Tauc Plot Calculator
Methodology & Docs

The theory behind the plot

The Tauc–Davis–Mott relation, the transition selection rules, the regression standard used to extract Eg, and the exact input conventions the calculator expects.

Docs · Rev 1.0

1. The Tauc relation

Originally formulated by Jan Tauc (1966) for amorphous semiconductors and generalized by Davis and Mott (1970), the optical absorption near the fundamental absorption edge satisfies:

(α · hν)n = B · (hν − Eg)

α is the absorption coefficient,hν is the photon energy in electronvolts,B is an energy-independent transition constant,Eg is the optical band gap, andn encodes the nature of the electronic transition. Plotting (αhν)n againsthν therefore yields a linear onset whose extrapolation to the energy axis gives Eg. A term-by-term walkthrough of this equation, its axes and the intercept calculation lives on theTauc plot equation page.

2. Transition models & exponents (n)

Electronic transitionExponent (n)Selection rules & mechanismCanonical materials
Direct allowed2Δk = 0; vertical electric dipole transition at identical k-vectorZnO, GaAs, CdTe, MAPbI₃
Indirect allowed1/2 (0.5)Δk ≠ 0; requires simultaneous phonon absorption/emissionSi, Ge, Anatase TiO₂, GaP
Direct forbidden3/2 (1.5)Dipole matrix element vanishes at k = 0; higher-order transitionsCu₂O, SnO
Indirect forbidden2/3 (~0.67)Phonon-assisted transition with dipole forbidden matrix elementSnO₂, rare-earth oxides

In practice the plotted quantity is written asF(R)hν or(αhν)n depending on the unit mode selected in the workspace; the exponent is applied after the unit conversion, never before.

3. Absorbance proxy vs. true absorption coefficient

Absorbance proxy mode

When film thickness is unknown, or when analysing colloidal suspensions and powders, the absorbance A serves as an experimental proxy for α:

y = (A · hν)n

Assumes constant optical path length and negligible wavelength-dependent scattering.

True absorption coefficient (α)

Calculated using the Beer–Lambert transmission law through a sample of thickness d:

α = 2.302585 · A / d [cm−1]

Assumes normal incidence, negligible specular/diffuse surface reflectance, and non-interfering sample boundaries.

4. Linear region selection & regression standard

Fitting must occur strictly in the linear onset region of the Tauc curve:

  • Exclude the Urbach tail: sub-bandgap exponential absorption tails from structural defects, grain boundaries and thermal phonons must be excluded.
  • Exclude detector saturation: spectrophotometers saturate at high absorbance (typically A > 2.0–2.5), flattening the curve at high energies.
  • Stay inside the measured range: an intercept far outside the scanned energy window signals a misplaced fit window rather than a real gap.

Within the selected window the calculator performs an ordinary least-squares fit ofy = mx + b and reports the coefficient of determination R². The fitted line is extrapolated to y = 0, giving the optical band gap Eg = −b / m.

5. Input formats & conversions

File types

Plain-text instrument exports with a .txt, .dat or .csv extension. Two columns are required: the horizontal axis and the measured intensity.

Delimiter detection

Comma, semicolon, tab and whitespace separators are detected automatically, as are header rows, comment lines and blank rows.

Axis units

Wavelength (nm), photon energy (eV) or wavenumber (cm⁻¹). Wavelength is converted internally with E = hc / λ, using hc = 1239.841984 eV·nm.

Intensity units

Absorbance, transmittance (%) or a pre-computed absorption coefficient. Transmittance is converted with A = −log₁₀(T / 100).

E (eV) = 1239.841984 / λ (nm)
A = −log10(T% / 100)
α (cm−1) = 2.302585 · A / d (cm)
Eg (eV) = −b / m, with m the fitted slope and b the intercept

6. Outputs & export

OutputDescription
Eg (eV)Optical band gap from the extrapolated x-intercept
m, bSlope and intercept of the linear fit within the selected window
R²Coefficient of determination for the fit window
PNG / SVGPlot export including curve, fit line, dashed extrapolation and Eg annotation

7. Assumptions & limitations

  • The analysis yields an optical gap; it is not a substitute for transport measurements.
  • Scattering, interference fringes in thin films and surface reflectance are not modelled.
  • Amorphous, polycrystalline and heavily defective samples may show Urbach tails that bias a naive fit.
  • Results are only comparable between samples measured with the same instrument configuration and unit mode.
  • The calculator performs no automated model selection — the exponent n is always your choice.

8. References & recommended reading

  1. Tauc, J., Grigorovici, R., & Vancu, A. (1966). Optical Properties and Electronic Structure of Amorphous Germanium. Phys. Status Solidi B, 15(2), 627–637.
  2. Davis, E. A., & Mott, N. F. (1970). Conduction in non-crystalline systems V.Philosophical Magazine, 22(179), 0903–0922.
  3. Makuła, P., Pacia, M., & Macyk, W. (2018). How To Correctly Determine the Band Gap Energy of Modified Semiconductor Photocatalysts. J. Phys. Chem. Lett., 9(23), 6814–6817.
  4. Sheetz, R. M., Savelev, I., & Kosaki, A. (2011). Indirect optical gap in low temperature grown GaAs. Semiconductor Science and Technology, 26, 125004.

Apply the method

Open the calculatorStep-by-step guide