Optical dielectric function of semiconductors

Djurišić, A; Li, E.H.

doi:10.1016/s0040-6090(99)00919-0

Cited by 13 publications

(18 citation statements)

References 14 publications

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“…The tanΨ and cosΔ spectra were fitted by the AC model. 21,[26][27][28][29][30][31][32] The AC model consists of the sum of the dielectric functions for each critical-point, as follows: ex are the one-electron contribution and 2D excitonic transition at the E 1 gap, which have been observed at a higher energy than the E 0 gap. In the case of GaN, AlN, AlGaN, and low-indium content Al 1−x In x N alloys, three E 1 transitions (β = A, B, and C) were observed in the range of 7−9 eV in the imaginary part of dielectric function spectra.…”

Section: Resultsmentioning

confidence: 99%

“…In the case of GaN, AlN, AlGaN, and low-indium content Al 1−x In x N alloys, three E 1 transitions (β = A, B, and C) were observed in the range of 7−9 eV in the imaginary part of dielectric function spectra. 20,[26][27][28][29] e ¥ is the constant. It has been reported that the e b 1 ex dominates and that the e b 1 could be ignored in II-VI, III-V, and III-nitride semiconductors.…”

Section: Resultsmentioning

confidence: 99%

“…It has been reported that the e b 1 ex dominates and that the e b 1 could be ignored in II-VI, III-V, and III-nitride semiconductors. [26][27][28][29][30][31][32] In Al 1−x In x N alloys, the e b 1 ex is also considered to be dominant in the imaginary part of dielectric function spectra. 20,21) The E 1 transitions are generally observed by SE system attached to synchrotron radiation facilities and difficult to observe by a typical SE system.…”

Section: Resultsmentioning

confidence: 99%

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Near-bandgap optical properties of Al_1−xIn_xN thin films grown on a c-plane freestanding GaN substrate

Toyoda

Murakami

Miyata

et al. 2021

Jpn. J. Appl. Phys.

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We investigated the relationship between the optical constants and localized states near the band-edge in high-quality crystalline Al1−x In x N alloys, with an indium content x ranging from 0.12 to 0.22, grown on a c-plane freestanding GaN substrate. Optical constants were obtained by spectroscopic ellipsometry. The tanΨ and cosΔ spectra were fitted by the Adachi’s critical-point (AC) model. The effects of the near-band-edge localized states on the optical constants were characterized by the spectral broadening factor γ, which was obtained by the AC model. The γ increased with increasing x and this tendency also confirmed by the γ obtained by the photoluminescence excitation (PLE). The bandgap energies obtained by the AC model agree well with those obtained by the PLE. It is suggested that the indium-related near-band-edge localized states cause the spectral broadening of the refractive index and extinction coefficient spectra in Al1−x In x N alloys.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Near-bandgap optical properties of Al_1−xIn_xN thin films grown on a c-plane freestanding GaN substrate

Toyoda

Murakami

Miyata

et al. 2021

Jpn. J. Appl. Phys.

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“…In this model most of the negative values are just below zero, so fixing the values at zero doesn't affect much the dielectric function of the layer (and the fit quality). However, these discrepancies point out the necessity of using more complex parameterization, like that of Adachi [9][10][11][12]. Table 2.…”

Section: Discussionmentioning

confidence: 99%

Optical characterization using ellipsometry of Si nanocrystal thin layers embedded in silicon oxide

et al. 2011

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We have developed optical models for the characterization of grain size in nanocrystal thin films embedded in SiO 2 and fabricated using low pressure chemical vapor deposition of Si from silane on a quartz substrate, followed by thermal oxidation. The as-grown nanocrystals thin film on quartz was composed of a two-dimensional array of Si nanocrystals (Si-NC) showing columnar structure in the z-direction and touching each other in the x-y plane. The nanocrystal size in the z-direction was equal to the Si nanocrystal film thickness, changing by the deposition time, while their x-y size was almost equal in all the samples, with small size dispersion. After high temperature thermal oxidation, a thin silicon oxide film was formed on top of the nanocrystals layer. The aim of this work was to measure the grain size and the nanocrystallinity of the Si nanocrystal thin films, a quantity related to the change of the dielectric function. We used a definition for the nanorcystallinity that is related to the effective medium analysis (EMA) of the material. The optical technique used for the investigations was spectroscopic ellipsometry. To measure the above sample properties the thickness and composition of several layers on a quartz substrate had to be determined by proper modeling of this complex system. We found that the nanocrystallinity (defined as the ratio of nc-Si/(c-Si+nc-Si) decreases systematically with increasing the Si-NC layer thickness. Using this approach we are sensitive to the lifetime broadening of electrons caused by the scattering on the grain boundaries, and not to the shift of the direct interband transition energies due to quantum confinement.

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“…where P cv (k) is the matrix element of the electron transition from the top of the valence band v to the bottom of conduction band c; E cv (k) = E c (k) E v (k) is the energy of the transition; k 1 and k 2 are variables that locate a point on the constant-energy surface S and which are determined from relation E cv (k) = E; m is the electron effective mass; ê is the unit polarization vector of the photon electric field; Ã is the phenomenological broadening parameter (damping constant). As in the works [4][5][6][7][8][9], one can integrate the formula (1) having previously made the substitution E cv (k) = E j , Ã = Ã j (j = 0,1,2,3,4 is the index of electron transition). Integrating gives the following expression for the complex dielectric function:…”

Section: Model Descriptionmentioning

confidence: 99%

Analysis of exciton reflection spectrum of 2H-PbI2 layered single crystals with atomically clean surface

Dorogan¹

2003

Semicond. Phys. Quantum Electron. Optoelectron.

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We performed the computer modelling of the dispersion dependences of real ε 1 (E) and imaginary ε 2 (E) parts of complex dielectric function ε(E) for 2H-PbI 2 crystals with atomically clean surface at the temperature 5 K and the light polarization C E H H ⊥ and determined the energy position of the exciton bands and the parameters of the critical points. The obtained data allowed us to conclude the exciton spectra of this semiconductor can be described in terms of a single Wannier series with a large ground-state anomaly caused by a repulsive central-cell correction due to the cationic character of the exciton.

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Optical dielectric function of semiconductors

Cited by 13 publications

References 14 publications

Near-bandgap optical properties of Al_1−xIn_xN thin films grown on a c-plane freestanding GaN substrate

Near-bandgap optical properties of Al_1−xIn_xN thin films grown on a c-plane freestanding GaN substrate

Optical characterization using ellipsometry of Si nanocrystal thin layers embedded in silicon oxide

Analysis of exciton reflection spectrum of 2H-PbI2 layered single crystals with atomically clean surface

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Optical dielectric function of semiconductors

Cited by 13 publications

References 14 publications

Near-bandgap optical properties of Al1−x In x N thin films grown on a c-plane freestanding GaN substrate

Near-bandgap optical properties of Al1−x In x N thin films grown on a c-plane freestanding GaN substrate

Optical characterization using ellipsometry of Si nanocrystal thin layers embedded in silicon oxide

Analysis of exciton reflection spectrum of 2H-PbI2 layered single crystals with atomically clean surface

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Near-bandgap optical properties of Al_1−xIn_xN thin films grown on a c-plane freestanding GaN substrate

Near-bandgap optical properties of Al_1−xIn_xN thin films grown on a c-plane freestanding GaN substrate