How to Calculate Band Gap Using Tauc Plot
Optical Property Analysis for Semiconductors & Thin Films
Choose based on the electronic structure of your material.
Input Absorption Data (Linear Region):
| Point | Wavelength (nm) | Absorption Coeff (α) |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 |
— eV
Tauc Plot Visualization
X-axis: Photon Energy (eV) | Y-axis: (αhν)1/n
What is how to calculate band gap using tauc plot?
Determining the electronic properties of materials is fundamental in semiconductor physics and materials science. The process of how to calculate band gap using tauc plot involves analyzing UV-Visible absorption spectra to find the energy difference between the valence band and the conduction band. A Tauc plot specifically visualizes the relationship between the absorption coefficient and the energy of incident photons.
Researchers, students, and engineers should use this method when characterizing thin films, nanoparticles, or bulk crystalline materials. A common misconception is that the band gap can be found simply by looking at the peak of an absorption spectrum; however, the Tauc method provides a more rigorous linear extrapolation to the energy axis, accounting for the specific nature of the electronic transition (direct vs. indirect).
how to calculate band gap using tauc plot Formula and Mathematical Explanation
The calculation is based on Tauc’s equation, which relates the absorption coefficient (α) to the photon energy (hν). The derivation stems from the electronic transition probability between bands.
The fundamental equation used in how to calculate band gap using tauc plot is:
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| α | Absorption Coefficient | cm⁻¹ | 10² to 10⁶ |
| hν | Photon Energy | eV | 1.0 to 5.0 |
| Eg | Optical Band Gap | eV | 0.5 to 4.5 |
| n | Transition Constant | Dimensionless | 0.5 (Direct) or 2 (Indirect) |
Practical Examples (Real-World Use Cases)
Example 1: Direct Band Gap Semiconductor (ZnO)
Suppose you are investigating Zinc Oxide (ZnO) thin films. You collect UV-Vis data showing a sharp absorption edge around 370 nm. Using how to calculate band gap using tauc plot for direct transitions (n=0.5), you plot (αhν)² versus hν. By fitting a straight line to the linear portion of the curve, the intercept on the energy axis yields approximately 3.37 eV, confirming its UV-active nature.
Example 2: Indirect Band Gap Material (Silicon)
For crystalline silicon, the transition is indirect. To understand how to calculate band gap using tauc plot in this context, you set n=2 and plot (αhν)1/2. The extrapolation leads to a band gap value of roughly 1.12 eV. This lower value and the indirect nature explain why silicon is less efficient for light emission compared to direct gap materials.
How to Use This how to calculate band gap using tauc plot Calculator
- Select Transition Type: Choose ‘Direct’ if your material has aligned band extrema, or ‘Indirect’ if they are offset.
- Enter Wavelength Data: Provide at least 5 data points (Wavelength in nm) from the region where absorption begins to rise sharply.
- Enter Absorption Coefficient: Input the corresponding α values (usually derived from Absorbance and film thickness).
- Review the Plot: Check the generated Tauc plot. The red line represents the linear regression used for extrapolation.
- Read the Intercept: The primary result shows the Eg value where the extrapolated line crosses the X-axis (Energy).
Key Factors That Affect how to calculate band gap using tauc plot Results
- Film Thickness: An incorrect thickness measurement leads to errors in calculating the absolute absorption coefficient α.
- Scattering Effects: In nanoparticle samples, light scattering can mimic absorption, leading to an underestimation of the band gap.
- Urbach Tail: Sub-band gap absorption due to defects can make the linear region difficult to identify in how to calculate band gap using tauc plot.
- Transition Nature: Using the wrong ‘n’ value (e.g., direct instead of indirect) will produce a mathematically valid but physically incorrect band gap.
- Instrumental Noise: Noise at high absorbance values can distort the linear fitting process.
- Data Range Selection: Choosing a range that is too wide or too narrow for the linear fit can significantly shift the intercept.
Frequently Asked Questions (FAQ)
In a direct band gap, the maximum of the valence band and the minimum of the conduction band occur at the same momentum. In an indirect gap, they are offset, requiring a phonon for transition.
If the thickness is constant, (Ahν)1/n can be plotted, but the slope will not represent the true constant A. The intercept Eg remains the same.
Use the formula E(eV) = 1240 / λ(nm). This is a standard conversion used in how to calculate band gap using tauc plot.
A low R² indicates the chosen data points do not lie on a straight line, possibly because you haven’t selected the true linear absorption edge.
Yes, most semiconductors show a decrease in band gap as temperature increases due to lattice expansion and electron-phonon interactions.
n = 1/2 for direct allowed, n = 3/2 for direct forbidden, n = 2 for indirect allowed, and n = 3 for indirect forbidden transitions.
While 3 points can form a line, 5-10 points in the steepest part of the absorption edge are recommended for an accurate how to calculate band gap using tauc plot result.
It is primarily valid for crystalline and amorphous semiconductors. It may not be suitable for metals or highly complex molecular crystals.
Related Tools and Internal Resources
- UV-Vis Spectroscopy Guide – A comprehensive look at the instrumentation behind the data.
- Semiconductor Physics Basics – Learn about carrier concentrations and band structures.
- Thin Film Thickness Calculator – Tools to determine thickness using interference patterns.
- Molar Extinction Coefficient Tool – Related analysis for liquid-phase samples.
- Refractive Index Analysis – How optical constants relate to band gap.
- Crystal Structure and Lattice Calculator – Exploring how lattice parameters influence Eg.