand alone and have a efficieny of 30 percent. You could also have a layer of Perovskite on top of the silicon layer to improve efficiency or have it in tandem with other perovskites.
The high efficiency of perovskites comes from high carrier lifetimes, high carrier mobility and few defects.
I would say Perovskites too; lead and iodine based Perovskites I believe are some of the promising alternatives.
Also, another novel technology which may have a lot of potential is the one of Organic Solar Cells, as well as Organic cells using flexible substrates.
A new class of materials called perovskites, especially lead-free perovskite emerged as a promising materials for making an inexpensive and high-efficient solar cells. Four halide double perovskites structure such as Cs2BiAgCl6 and Cs2BiAgBr6 are also found as promising materials.