I am working on band gap calculation using UV vis spectroscopy of ZnO nanorods that i grown on gold coated glass . As it is non transmittance so it has 100% absorbance and 0% transmittance. the only thing i can use for the band gape is reflectance. But i did not find any relation (mathematical formula) to calculate the band gap from reflectance. Can anyone help me how to calculte the energy band gap in such situation?
On a side note, zero transmittance does not mean 100 % absorption (not absorbance, since this is in most cases defined as -lg T, whereas absorption is 1-R-T with R being reflectance and T being transmittance). In your system zero transmittance means a very high specular reflectance due to gold coated substrate and does not imply a high absorbance or a 100 % absorption.
you have to get rid of the the angle dependance of the scattering. That means you have to use a Integration sheres (Ulbrich). Than you can use the data to calculate the Band gab by linear interpolation. Of course the same laws are also valid for such kind of measurements = sufficient amount of light should reach the detector which might be problematic for your sample. Otherwise the bandgab seems to be larger than it really is.
On a side note, zero transmittance does not mean 100 % absorption (not absorbance, since this is in most cases defined as -lg T, whereas absorption is 1-R-T with R being reflectance and T being transmittance). In your system zero transmittance means a very high specular reflectance due to gold coated substrate and does not imply a high absorbance or a 100 % absorption.
Dear Younas,
in particulate systems, the answer to your problem would be best described in terms of KUBELKA-MUNK theory of diffuse reflectance from the late 1920s. Therein DIFFUSELY reflected light is gathered in an integrating sphere (covered with BaSO4), as Prof. Schmitt noted. The theory itself is described in much detail in the famous book "Reflexionsspektroskopie" by Gustav Kortüm...unfortunaley written in german language.
If in your system the reflected light hopefully lacks of much specular reflectance, due to the nanostructured surface covered with ZnO, when you can record diffuse reflectance just like a transmission-based electronic spectrum. The particulate nature of your sample then introduces a second factor besides the wavelength dependence of absorption (named absorption coefficient K), namely the wavelength dependence of light scattering (named scattering coefficient S). Within KM-theory, the measured reflectance R(lamda) is transformed as follows:
F(R) = (1-R)² / 2R = K/S
If you plot these transformed data vs. wavelength or energy, you will receive the typical step-like behaviour of a semiconducting material and can extract the band-gap energy from the onset of the step (there are more sophisticated ways to get these data). Note that there are several ways to plot F(R), which depend on the nature of the semiconductor (direct vs. indirect).
Hope this helps...good luck!
Thomas Mayerhöfer please elaborate more on "absorption = 1-R-T". I have 100s of cases where measured R(specular included) and T already sum to >1, does that mean negative absorption? No, right? What is it then? Thanks in anticipation!
Muhammad Safdar Energy conservation requires that R+T+A=1 or IR+IT+IA=I0 where I0 is the irradiance from the light source (all in the absence of scattering) and A is better called absorptance (instead of absorption). If R and T sum already up to more than 1, your sample is either a light source or your measurements went wrong (also, note that often T is expressed in %T... ).
Hi Thomas Mayerhöfer , thank you for your kind answer. I was actually adding T and R at each wavelength that was giving sum>1 at some of the wavelengths. Sum of T_mean and R_mean is of course not >1, so law of conservation of energy was still valid I believe. R+T can be >1 at some of the wavelengths, right? But the actual question is that if absorptance (A), generally, fits in a linear equation (R+T+A=1)? Or is there any assumption made here?
A last question is that if we have measured values of R(λ) and T(λ), what general relations we would use to find absorption coefficient (K(λ)) and scattering coefficient (S(λ))?
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