There are two broad classes of charge carriers in semiconductors: polarons and bands. Polarons occur as electrons or holes in semiconductors distort the lattice and become localized within the lattice. This slows down the mobility of charge carriers relative to bands, and leads to a distortion around the polaron site. Both large and small polarons occur, depending on the extent of the distortion, and each has unique properties. Furthermore, polarons may be negatively charged (electrons) or positively charged (holes). Several reviews[efn_note][/efn_note],[efn_note]Devreese, Jozef T. “Polarons.” Encycl. Appl. Phys. 14.cond-mat/0004497 (1996): 383-409.[/efn_note],[efn_note]Alexandrov, Alexandre S., and Jozef T. Devreese. Advances in polaron physics. Vol. 159. Berlin: Springer, 2010.[/efn_note],[efn_note]Shluger, A. L., and A. M. Stoneham. “Small polarons in real crystals: concepts and problems.” Journal of Physics: Condensed Matter 5.19 (1993): 3049.[/efn_note],[efn_note]Emin, David. Polarons. Cambridge University Press, 2013.[/efn_note],[efn_note]Franchini, C., Reticcioli, M., Setvin, M., & Diebold, U. (2021). Polarons in materials. Nature Reviews Materials, 0123456789.[/efn_note] exist on the study of polarons.

Polarons may occur in materials as excess electrons or holes form. Photoexcitation may create polarons, where excited electrons and holes are created. Defects in a material may also create polarons, either excess electrons or a deficit of electrons (hole). For example, formation of an oxygen vacancy in a metal oxide such as TiO2 creates excess electrons that may localize as polarons. A dopant, like Nb in TiO2, may also create an excess electron that forms a polaron.

The nature and properties of polarons (such as size, mobility, and stability) are all important, as they strongly influence the applicability of a material for a given application. For example, polarons may limit or determine the conductivity within a semiconductor used in electronic devices. Polarons may also enable reduction or oxidation reactions, such as in photocatalysis. Polarons may also play an important role in geochemical processes that occur with minerals. Thus, the study of characterization of polarons is an on-going area of research.

Polarons can be modeled using electronic structure methods, such as density functional theory. Challenges, however, do exist in modeling polarons, as discussed here. An example polaron in TiO2 is shown below. Note that the electron polaron exists as a d orbital localized on a Ti atom. Further examples abound in the literature, and polarons have been observed in many materials, such as HfO2, FeO, FePO4, BaTiO3, BiVO4, and others. A literature search (such as “polarons density functional theory”) will give many examples of modeling polarons.

A polaron in TiO2. An electron (d-orbital) is localized on a Ti atom within the lattice.