Optical properties of crystalline semiconductors and dielectrics

Forouhi, A. Rahim; Bloomer, Iris

doi:10.1103/physrevb.38.1865

Cited by 427 publications

(288 citation statements)

References 11 publications

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“…The experimental data are represented with open circles; the solid line represents our calculations, the dotted line represents the results of Adachi, 11 and the dashed line represents the calculations of Forouhi and Bloomer. 19 The refractive index rms error obtained for our model is 1.2%, compared with the values of 13.6% for Adachi's MDF and 5.8% for the model of Forouhi and Bloomer. The conventional Adachi model gives the poorest agreement with the experimental data.…”

Section: Resultsmentioning

confidence: 89%

“…[9][10][11][12][13][14][15][16][17][18] Forouhi and Bloomer 19 have proposed a model which is also related to the band structure and requires fewer parameters ͑up to 14͒. However, for the materials investigated here, this model does not bring about significant improvement in accuracy over the conventional Adachi's model, especially around the fundamental band-gap E 0 .…”

Section: Introductionmentioning

confidence: 72%

“…Agreement with experiment is better for the calculations of Forouhi and Bloomer. 19 However, it can be observed that this model fails to describe accurately the optical properties of GaP below and around the fundamental band-gap E 0 . The discrepancy present at the end of the investigated spectral range is probably due to the fact that data for energies higher than 5.5 eV are not taken into account on the determination of the model parameters.…”

Section: Resultsmentioning

confidence: 99%

“…2. The experimental data are represented by open circles; the solid line represents our calculations, the dotted line represents the results of Adachi, 11 and the dashed line represents the calcula- 19 For InAs, we obtain 1.6% relative rms error for the refractive index, while errors for the calculations of Adachi 11 and Forouhi and Bloomer 19 equal 6.5% and 2.3%, respectively. In this case, the results of Forouhi and Bloomer 19 are comparable to ours, i.e., their calculations give a rms error at 1.5 times higher than ours.…”

Section: Resultsmentioning

confidence: 99%

See 3 more Smart Citations

Modeling the optical constants of GaP, InP, and InAs

Djurišić¹,

Rakić

Kwok³

et al. 1999

Journal of Applied Physics

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An extension of the Adachi model with the adjustable broadening function, instead of the Lorentzian one, is employed to model the optical constants of GaP, InP, and InAs. Adjustable broadening is modeled by replacing the damping constant with the frequency-dependent expression. The improved flexibility of the model enables achieving an excellent agreement with the experimental data. The relative rms errors obtained for the refractive index equal 1.2% for GaP, 1.0% for InP, and 1.6% for InAs.

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Section: Resultsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 72%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Modeling the optical constants of GaP, InP, and InAs

Djurišić¹,

Rakić

Kwok³

et al. 1999

Journal of Applied Physics

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“…A common approach is the indirect (inverse) synthesis technique { , }⟶{ , }, which is based on inserting multi-constant dispersion function for and (Tan, 2006;Tan et al, 2007;Tan et al, 2006;Theiss, 2012;Forouhi & Bloomer, 1986;Forouhi & Bloomer, 1988;Adachi, 1991;Jellison & Modine, 1996;Chambouleyron & Martínez, 2001;Truong & Tanemura, 2006;Kasap & Capper, 2006;Christman, 1988;Rogalski & Palmer, 2000;Palik, 1998;Dressel & Grüner, 2002;Reitz et al, 1993) into theoretical formulas of transmittance and/or reflectance of a multi-layered structure including the film, and then use a powerful statistical curve-fitting program to attain simulated transmittance and reflectance curves to the entire and data (Solieman et al, 2014;Navarrete et al, 1990;Solieman & Abu-Sehly, 2010;Joo et al, 1999;Dobrowolski et al, 1983;Klein et al, 1990;Kukinyi et al, 1996;Chiao et al, 1995;Theiss, 2012). Numeric inversion approaches, armed with dielectric models, are also used for analyzing optical data acquired from spectroscopic ellipsometry, which are based on measured polarized-light reflection quantities of a structure that are directly related its optical functions.…”

Section: Measurements and Analytical Techniques For Determining Opticmentioning

confidence: 99%

Determination of Optical Properties of Undoped Amorphous Selenium (a-Se) Films by Dielectric Modeling of Their Normal-Incidence Transmittance Spectra

