I am working with Alumina & Zirconia thin films by reactive dc magnetron sputtering on silicon & soda lime glass substrates. Is it possible to use the Kubelka-Munk method from diffuse reflection spectra to calculate band gap? I know that photoelectron spectroscopy can do this job, but we don't have that facility. So please show some light in optical measurements technique regarding this.
Note: thickness= 100nm.
Dear Muhammed
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: The following relational expression proposed by Tauc, Davis, and Mott is used. (hνα)1/n = A(hν - Eg) (1) 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 = 1/2
For direct forbidden transition•••••••••• n = 3/2
For indirect allowed transition•••••••••• n = 2
For indirect forbidden transition•••••••• n = 3
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: (hνF(R∞))2 = A(hν - Eg) (2) Using the Kubelka-Munk function, the (hνF(R∞))2 can be 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. A line is drawn tangent to the point of inflection on the curve and the hν value at the point of intersection of the tangent line and the
horizontal axis is the band gap Eg value.
If you have reflection measurement accessibility, then yes. With help of R, T and thickness you can measure band gap using Tauc's plots. For this you need to deposit on quartz substrate in place of glass.
Thanks for your Concern!. I have already coated films on silicon and soda lime glass. using these samples, is it possible to measure the band gap (>4eV)?
I am also interested to know that, is it possible to measure a band gap of 8-8.5eV films, which is coated on a quartz substrate?
On Silicon and soda lime glass, possiblity is very very less because of their band edge. With quartz usually you can measure upto 7 eV reliably. For more than this 7 eV, quartz isnot the appropriate choice.
You can use spectroscopic ellipsometry method (reflectance measurements). The energy ban-gap you can determine from the optical model of sample: dielectric layer/substrate (the simplest form). You can use both transparent and non-transparent substrates.
@ Lukasz Skowronski, Is it possible to calculate band gap from Kubelka-Munk method using diffuse reflection spectra(UV-VIS) of the sample?
Dear Muhammed
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: The following relational expression proposed by Tauc, Davis, and Mott is used. (hνα)1/n = A(hν - Eg) (1) 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 = 1/2
For direct forbidden transition•••••••••• n = 3/2
For indirect allowed transition•••••••••• n = 2
For indirect forbidden transition•••••••• n = 3
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: (hνF(R∞))2 = A(hν - Eg) (2) Using the Kubelka-Munk function, the (hνF(R∞))2 can be 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. A line is drawn tangent to the point of inflection on the curve and the hν value at the point of intersection of the tangent line and the
horizontal axis is the band gap Eg value.
Spectroscopic ellipsometry (SE) is an alternative method to determine e.g. thickness of layer(s), parameters of disperssion relation of refractive index (e.g. Sellmeier relation) and extinction coefficient, the energy of band gap and others. In my opinion (in general) SE is a powerfull method to examine optical properties of layers and some microstructural properties of materials.
Obviously, if you performed R and T measurements, the method presented by Maria Vasilopoulou is sufficient.
Kubelka-Munk method, based on diffuse reflection spectra, is a fair way to calculate a band gap for the first orientation (see some of our previous works on PZT).
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