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Direct ingest for raw ASCII exports from Shimadzu, PerkinElmer, Cary, Jasco, Ocean Optics (.txt, .dat, .csv, .tsv, .asc)
| Column 1 | Column 2 |
|---|
Analysis settings
Step 2 · ParameterizeConversion to photon energy (hν) is applied automatically.
Direct dipole-allowed electronic transition across the band edge (n = 2). Typical for: ZnO, GaAs, CdTe, Perovskites.
Linear fitting region
Select the fundamental absorption onset
Automatic suggestion — verify the range manually before publishing.
| R² (determination) | 0.9972 |
| Linear slope (m) | 12.450 |
| Y-intercept (b) | -30.751 |
| Fit range | 2.31–2.82 eV |
| Fitted points | 42 |
| Fit quality | Good |
| Transition | Direct allowed |
| Method | Absorbance-based |
Advanced analytical options▼
Processed Scientific Coordinates
Tabular numerical dataset transformed for regression and export
Understanding Tauc Plot Analysis & Optical Band Gap Calculation
Authoritative physics reference for solid-state physicists, materials scientists, and nanotechnologists
1. Davis–Mott and Tauc Formulation
The optical absorption coefficient α of amorphous and crystalline semiconductors near the absorption edge is governed by the Davis–Mott power law:
In a standard Tauc plot, photon energy hν (in eV) is plotted on the abscissa (X-axis), and (αhν)n is plotted on the ordinate (Y-axis). By performing linear regression along the fundamental absorption onset and extrapolating the line down to y = 0, the optical band gap Eg is precisely determined as Eg = −b / m.
2. How to Choose Transition Exponent (n)
The exponent n depends directly on the electronic band structure of the material:
- Direct Allowed (n = 2): Valence band maximum and conduction band minimum coincide at the same k-vector (Γ point). Photons excite electrons directly without lattice phonons. Common examples include ZnO, GaAs, InP, CdTe, and metal halide perovskites.
- Indirect Allowed (n = 1/2): The band extrema occur at differing crystal momentum vectors (Δk ≠ 0). Conservation of momentum requires simultaneous emission or absorption of a crystal phonon. Examples: Silicon (Si), Germanium (Ge), and Anatase TiO2.
- Direct Forbidden (n = 2/3): Transitions where the electric dipole matrix element vanishes at k = 0 by parity selection rules (e.g. Cu2O).
- Indirect Forbidden (n = 1/3): Phonon-assisted transitions whose dipole matrix element also vanishes (e.g. SnO2 and some metal oxides).
3. Avoiding Common Pitfalls: The Urbach Tail
Real semiconductor samples possess localized defect states, grain boundaries, and thermal lattice vibrations that cause exponential absorption below the nominal band gap (known as the Urbach tail).
Fitting the sub-bandgap tail rather than the true interband absorption edge will systematically underestimate Eg. Our calculator's interactive fitting sliders allow researchers to visually restrict the regression span exclusively to the steep, linear onset.
4. UV–Vis Spectrophotometer Data Compatibility
This web application parses ASCII numerical data tables exported from major optical spectroscopy systems:
- Shimadzu UV-2600 / UV-3600 (UVProbe / LabSolutions)
- PerkinElmer Lambda 750 / 950 / 1050 (UV WinLab)
- Agilent Cary 60 / 5000 (Cary WinUV)
- Jasco V-770 / V-670 (Spectra Manager)
- Ocean Optics / Ocean Insight spectrometers