One measurement is made at normal incidence and the other at an arbitrary angle of incidence greater than zero, but less than 90. Refractive index dispersion of chalcogenide glasses for. In more complicated situations, numerical solutions are nec. The refractive indices for these semiconductors are calculated to be 3. Use the link below to share a fulltext version of this article with your friends and colleagues. B 6, 43704379 1972 silver is often used as a coating material for broadband mirrors for visible and infrared spectral regions. Relations between the refractive index and energy gap of. The refractive index determines how much the path of light is bent, or refracted, when entering a material. The handbook on optical constants of semiconductors.
This ef fectively excludes the microwave and radiofrequency ranges from being discussed in a chapter on the optical properties of semiconductors. Simulation results demonstrate that complex sellmeier equations can accurately. The fact that dielectric loss increases ith frequency in the millimeter, unlike the microwave, is an important feature of ur data. Model for calculating the refractive index of different. The interrelation between the real and imaginary parts of the dielectric constant.
Measurement of the complex refractive index and the band gap of a. Tripathy abstract an empirical relation based on energy gap and refractive index data has been proposed in the present study to calculate the refractive index of semiconductors. The complex dielectric constant and refractive index of binary alloys were first calculated and the results were then used in the calculations for quaternary alloys. Empirical temperature dependence of the refractive index. The method depends on making two reflection measurements from a bulk sample of material. Modeling of semiconductors refractive indices using hybrid. Ravindran, phy02e semiconductor physics, autum 20 17 december. Owolabi2,3,6, sola fayose2, muideen adegoke4, kabiru o. An empirical relation based on energy gap and refractive index data has been proposed in the present study to calculate the refrac.
The results of this paper are very interesting for many applications including optical simulation software and waveguide design. A simple method is presented for measuring boththe real and imaginary parts of low resistivity semiconductors. Refractive index dispersion of chalcogenide glasses for ultrahigh numericalaperture fiber for midinfrared supercontinuum generation harshana g. Recall that in nonattenuating media, the refractive index and angular wavenumber are related by. The method is shown to work well for powders with a narrow size distribution exemplified by fe 2 o 3 and to be ineffective for semiconductors with a broad size distribution. For example, it is used in the sugar processing industry to determine the mass. Measurements of electrically tunable refractive index of. Refractive index of gapinp gallium indium phosphide. Complex refractiveindex measurement based on fresnels equations and the uses of heterodyne interferometry article pdf available in applied optics 3819. Refractive index of iiiv group semiconductors as function of en ergy gap using our modi ed relation in eq. Empirical temperature dependence of the refractive index of. The refractive index obtained for inn within the photon energy range 2. Using this and maxwells equations, one obtains the well known maxwells formula for the refractive index of a substance as, where e.
Osa temperature dependence of the refractive index in. Determination of the complex refractive index and optical. The book will aid many who are interested to know the optical constants of the elemental and compound semiconductors in the course of their work. The straininduced bandgap shrinkage and absorption. Selfreferenced method for estimating refractive index and. This article presents a comprehensive model, which includes the exciton effect and most of the major critical points, to calculate the complex index of refraction of the ingangan qw at room temperature. Olatunji6 1 department of physics and engineering physics, obafemi awolowo university, ileife a234, nigeria 2 physics and electronics department, adekunle ajasin university, akungba akoko 342111, nigeria.
Modeling the dispersion relation of semiconductors using a complex sellmeier equation is reported for the first time. Refractive indices of semiconductors from energy gaps s. Nov 20, 2002 a simple method is presented for measuring boththe real and imaginary parts of low resistivity semiconductors. Simulation results demonstrate that complex sellmeier equations can accurately model the refractive index dispersion of different semiconductors at wavelengths shorter than the band gap wavelengths, where the conventional sellmeier equations are not. Magnetooptical kerr spectroscopy in ferromagnetic semiconductors. Pdf model for calculating the refractive index of a iiiv. Energy gaprefractive index relations in semiconductors. Moss 9 showed that the refractive index and absorption edge are related by. This is described by snells law of refraction, n 1 sin. The refractive index usually has real and imaginary parts. Complex refractive index tunability of graphene at 1550 nm. Handbook on optical constants of semiconductors, the. Complex dielectric function and refractive index spectra. Refractive index of solids the refractive index of a material is defined as.
From the maxwell equations, a dispersion relation k2. It is commonly used to identify a particular substance, determine its purity, or measure concentration. A lower limit of the optical frequency range might correspond to wavelengths of about 1 mm photon energy of 1. The proposed model is then applied to binary as well as ternary semiconductors for a wide range of energy gap. Ab initio calculations of the reflectanceanisotropyofgaas110. The real and imaginary parts of the refractive index, n and k. The complex dielectric function and complex optical conductivity are introduced through.
