Calculation of energy gap using Tauc plot

The Tauc plot is a method that is widely used for the determination of band gap. Shown next is the

procedure for determining the band gap from a diffuse reflectance spectrum using the Tauc plot.

 

Process for Obtaining Band Gap Using Tauc Plot

 

 

1. The following relational expression proposed by Tauc, Davis, and Mott is used.

where h: Planck's constant, ν: frequency of vibration, α: absorption coefficient, Eg: band gap, 

A: proportional constant. The value of the exponent n denotes the nature of the sample transition.
For direct allowed transition   n = 2, for direct forbidden transition    n = 2/3, for indirect allowed transition    n = 1/2, and for indirect forbidden transition   n = 1/3
Since the direct allowed sample transition is used in this experiment, n = 2 is used for these samples.

 

2.  The acquired diffuse reflectance spectrum is converted to Kubelka-Munk function. Thus, the vertical axis is converted to quantity F(R∞), which is proportional to the absorption coefficient. The α in the Tauc equation is substituted with F(R∞). Thus, in the actual experiment, the relational expression becomes:

 

3.  Using the Kubelka-Munk function, the (hνF(R∞))^2 was plotted against the hν. The curve that plots the value of (hν - (hνF(R∞))2) on the horizontal axis hν and vertical axis (hνF(R∞))2 is drawn. Here, the unit for hν is eV (electron volts), and its relationship to the wavelength λ (nm) becomes hν = 1239.7/λ.

 

 

 

4. A line is drawn tangent to the point of inflection on the curve of step (3), and the hν value at the point of intersection of the tangent line and the horizontal axis is the band gap Eg value.

 

Note: The point of inflection is found by taking the first derivative of the curve. The point at which the value of the first derivative coefficient begins to decrease after increasing is the point of inflection.