(αhν)ⁿ = B(hν − Eg) — every symbol, both axes, the exponent values and the arithmetic that turns a fitted line into a band gap.
The Tauc relation describes absorption near the fundamental edge of a semiconductor. It was formulated by Jan Tauc in 1966 for amorphous materials and generalized by Davis and Mott in 1970. Rearranged as y = mx + b — withy = (αhν)ⁿ andx = hν — the equation becomes a straight line whose extrapolation crosses the energy axis exactly at the optical band gap.
How strongly the material absorbs per unit length, in cm⁻¹. Replace with absorbance A when thickness is unknown.
Energy of the incident photon in electronvolts (eV). This is the x-axis of the Tauc plot.
Encodes the transition: 2 (direct allowed), 1/2 (indirect allowed), 3/2 (direct forbidden), 2/3 (indirect forbidden).
An energy-independent probability factor. It scales the curve vertically but does not move the intercept.
The value you are solving for — the x-axis intercept of the extrapolated linear fit, in eV.
| Axis | Quantity | Units |
|---|---|---|
| x-axis | hν (photon energy) | eV |
| y-axis | (αhν)ⁿ or (Ahν)ⁿ | arbitrary / (eV·cm⁻¹)ⁿ |
Wavelength data must be converted before plotting — see the photon energy calculation below — because the Tauc relation is written in energy, not wavelength.
The calculator uses the NIST value hc = 1239.841984 eV·nm; 1240 is the common two-significant-figure shorthand and gives the same result to within a few meV.
| Transition | n | Plotted quantity |
|---|---|---|
| Direct allowed | 2 | (αhν)² |
| Indirect allowed | 1/2 | (αhν)^(1/2) |
| Direct forbidden | 3/2 | (αhν)^(3/2) |
| Indirect forbidden | 2/3 | (αhν)^(2/3) |
More on choosing between them indirect vs indirect band gap Tauc plots.
Within the fitted window the relation is a straight line, so the Tauc equation maps ontoy = mx + b. Setting y = 0 gives the extrapolation to the energy axis:
Worked numbers: a fit with slope m = 4.20 and intercept b = −8.61 givesEg = 8.61 / 4.20 = 2.05 eV. The calculator performs this arithmetic automatically and reports m, b and R² next to the result.
The general Tauc relationship is (αhν)ⁿ = B(hν − Eg), where α is the absorption coefficient, hν is photon energy, Eg is the optical band gap, and n depends on the type of electronic transition.
The x-axis is photon energy hν in electron volts. The y-axis is (αhν)ⁿ — or (Ahν)ⁿ when only absorbance is available — for the exponent n of the chosen transition model.
Direct allowed n = 2, indirect allowed n = 1/2, direct forbidden n = 3/2 and indirect forbidden n = 2/3.
Fit y = mx + b to the linear region and set y = 0. The intercept on the energy axis is Eg = −b/m, in electronvolts.
Load a spectrum and the calculator builds the (αhν)ⁿ vs hν plot, fits the linear region and returns Eg = −b/m for you.