This document summarizes a study that determined the optical constants of thin rhodium films using spectral reflectance measurements. The study used Kramers-Kronig relations to calculate the phase angle from reflectance measurements. This allowed determining the real refractive index. The extinction coefficient was then estimated using equations relating reflectance, refractive index, and film thickness. The determined optical constants compared well to values from an interference method. The method provides an accurate way to determine optical constants of highly absorbing thin films using normal incidence reflectance measurements alone.
Linear attenuation coefficient (휇) is a measure of the ability of a medium to diffuse and absorb radiation. In the interaction of radiation with matter, the linear absorption coefficient plays an important role because during the passage of radiation through a medium, its absorption depends on the wavelength of the radiation and the thickness and nature of the medium. Experiments to determine linear absorption coefficient for Lead, Copper and Aluminum were carried out in air. The result showed that linear absorption Coefficient for Lead is 0.545cm – 1, Copper is 0.139cm-1 and Aluminum is 0.271cm-1 using gamma-rays. The results agree with standard values.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
A method of obtaining an Infrared spectrum by measuring the interferogram of a sample using an interferometer, then performing a Fourier Transform upon the interferogram to obtain the spectrum.
Linear attenuation coefficient (휇) is a measure of the ability of a medium to diffuse and absorb radiation. In the interaction of radiation with matter, the linear absorption coefficient plays an important role because during the passage of radiation through a medium, its absorption depends on the wavelength of the radiation and the thickness and nature of the medium. Experiments to determine linear absorption coefficient for Lead, Copper and Aluminum were carried out in air. The result showed that linear absorption Coefficient for Lead is 0.545cm – 1, Copper is 0.139cm-1 and Aluminum is 0.271cm-1 using gamma-rays. The results agree with standard values.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
A method of obtaining an Infrared spectrum by measuring the interferogram of a sample using an interferometer, then performing a Fourier Transform upon the interferogram to obtain the spectrum.
It is an analytical technique uselful for detection of functional groups present in particular molecules and compounds.
It is highly applicable in pharmaceutical and chemical engineering.
It is an analytical technique uselful for detection of functional groups present in particular molecules and compounds.
It is highly applicable in pharmaceutical and chemical engineering.
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Experimental Study of Third Order Nonlinear Absorption in Pure and MG Doped L...ijtsrd
With the discovery of laser in 1960 various nonlinear effect arises, the origin of nonlinear optics lies in the nonlinear response of materials to the incident coherent radiation. Using pulsed Q switched Nd YAG Laser, we have observed the important phenomena i.e. third order nonlinear effect in the LiNbO3 crystals. In present work, I have performed an experiment using simple and sensitive single beam Z scan technique to measure nonlinear absorption in LiNbO3 crystals samples such as pure LiNbO3 crystal, 5mol Mg doped LiNbO3 crystal, and 7mol Mg doped LiNbO3 crystal. Vijay Aithekar | Dr. Vishal Saxana "Experimental Study of Third Order Nonlinear Absorption in Pure and MG Doped Lithium Niobate Crystals" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26370.pdf Paper URL: https://www.ijtsrd.com/physics/engineering-physics/26370/experimental-study-of-third-order-nonlinear-absorption-in-pure-and-mg-doped-lithium-niobate-crystals/vijay-aithekar
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In this paper, we show theoretically that the reflectance spectra of one dimensional multilayer metal-organic periodic structure (1D MOPS) can be enhanced due to the addition of the organic constituents. We have used simple transfer matrix method to calculate the absorption, transmittance and reflectance of the 1D MOPS systems. The organic component like N,N’-bis-(1-naphthyl)-N,N’diphenyl-1; 1biphenyl-4; 4diamine (NPB) absorbs the light in ultra-violet, visible and infrared electromagnetic region and the structure with Ag-metal also having the tendency to absorb the light by the plasmaonic action and their refractive can be calculated from Drude equation. The reflectance spectra of multilayer 1D MOPS containing a variable number periodic of Ag/N,N’-bis-(1-naphthyl)-N,N’diphenyl-1; 1biphenyl-4; 4diamine (NPB) structure are calculated taking optical constant of NPB and Ag. The optical band gap and reflectance spectra of 1D MOPS of the considered structure is obtained in the visible and near infrared regions either with the variation of the metal layer thickness or thickness of the organic layer. From the results under investigation through TMM, tunability in the optical band gap was observed either change in thickness of the other layer 1/ or 2 or the angle of the incident. Due to optical absorption of the light in the different region of electromagnetic spectrum due to either N,N’-bis-(1-naphthyl)-N,N’diphenyl-1; 1biphenyl-4; 4diamine (NPB) or silver metal, the optical band gap of 1DMOPS shows the shift of band edges of λL and λR from ultra-violet to visible and the infrared with change the optical constant.
