Engineering & Science
Tauc Plot Optical Bandgap Calculator: Photon Energy & (alpha*h*nu)^n
Transform UV-Vis spectrophotometer wavelength (nm) and absorption coefficient alpha (cm^-1) into Tauc abscissa h*nu = 1239.842 / lambda_nm (eV) and direct ((alpha * h*nu)^2) vs. indirect (SQRT(alpha * h*nu)) ordinates.
Convert raw UV-Vis thin-film spectra into linear Tauc bandgap plots!
Materials scientists characterizing TiO2 photocatalysts, ZnO transparent conductors, and perovskite thin films determine optical bandgap E_g by plotting Jan Tauc’s (1966) relation (alpha * h * nu)^(1 / r) against photon energy h * nu (eV) and extrapolating the linear absorption edge to zero! Here photon energy is h * nu = 1239.842 / lambda_nm (eV), while exponent 1 / r = 2 for Direct-Allowed transitions (ZnO, GaN, MAPbI3) and 1 / r = 1/2 (SQRT) for Indirect-Allowed transitions (anatase TiO2, crystalline/amorphous Si)!
Because raw alpha in thin films reaches 10^4–10^5 cm^-1, scaling alpha into units of 10^4 cm^-1 (alpha_4 = alpha_cm / 10,000) keeps Tauc Y-axis values clean and readable instead of overflowing 10^10! At lambda = 450 nm (h * nu = 2.7552 eV) with alpha = 25,000 cm^-1 (alpha_4 = 2.50), the direct Tauc ordinate is (2.50 * 2.7552)^2 = 47.445 (10^4 eV/cm)^2!
| UV-Vis Wavelength lambda (nm) | Photon Energy h*nu (eV) | Normalized Direct Ordinate ((alpha/1e4)*h*nu)^2 | Band-Edge Transition Use |
|---|---|---|---|
| 450 nm Blue Edge (alpha = 25,000 cm^-1) | 2.7552 eV | 47.445 (10^4 eV/cm)^2 | Direct Allowed (r = 1/2 -> Power 2) |
| 380 nm Near-UV (alpha = 25,000 cm^-1) | 3.2627 eV | 66.534 (10^4 eV/cm)^2 | Wide-Gap Oxide Edge (ZnO / GaN) |
| Invalid Wavelength (lambda <= 0 or alpha < 0) | Spectra Guard | "Invalid UV-Vis Input" | Requires lambda > 0, alpha >= 0 |
Tauc X-Axis Photon Energy h * nu (eV) = 1239.842 / Wavelength_nm
Uses CODATA Planck-Einstein constant h * c = 1239.84198 eV*nm.
=IF(OR(B2 <= 0, B3 < 0), "Invalid UV-Vis Input", ROUND(1239.842 / B2, 4))Direct-Bandgap Tauc Y-Axis Ordinate ((alpha / 10^4) * h * nu)^2
Scales absorption coefficient B3 (cm^-1) by 10,000 and squares the product with photon energy for direct-allowed extrapolation.
=IF(OR(B2 <= 0, B3 < 0), "Invalid UV-Vis Input", ROUND(((B3 / 10000) * (1239.842 / B2)) ^ 2, 3))Try the example
Use the original values or change them to test your understanding.