UV–vis spectroscopy: how it works, the Beer–Lambert law, band gaps from Tauc plots and plasmon bands

A spectrometer passes ultraviolet and visible light through a sample, usually a solution in a cuvette, and compares the light that comes out with the light that went in. The ratio is the transmittance T, and the quantity plotted is the absorbance, A = −log₁₀T; in routine work the transmittance of the solution is ratioed to that of the pure solvent, which removes the baseline (Mayerhöfer et al. 2019).

The Beer–Lambert law links absorbance to the amount of absorber: A = εcl, where ε is the molar attenuation coefficient, c the concentration and l the path length. Beer showed in 1852 that the transmittance stays the same when the product of cell thickness and concentration stays the same (Mayerhöfer et al. 2019). The law assumes monochromatic light and absorbers that do not interact; finite spectral resolution, detector nonlinearity, chemical interactions, scattering and plasmonic field enhancement all make it fail (Mayerhöfer et al. 2019).

For a semiconductor, light is absorbed once the photon energy reaches the band gap, so the spectrum has an absorption edge. ZnO, for instance, absorbs below about 380 nm, which corresponds to its gap of about 3.3 eV (Escobedo-Morales et al. 2019). UV–vis sits with the other characterisation techniques as the quickest optical measurement.

Solutions. A UV–vis spectrum plots absorbance against wavelength. Read the wavelength of maximum absorbance and its height; at a fixed wavelength, absorbance rises linearly with concentration, so a calibration line of A against c gives unknown concentrations (Mayerhöfer et al. 2019).

Band gap from a Tauc plot. The Tauc method relates the absorption coefficient α to the photon energy hν:

(αhν)^(1/n) = C(hν − Eg)

where n = 1/2 for a direct allowed transition, 3/2 for direct forbidden, 2 for indirect allowed and 3 for indirect forbidden (Escobedo-Morales et al. 2019). Plot (αhν)^(1/n) against hν, fit a straight line to the steep part of the absorption edge (the Tauc segment) and read Eg where that line meets the energy axis (Escobedo-Morales et al. 2019). Convert wavelength to energy with E (eV) ≈ 1240 / λ (nm) (calculated from E = hc/λ; it reproduces ZnO's 3.3 eV ≈ 375 nm in Escobedo-Morales et al. 2019).

You can do this without a spreadsheet: the free LabCanvas Tauc plot band gap calculator takes absorbance against wavelength or photon energy (or Kubelka–Munk F(R) values for powders, pasted in place of absorbance), lets you choose a direct or indirect allowed transition, subtracts a flat baseline below the gap, suggests the linear region of the edge and gives Eg from the intercept, with the plot as PNG or SVG and the data as CSV.

Powders: diffuse reflectance. Because the Tauc method uses α, it needs negligible scattering, and powders scatter strongly. For them, measure diffuse reflectance against a white standard (PTFE or BaSO₄), take R∞ as the ratio of sample to standard reflectance, and use the Kubelka–Munk function F(R∞) = (1 − R∞)² / 2R∞, which is proportional to the ratio of the absorption and scattering coefficients, in place of α (Escobedo-Morales et al. 2019).

Gold nanoparticles. Dispersed gold nanoparticles show a localised surface plasmon band near 520 nm, the source of their wine-red colour; when they aggregate, the band red-shifts and broadens and a new band can appear further to the red, turning the dispersion purple or blue (Wang et al. 2026). Because the band depends on particle size, the spectrum alone can give the size and concentration of spherical gold particles from 5 to 100 nm (Haiss et al. 2007).

• Solutions. Use a matched cuvette of pure solvent as the reference, so the reported absorbance is ratioed to the solvent (Mayerhöfer et al. 2019).
• Stay in the linear range. Deviations from Beer–Lambert grow with higher concentration × path length and with poorer spectral resolution and lower light intensity (Li et al. 2022); dilute until A is proportional to c.
• Powders. Fill a holder deep enough (more than about 2 mm) that the holder does not contribute, and measure against a PTFE or BaSO₄ reflectance standard (Escobedo-Morales et al. 2019).
• Nanoparticle dispersions. Measure them well dispersed; aggregation changes the plasmon band itself (Wang et al. 2026). Check the hydrodynamic size and stability with DLS and zeta potential.

Band gaps of semiconductors and photocatalysts. Optical spectroscopy with the Tauc method is by far the most widely used way to determine the band gap of a material (Escobedo-Morales et al. 2019). The same procedure applies to any semiconductor film or powder, for example the halide perovskites such as MAPbI₃ and CsPbBr₃ or layered MoS₂; automated algorithms now fit Tauc plots, including the choice between direct and indirect gaps, across many spectra at once (Suram et al. 2016).

Mixtures and composites. In a powder with more than one absorbing phase, the edge of the narrower-gap phase raises the background under the wider-gap edge. Intersecting the Tauc line with the energy axis then underestimates the wider gap: ZnO mixed with CoO gave 3.15 eV instead of 3.25 eV, while intersecting with a baseline segment recovered 3.24 eV (Escobedo-Morales et al. 2019).

Nanoparticles. For gold, the plasmon band gives particle size and concentration (Haiss et al. 2007) and shows aggregation as a red shift and broadening, the basis of colorimetric sensors (Wang et al. 2026).

Concentration. In solution chemistry, UV–vis with a Beer–Lambert calibration is the routine way to measure how much of a species is present (Mayerhöfer et al. 2019).

• Using the wrong exponent. The Tauc exponent must match the transition (n = 1/2 direct allowed, 2 indirect allowed); the wrong one gives the wrong gap (Escobedo-Morales et al. 2019).
• Ignoring the baseline. Absorption below the gap (defects, other phases, scattering) bends the Tauc plot; extrapolating to the axis can give large errors, and removing the baseline first gives a converging value, as for cubic BAs at 1.835 eV (Zhong et al. 2023). In mixtures, intersect with a baseline segment rather than the axis (Escobedo-Morales et al. 2019).
• Measuring powders in transmission. Scattering makes the absorbance of a powder meaningless for a Tauc plot; use diffuse reflectance with Kubelka–Munk (Escobedo-Morales et al. 2019).
• Trusting Beer–Lambert at high absorbance. Linearity fails at high concentration, poor resolution and low light levels (Li et al. 2022) and when absorbers interact (Mayerhöfer et al. 2019); integrated band area stays linear longer than peak height (Mayerhöfer et al. 2019).
• Reading a plasmon shift as a size change. Aggregation also red-shifts and broadens the gold band (Wang et al. 2026); confirm with TEM or DLS.
• UV–vis does not identify functional groups. It records electronic absorption; for bonds and functional groups use vibrational spectroscopy, FTIR or Raman.

In the LabCanvas figure editor, the Library has a UV–vis spectrometer as an editable object, including a cutaway of the light path from lamp through monochromator, cuvette and detector, plus an editable data plot for absorbance spectra and Tauc plots. You can label the absorption maximum or the plasmon band, draw the Tauc fit line and Eg, and export for a methods figure or a graphical abstract. To get the band gap itself, run your data through the Tauc plot band gap calculator first.