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Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
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Twitter: https://x.com/albumentations
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!SOFTTECHHUB
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Building RAG with self-deployed Milvus vector database and Snowpark Container...Zilliz
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Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
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The optical constants of highly absorbing films using the spectral reflectance measured by double beam spectrophotometer
1. Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.2, 2011
The Optical Constants of Highly Absorbing Films Using the
Spectral Reflectance Measured By Double Beam
Spectrophotometer
ElSayed Moustafa1*
1. Faculty of science , El-Azhar university, physics department, Assuit, 71511, Egypt
* e-mail of the corresponding author: Sayed19652000@yahoo.com
Abstract
The optical constants of the metal thin films of Rhodium have been determined, the phase angles was
determined using the measured spectral reflectance R(λ) by Kramers-Kronig relations. Then, the real part
of the refractive index is calculated by the approach of Heavens when the film is highly absorbing, in that
range the real refractive was found to be in order of the extinction coefficient k.
The interference reflectance spectra at normal incidence for different thicknesses of amorphous metal films
deposited by thermal evaporation have been obtained in the spectral range 400–800 nm. We propose a
method for determination of the refractive index and extinction coefficients of highly absorbing films. This
method is based on measurements of reflectance of the film at normal incidence alone, simulations of the
theoretical accuracy and the effect of the error of the spectral reflectance measurements in the
determination of the optical constants of the film are analyzed.
Keywords: optical constants , refractive index , thin film ,reflectance and absorption coefficient .
1. Introduction
The determination of the optical properties of thin films is a topic of fundamental and technological
importance ( Jyh-Jian Chen, et al ,1999 ). Most of the optical applications of metal coating are based on the
knowledge of the optical constants. For the metal coating (Rh) film which was used, this metal is inert , so
changes due to oxidations should be minimal. The optical constants are important parameters for predicting
the performance of an optical system. The optical constants are sensitive to the microstructure, which is
effected by the deposition conditions.
A good knowledge of film parameters is necessary for the design and manufacture of new optical coatings
and devices such as multilayers coatings and regulate filters[ Manifacier.J.C, et al 1976]. An optical
constant is sometimes called a complex refractive index and is described by the expression of (n-ik), where
n and k are the refractive index and the extinction coefficient respectively of the film. Measurements of
the optical constants of highly absorbing thin films on transparent or slightly absorbing substrates have
been extensively investigated. Especially the method based on only a single measurements of the
transmission spectrum at normal incidence is widely used to determine the refractive index and extinction
coefficient of a film( Swanepoel. R, 1984). Also, there are the method of interference of the spectral
transmittance and reflectance ( Özcan Bazkir,2007 ).
2.Theoretical considerations
In the highly absorbing films, according to the notation of Heaven, the reflectance can
approach to the following formula :
(n − 1) 2 − k 2
Rf = (1)
(n + 1) 2 + k 2
In the above approach the sample is considered to be in air so n0=1, the refractive index
of vacuum and practically the incident rays are quasi-parallel.
