Tauc Plot Band Gap Calculator

An expert tool to analyze semiconductor properties by determining the optical band gap.

Calculate Tauc Plot Y-Axis Value

What is How to Calculate Band Gap Using Tauc Plot?

A Tauc plot is a widely used graphical method in materials science and physics to determine the optical band gap of a semiconductor material. The minimum energy required to excite an electron from the valence band to the conduction band is known as the band gap (Eg). This property is crucial for understanding a material’s electronic and optical behavior, particularly for applications like LEDs, solar cells, and photodetectors. The process involves analyzing the material’s light absorption spectrum, obtained via UV-Vis spectroscopy, and plotting the data in a specific way to reveal the band gap energy. Learning how to calculate band gap using Tauc plot is a fundamental skill for researchers in these fields.

The Tauc Plot Formula and Explanation

The relationship between the absorption coefficient (α), the photon energy (hν), and the band gap (Eg) is described by the Tauc equation. The core idea is to plot a function of absorption and energy against the energy itself, which linearizes a specific part of the spectrum. The formula is:

(αhν)¹/ⁿ = A(hν – Eg)

By plotting (αhν)¹/ⁿ on the y-axis and hν (photon energy) on the x-axis, the linear portion of the graph can be extrapolated to the x-axis. The point where the line intercepts the x-axis (y=0) gives the value of the optical band gap, Eg. The exponent ‘n’ depends on the nature of the electronic transition. If you need to analyze semiconductor properties, understanding the {related_keywords} is crucial.

Variables Table

Description of variables used in the Tauc plot formula.

Variable	Meaning	Unit (Typical)	Typical Range
α	Absorption Coefficient	cm⁻¹	10³ – 10⁶
hν	Photon Energy	eV (electron Volts)	1.0 – 6.0
Eg	Optical Band Gap	eV	0.5 – 4.0
A	A proportionality constant (band tailing parameter)	Varies	–
n	Transition exponent	Unitless	1/2, 3/2, 2, or 3

Practical Examples

Example 1: Direct Band Gap Semiconductor

Let’s assume we are analyzing a direct allowed transition material like Gallium Arsenide (GaAs). We have a data point from our UV-Vis spectrum where the photon energy (hν) is 1.5 eV and the measured absorption coefficient (α) is 10⁴ cm⁻¹.

• Inputs: α = 10000 cm⁻¹, hν = 1.5 eV, n = 1/2 (for direct allowed)
• Calculation: (10000 * 1.5)¹/⁽¹/²⁾ = (15000)² = 225,000,000
• Result: The value on the y-axis of the Tauc plot for this point is 2.25 x 10⁸. To find the band gap, one must plot multiple points and extrapolate the linear trend.

Example 2: Indirect Band Gap Semiconductor

Now consider an indirect allowed transition material like Silicon (Si). We have a data point where hν = 1.2 eV and α = 500 cm⁻¹.

• Inputs: α = 500 cm⁻¹, hν = 1.2 eV, n = 2 (for indirect allowed)
• Calculation: (500 * 1.2)¹/² = (600)⁰.⁵ ≈ 24.5
• Result: The y-axis value is approximately 24.5. Again, this is a single point on the plot used to determine the final band gap energy. The mastery of how to calculate band gap using Tauc plot enables precise material characterization. For further reading on material properties, consider exploring the {related_keywords}.

How to Use This Tauc Plot Calculator

1. Enter Absorption Coefficient (α): Input the value obtained from your experimental data, typically measured in cm⁻¹.
2. Enter Photon Energy (hν): Input the corresponding photon energy in electron volts (eV). If you have wavelength (λ) in nm, use the formula E(eV) = 1240 / λ(nm).
3. Select Transition Type (n): Choose the correct value of ‘n’ based on your material’s expected properties. This is the most critical step for an accurate analysis.
4. Calculate: Click the “Calculate” button. The calculator will compute the (αhν)¹/ⁿ value, which is the y-coordinate on a Tauc plot.
5. Interpret the Result: The calculator provides one point. The actual process of finding the band gap involves plotting many such points and performing a linear fit. The primary result reminds you that the final band gap is the x-intercept of this line.

Key Factors That Affect How to Calculate Band Gap Using Tauc Plot

• Choice of ‘n’ value: The most significant factor. An incorrect ‘n’ will lead to an incorrect band gap value as it determines the shape of the plot.
• Linear Fit Region: Choosing the correct linear region on the plot to extrapolate is subjective and can introduce errors. The fit should only be applied to the part of the curve corresponding to band-to-band absorption.
• Data Quality: Noise in the UV-Vis absorption spectrum can make it difficult to identify the linear region, affecting the accuracy of the extrapolation.
• Baseline Correction: The presence of an “Urbach tail” or sub-band gap absorption can shift the baseline, leading to an underestimation of the band gap if not corrected.
• Film Thickness: An accurate measurement of the sample’s thickness is required to correctly calculate the absorption coefficient (α), directly impacting the entire calculation.
• Material Phase: Amorphous and crystalline phases of the same material will have different absorption characteristics and thus different Tauc plots and band gaps. A deep dive into the {related_keywords} can provide more context.

Frequently Asked Questions (FAQ)

1. What is the difference between a direct and indirect band gap?

In a direct band gap material, an electron can be excited by a photon alone. In an indirect band gap material, the transition also requires interaction with a phonon (a lattice vibration), making the absorption process less efficient. This is reflected in the ‘n’ value used in the Tauc plot. For more on this, the {related_keywords} is a good resource.

2. Why can’t I just find the wavelength where absorption starts?

Absorption doesn’t start at a sharp, single point. It begins gradually, often with a tail of weak absorption (Urbach tail) caused by defects and thermal effects. The Tauc plot method is a standardized way to get a more accurate and reproducible value by focusing on the strong absorption region.

3. How do I know which ‘n’ value to use?

This often comes from prior knowledge of the material or theoretical calculations. If unknown, you can create Tauc plots for different ‘n’ values and see which one yields the best linear fit in the high-absorption region.

4. What does the Y-axis value calculated here represent?

It represents the transformed absorption value for a single photon energy. Plotting this Y-value against its corresponding X-value (photon energy) for your whole dataset creates the Tauc plot.

5. What is an Urbach Tail?

It’s an exponential tail on the absorption spectrum below the main absorption edge, often caused by structural disorder, defects, or thermal effects in the material. It can complicate the Tauc analysis.

6. Can this method be used for non-semiconductors?

The Tauc plot method is specifically designed for amorphous and crystalline semiconductors. It is generally not applicable to metals (which have no band gap) or insulators with very large band gaps where band-edge absorption is not easily measured.

7. How do I convert wavelength (nm) to photon energy (eV)?

Use the simple conversion formula: E (eV) = 1240 / λ (nm), where λ is the wavelength in nanometers. This is a vital first step in knowing how to calculate band gap using Tauc plot. For related calculations, see our {related_keywords} page.

8. What if my plot has two linear slopes?

This can sometimes occur in complex materials or composites, potentially indicating multiple phases or different types of electronic transitions. It requires careful interpretation, but often the slope at higher energy is taken for the primary band gap.