Band Gap Energy Calculator

The band gap is the energy separating the top of the valence band from the bottom of the conduction band in a periodic solid. It arises because electron waves travelling through a lattice are Bragg-reflected at the Brillouin zone boundary, opening forbidden energy ranges between the allowed bands. If the highest occupied band is only partly filled the material conducts as a metal; if it is exactly full, conduction requires promoting an electron across the gap, and the size of that gap sets everything from colour to carrier density. The conversion between energy and the optical absorption edge is Eg in eV equals 1240 divided by the wavelength in nanometres. Reference values at 300 K include germanium 0.66 eV, silicon 1.12 eV, gallium arsenide 1.42 eV, cadmium telluride 1.50 eV, gallium nitride 3.4 eV, diamond 5.47 eV and fused silica near 9 eV. The common cut-offs place metals and semimetals below about 0.1 eV, semiconductors between roughly 0.1 and 4 eV, and insulators above 4 eV, though the boundaries are conventions rather than physics. Intrinsic carrier concentration falls exponentially with Eg, which is why silicon holds only about 1e10 carriers per cm3 at 300 K while germanium holds 1e13. Band gaps shrink as temperature rises, following the Varshni relation, with silicon losing roughly 0.27 meV per kelvin. Two cautions are important. Absorption-edge fitting depends on whether the transition is direct or indirect, since the Tauc exponent differs, and exciton binding can put the optical gap tens or hundreds of meV below the true electronic gap.

Band theory emerged from quantum mechanics within a few years of its formulation. Felix Bloch showed in 1928 that an electron in a periodic potential has wavefunctions modulated by the lattice periodicity, and Rudolf Peierls and Leon Brillouin worked out around 1929 and 1930 how zone boundaries produce forbidden energy ranges. Alan Herries Wilson drew the decisive conclusion in 1931, in two papers on the theory of electronic semiconductors, arguing that metals, semiconductors and insulators differ only in band filling and gap width, and that the conductivity of semiconductors is governed by thermal excitation across the gap and by impurities. This resolved why some crystalline solids conduct poorly yet conduct better on heating. Measurement caught up during the 1940s, when the wartime effort to make reliable radar detectors pushed Bell Telephone Laboratories and Purdue to purify germanium and silicon far enough for intrinsic properties to be seen, work that led to the transistor in 1947. Systematic optical determination of gaps followed, with Jan Tauc introducing in the 1960s the absorption-edge plotting method still used for thin films, and Y. P. Varshni publishing his empirical temperature-dependence equation in 1967. Applications drove further interest: William Shockley and Hans Queisser derived the detailed-balance efficiency limit for single-junction solar cells in 1961, peaking near 33.7 percent for a gap around 1.34 eV, and the development of gallium nitride devices by Isamu Akasaki, Hiroshi Amano and Shuji Nakamura made wide-gap semiconductors central to lighting.