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2. Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.2, 2011
In the fundamental absorption region (i.e., αf ≥ 105 cm-1 or αfdf ≥ 1), transmission
measurements become impractical and the optical constants have to be determined from
reflectivity measurements alone. This is possible, in principle, when the amplitude r and phase angle θ of
the complex reflectivity are both determined as a function of hω as follows:
r (ω ) = r (ω )e iθ
ˆ (2)
It is achieved in ellipsometry where the polarization state of a light beam impinging at non-normal
incidence onto the specimen surface is a analyzed ( J.D .Joannopoulos & G.Lucovsky, 1984). Since
ellipsometry is very surface sensitive, it has so far been applied to study the growth and the oxidation of
plasma deposited amorphous films. An ε2 spectrum of HF etched a-SiH is given in (J.D .Joannopoulos &
G.Lucovsky ,1984). It is possible to derive both r(ω) and θ(ω) from measurements of |r2|2 at normal
incidence alone using the Kramers-Kronig dispersion relationship between r and θ (Özcan Bazkir,2007 ), as
follows:
ω0 ln r (ω )
θ (ω0 ) = − ∫
∞
dω (3)
π 0
ω 2 − ω02
On the other hand the phase angle θ = 2π/λ( n - ik ).d ( 4)
d is the film thickness.
df nf film nf = (n -ik)
n1 ≡ ns substrate
no =1 d2
Figure ( 1 ) demonstrates the optical constants used in the calculation of thin highly absorbing
film
The Kramers-Kronig relationship links the value of θ at a particular frequency ω0 to an integral over
reflectivities extending over all energies hω. The latter is, however, only known over a limited region in ω
and methods have therefore been developed to extrapolate r(ω) to very low or very high frequencies in a
physically reasonable way.
The sum rules relations are considerable help in this procedure. The most useful of these in the present
work is that which relates ε∞, the long wavelength dielectric constant to an integral over ε2 (ω) .
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3. Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.2, 2011
The advantage of the methods that use the envelope of transmittance or reflectance measurements is that
the dispersion of the complex refractive index of the index of a thin film is obtained easily. The
disadvantage. However, is that the thin film must be thick (J.M.Gonzalez-leal et al, 2004 ). Here there is no
new method for n and k determination of the film . But an improvement to obtain the accurate values of
the optical constants by comparing two methods, one of them is the interference method and the other is a
method depends on the spectral reflectance of the film involved the correction of the multi-reflections
inside the substrate.
The theoretical idea of this work is the determination of the optical constants nf and kf for the highly
absorbing films using the measured reflectance Rf at normal incidence using KK relations.
3.Results and discussions
The reflectance of the samples has been measured by double beam spectrophotometer with high accuracy
± 1% as shown in figure ( 2 ). To obtain the accurate values of the optical constants by comparing two
methods, one of them is the interference method which depends on the maxima and minima of the
transmittance and reflectance (Yanfi Zheng & Kazuo kikuchi,1997), the other is a method depends on the
spectral reflectance of the film involved the correction of the multi-reflections inside the substrate. Figures
( 2 ) shows the experimental spectral reflectance of Rh film, by applying equation (3),we calculated the
values of the phase angle using the measured reflectance data, the value of θ has been found to be 1.8435 .
Then by substitution in equation ( 2 ) and computing the Fresnel coefficients, the real refractive index n
and k have been determined, it is noted that the values of n and k are nearly equal as the thickness of the
film decreases and the wavelength λ increases.
In this work the values of θ have been calculated from the integral ( 3 ) over the range from 1.55 - 4.14
eV. By solving equations ( 1 ) and ( 4 ), the real refractive index n can be determined , then the extinction
coefficient k can be estimated by equation ( 1 ). Where d is the film thickness and λ is the incidence
wavelength.
ω0 in the calculations has been taken to be around 0.75*1015 Hz , and the interval dω was 1 Hz. As the
extrapolation of the reflectance increases , this means more accuracy.
The integral ( 3 ) has been estimated numerically using a computerizing program, the uncertainty of
estimation within ± 2%.
Table (1) illustrates the values of the calculated refractive index nkk and the extinction coefficient kkk of the
absorbing film comparing them with that determined by interference method of R(λ) and T(λ). It is clear
that the error between the two values is acceptable with respect to this type of measurements around ± 5%.
The advantage of this method its accuracy because the optical constants directly determine from the
measured spectral reflectance R(λ) of the film especially the metal films at normal incidence.
