Tauc plot

A Tauc plot is a graphical method used to determine the optical band gap of thin films or semiconductors. It is particularly useful for materials with indirect band gaps, where the absorption edge is not as sharp as in direct band gap materials. The plot is based on the Tauc equation, which relates the absorption coefficient (α) to the photon energy (hν) near the band edge.

The Tauc equation generally takes the form:

(αhν)^n = A(hν - Eg)

Where:

• α is the absorption coefficient.
• hν is the photon energy.
• Eg is the optical band gap energy.
• A is a constant that depends on the material.
• n is a factor that depends on the nature of the electronic transition. It takes values of 2 for indirect allowed transitions, 1/2 for direct allowed transitions, 3 for indirect forbidden transitions, and 3/2 for direct forbidden transitions.

To create a Tauc plot, (αhν)^n is plotted against hν. The appropriate value of 'n' is selected based on the expected electronic transition type. The linear portion of the curve, corresponding to the region where the absorption is increasing rapidly near the band edge, is extrapolated to the x-axis (hν axis). The x-intercept of this extrapolated line is taken as the optical band gap energy (Eg).

The absorption coefficient (α) is typically calculated from the measured transmittance (T) and reflectance (R) of the thin film, along with its thickness (d), using the following equation:

α = (1/d) * ln((1-R)/T)

The Tauc plot is a widely used technique for estimating the optical band gap of various materials, offering a relatively simple and convenient method for characterization. It is important to note that the accuracy of the determined band gap relies on the correct assignment of the 'n' value and the quality of the measured optical data. Deviations from ideal behavior and complexities in the electronic structure can lead to inaccuracies in the extracted band gap.