Saleh¹,

Jafar²,

Bulos³

et al. 2014

APR

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Normal-incidence specular transmittance of undoped amorphous selenium (a-Se) films of several thicknesses ( 0.25 1 μm ) thermally evaporated on thick microscopic glass-slide substrates upheld at temperatures near 30 (below glass transition temperature of undoped Se) has been measured at room temperature in the spectral wavelength range 300 1100 nm. Above a threshold wavelength (~ 600 nm), their as-measured curves display transmittance values near that of glass substrates and exhibit well-resolved interference-fringe maxima and minima, signifying good uniformity of fabricated a-Se films. Below , the curves decline progressively to zero transmittance, preceded by a tailing-like trend of possible structural disorder origin. The spectral dependencies of optical constants and of the studied a-Se films on were retrieved from iterative curve-fitting of their -data to theoretical -formulations of an air-supported {thin film/thick substrate}-stack using the O'Leary-Johnson-Lim (OJL) interband-transition dielectric model, combined with a dielectric constant , representing the dielectric background at very high photon energies (at spectral wavelengths much smaller than measured). Regardless of the number of observed interference fringes, reliable simulation to the as-measured normal-incidence -spectra has been achieved, but were remarkably curve-fitted if we presume that a thin roughness layer ( 5 nm) of selenium was formed on top of the fabricated undoped a-Se films. The retrieved spectra display a broad peak around ≅ 0.52 μm, below which was found to vary with wavelength in accordance with a Sellmeier-like (Wemple-DiDominco) single-oscillator (normal) dispersion formula, with a static index of refraction 0 ≅ 2.42, where is the static dielectric constant of the material at zero photon energy , and an oscillator "average" bandgap energy of ≅ 3.93 eV ≅ 2 , the optical (Tauc) bandgap energy. The values of of studied undoped a-Se films deduced from Tauc-like plots were around 1.92 eV ( 0.02 eV) and the retrieved values of OJL band-tailing energy parameter (Urbach-tail parameter Γ ) was found to be in the range 40 50 meV, slightly dependent on film thickness.

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Extraction Efficiency of GaN-Based LEDs

Schad

Scherer

Seyboth

et al. 2001

phys. stat. sol. (a)

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In this work, we investigate the extraction efficiency for UV emitting rectangular 300 Â 300 mm 2 gallium nitride (GaN) based light emitting diodes (LEDs) by simulation with a raytracer tool. It is shown that the extraction efficiency depends strongly on slight variations of the absorption in the GaN layers. Furthermore, the influence of the substrate shape is studied. For standard rectangular sapphire substrate based LEDs the calculated extraction efficiency is 12.4%, whereas for silicon carbide substrate based devices the higher refractive index causes a lower efficiency (4.5%). Using a shaped SiC substrate the extraction efficiency can be improved to 17.2% and 19.9% for a sapphire substrate. The influence of geometric design parameters like sidewall angle are analyzed as well.Introduction High brightness light emitting diodes (LEDs) have proven their suitability for a variety of applications such as large area outdoor displays or the generation of white light. GaN based LEDs offer a high efficiency and cover nearly the full visible wavelength range. However, internal losses and total internal reflections (TIR) limit the device performance. OSRAM-OS invented the ATON technology and improved the external quantum efficiency of GaN LEDs grown on SiC by a modified substrate geometry [1, 2]. The high refractive index of silicon carbide (n % 2:77 at 410 nm [4]) causes a small extraction cone of 42 for an unencapsulated device, whereas for sapphire substrates due to n ¼ 1:7 the cone is 72 . In the visible range both materials are transparent, but the still present low absorption reduces the extraction efficiency. The intensity decay for rays which are within the extraction cone is small for a low absorption coefficient. On the other hand, for TIR rays which propagate long distances within the device, the intensity is strongly reduced. In the ideal case, where no surface roughness and bulk scattering is present, the intensity is decreased to zero. In reality these rays contribute to the extraction efficiency due to scattering. The smaller escape cone and the higher absorption coefficient yield a lower extraction efficiency for SiC based devices compared to sapphire based LEDs. To overcome the problem of extraction, several LED designs have been proposed [5][6][7] for other material systems than IIInitrides. However, the implementation requires material specific processing steps. In this work, a structured substrate geometry is considered which can improve the efficiency in both, more rays in the extraction cone and a shorter average propagation distance.

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Optical properties of crystalline semiconductors and dielectrics

Cited by 427 publications

References 11 publications

Modeling the optical constants of GaP, InP, and InAs

Modeling the optical constants of GaP, InP, and InAs

Determination of Optical Properties of Undoped Amorphous Selenium (a-Se) Films by Dielectric Modeling of Their Normal-Incidence Transmittance Spectra

Extraction Efficiency of GaN-Based LEDs

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