5. Conclusions
-From the previous analysis it was conclude that the optical constants of film depend on the method of
calculation. The accuracy of the suggested method depends on the extrapolation of the curve of the
spectral reflectance of the sample.
-It is preferable to use the spectral reflectance measured by the spectrophotometer at normal incidence as
the film is highly absorbing and the thickness is thin.
-Table ( 1 ) are very important in the calculation of the optical constants of the highly absorbing films.
References:
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4. Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.2, 2011
Arndt.D.P, Borgongo.J.P.,Azzam.R.M & Bennett.J.P,(1984), "Multiple determination of the optical
constants of thin-film coating materials ", Applied Optics,vol.23,No.20,3571-3580.
Borgongo . J. P , Lazarides . B, & Pelletier . E,(1982), "Automatic determination of the optical constants
of inhomogeneous thin films", Applied optics , vol . 21, No. 22, 4020.
Minkov. D. A, (1989) , " Calculation of the optical constants of a layer upon a transparent substrate from
the reflection spectra ", J.Phys.D:Appl.Phys.22,1157.
Manifacier. J.C, Gasiot. J & Fillard. J.P, (1976 ), " A simple method for the determination of the optical
constants and thickness of weakly absorbing films ", J. Phys. E., 9, 1002-1004 .
Joannopoulos. J.D and Lucovsky. G, (1984)," The physics of hydrogenated amorphous silicon II ",
Springer- Verlag ,Berlin Heidelberg.
Jyh-Jian Chen, Jenn- Der Lin, & Long-Jye Sheu, (1999), " Simultaneous measurements of spectral optical
properties and thickness of an absorbing thin films on a substrate ",Thin Solid Films, 354, 176 -186.
Gonzalez-Leal. J.M, Pr ieto-Alcon. R, Stuchlik. M, Vlcek. M, Elliott. S.R, and Marquez. E,(2004),
"Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by
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5. Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.2, 2011
*The Author had been born in 1965, Egypt ,and has BSc in 1986 in physics, Msc in experimental physics
1993, and the ph.D in solid state and optical properties of films in 2000. Associated prof. in physics in 2006
,the field of research is the optical and electrical properties of solids ( glasses , coating films, solar cells ).
My institution is Faculty of science , El-Azhar university, physics department, Assuit, 71511, Egypt.
0 2 4 6 8 10
0.44 10
Rh-film 14 nm
8
reflectaance %
6
0.43
4
2
0.42 0
400 500 600 700 800
wavelength λ
Figure ( 2a) illustrates the spectral reflectance of Rh film (14nm ) meaured
by the spectrophotometer
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ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.2, 2011
0 2 4 6 8 10
10
0.59
Rh-27.1 nm
8
0.58
Reflectance %
0.57 6
0.56 4
0.55
2
0.54
0
350 400 450 500 550 600 650 700 750 800
wavelength λ
Figure ( 2b) illustrates the spectral reflectance of Rh film (27.1 nm ) meaured
by the spectrophotometer
Table. ( 1 ) : A comparison between the calculated and reported values of the refractive index n and the
extinction coefficient K for the Rh films
Material Wavelength Thickness Measured Refractive Extinction
λ t reflectivity index nkk coefficient nf Kf
nm R k kk
Rh 450 0.4367 2.550 2.551 2.4 3.28
500 0.4322 2.500 2.522 2.6 3.40
550 14.2 0.4311 2.50 2.51 2.78 3.53
600 0.4294 2.50 2.51 2.95 3.65
650 0.4284 2.50 2.50 3.11 3.77
700 0.4282 2.497 2.50 3.23 3.91
450 0.5597 2.50 3.54 2.27 3.25
500 0.5649 2.56 3.58 2.39 3.41
Rh 550 27.1 0.5698 2.60 3.62 2.51 3.58
600 0.5745 2.62 3.69 2.62 3.74
650 0.5770 2.65 3.70 2.75 3.88
700 0.5797 2.70 3.76 2.78 4.03
*Reported n and k according to ( Arndt D.P, Borgongo . J. P. et al,1984).
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