Refractive index measurements are performed by determining the critical angle of internal reflection between the fluid being measured and a medium with a known refractive index. For this purpose, the refractive indices of gaas and inasbi were measured using spectroscopic ellipsometry. Semiconductor physics related content optical properties of gaas. Handout 06 dielectric constant and refractive index of. The refractive index dispersions of semiconductors at wavelengths longer than the fundamental absorption edge have been analyzed with a theoretical prediction which is based on a modification of the simplified models of the interband transitions by taking into account the contribution of the free. Model for calculating the refractive index of a iiiv semiconductor. The complex sellmeier coefficients were then obtained by a leastsquare fitting procedure.
Moss 9 pointed out that the absorption edge can be calculated using the refractive index. The experiment allows us to obtain, from the real part of the refractive index, the n dispersive law, and from the imaginary part, the absorption coefficient an energy dependence analysis of. Optical constants of gapinp gallium indium phosphide, gainp schubert et al. Hui1 1department of electrical engineering and computer science, the university of kansas, lawrence kansas 66045, usa 2school of physics and materials science, anhui university, hefei 230039, china 3department of physics and astronomy, the. They proposed a linear relationship between the index of refraction and the energy gap. Energy gaprefractive index relations in semiconductors an. The results of photoluminescence show that with the strain applied, the silicon bandgap can be adjusted to 0. Measurement of the complex refractive index and the band gap of a thin film semiconductor article pdf available in american journal of physics 601. Dantanarayana,1 nabil abdelmoneim, 1,2 zhuoqi tang,1,2 lukasz sojka, slawomir sujecki,1 david furniss, 1,2 angela b. Introduction to semiconductors 3 we want to develop a set of equations to describe the absorption of a photon in semiconductor material. The two most interesting optical properties of a semiconductor are the absorption.
For cubic materials, the index of refraction is the same along the two transverse directions. Simulation results demonstrated that the complex sellmeier equation is an accurate model for modeling the refractive index dispersion of semiconductors at energies higher than the band gap. Complex refractive index tunability of graphene at 1550nm wavelength f. Numerical values of equivalent oscillator parameters describing the n. Calculations of optical properties for quaternary iiiv semiconductor. Refractive indices of semiconductors from energy gaps arxiv. The basic rule for obtaining the trasnition rates is given by fermis golden rule. However, even in the case where analytic calculations. Knowledge of the complex refractive index is essential for designing photonic devices based on ch3nh3pbi3 thin films such as solar cells, lightemitting diodes, or lasers. Benson1, 1george green institute for electromagnetics research faculty of. Chapter 3 optical transitions in bulk semiconductors.
Three relations for the temperature dependence of the refractive. Pdf model for calculating the refractive index of a iii. And n is the refractive index of the medium in which the wave is travelling. Model for calculating the refractive index of different materials. Modeling of semiconductors refractive indices using hybrid chemometric model luqman e. The electromagnetic field is a quantized system with a set of modes, each of which is a harmonic oscillator.
Yet, the refractive index of the ingangan qw system over a wide spectral range has been unavailable so far. In more complicated situations, numerical solutions are necessary. So, we can describe light in a medium just like light in vacuum, as long as we take into account the possibly complex refractive index correction to the speed. When optical absorption is present, the wave vector and the index are complex quantities.
The refractive index and energy gap of semiconductors. Measurement of the complex index of refraction of semiconductors. A complex refractive index can therefore be defined in terms of the complex angular wavenumber defined above. The complex refractive index n, with real part n and imaginary part k called the extinction coefficient. Yu and cardona, fundamentals of semiconductors, springer verlag 1996. The free carrier contribution to the complex refractive index.
Article pdf available in computational materials science 414. Measurements of electrically tunable refractive index of mos. In this paper we have proposed a complex sellmeier equation which can be used for modeling the material dispersion in the opaque region of the dispersion curve. The refractive index of a semiconductor material typically decreases with increasing bandgap energy eg. Pdf complex refractiveindex measurement based on fresnels. Refractive indices of semiconductors from energy gaps request pdf. Metrology of complex refractive index for solids in the. In this work, a simple selfreferenced method for estimating both the refractive indices, ne, and absolute.
Optical properties of dielectric and semiconductor thin films 3 analytic solutions can be given if we assume that the incident wave is a pure wave and that the boundary layers are regular. A singleoscillator lorentz model is applied to four different semiconductors having diamondlike crystal structure to describe the temperature dependence of their refractive index between 300 and 600 k. Complex sellmeier equation for the refractive index of. Solid state physics part ii optical properties of solids.
Complex refractive index spectra of ch3nh3pbi3 perovskite. We present a study of the influence of high strain on the bandgap and the refractive index of silicon. Determination of the complex refractive index and optical bandgap of ch 3 nh 3 pbi 3 thin films. A simple experiment to determine the complex refractive index of a semiconductor in thin film form through transmittance measurements is presented.
Solid state physics part ii optical properties of solids m. Hui1 1department of electrical engineering and computer science, the university of kansas, lawrence kansas 66045, usa 2school of physics and materials science, anhui university, hefei 230039, china. The refractive index and electronic gap of water and ice. Optical properties of semiconductors photonics research group.
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