As you know, Beer-Lambert law is
I=I0exp(-a*d)
where a is absorption coefficient and d is sample thickness.
my question is if a ~104 cm-1 and d ~ 100 um, the I would be quite small compare to the I0. that makes hard to obtain
is there a way to measure absorption coefficient except ellipsometry in single crsytal?
Dear friend Jeong Bin Cho
The Beer-Lambert law is used to calculate the absorption coefficient of a sample. However, if the absorption coefficient is too high and the sample thickness is too large, it can be difficult to obtain accurate measurements. There are several methods to measure the absorption coefficient of a single crystal. One method is to use ellipsometry, which measures the change in polarization of light as it passes through the sample (How can we calculate...).
Another method is to use transmittance (T) and reflectance (R) spectra to calculate the absorption coefficient of a single crystal. The linear absorption coefficient can be estimated using the following formula: α = − ln [ T0 / (1 − R) 2] / L where T0, R, and L are the linear transmittance, reflectivity, and thickness of the sample, respectively (Frontiers research on the.....).
I hope this helps! Let me know if you have any more questions.
Source:
(1) How can we calculate the absorption coefficient of the single crystal .... https://www.researchgate.net/post/How_can_we_calculate_the_absorption_coefficient_of_the_single_crystal_wafer.
(2) Frontiers | Research on the Nonlinear Absorption Coefficient of 98% .... https://www.frontiersin.org/articles/10.3389/fphy.2022.901370/full.
(3) Saturation of optical absorption in CdS single crystals. https://www.researchgate.net/publication/281525678_Saturation_of_optical_absorption_in_CdS_single_crystals.
(4) Absorption Coefficient of Bulk III-V Semiconductor Materials ... - Springer. https://link.springer.com/article/10.1007/s11664-022-09846-7.
(5) Absorption coefficient, explained by RP Photonics Encyclopedia .... https://www.rp-photonics.com/absorption_coefficient.html.
Just to add, there are two different levels of theory, namely the (Bouguer-)Beer-Lambert (BBL) approximation and the combination of Wave Optics and Dispersion Theory. The BBL approximation assumes that light has no wave properties (e.g., no interference effects, but also no reflection) and it also assumes that light does not polarize matter. Depending on the nature of your sample, such simplifications may be admissible. Additionally, most single crystals are anisotropic. This usually kills the concept of an absorption coefficient, because it only makes sense on the BBL level of theory (refractive index and absorption coefficient are wave properties!). Instead you have to determine the (complex) dielectric function tensor.
the absorption coefficient and the sample thickness are related , the transmitted light intensity will be significantly reduced if the thickness is importante making it difficult to measure the absorption coefficient accurately. You can work using samples of different thicknesses or the best is to use a technique called attenuated total reflection (ATR) spectroscopy. ATR spectroscopy measures the absorption of light in a thin layer of sample material that is in contact with an optically dense material, such as a crystal or prism.
Eric Finot One problem with ATR is that most modern accessories no longer have the possibility to employ a polarizer, which makes the analysis of anisotropic single crystals complicated. I would assume that it is also not so easy to establish the necessary intimate contact between ATR crystal and the single crystal sample...
If your sample shows an absorption coefficient of 10^4, and your sample is 100 um thick, then, necessarily, Io has a very low value. To obtain the absorption coefficient properly, you must reduce the sample thickness to 1-10 um.
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