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Semiconductors, perovskites Connect band structure and charge-carrier populations to semiconductor behavior, then examine why halide perovskites are promising yet challenging optoelectronic materials.
Intuition From insulator to conductor Explore the ideal ABX₃ framework: A-site cations occupy cavities, B cations sit in BX₆ octahedra, and X anions connect the octahedra. School Bands and charge carriers
Example
Solution σ ≈ qnμn = (1.602×10⁻¹⁹)(2.0×10²¹)(0.10) ≈ 32 S m⁻¹.
Typical roles of perovskite constituents Site Typical role A Cavity-filling cation; tunes structure and stability B Octahedral cation; contributes strongly to band-edge states X Anion linking BX₆ octahedra
Undergraduate Quantitative optoelectronic picture
Historical note
In 1833 Michael Faraday noticed that the conductivity of silver sulfide rises with temperature, the first hint of semiconducting behaviour, but the field only took off after quantum band theory in the 1930s. In 1947 John Bardeen, Walter Brattain and William Shockley built the first transistor at Bell Labs, and ultrapure silicon and germanium became the foundation of electronics. The mineral perovskite (CaTiO3) was described by Gustav Rose in 1839 and named after the mineralogist Lev Perovski; halide perovskites showed 3.8 % solar-cell efficiency in 2009 (Tsutomu Miyasaka) and exceeded 25 % within about a decade.
Michael Faraday
The band gap of a semiconductor is best defined as
the energy of the Fermi level the energy difference between the conduction-band minimum and the valence-band maximum; it sets the minimum photon energy for band-to-band absorption the energy needed to melt the crystal the binding energy of the deepest defect state
Doping a semiconductor n-type mainly
adds donor states that supply excess electrons as majority carriers adds excess holes removes all lattice defects increases the band gap
References The emergence of perovskite solar cells · H. J. Snaith, 2013