Four worked cases: two direct, one indirect, and one deliberately wrong — each with the fit window, the regression statistics and the resulting band gap.
A Tauc plot example is worth more than a page of theory: the same numbers every manual analysis reports — fit window, slope, intercept, R² — and the band gap that falls out of Eg = −b/m. Below are four illustrative cases, including one that looks statistically fine but is physically wrong.
Every value here is reproducible with theTauc plot calculator, which ships sample datasets so you can follow the fits yourself.
| Axis | Wavelength 300–700 nm → E = 1239.84 / λ |
| Input | Absorbance column |
| Mode | α = 2.302585 · A / d |
| Fit window | 3.18 – 3.42 eV |
| Slope m | 2.14 × 10¹⁵ eV⁻¹cm⁻¹ |
| Intercept b | −6.86 × 10¹⁵ |
| R² | 0.9987 |
Matches the literature range for wurtzite ZnO (3.2–3.4 eV). The window excludes the Urbach tail below 3.18 eV.
| Axis | 400–800 nm → eV |
| Input | Absorbance (no thickness) |
| Mode | (Ahν)^(1/2) proxy |
| Fit window | 3.10 – 3.45 eV |
| Slope m | 4.42 |
| Intercept b | −13.70 |
| R² | 0.9952 |
Consistent with anatase-rich titania (≈3.2 eV); the slight underestimate is typical when scattering is present in dispersions.
| Axis | 1100–400 nm → eV |
| Input | %T → T = %T/100 → A = −log₁₀(T) |
| Mode | Absorbance proxy (wafer back-reflection ignored) |
| Fit window | 1.18 – 1.40 eV |
| Slope m | 3.08 |
| Intercept b | −3.63 |
| R² | 0.9941 |
Close to the accepted indirect gap of crystalline silicon (≈1.12–1.17 eV). The transmittance conversion step is what makes this work.
| Axis | Same as case 1 |
| Input | Absorbance |
| Mode | (Ahν)^(1/2) — wrong exponent |
| Fit window | 2.90 – 3.60 eV (too wide) |
| Slope m | 0.94 |
| Intercept b | −2.31 |
| R² | 0.9740 |
R² still looks respectable, yet the answer is off by 0.75 eV. Cause: wrong transition model plus a window spanning the exponential tail and the saturation plateau.
| Statistic | What it tells you |
|---|---|
| Slope m | Steepness of the edge — sets how sensitive Eg is to the window. |
| Intercept b | Together with m gives Eg = −b/m. |
| R² | Linearity of the window. High R² is necessary but never sufficient. |
| Fit window | The point range used. Always report it alongside Eg. |
Values on this page are illustrative and rounded; reproduce them with your own spectra before citing anything.
No. A high R² alone does not guarantee a physically meaningful Tauc fit. The fitting region, number of points, slope, transition model, and optical spectrum should also be considered.
Enough to define a straight segment robustly — typically at least 10–20 points inside a clearly linear onset. Too few points makes R² meaningless; too many usually means the window spans a curved region.
There is no universal threshold. Values above roughly 0.99 are common for clean data, but R² must always be judged alongside a visibly linear region, a sensible slope and a physically plausible Eg.
Common causes are fitting inside the Urbach tail, using the wrong exponent n, forgetting to convert transmittance to absorbance, or measuring a material with strong scattering or quantum confinement effects.
The workspace includes bundled experimental datasets — load one, adjust the window, and watch slope, R² and Eg respond.